id	sid	tid	token	lemma	pos
cjfa-35471	1	1	date	date	NOUN
cjfa-35471	1	2	of	of	ADP
cjfa-35471	1	3	submission	submission	NOUN
cjfa-35471	1	4	:	:	PUNCT
cjfa-35471	1	5	april	april	PROPN
cjfa-35471	1	6	15	15	NUM
cjfa-35471	1	7	,	,	PUNCT
cjfa-35471	1	8	2021	2021	NUM
cjfa-35471	1	9	;	;	PUNCT
cjfa-35471	1	10	date	date	NOUN
cjfa-35471	1	11	of	of	ADP
cjfa-35471	1	12	acceptance	acceptance	NOUN
cjfa-35471	1	13	:	:	PUNCT
cjfa-35471	1	14	june	june	PROPN
cjfa-35471	1	15	10	10	NUM
cjfa-35471	1	16	,	,	PUNCT
cjfa-35471	1	17	2021	2021	NUM
cjfa-35471	1	18	.	.	PUNCT
cjfa-35471	2	1	*	*	PUNCT
cjfa-35471	2	2	contact	contact	NOUN
cjfa-35471	2	3	information	information	NOUN
cjfa-35471	2	4	:	:	PUNCT
cjfa-35471	2	5	mustafaakan@halic.edu.tr	mustafaakan@halic.edu.tr	ADJ
cjfa-35471	2	6	,	,	PUNCT
cjfa-35471	3	1	halic	halic	ADJ
cjfa-35471	3	2	university	university	NOUN
cjfa-35471	3	3	sutluce	sutluce	NOUN
cjfa-35471	3	4	mh	mh	PROPN
cjfa-35471	3	5	.	.	PUNCT
cjfa-35471	3	6	imrahor	imrahor	NOUN
cjfa-35471	3	7	sk	sk	PROPN
cjfa-35471	3	8	.	.	PUNCT
cjfa-35471	4	1	no	no	PRON
cjfa-35471	4	2	:	:	PUNCT
cjfa-35471	4	3	82	82	NUM
cjfa-35471	4	4	34445	34445	NUM
cjfa-35471	4	5	beyoglu	beyoglu	PROPN
cjfa-35471	4	6	/	/	SYM
cjfa-35471	4	7	istanbul	istanbul	PROPN
cjfa-35471	4	8	,	,	PUNCT
cjfa-35471	4	9	turkey	turkey	PROPN
cjfa-35471	4	10	,	,	PUNCT
cjfa-35471	4	11	phone	phone	NOUN
cjfa-35471	4	12	:	:	PUNCT
cjfa-35471	4	13	+905333119405	+905333119405	NUM
cjfa-35471	4	14	;	;	PUNCT
cjfa-35471	4	15	orcid	orcid	NOUN
cjfa-35471	5	1	i	i	NOUN
cjfa-35471	5	2	d	d	NOUN
cjfa-35471	5	3	:	:	PUNCT
cjfa-35471	6	1	https://orcid.org/0000-0002-2900-4932	https://orcid.org/0000-0002-2900-4932	INTJ
cjfa-35471	6	2	.	.	PUNCT
cjfa-35471	7	1	*	*	PUNCT
cjfa-35471	7	2	*	*	PUNCT
cjfa-35471	7	3	contact	contact	NOUN
cjfa-35471	7	4	information	information	NOUN
cjfa-35471	7	5	:	:	PUNCT
cjfa-35471	7	6	natalija.konovalova@riseba.lv	natalija.konovalova@riseba.lv	ADJ
cjfa-35471	7	7	,	,	PUNCT
cjfa-35471	7	8	riseba	riseba	NOUN
cjfa-35471	7	9	university	university	PROPN
cjfa-35471	7	10	of	of	ADP
cjfa-35471	7	11	applied	apply	VERB
cjfa-35471	7	12	sciences	science	NOUN
cjfa-35471	7	13	,	,	PUNCT
cjfa-35471	7	14	meza	meza	PROPN
cjfa-35471	7	15	street	street	NOUN
cjfa-35471	7	16	3	3	NUM
cjfa-35471	7	17	,	,	PUNCT
cjfa-35471	7	18	riga	riga	ADJ
cjfa-35471	7	19	,	,	PUNCT
cjfa-35471	7	20	latvia	latvia	PROPN
cjfa-35471	7	21	,	,	PUNCT
cjfa-35471	7	22	phone	phone	NOUN
cjfa-35471	7	23	:	:	PUNCT
cjfa-35471	7	24	+37129215208	+37129215208	NUM
cjfa-35471	7	25	;	;	PUNCT
cjfa-35471	7	26	orcid	orcid	NOUN
cjfa-35471	8	1	i	i	NOUN
cjfa-35471	8	2	d	d	NOUN
cjfa-35471	8	3	:	:	PUNCT
cjfa-35471	8	4	https://orcid	https://orcid	PROPN
cjfa-35471	8	5	.	.	PUNCT
cjfa-35471	8	6	org/0000	org/0000	NOUN
cjfa-35471	8	7	-	-	PUNCT
cjfa-35471	8	8	0003	0003	NUM
cjfa-35471	8	9	-	-	PUNCT
cjfa-35471	8	10	4072	4072	NUM
cjfa-35471	8	11	-	-	SYM
cjfa-35471	8	12	4479	4479	NUM
cjfa-35471	8	13	.	.	PUNCT
cjfa-35471	9	1	copernican	copernican	PROPN
cjfa-35471	9	2	journal	journal	PROPN
cjfa-35471	9	3	of	of	ADP
cjfa-35471	9	4	finance	finance	PROPN
cjfa-35471	9	5	&	&	CCONJ
cjfa-35471	9	6	accounting	accounting	PROPN
cjfa-35471	9	7	e	e	PROPN
cjfa-35471	9	8	-	-	PROPN
cjfa-35471	9	9	issn	issn	PROPN
cjfa-35471	9	10	2300	2300	NUM
cjfa-35471	9	11	-	-	SYM
cjfa-35471	9	12	3065	3065	NUM
cjfa-35471	9	13	p	p	PROPN
cjfa-35471	9	14	-	-	PUNCT
cjfa-35471	9	15	issn	issn	PROPN
cjfa-35471	9	16	2300	2300	NUM
cjfa-35471	9	17	-	-	SYM
cjfa-35471	9	18	12402021	12402021	NUM
cjfa-35471	9	19	,	,	PUNCT
cjfa-35471	9	20	volume	volume	NOUN
cjfa-35471	9	21	10	10	NUM
cjfa-35471	9	22	,	,	PUNCT
cjfa-35471	9	23	issue	issue	NOUN
cjfa-35471	9	24	3	3	NUM
cjfa-35471	9	25	akan	akan	PROPN
cjfa-35471	9	26	,	,	PUNCT
cjfa-35471	9	27	m.	m.	NOUN
cjfa-35471	9	28	,	,	PUNCT
cjfa-35471	9	29	&	&	CCONJ
cjfa-35471	9	30	konovalova	konovalova	PROPN
cjfa-35471	9	31	,	,	PUNCT
cjfa-35471	9	32	n.	n.	NOUN
cjfa-35471	9	33	(	(	PUNCT
cjfa-35471	9	34	2021	2021	NUM
cjfa-35471	9	35	)	)	PUNCT
cjfa-35471	9	36	.	.	PUNCT
cjfa-35471	10	1	optimal	optimal	ADJ
cjfa-35471	10	2	incentives	incentive	NOUN
cjfa-35471	10	3	for	for	ADP
cjfa-35471	10	4	economic	economic	ADJ
cjfa-35471	10	5	growth	growth	NOUN
cjfa-35471	10	6	in	in	ADP
cjfa-35471	10	7	central	central	ADJ
cjfa-35471	10	8	european	european	ADJ
cjfa-35471	10	9	countries	country	NOUN
cjfa-35471	10	10	:	:	PUNCT
cjfa-35471	10	11	a	a	DET
cjfa-35471	10	12	micro	micro	ADJ
cjfa-35471	10	13	approach	approach	NOUN
cjfa-35471	10	14	.	.	PUNCT
cjfa-35471	11	1	copernican	copernican	PROPN
cjfa-35471	11	2	journal	journal	PROPN
cjfa-35471	11	3	of	of	ADP
cjfa-35471	11	4	finance	finance	PROPN
cjfa-35471	11	5	&	&	CCONJ
cjfa-35471	11	6	accounting	accounting	PROPN
cjfa-35471	11	7	,	,	PUNCT
cjfa-35471	11	8	10(3	10(3	NUM
cjfa-35471	11	9	)	)	PUNCT
cjfa-35471	11	10	,	,	PUNCT
cjfa-35471	11	11	9–31	9–31	PROPN
cjfa-35471	11	12	.	.	PUNCT
cjfa-35471	12	1	http://	http://	PROPN
cjfa-35471	12	2	dx.doi.org/10.12775/cjfa.2021.009	dx.doi.org/10.12775/cjfa.2021.009	PROPN
cjfa-35471	12	3	mustafa	mustafa	PROPN
cjfa-35471	12	4	akan	akan	PROPN
cjfa-35471	12	5	*	*	PROPN
cjfa-35471	12	6	haliç	haliç	PROPN
cjfa-35471	12	7	university	university	PROPN
cjfa-35471	12	8	natalia	natalia	PROPN
cjfa-35471	12	9	konovalova	konovalova	PROPN
cjfa-35471	12	10	*	*	PUNCT
cjfa-35471	12	11	*	*	PROPN
cjfa-35471	12	12	riseba	riseba	PROPN
cjfa-35471	12	13	university	university	NOUN
cjfa-35471	12	14	of	of	ADP
cjfa-35471	12	15	applied	apply	VERB
cjfa-35471	12	16	sciences	science	NOUN
cjfa-35471	12	17	optimal	optimal	ADJ
cjfa-35471	12	18	incentives	incentive	NOUN
cjfa-35471	12	19	for	for	ADP
cjfa-35471	12	20	economic	economic	ADJ
cjfa-35471	12	21	growth	growth	NOUN
cjfa-35471	12	22	in	in	ADP
cjfa-35471	12	23	central	central	ADJ
cjfa-35471	12	24	european	european	ADJ
cjfa-35471	12	25	countries	country	NOUN
cjfa-35471	12	26	:	:	PUNCT
cjfa-35471	12	27	a	a	DET
cjfa-35471	12	28	micro	micro	ADJ
cjfa-35471	12	29	approach	approach	NOUN
cjfa-35471	12	30	keywords	keyword	NOUN
cjfa-35471	12	31	:	:	PUNCT
cjfa-35471	12	32	optimal	optimal	ADJ
cjfa-35471	12	33	control	control	NOUN
cjfa-35471	12	34	theory	theory	NOUN
cjfa-35471	12	35	,	,	PUNCT
cjfa-35471	12	36	incentives	incentive	NOUN
cjfa-35471	12	37	for	for	ADP
cjfa-35471	12	38	economic	economic	ADJ
cjfa-35471	12	39	growth	growth	NOUN
cjfa-35471	12	40	,	,	PUNCT
cjfa-35471	12	41	fluctuating	fluctuate	VERB
cjfa-35471	12	42	demand	demand	NOUN
cjfa-35471	12	43	.	.	PUNCT
cjfa-35471	13	1	j	j	PROPN
cjfa-35471	13	2	e	e	NOUN
cjfa-35471	13	3	l	l	NOUN
cjfa-35471	13	4	classification	classification	NOUN
cjfa-35471	13	5	:	:	PUNCT
cjfa-35471	14	1	d90	d90	NOUN
cjfa-35471	14	2	,	,	PUNCT
cjfa-35471	14	3	f43	f43	NOUN
cjfa-35471	14	4	,	,	PUNCT
cjfa-35471	14	5	f63	f63	PROPN
cjfa-35471	14	6	,	,	PUNCT
cjfa-35471	14	7	c61	c61	PROPN
cjfa-35471	14	8	.	.	PUNCT
cjfa-35471	15	1	abstract	abstract	ADJ
cjfa-35471	15	2	:	:	PUNCT
cjfa-35471	15	3	financial	financial	ADJ
cjfa-35471	15	4	crisis	crisis	NOUN
cjfa-35471	15	5	of	of	ADP
cjfa-35471	15	6	2008	2008	NUM
cjfa-35471	15	7	and	and	CCONJ
cjfa-35471	15	8	the	the	DET
cjfa-35471	15	9	ongoing	ongoing	ADJ
cjfa-35471	15	10	pandemic	pandemic	NOUN
cjfa-35471	15	11	are	be	AUX
cjfa-35471	15	12	continuing	continue	VERB
cjfa-35471	15	13	to	to	PART
cjfa-35471	15	14	have	have	VERB
cjfa-35471	15	15	a	a	DET
cjfa-35471	15	16	negative	negative	ADJ
cjfa-35471	15	17	impact	impact	NOUN
cjfa-35471	15	18	on	on	ADP
cjfa-35471	15	19	the	the	DET
cjfa-35471	15	20	economies	economy	NOUN
cjfa-35471	15	21	of	of	ADP
cjfa-35471	15	22	all	all	DET
cjfa-35471	15	23	countries	country	NOUN
cjfa-35471	15	24	even	even	ADV
cjfa-35471	15	25	tough	tough	ADJ
cjfa-35471	15	26	interest	interest	NOUN
cjfa-35471	15	27	rates	rate	NOUN
cjfa-35471	15	28	have	have	AUX
cjfa-35471	15	29	been	be	AUX
cjfa-35471	15	30	decreased	decrease	VERB
cjfa-35471	15	31	significantly	significantly	ADV
cjfa-35471	15	32	.	.	PUNCT
cjfa-35471	16	1	this	this	DET
cjfa-35471	16	2	paper	paper	NOUN
cjfa-35471	16	3	attempted	attempt	VERB
cjfa-35471	16	4	to	to	PART
cjfa-35471	16	5	view	view	VERB
cjfa-35471	16	6	the	the	DET
cjfa-35471	16	7	problem	problem	NOUN
cjfa-35471	16	8	from	from	ADP
cjfa-35471	16	9	a	a	DET
cjfa-35471	16	10	micro	micro	ADJ
cjfa-35471	16	11	point	point	NOUN
cjfa-35471	16	12	of	of	ADP
cjfa-35471	16	13	view	view	NOUN
cjfa-35471	16	14	to	to	PART
cjfa-35471	16	15	suggest	suggest	VERB
cjfa-35471	16	16	more	more	ADV
cjfa-35471	16	17	effective	effective	ADJ
cjfa-35471	16	18	incentives	incentive	NOUN
cjfa-35471	16	19	for	for	ADP
cjfa-35471	16	20	growth	growth	NOUN
cjfa-35471	16	21	.	.	PUNCT
cjfa-35471	17	1	the	the	DET
cjfa-35471	17	2	specific	specific	ADJ
cjfa-35471	17	3	objective	objective	NOUN
cjfa-35471	17	4	of	of	ADP
cjfa-35471	17	5	the	the	DET
cjfa-35471	17	6	study	study	NOUN
cjfa-35471	17	7	is	be	AUX
cjfa-35471	17	8	to	to	PART
cjfa-35471	17	9	determine	determine	VERB
cjfa-35471	17	10	and	and	CCONJ
cjfa-35471	17	11	examine	examine	VERB
cjfa-35471	17	12	the	the	DET
cjfa-35471	17	13	effects	effect	NOUN
cjfa-35471	17	14	of	of	ADP
cjfa-35471	17	15	these	these	DET
cjfa-35471	17	16	incentives	incentive	NOUN
cjfa-35471	17	17	on	on	ADP
cjfa-35471	17	18	economic	economic	ADJ
cjfa-35471	17	19	growth	growth	NOUN
cjfa-35471	17	20	in	in	ADP
cjfa-35471	17	21	central	central	ADJ
cjfa-35471	17	22	european	european	ADJ
cjfa-35471	17	23	countries	country	NOUN
cjfa-35471	17	24	.	.	PUNCT
cjfa-35471	18	1	mustafa	mustafa	PROPN
cjfa-35471	18	2	akan	akan	PROPN
cjfa-35471	18	3	,	,	PUNCT
cjfa-35471	18	4	natalia	natalia	PROPN
cjfa-35471	18	5	konovalova10	konovalova10	VERB
cjfa-35471	18	6	an	an	DET
cjfa-35471	18	7	optimal	optimal	ADJ
cjfa-35471	18	8	control	control	NOUN
cjfa-35471	18	9	theoretic	theoretic	NOUN
cjfa-35471	18	10	model	model	NOUN
cjfa-35471	18	11	was	be	AUX
cjfa-35471	18	12	employed	employ	VERB
cjfa-35471	18	13	as	as	ADP
cjfa-35471	18	14	a	a	DET
cjfa-35471	18	15	method	method	NOUN
cjfa-35471	18	16	of	of	ADP
cjfa-35471	18	17	analysis	analysis	NOUN
cjfa-35471	18	18	with	with	ADP
cjfa-35471	18	19	data	datum	NOUN
cjfa-35471	18	20	from	from	ADP
cjfa-35471	18	21	countries	country	NOUN
cjfa-35471	18	22	in	in	ADP
cjfa-35471	18	23	question	question	NOUN
cjfa-35471	18	24	.	.	PUNCT
cjfa-35471	19	1	results	result	NOUN
cjfa-35471	19	2	showed	show	VERB
cjfa-35471	19	3	,	,	PUNCT
cjfa-35471	19	4	generally	generally	ADV
cjfa-35471	19	5	,	,	PUNCT
cjfa-35471	19	6	that	that	PRON
cjfa-35471	19	7	incentives	incentive	VERB
cjfa-35471	19	8	such	such	ADJ
cjfa-35471	19	9	as	as	ADP
cjfa-35471	19	10	interest	interest	NOUN
cjfa-35471	19	11	rates	rate	NOUN
cjfa-35471	19	12	,	,	PUNCT
cjfa-35471	19	13	investments	investment	NOUN
cjfa-35471	19	14	in	in	ADP
cjfa-35471	19	15	production	production	NOUN
cjfa-35471	19	16	technologies	technology	NOUN
cjfa-35471	19	17	,	,	PUNCT
cjfa-35471	19	18	labor	labor	NOUN
cjfa-35471	19	19	productivity	productivity	NOUN
cjfa-35471	19	20	,	,	PUNCT
cjfa-35471	19	21	and	and	CCONJ
cjfa-35471	19	22	the	the	DET
cjfa-35471	19	23	cost	cost	NOUN
cjfa-35471	19	24	of	of	ADP
cjfa-35471	19	25	inventory	inventory	NOUN
cjfa-35471	19	26	were	be	AUX
cjfa-35471	19	27	important	important	ADJ
cjfa-35471	19	28	factors	factor	NOUN
cjfa-35471	19	29	to	to	PART
cjfa-35471	19	30	induce	induce	VERB
cjfa-35471	19	31	growth	growth	NOUN
cjfa-35471	19	32	with	with	ADP
cjfa-35471	19	33	different	different	ADJ
cjfa-35471	19	34	impact	impact	NOUN
cjfa-35471	19	35	in	in	ADP
cjfa-35471	19	36	each	each	DET
cjfa-35471	19	37	country	country	NOUN
cjfa-35471	19	38	.	.	PUNCT
cjfa-35471	20	1	results	result	NOUN
cjfa-35471	20	2	showed	show	VERB
cjfa-35471	20	3	that	that	SCONJ
cjfa-35471	20	4	changes	change	NOUN
cjfa-35471	20	5	in	in	ADP
cjfa-35471	20	6	interest	interest	NOUN
cjfa-35471	20	7	rates	rate	NOUN
cjfa-35471	20	8	will	will	AUX
cjfa-35471	20	9	not	not	PART
cjfa-35471	20	10	cause	cause	VERB
cjfa-35471	20	11	significant	significant	ADJ
cjfa-35471	20	12	economic	economic	ADJ
cjfa-35471	20	13	growth	growth	NOUN
cjfa-35471	20	14	in	in	ADP
cjfa-35471	20	15	poland	poland	PROPN
cjfa-35471	20	16	,	,	PUNCT
cjfa-35471	20	17	hungary	hungary	PROPN
cjfa-35471	20	18	,	,	PUNCT
cjfa-35471	20	19	and	and	CCONJ
cjfa-35471	20	20	the	the	DET
cjfa-35471	20	21	czech	czech	PROPN
cjfa-35471	20	22	republic	republic	NOUN
cjfa-35471	20	23	where	where	SCONJ
cjfa-35471	20	24	interest	interest	NOUN
cjfa-35471	20	25	rates	rate	NOUN
cjfa-35471	20	26	are	be	AUX
cjfa-35471	20	27	already	already	ADV
cjfa-35471	20	28	low	low	ADJ
cjfa-35471	20	29	.	.	PUNCT
cjfa-35471	21	1	however	however	ADV
cjfa-35471	21	2	,	,	PUNCT
cjfa-35471	21	3	countries	country	NOUN
cjfa-35471	21	4	such	such	ADJ
cjfa-35471	21	5	as	as	ADP
cjfa-35471	21	6	croatia	croatia	PROPN
cjfa-35471	21	7	and	and	CCONJ
cjfa-35471	21	8	romania	romania	PROPN
cjfa-35471	21	9	where	where	SCONJ
cjfa-35471	21	10	interest	interest	NOUN
cjfa-35471	21	11	rates	rate	NOUN
cjfa-35471	21	12	are	be	AUX
cjfa-35471	21	13	relatively	relatively	ADV
cjfa-35471	21	14	high	high	ADJ
cjfa-35471	21	15	,	,	PUNCT
cjfa-35471	21	16	reducing	reduce	VERB
cjfa-35471	21	17	interest	interest	NOUN
cjfa-35471	21	18	rates	rate	NOUN
cjfa-35471	21	19	may	may	AUX
cjfa-35471	21	20	lead	lead	VERB
cjfa-35471	21	21	to	to	ADP
cjfa-35471	21	22	economic	economic	ADJ
cjfa-35471	21	23	growth	growth	NOUN
cjfa-35471	21	24	.	.	PUNCT
cjfa-35471	22	1	the	the	DET
cjfa-35471	22	2	investment	investment	NOUN
cjfa-35471	22	3	in	in	ADP
cjfa-35471	22	4	production	production	NOUN
cjfa-35471	22	5	technologies	technology	NOUN
cjfa-35471	22	6	will	will	AUX
cjfa-35471	22	7	have	have	VERB
cjfa-35471	22	8	a	a	DET
cjfa-35471	22	9	significant	significant	ADJ
cjfa-35471	22	10	impact	impact	NOUN
cjfa-35471	22	11	on	on	ADP
cjfa-35471	22	12	economic	economic	ADJ
cjfa-35471	22	13	growth	growth	NOUN
cjfa-35471	22	14	in	in	ADP
cjfa-35471	22	15	bulgaria	bulgaria	PROPN
cjfa-35471	22	16	,	,	PUNCT
cjfa-35471	22	17	hungary	hungary	PROPN
cjfa-35471	22	18	and	and	CCONJ
cjfa-35471	22	19	croatia	croatia	PROPN
cjfa-35471	22	20	.	.	PUNCT
cjfa-35471	23	1	for	for	ADP
cjfa-35471	23	2	the	the	DET
cjfa-35471	23	3	czech	czech	PROPN
cjfa-35471	23	4	republic	republic	NOUN
cjfa-35471	23	5	,	,	PUNCT
cjfa-35471	23	6	slovenia	slovenia	PROPN
cjfa-35471	23	7	and	and	CCONJ
cjfa-35471	23	8	poland	poland	PROPN
cjfa-35471	23	9	,	,	PUNCT
cjfa-35471	23	10	which	which	PRON
cjfa-35471	23	11	are	be	AUX
cjfa-35471	23	12	already	already	ADV
cjfa-35471	23	13	quite	quite	ADV
cjfa-35471	23	14	advanced	advanced	ADJ
cjfa-35471	23	15	in	in	ADP
cjfa-35471	23	16	the	the	DET
cjfa-35471	23	17	field	field	NOUN
cjfa-35471	23	18	of	of	ADP
cjfa-35471	23	19	production	production	NOUN
cjfa-35471	23	20	technology	technology	NOUN
cjfa-35471	23	21	,	,	PUNCT
cjfa-35471	23	22	the	the	DET
cjfa-35471	23	23	impact	impact	NOUN
cjfa-35471	23	24	of	of	ADP
cjfa-35471	23	25	this	this	DET
cjfa-35471	23	26	factor	factor	NOUN
cjfa-35471	23	27	on	on	ADP
cjfa-35471	23	28	economic	economic	ADJ
cjfa-35471	23	29	growth	growth	NOUN
cjfa-35471	23	30	will	will	AUX
cjfa-35471	23	31	be	be	AUX
cjfa-35471	23	32	less	less	ADV
cjfa-35471	23	33	significant	significant	ADJ
cjfa-35471	23	34	.	.	PUNCT
cjfa-35471	24	1	incentives	incentive	NOUN
cjfa-35471	24	2	to	to	PART
cjfa-35471	24	3	increase	increase	VERB
cjfa-35471	24	4	labor	labor	NOUN
cjfa-35471	24	5	productivity	productivity	NOUN
cjfa-35471	24	6	in	in	ADP
cjfa-35471	24	7	hungary	hungary	PROPN
cjfa-35471	24	8	,	,	PUNCT
cjfa-35471	24	9	bulgaria	bulgaria	PROPN
cjfa-35471	24	10	,	,	PUNCT
cjfa-35471	24	11	estonia	estonia	PROPN
cjfa-35471	24	12	,	,	PUNCT
cjfa-35471	24	13	latvia	latvia	PROPN
cjfa-35471	24	14	,	,	PUNCT
cjfa-35471	24	15	and	and	CCONJ
cjfa-35471	24	16	lithuania	lithuania	PROPN
cjfa-35471	24	17	will	will	AUX
cjfa-35471	24	18	have	have	VERB
cjfa-35471	24	19	significant	significant	ADJ
cjfa-35471	24	20	impact	impact	NOUN
cjfa-35471	24	21	on	on	ADP
cjfa-35471	24	22	economic	economic	ADJ
cjfa-35471	24	23	growth	growth	NOUN
cjfa-35471	24	24	as	as	ADP
cjfa-35471	24	25	productivity	productivity	NOUN
cjfa-35471	24	26	in	in	ADP
cjfa-35471	24	27	these	these	DET
cjfa-35471	24	28	countries	country	NOUN
cjfa-35471	24	29	is	be	AUX
cjfa-35471	24	30	relatively	relatively	ADV
cjfa-35471	24	31	low	low	ADJ
cjfa-35471	24	32	.	.	PUNCT
cjfa-35471	25	1	incentives	incentive	NOUN
cjfa-35471	25	2	regarding	regard	VERB
cjfa-35471	25	3	holding	hold	VERB
cjfa-35471	25	4	costs	cost	NOUN
cjfa-35471	25	5	will	will	AUX
cjfa-35471	25	6	be	be	AUX
cjfa-35471	25	7	effective	effective	ADJ
cjfa-35471	25	8	on	on	ADP
cjfa-35471	25	9	sectoral	sectoral	ADJ
cjfa-35471	25	10	basis	basis	NOUN
cjfa-35471	25	11	.	.	PUNCT
cjfa-35471	25	12	 	 	SPACE
cjfa-35471	26	1	introduction	introduction	NOUN
cjfa-35471	26	2	governments	government	NOUN
cjfa-35471	26	3	have	have	AUX
cjfa-35471	26	4	taken	take	VERB
cjfa-35471	26	5	actions	action	NOUN
cjfa-35471	26	6	to	to	PART
cjfa-35471	26	7	stabilize	stabilize	VERB
cjfa-35471	26	8	the	the	DET
cjfa-35471	26	9	financial	financial	ADJ
cjfa-35471	26	10	sector	sector	NOUN
cjfa-35471	26	11	by	by	ADP
cjfa-35471	26	12	principally	principally	ADV
cjfa-35471	26	13	increasing	increase	VERB
cjfa-35471	26	14	money	money	NOUN
cjfa-35471	26	15	supply	supply	NOUN
cjfa-35471	26	16	and	and	CCONJ
cjfa-35471	26	17	other	other	ADJ
cjfa-35471	26	18	measures	measure	NOUN
cjfa-35471	26	19	such	such	ADJ
cjfa-35471	26	20	as	as	ADP
cjfa-35471	26	21	taking	take	VERB
cjfa-35471	26	22	over	over	ADP
cjfa-35471	26	23	some	some	PRON
cjfa-35471	26	24	of	of	ADP
cjfa-35471	26	25	the	the	DET
cjfa-35471	26	26	financial	financial	ADJ
cjfa-35471	26	27	institutions	institution	NOUN
cjfa-35471	26	28	affected	affect	VERB
cjfa-35471	26	29	by	by	ADP
cjfa-35471	26	30	the	the	DET
cjfa-35471	26	31	crisis	crisis	NOUN
cjfa-35471	26	32	.	.	PUNCT
cjfa-35471	27	1	growth	growth	NOUN
cjfa-35471	27	2	rates	rate	NOUN
cjfa-35471	27	3	in	in	ADP
cjfa-35471	27	4	advanced	advanced	ADJ
cjfa-35471	27	5	countries	country	NOUN
cjfa-35471	27	6	are	be	AUX
cjfa-35471	27	7	low	low	ADJ
cjfa-35471	27	8	and	and	CCONJ
cjfa-35471	27	9	are	be	AUX
cjfa-35471	27	10	forecasted	forecast	VERB
cjfa-35471	27	11	to	to	PART
cjfa-35471	27	12	remain	remain	VERB
cjfa-35471	27	13	low	low	ADJ
cjfa-35471	27	14	for	for	ADP
cjfa-35471	27	15	several	several	ADJ
cjfa-35471	27	16	more	more	ADJ
cjfa-35471	27	17	years	year	NOUN
cjfa-35471	27	18	.	.	PUNCT
cjfa-35471	28	1	the	the	DET
cjfa-35471	28	2	trade	trade	NOUN
cjfa-35471	28	3	war	war	NOUN
cjfa-35471	28	4	between	between	ADP
cjfa-35471	28	5	the	the	DET
cjfa-35471	28	6	usa	usa	PROPN
cjfa-35471	28	7	and	and	CCONJ
cjfa-35471	28	8	china	china	PROPN
cjfa-35471	28	9	will	will	AUX
cjfa-35471	28	10	surely	surely	ADV
cjfa-35471	28	11	have	have	VERB
cjfa-35471	28	12	a	a	DET
cjfa-35471	28	13	negative	negative	ADJ
cjfa-35471	28	14	impact	impact	NOUN
cjfa-35471	28	15	on	on	ADP
cjfa-35471	28	16	the	the	DET
cjfa-35471	28	17	growth	growth	NOUN
cjfa-35471	28	18	rates	rate	NOUN
cjfa-35471	28	19	.	.	PUNCT
cjfa-35471	29	1	outbreak	outbreak	NOUN
cjfa-35471	29	2	of	of	ADP
cjfa-35471	29	3	a	a	DET
cjfa-35471	29	4	virus	virus	NOUN
cjfa-35471	29	5	in	in	ADP
cjfa-35471	29	6	china	china	PROPN
cjfa-35471	29	7	will	will	AUX
cjfa-35471	29	8	probably	probably	ADV
cjfa-35471	29	9	have	have	VERB
cjfa-35471	29	10	a	a	DET
cjfa-35471	29	11	negative	negative	ADJ
cjfa-35471	29	12	impact	impact	NOUN
cjfa-35471	29	13	on	on	ADP
cjfa-35471	29	14	growth	growth	NOUN
cjfa-35471	29	15	.	.	PUNCT
cjfa-35471	30	1	afp	afp	PROPN
cjfa-35471	30	2	(	(	PUNCT
cjfa-35471	30	3	2020	2020	NUM
cjfa-35471	30	4	)	)	PUNCT
cjfa-35471	30	5	estimates	estimate	VERB
cjfa-35471	30	6	that	that	SCONJ
cjfa-35471	30	7	the	the	DET
cjfa-35471	30	8	impact	impact	NOUN
cjfa-35471	30	9	could	could	AUX
cjfa-35471	30	10	be	be	AUX
cjfa-35471	30	11	0.1	0.1	NUM
cjfa-35471	30	12	-	-	SYM
cjfa-35471	30	13	0.2	0.2	NUM
cjfa-35471	30	14	%	%	NOUN
cjfa-35471	30	15	.	.	PUNCT
cjfa-35471	31	1	giles	gile	NOUN
cjfa-35471	31	2	,	,	PUNCT
cjfa-35471	31	3	arnold	arnold	PROPN
cjfa-35471	31	4	and	and	CCONJ
cjfa-35471	31	5	greely	greely	PROPN
cjfa-35471	31	6	(	(	PUNCT
cjfa-35471	31	7	2020	2020	NUM
cjfa-35471	31	8	)	)	PUNCT
cjfa-35471	31	9	have	have	AUX
cjfa-35471	31	10	reported	report	VERB
cjfa-35471	31	11	that	that	SCONJ
cjfa-35471	31	12	oecd	oecd	PROPN
cjfa-35471	31	13	lowered	lower	VERB
cjfa-35471	31	14	its	its	PRON
cjfa-35471	31	15	growth	growth	NOUN
cjfa-35471	31	16	estimates	estimate	NOUN
cjfa-35471	31	17	for	for	ADP
cjfa-35471	31	18	the	the	DET
cjfa-35471	31	19	world	world	NOUN
cjfa-35471	31	20	from	from	ADP
cjfa-35471	31	21	2.9	2.9	NUM
cjfa-35471	31	22	%	%	NOUN
cjfa-35471	31	23	to	to	ADP
cjfa-35471	31	24	2.4	2.4	NUM
cjfa-35471	31	25	%	%	NOUN
cjfa-35471	31	26	for	for	ADP
cjfa-35471	31	27	2020	2020	NUM
cjfa-35471	31	28	.	.	PUNCT
cjfa-35471	32	1	all	all	DET
cjfa-35471	32	2	major	major	ADJ
cjfa-35471	32	3	economies	economy	NOUN
cjfa-35471	32	4	of	of	ADP
cjfa-35471	32	5	the	the	DET
cjfa-35471	32	6	world	world	NOUN
cjfa-35471	32	7	have	have	AUX
cjfa-35471	32	8	taken	take	VERB
cjfa-35471	32	9	monetary	monetary	ADJ
cjfa-35471	32	10	measures	measure	NOUN
cjfa-35471	32	11	to	to	PART
cjfa-35471	32	12	minimize	minimize	VERB
cjfa-35471	32	13	the	the	DET
cjfa-35471	32	14	impact	impact	NOUN
cjfa-35471	32	15	of	of	ADP
cjfa-35471	32	16	financial	financial	ADJ
cjfa-35471	32	17	crisis	crisis	NOUN
cjfa-35471	32	18	on	on	ADP
cjfa-35471	32	19	the	the	DET
cjfa-35471	32	20	real	real	ADJ
cjfa-35471	32	21	sector	sector	NOUN
cjfa-35471	32	22	.	.	PUNCT
cjfa-35471	33	1	these	these	DET
cjfa-35471	33	2	policies	policy	NOUN
cjfa-35471	33	3	worked	work	VERB
cjfa-35471	33	4	well	well	ADV
cjfa-35471	33	5	in	in	ADP
cjfa-35471	33	6	most	most	ADJ
cjfa-35471	33	7	countries	country	NOUN
cjfa-35471	33	8	to	to	PART
cjfa-35471	33	9	contain	contain	VERB
cjfa-35471	33	10	the	the	DET
cjfa-35471	33	11	financial	financial	ADJ
cjfa-35471	33	12	crisis	crisis	NOUN
cjfa-35471	33	13	but	but	CCONJ
cjfa-35471	33	14	not	not	PART
cjfa-35471	33	15	so	so	ADV
cjfa-35471	33	16	well	well	ADV
cjfa-35471	33	17	to	to	PART
cjfa-35471	33	18	induce	induce	VERB
cjfa-35471	33	19	growth	growth	NOUN
cjfa-35471	33	20	which	which	PRON
cjfa-35471	33	21	is	be	AUX
cjfa-35471	33	22	evident	evident	ADJ
cjfa-35471	33	23	from	from	ADP
cjfa-35471	33	24	the	the	DET
cjfa-35471	33	25	growth	growth	NOUN
cjfa-35471	33	26	rates	rate	NOUN
cjfa-35471	33	27	in	in	ADP
cjfa-35471	33	28	2009	2009	NUM
cjfa-35471	33	29	and	and	CCONJ
cjfa-35471	33	30	thereafter	thereafter	ADV
cjfa-35471	33	31	.	.	PUNCT
cjfa-35471	34	1	the	the	DET
cjfa-35471	34	2	interest	interest	NOUN
cjfa-35471	34	3	rates	rate	NOUN
cjfa-35471	34	4	in	in	ADP
cjfa-35471	34	5	major	major	ADJ
cjfa-35471	34	6	economies	economy	NOUN
cjfa-35471	34	7	of	of	ADP
cjfa-35471	34	8	the	the	DET
cjfa-35471	34	9	world	world	NOUN
cjfa-35471	34	10	are	be	AUX
cjfa-35471	34	11	already	already	ADV
cjfa-35471	34	12	low	low	ADJ
cjfa-35471	34	13	.	.	PUNCT
cjfa-35471	35	1	they	they	PRON
cjfa-35471	35	2	are	be	AUX
cjfa-35471	35	3	zero	zero	NUM
cjfa-35471	35	4	in	in	ADP
cjfa-35471	35	5	eurozone	eurozone	NOUN
cjfa-35471	35	6	,	,	PUNCT
cjfa-35471	35	7	negative	negative	ADJ
cjfa-35471	35	8	in	in	ADP
cjfa-35471	35	9	japan	japan	PROPN
cjfa-35471	35	10	.	.	PUNCT
cjfa-35471	36	1	inflation	inflation	NOUN
cjfa-35471	36	2	rates	rate	NOUN
cjfa-35471	36	3	in	in	ADP
cjfa-35471	36	4	almost	almost	ADV
cjfa-35471	36	5	all	all	PRON
cjfa-35471	36	6	major	major	ADJ
cjfa-35471	36	7	economies	economy	NOUN
cjfa-35471	36	8	are	be	AUX
cjfa-35471	36	9	low	low	ADV
cjfa-35471	36	10	implying	implying	ADJ
cjfa-35471	36	11	that	that	SCONJ
cjfa-35471	36	12	the	the	DET
cjfa-35471	36	13	consumers	consumer	NOUN
cjfa-35471	36	14	are	be	AUX
cjfa-35471	36	15	not	not	PART
cjfa-35471	36	16	borrowing	borrow	VERB
cjfa-35471	36	17	for	for	ADP
cjfa-35471	36	18	consumption	consumption	NOUN
cjfa-35471	36	19	even	even	ADV
cjfa-35471	36	20	though	though	SCONJ
cjfa-35471	36	21	the	the	DET
cjfa-35471	36	22	interest	interest	NOUN
cjfa-35471	36	23	rates	rate	NOUN
cjfa-35471	36	24	are	be	AUX
cjfa-35471	36	25	generally	generally	ADV
cjfa-35471	36	26	very	very	ADV
cjfa-35471	36	27	low	low	ADJ
cjfa-35471	36	28	.	.	PUNCT
cjfa-35471	37	1	these	these	DET
cjfa-35471	37	2	two	two	NUM
cjfa-35471	37	3	facts	fact	NOUN
cjfa-35471	37	4	are	be	AUX
cjfa-35471	37	5	good	good	ADJ
cjfa-35471	37	6	indications	indication	NOUN
cjfa-35471	37	7	of	of	ADP
cjfa-35471	37	8	the	the	DET
cjfa-35471	37	9	end	end	NOUN
cjfa-35471	37	10	of	of	ADP
cjfa-35471	37	11	effectiveness	effectiveness	NOUN
cjfa-35471	37	12	of	of	ADP
cjfa-35471	37	13	monetary	monetary	ADJ
cjfa-35471	37	14	(	(	PUNCT
cjfa-35471	37	15	easy	easy	ADJ
cjfa-35471	37	16	money	money	NOUN
cjfa-35471	37	17	,	,	PUNCT
cjfa-35471	37	18	low	low	ADJ
cjfa-35471	37	19	interest	interest	NOUN
cjfa-35471	37	20	rate	rate	NOUN
cjfa-35471	37	21	)	)	PUNCT
cjfa-35471	37	22	policies	policy	NOUN
cjfa-35471	37	23	.	.	PUNCT
cjfa-35471	38	1	optimal	optimal	ADJ
cjfa-35471	38	2	incentives	incentive	NOUN
cjfa-35471	38	3	for	for	ADP
cjfa-35471	38	4	economic	economic	ADJ
cjfa-35471	38	5	growth	growth	NOUN
cjfa-35471	38	6	…	…	PUNCT
cjfa-35471	38	7	11	11	NUM
cjfa-35471	38	8	a	a	DET
cjfa-35471	38	9	brief	brief	ADJ
cjfa-35471	38	10	review	review	NOUN
cjfa-35471	38	11	of	of	ADP
cjfa-35471	38	12	literature	literature	NOUN
cjfa-35471	38	13	shows	show	VERB
cjfa-35471	38	14	such	such	ADJ
cjfa-35471	38	15	measures	measure	NOUN
cjfa-35471	38	16	have	have	AUX
cjfa-35471	38	17	either	either	ADV
cjfa-35471	38	18	been	be	AUX
cjfa-35471	38	19	ineffective	ineffective	ADJ
cjfa-35471	38	20	,	,	PUNCT
cjfa-35471	38	21	insignificant	insignificant	ADJ
cjfa-35471	38	22	,	,	PUNCT
cjfa-35471	38	23	or	or	CCONJ
cjfa-35471	38	24	even	even	ADV
cjfa-35471	38	25	negative	negative	ADJ
cjfa-35471	38	26	.	.	PUNCT
cjfa-35471	39	1	carlianne	carlianne	NOUN
cjfa-35471	39	2	(	(	PUNCT
cjfa-35471	39	3	2014	2014	NUM
cjfa-35471	39	4	)	)	PUNCT
cjfa-35471	39	5	found	find	VERB
cjfa-35471	39	6	that	that	SCONJ
cjfa-35471	39	7	governments	government	NOUN
cjfa-35471	39	8	aiding	aid	VERB
cjfa-35471	39	9	private	private	ADJ
cjfa-35471	39	10	enterprises	enterprise	NOUN
cjfa-35471	39	11	has	have	VERB
cjfa-35471	39	12	significant	significant	ADJ
cjfa-35471	39	13	negative	negative	ADJ
cjfa-35471	39	14	mid	mid	ADJ
cjfa-35471	39	15	-	-	ADJ
cjfa-35471	39	16	term	term	ADJ
cjfa-35471	39	17	effect	effect	NOUN
cjfa-35471	39	18	on	on	ADP
cjfa-35471	39	19	employment	employment	NOUN
cjfa-35471	39	20	and	and	CCONJ
cjfa-35471	39	21	growth	growth	NOUN
cjfa-35471	39	22	.	.	PUNCT
cjfa-35471	40	1	osario	osario	PROPN
cjfa-35471	40	2	and	and	CCONJ
cjfa-35471	40	3	florida	florida	PROPN
cjfa-35471	40	4	(	(	PUNCT
cjfa-35471	40	5	2017	2017	NUM
cjfa-35471	40	6	)	)	PUNCT
cjfa-35471	40	7	showed	show	VERB
cjfa-35471	40	8	that	that	SCONJ
cjfa-35471	40	9	business	business	NOUN
cjfa-35471	40	10	incentives	incentive	NOUN
cjfa-35471	40	11	have	have	VERB
cjfa-35471	40	12	different	different	ADJ
cjfa-35471	40	13	impacts	impact	NOUN
cjfa-35471	40	14	in	in	ADP
cjfa-35471	40	15	different	different	ADJ
cjfa-35471	40	16	areas	area	NOUN
cjfa-35471	40	17	and	and	CCONJ
cjfa-35471	40	18	are	be	AUX
cjfa-35471	40	19	usually	usually	ADV
cjfa-35471	40	20	ineffective	ineffective	ADJ
cjfa-35471	40	21	,	,	PUNCT
cjfa-35471	40	22	costly	costly	ADJ
cjfa-35471	40	23	,	,	PUNCT
cjfa-35471	40	24	and	and	CCONJ
cjfa-35471	40	25	wasteful	wasteful	ADJ
cjfa-35471	40	26	.	.	PUNCT
cjfa-35471	41	1	peters	peters	PROPN
cjfa-35471	41	2	and	and	CCONJ
cjfa-35471	41	3	fisher	fisher	PROPN
cjfa-35471	41	4	(	(	PUNCT
cjfa-35471	41	5	2004	2004	NUM
cjfa-35471	41	6	)	)	PUNCT
cjfa-35471	41	7	have	have	AUX
cjfa-35471	41	8	concluded	conclude	VERB
cjfa-35471	41	9	that	that	SCONJ
cjfa-35471	41	10	incentives	incentive	NOUN
cjfa-35471	41	11	are	be	AUX
cjfa-35471	41	12	costly	costly	ADJ
cjfa-35471	41	13	and	and	CCONJ
cjfa-35471	41	14	do	do	AUX
cjfa-35471	41	15	not	not	PART
cjfa-35471	41	16	encourage	encourage	VERB
cjfa-35471	41	17	investment	investment	NOUN
cjfa-35471	41	18	.	.	PUNCT
cjfa-35471	42	1	kosonen	kosonen	NOUN
cjfa-35471	42	2	(	(	PUNCT
cjfa-35471	42	3	2012	2012	NUM
cjfa-35471	42	4	)	)	PUNCT
cjfa-35471	42	5	,	,	PUNCT
cjfa-35471	42	6	in	in	ADP
cjfa-35471	42	7	a	a	DET
cjfa-35471	42	8	study	study	NOUN
cjfa-35471	42	9	on	on	ADP
cjfa-35471	42	10	finnish	finnish	ADJ
cjfa-35471	42	11	firms	firm	NOUN
cjfa-35471	42	12	,	,	PUNCT
cjfa-35471	42	13	have	have	AUX
cjfa-35471	42	14	found	find	VERB
cjfa-35471	42	15	that	that	SCONJ
cjfa-35471	42	16	decreasing	decrease	VERB
cjfa-35471	42	17	taxes	taxis	NOUN
cjfa-35471	42	18	would	would	AUX
cjfa-35471	42	19	increase	increase	VERB
cjfa-35471	42	20	the	the	DET
cjfa-35471	42	21	production	production	NOUN
cjfa-35471	42	22	but	but	CCONJ
cjfa-35471	42	23	the	the	DET
cjfa-35471	42	24	tax	tax	NOUN
cjfa-35471	42	25	elasticity	elasticity	NOUN
cjfa-35471	42	26	of	of	ADP
cjfa-35471	42	27	production	production	NOUN
cjfa-35471	42	28	is	be	AUX
cjfa-35471	42	29	only	only	ADV
cjfa-35471	42	30	-0.17	-0.17	ADJ
cjfa-35471	42	31	.	.	PUNCT
cjfa-35471	42	32	petrin	petrin	PROPN
cjfa-35471	42	33	(	(	PUNCT
cjfa-35471	42	34	2018	2018	NUM
cjfa-35471	42	35	)	)	PUNCT
cjfa-35471	42	36	concluded	conclude	VERB
cjfa-35471	42	37	that	that	SCONJ
cjfa-35471	42	38	incentives	incentive	VERB
cjfa-35471	42	39	for	for	ADP
cjfa-35471	42	40	r	r	NOUN
cjfa-35471	42	41	/	/	SYM
cjfa-35471	42	42	d	d	NOUN
cjfa-35471	42	43	and	and	CCONJ
cjfa-35471	42	44	innovation	innovation	NOUN
cjfa-35471	42	45	might	might	AUX
cjfa-35471	42	46	have	have	VERB
cjfa-35471	42	47	positive	positive	ADJ
cjfa-35471	42	48	impact	impact	NOUN
cjfa-35471	42	49	but	but	CCONJ
cjfa-35471	42	50	not	not	PART
cjfa-35471	42	51	always	always	ADV
cjfa-35471	42	52	.	.	PUNCT
cjfa-35471	43	1	a	a	DET
cjfa-35471	43	2	report	report	NOUN
cjfa-35471	43	3	by	by	ADP
cjfa-35471	43	4	dpme	dpme	PROPN
cjfa-35471	43	5	/	/	SYM
cjfa-35471	43	6	dsbo	dsbo	PROPN
cjfa-35471	43	7	(	(	PUNCT
cjfa-35471	43	8	2018	2018	NUM
cjfa-35471	43	9	)	)	PUNCT
cjfa-35471	43	10	could	could	AUX
cjfa-35471	43	11	not	not	PART
cjfa-35471	43	12	make	make	VERB
cjfa-35471	43	13	a	a	DET
cjfa-35471	43	14	conclusion	conclusion	NOUN
cjfa-35471	43	15	on	on	ADP
cjfa-35471	43	16	the	the	DET
cjfa-35471	43	17	impact	impact	NOUN
cjfa-35471	43	18	of	of	ADP
cjfa-35471	43	19	government	government	NOUN
cjfa-35471	43	20	incentives	incentive	VERB
cjfa-35471	43	21	on	on	ADP
cjfa-35471	43	22	business	business	NOUN
cjfa-35471	43	23	.	.	PUNCT
cjfa-35471	44	1	conroy	conroy	PROPN
cjfa-35471	44	2	(	(	PUNCT
cjfa-35471	44	3	2019	2019	NUM
cjfa-35471	44	4	)	)	PUNCT
cjfa-35471	44	5	,	,	PUNCT
cjfa-35471	44	6	in	in	ADP
cjfa-35471	44	7	her	her	PRON
cjfa-35471	44	8	master	master	NOUN
cjfa-35471	44	9	thesis	thesis	NOUN
cjfa-35471	44	10	,	,	PUNCT
cjfa-35471	44	11	concluded	conclude	VERB
cjfa-35471	44	12	that	that	SCONJ
cjfa-35471	44	13	there	there	PRON
cjfa-35471	44	14	is	be	VERB
cjfa-35471	44	15	a	a	DET
cjfa-35471	44	16	positive	positive	ADJ
cjfa-35471	44	17	impact	impact	NOUN
cjfa-35471	44	18	of	of	ADP
cjfa-35471	44	19	incentives	incentive	NOUN
cjfa-35471	44	20	on	on	ADP
cjfa-35471	44	21	attracting	attract	VERB
cjfa-35471	44	22	investment	investment	NOUN
cjfa-35471	44	23	to	to	ADP
cjfa-35471	44	24	a	a	DET
cjfa-35471	44	25	state	state	NOUN
cjfa-35471	44	26	but	but	CCONJ
cjfa-35471	44	27	it	it	PRON
cjfa-35471	44	28	depends	depend	VERB
cjfa-35471	44	29	on	on	ADP
cjfa-35471	44	30	the	the	DET
cjfa-35471	44	31	type	type	NOUN
cjfa-35471	44	32	of	of	ADP
cjfa-35471	44	33	incentives	incentive	NOUN
cjfa-35471	44	34	.	.	PUNCT
cjfa-35471	45	1	prillaman	prillaman	NOUN
cjfa-35471	45	2	and	and	CCONJ
cjfa-35471	45	3	meier	meier	PROPN
cjfa-35471	45	4	(	(	PUNCT
cjfa-35471	45	5	2014	2014	NUM
cjfa-35471	45	6	)	)	PUNCT
cjfa-35471	45	7	concluded	conclude	VERB
cjfa-35471	45	8	that	that	SCONJ
cjfa-35471	45	9	state	state	NOUN
cjfa-35471	45	10	tax	tax	NOUN
cjfa-35471	45	11	cuts	cut	NOUN
cjfa-35471	45	12	have	have	VERB
cjfa-35471	45	13	little	little	ADJ
cjfa-35471	45	14	to	to	ADP
cjfa-35471	45	15	no	no	DET
cjfa-35471	45	16	positive	positive	ADJ
cjfa-35471	45	17	on	on	ADP
cjfa-35471	45	18	the	the	DET
cjfa-35471	45	19	growth	growth	NOUN
cjfa-35471	45	20	of	of	ADP
cjfa-35471	45	21	the	the	DET
cjfa-35471	45	22	state	state	NOUN
cjfa-35471	45	23	,	,	PUNCT
cjfa-35471	45	24	job	job	NOUN
cjfa-35471	45	25	creation	creation	NOUN
cjfa-35471	45	26	,	,	PUNCT
cjfa-35471	45	27	personal	personal	ADJ
cjfa-35471	45	28	income	income	NOUN
cjfa-35471	45	29	,	,	PUNCT
cjfa-35471	45	30	poverty	poverty	NOUN
cjfa-35471	45	31	rates	rate	NOUN
cjfa-35471	45	32	,	,	PUNCT
cjfa-35471	45	33	and	and	CCONJ
cjfa-35471	45	34	formation	formation	NOUN
cjfa-35471	45	35	of	of	ADP
cjfa-35471	45	36	new	new	ADJ
cjfa-35471	45	37	businesses	business	NOUN
cjfa-35471	45	38	.	.	PUNCT
cjfa-35471	46	1	a	a	DET
cjfa-35471	46	2	report	report	NOUN
cjfa-35471	46	3	by	by	ADP
cjfa-35471	46	4	christian	christian	PROPN
cjfa-35471	46	5	,	,	PUNCT
cjfa-35471	46	6	karlin	karlin	PROPN
cjfa-35471	46	7	,	,	PUNCT
cjfa-35471	46	8	schaff	schaff	NOUN
cjfa-35471	46	9	and	and	CCONJ
cjfa-35471	46	10	tucker	tucker	PROPN
cjfa-35471	46	11	-	-	PUNCT
cjfa-35471	46	12	roy	roy	PROPN
cjfa-35471	46	13	(	(	PUNCT
cjfa-35471	46	14	2019	2019	NUM
cjfa-35471	46	15	)	)	PUNCT
cjfa-35471	46	16	found	find	VERB
cjfa-35471	46	17	a	a	DET
cjfa-35471	46	18	positive	positive	ADJ
cjfa-35471	46	19	relationship	relationship	NOUN
cjfa-35471	46	20	between	between	ADP
cjfa-35471	46	21	incentive	incentive	NOUN
cjfa-35471	46	22	spending	spending	NOUN
cjfa-35471	46	23	and	and	CCONJ
cjfa-35471	46	24	jobs	job	NOUN
cjfa-35471	46	25	created	create	VERB
cjfa-35471	46	26	only	only	ADV
cjfa-35471	46	27	if	if	SCONJ
cjfa-35471	46	28	specific	specific	ADJ
cjfa-35471	46	29	objectives	objective	NOUN
cjfa-35471	46	30	are	be	AUX
cjfa-35471	46	31	set	set	VERB
cjfa-35471	46	32	,	,	PUNCT
cjfa-35471	46	33	measurable	measurable	ADJ
cjfa-35471	46	34	goals	goal	NOUN
cjfa-35471	46	35	are	be	AUX
cjfa-35471	46	36	defined	define	VERB
cjfa-35471	46	37	,	,	PUNCT
cjfa-35471	46	38	and	and	CCONJ
cjfa-35471	46	39	investment	investment	NOUN
cjfa-35471	46	40	is	be	AUX
cjfa-35471	46	41	made	make	VERB
cjfa-35471	46	42	in	in	ADP
cjfa-35471	46	43	staff	staff	NOUN
cjfa-35471	46	44	,	,	PUNCT
cjfa-35471	46	45	systems	system	NOUN
cjfa-35471	46	46	,	,	PUNCT
cjfa-35471	46	47	and	and	CCONJ
cjfa-35471	46	48	budget	budget	NOUN
cjfa-35471	46	49	.	.	PUNCT
cjfa-35471	47	1	bundrick	bundrick	PROPN
cjfa-35471	47	2	(	(	PUNCT
cjfa-35471	47	3	2016	2016	NUM
cjfa-35471	47	4	)	)	PUNCT
cjfa-35471	47	5	showed	show	VERB
cjfa-35471	47	6	that	that	SCONJ
cjfa-35471	47	7	incentives	incentive	NOUN
cjfa-35471	47	8	have	have	VERB
cjfa-35471	47	9	costs	cost	NOUN
cjfa-35471	47	10	and	and	CCONJ
cjfa-35471	47	11	they	they	PRON
cjfa-35471	47	12	create	create	VERB
cjfa-35471	47	13	market	market	NOUN
cjfa-35471	47	14	distortions	distortion	NOUN
cjfa-35471	47	15	.	.	PUNCT
cjfa-35471	48	1	in	in	ADP
cjfa-35471	48	2	a	a	DET
cjfa-35471	48	3	study	study	NOUN
cjfa-35471	48	4	for	for	ADP
cjfa-35471	48	5	center	center	NOUN
cjfa-35471	48	6	for	for	ADP
cjfa-35471	48	7	american	american	ADJ
cjfa-35471	48	8	progress	progress	NOUN
cjfa-35471	48	9	,	,	PUNCT
cjfa-35471	48	10	schwartz	schwartz	PROPN
cjfa-35471	48	11	(	(	PUNCT
cjfa-35471	48	12	2018	2018	NUM
cjfa-35471	48	13	)	)	PUNCT
cjfa-35471	48	14	concluded	conclude	VERB
cjfa-35471	48	15	that	that	SCONJ
cjfa-35471	48	16	subsidies	subsidy	NOUN
cjfa-35471	48	17	fail	fail	VERB
cjfa-35471	48	18	to	to	PART
cjfa-35471	48	19	meet	meet	VERB
cjfa-35471	48	20	promised	promise	VERB
cjfa-35471	48	21	results	result	NOUN
cjfa-35471	48	22	with	with	ADP
cjfa-35471	48	23	no	no	DET
cjfa-35471	48	24	net	net	ADJ
cjfa-35471	48	25	benefit	benefit	NOUN
cjfa-35471	48	26	to	to	ADP
cjfa-35471	48	27	the	the	DET
cjfa-35471	48	28	social	social	ADJ
cjfa-35471	48	29	welfare	welfare	NOUN
cjfa-35471	48	30	.	.	PUNCT
cjfa-35471	49	1	a	a	DET
cjfa-35471	49	2	report	report	NOUN
cjfa-35471	49	3	by	by	ADP
cjfa-35471	49	4	the	the	DET
cjfa-35471	49	5	pew	pew	NOUN
cjfa-35471	49	6	charitable	charitable	ADJ
cjfa-35471	49	7	trusts	trust	NOUN
cjfa-35471	49	8	(	(	PUNCT
cjfa-35471	49	9	2019	2019	NUM
cjfa-35471	49	10	)	)	PUNCT
cjfa-35471	49	11	states	state	NOUN
cjfa-35471	49	12	that	that	PRON
cjfa-35471	49	13	incentives	incentive	VERB
cjfa-35471	49	14	help	help	AUX
cjfa-35471	49	15	create	create	VERB
cjfa-35471	49	16	an	an	DET
cjfa-35471	49	17	unstable	unstable	ADJ
cjfa-35471	49	18	economy	economy	NOUN
cjfa-35471	49	19	.	.	PUNCT
cjfa-35471	50	1	mitschell	mitschell	NOUN
cjfa-35471	50	2	(	(	PUNCT
cjfa-35471	50	3	2019	2019	NUM
cjfa-35471	50	4	)	)	PUNCT
cjfa-35471	50	5	concluded	conclude	VERB
cjfa-35471	50	6	that	that	SCONJ
cjfa-35471	50	7	incentives	incentive	NOUN
cjfa-35471	50	8	lead	lead	VERB
cjfa-35471	50	9	to	to	ADP
cjfa-35471	50	10	a	a	DET
cjfa-35471	50	11	slower	slow	ADJ
cjfa-35471	50	12	growth	growth	NOUN
cjfa-35471	50	13	.	.	PUNCT
cjfa-35471	51	1	a	a	DET
cjfa-35471	51	2	review	review	NOUN
cjfa-35471	51	3	report	report	NOUN
cjfa-35471	51	4	by	by	ADP
cjfa-35471	51	5	world	world	PROPN
cjfa-35471	51	6	bank	bank	PROPN
cjfa-35471	51	7	(	(	PUNCT
cjfa-35471	51	8	1999	1999	NUM
cjfa-35471	51	9	)	)	PUNCT
cjfa-35471	51	10	has	have	AUX
cjfa-35471	51	11	shown	show	VERB
cjfa-35471	51	12	that	that	SCONJ
cjfa-35471	51	13	,	,	PUNCT
cjfa-35471	51	14	when	when	SCONJ
cjfa-35471	51	15	all	all	DET
cjfa-35471	51	16	other	other	ADJ
cjfa-35471	51	17	factors	factor	NOUN
cjfa-35471	51	18	such	such	ADJ
cjfa-35471	51	19	as	as	ADP
cjfa-35471	51	20	infrastructure	infrastructure	NOUN
cjfa-35471	51	21	,	,	PUNCT
cjfa-35471	51	22	transport	transport	NOUN
cjfa-35471	51	23	costs	cost	NOUN
cjfa-35471	51	24	,	,	PUNCT
cjfa-35471	51	25	and	and	CCONJ
cjfa-35471	51	26	political	political	ADJ
cjfa-35471	51	27	and	and	CCONJ
cjfa-35471	51	28	economic	economic	ADJ
cjfa-35471	51	29	stability	stability	NOUN
cjfa-35471	51	30	,	,	PUNCT
cjfa-35471	51	31	are	be	AUX
cjfa-35471	51	32	approximately	approximately	ADV
cjfa-35471	51	33	equal	equal	ADJ
cjfa-35471	51	34	,	,	PUNCT
cjfa-35471	51	35	the	the	DET
cjfa-35471	51	36	taxes	taxis	NOUN
cjfa-35471	51	37	may	may	AUX
cjfa-35471	51	38	have	have	VERB
cjfa-35471	51	39	significant	significant	ADJ
cjfa-35471	51	40	impact	impact	NOUN
cjfa-35471	51	41	on	on	ADP
cjfa-35471	51	42	investors	investor	NOUN
cjfa-35471	51	43	’	’	PART
cjfa-35471	51	44	location	location	NOUN
cjfa-35471	51	45	choices	choice	NOUN
cjfa-35471	51	46	.	.	PUNCT
cjfa-35471	52	1	the	the	DET
cjfa-35471	52	2	report	report	NOUN
cjfa-35471	52	3	also	also	ADV
cjfa-35471	52	4	concluded	conclude	VERB
cjfa-35471	52	5	that	that	SCONJ
cjfa-35471	52	6	this	this	DET
cjfa-35471	52	7	effect	effect	NOUN
cjfa-35471	52	8	depends	depend	VERB
cjfa-35471	52	9	on	on	ADP
cjfa-35471	52	10	the	the	DET
cjfa-35471	52	11	tax	tax	NOUN
cjfa-35471	52	12	instrument	instrument	NOUN
cjfa-35471	52	13	.	.	PUNCT
cjfa-35471	53	1	miller	miller	PROPN
cjfa-35471	53	2	and	and	CCONJ
cjfa-35471	53	3	atkinson	atkinson	PROPN
cjfa-35471	53	4	(	(	PUNCT
cjfa-35471	53	5	2014	2014	NUM
cjfa-35471	53	6	)	)	PUNCT
cjfa-35471	53	7	concluded	conclude	VERB
cjfa-35471	53	8	that	that	SCONJ
cjfa-35471	53	9	investment	investment	NOUN
cjfa-35471	53	10	in	in	ADP
cjfa-35471	53	11	information	information	NOUN
cjfa-35471	53	12	and	and	CCONJ
cjfa-35471	53	13	communication	communication	NOUN
cjfa-35471	53	14	technology	technology	NOUN
cjfa-35471	53	15	(	(	PUNCT
cjfa-35471	53	16	ict	ict	PROPN
cjfa-35471	53	17	)	)	PUNCT
cjfa-35471	53	18	brings	bring	VERB
cjfa-35471	53	19	about	about	ADP
cjfa-35471	53	20	a	a	DET
cjfa-35471	53	21	transformative	transformative	ADJ
cjfa-35471	53	22	change	change	NOUN
cjfa-35471	53	23	to	to	ADP
cjfa-35471	53	24	organizations	organization	NOUN
cjfa-35471	53	25	resulting	result	VERB
cjfa-35471	53	26	in	in	ADP
cjfa-35471	53	27	increased	increase	VERB
cjfa-35471	53	28	productivity	productivity	NOUN
cjfa-35471	53	29	.	.	PUNCT
cjfa-35471	54	1	buss	buss	PROPN
cjfa-35471	54	2	(	(	PUNCT
cjfa-35471	54	3	2001	2001	NUM
cjfa-35471	54	4	)	)	PUNCT
cjfa-35471	54	5	,	,	PUNCT
cjfa-35471	54	6	in	in	ADP
cjfa-35471	54	7	his	his	PRON
cjfa-35471	54	8	review	review	NOUN
cjfa-35471	54	9	of	of	ADP
cjfa-35471	54	10	literature	literature	NOUN
cjfa-35471	54	11	report	report	NOUN
cjfa-35471	54	12	on	on	ADP
cjfa-35471	54	13	state	state	NOUN
cjfa-35471	54	14	tax	tax	NOUN
cjfa-35471	54	15	incentives	incentive	NOUN
cjfa-35471	54	16	,	,	PUNCT
cjfa-35471	54	17	summarized	summarize	VERB
cjfa-35471	54	18	his	his	PRON
cjfa-35471	54	19	report	report	NOUN
cjfa-35471	54	20	by	by	ADP
cjfa-35471	54	21	stating	state	VERB
cjfa-35471	54	22	that	that	SCONJ
cjfa-35471	54	23	tax	tax	NOUN
cjfa-35471	54	24	studies	study	NOUN
cjfa-35471	54	25	offer	offer	VERB
cjfa-35471	54	26	little	little	ADJ
cjfa-35471	54	27	guidance	guidance	NOUN
cjfa-35471	54	28	as	as	ADP
cjfa-35471	54	29	tools	tool	NOUN
cjfa-35471	54	30	of	of	ADP
cjfa-35471	54	31	economic	economic	ADJ
cjfa-35471	54	32	development	development	NOUN
cjfa-35471	54	33	.	.	PUNCT
cjfa-35471	55	1	klemm	klemm	NOUN
cjfa-35471	55	2	and	and	CCONJ
cjfa-35471	55	3	parys	parys	PROPN
cjfa-35471	55	4	(	(	PUNCT
cjfa-35471	55	5	2012	2012	NUM
cjfa-35471	55	6	)	)	PUNCT
cjfa-35471	55	7	found	find	VERB
cjfa-35471	55	8	the	the	DET
cjfa-35471	55	9	evidence	evidence	NOUN
cjfa-35471	55	10	that	that	SCONJ
cjfa-35471	55	11	taxes	taxis	NOUN
cjfa-35471	55	12	were	be	AUX
cjfa-35471	55	13	effective	effective	ADJ
cjfa-35471	55	14	attracting	attract	VERB
cjfa-35471	55	15	foreign	foreign	ADJ
cjfa-35471	55	16	direct	direct	ADJ
cjfa-35471	55	17	investment	investment	NOUN
cjfa-35471	55	18	into	into	ADP
cjfa-35471	55	19	latin	latin	PROPN
cjfa-35471	55	20	america	america	PROPN
cjfa-35471	55	21	and	and	CCONJ
cjfa-35471	55	22	caribbean	caribbean	ADJ
cjfa-35471	55	23	but	but	CCONJ
cjfa-35471	55	24	not	not	PART
cjfa-35471	55	25	effective	effective	ADJ
cjfa-35471	55	26	on	on	ADP
cjfa-35471	55	27	increasing	increase	VERB
cjfa-35471	55	28	gross	gross	ADJ
cjfa-35471	55	29	private	private	ADJ
cjfa-35471	55	30	fixed	fix	VERB
cjfa-35471	55	31	capital	capital	NOUN
cjfa-35471	55	32	.	.	PUNCT
cjfa-35471	56	1	crespi	crespi	PROPN
cjfa-35471	56	2	,	,	PUNCT
cjfa-35471	56	3	guiliodori	guiliodori	ADJ
cjfa-35471	56	4	,	,	PUNCT
cjfa-35471	56	5	guiliodori	guiliodori	NOUN
cjfa-35471	56	6	and	and	CCONJ
cjfa-35471	56	7	rodriguez	rodriguez	NOUN
cjfa-35471	56	8	(	(	PUNCT
cjfa-35471	56	9	2016	2016	NUM
cjfa-35471	56	10	)	)	PUNCT
cjfa-35471	56	11	studied	study	VERB
cjfa-35471	56	12	the	the	DET
cjfa-35471	56	13	impacts	impact	NOUN
cjfa-35471	56	14	of	of	ADP
cjfa-35471	56	15	mustafa	mustafa	PROPN
cjfa-35471	56	16	akan	akan	PROPN
cjfa-35471	56	17	,	,	PUNCT
cjfa-35471	56	18	natalia	natalia	PROPN
cjfa-35471	56	19	konovalova12	konovalova12	PROPN
cjfa-35471	56	20	promoting	promote	VERB
cjfa-35471	56	21	firm	firm	ADJ
cjfa-35471	56	22	level	level	NOUN
cjfa-35471	56	23	investments	investment	NOUN
cjfa-35471	56	24	in	in	ADP
cjfa-35471	56	25	r	r	NOUN
cjfa-35471	56	26	/	/	SYM
cjfa-35471	56	27	d	d	NOUN
cjfa-35471	56	28	in	in	ADP
cjfa-35471	56	29	argentina	argentina	PROPN
cjfa-35471	56	30	and	and	CCONJ
cjfa-35471	56	31	found	find	VERB
cjfa-35471	56	32	that	that	SCONJ
cjfa-35471	56	33	elasticity	elasticity	NOUN
cjfa-35471	56	34	of	of	ADP
cjfa-35471	56	35	such	such	ADJ
cjfa-35471	56	36	investments	investment	NOUN
cjfa-35471	56	37	is	be	AUX
cjfa-35471	56	38	greater	great	ADJ
cjfa-35471	56	39	than	than	ADP
cjfa-35471	56	40	1	1	NUM
cjfa-35471	56	41	and	and	CCONJ
cjfa-35471	56	42	effects	effect	NOUN
cjfa-35471	56	43	vary	vary	VERB
cjfa-35471	56	44	on	on	ADP
cjfa-35471	56	45	the	the	DET
cjfa-35471	56	46	sector	sector	NOUN
cjfa-35471	56	47	and	and	CCONJ
cjfa-35471	56	48	the	the	DET
cjfa-35471	56	49	size	size	NOUN
cjfa-35471	56	50	of	of	ADP
cjfa-35471	56	51	the	the	DET
cjfa-35471	56	52	firm	firm	NOUN
cjfa-35471	56	53	.	.	PUNCT
cjfa-35471	57	1	the	the	DET
cjfa-35471	57	2	effects	effect	NOUN
cjfa-35471	57	3	vary	vary	VERB
cjfa-35471	57	4	depending	depend	VERB
cjfa-35471	57	5	on	on	ADP
cjfa-35471	57	6	the	the	DET
cjfa-35471	57	7	type	type	NOUN
cjfa-35471	57	8	of	of	ADP
cjfa-35471	57	9	investment	investment	NOUN
cjfa-35471	57	10	considered	consider	VERB
cjfa-35471	57	11	.	.	PUNCT
cjfa-35471	58	1	zee	zee	NOUN
cjfa-35471	58	2	,	,	PUNCT
cjfa-35471	58	3	stotsky	stotsky	ADJ
cjfa-35471	58	4	and	and	CCONJ
cjfa-35471	58	5	ley	ley	PROPN
cjfa-35471	58	6	(	(	PUNCT
cjfa-35471	58	7	2002	2002	NUM
cjfa-35471	58	8	)	)	PUNCT
cjfa-35471	58	9	concluded	conclude	VERB
cjfa-35471	58	10	that	that	SCONJ
cjfa-35471	58	11	tax	tax	NOUN
cjfa-35471	58	12	incentives	incentive	NOUN
cjfa-35471	58	13	should	should	AUX
cjfa-35471	58	14	be	be	AUX
cjfa-35471	58	15	directed	direct	VERB
cjfa-35471	58	16	towards	towards	ADP
cjfa-35471	58	17	rectification	rectification	NOUN
cjfa-35471	58	18	of	of	ADP
cjfa-35471	58	19	market	market	NOUN
cjfa-35471	58	20	failures	failure	NOUN
cjfa-35471	58	21	and	and	CCONJ
cjfa-35471	58	22	that	that	SCONJ
cjfa-35471	58	23	cost	cost	VERB
cjfa-35471	58	24	effectiveness	effectiveness	NOUN
cjfa-35471	58	25	of	of	ADP
cjfa-35471	58	26	such	such	ADJ
cjfa-35471	58	27	incentives	incentive	NOUN
cjfa-35471	58	28	are	be	AUX
cjfa-35471	58	29	inconclusive	inconclusive	ADJ
cjfa-35471	58	30	.	.	PUNCT
cjfa-35471	59	1	in	in	ADP
cjfa-35471	59	2	their	their	PRON
cjfa-35471	59	3	recent	recent	ADJ
cjfa-35471	59	4	paper	paper	NOUN
cjfa-35471	59	5	,	,	PUNCT
cjfa-35471	59	6	tadesse	tadesse	ADJ
cjfa-35471	59	7	and	and	CCONJ
cjfa-35471	59	8	melaku	melaku	NOUN
cjfa-35471	59	9	(	(	PUNCT
cjfa-35471	59	10	2019	2019	NUM
cjfa-35471	59	11	)	)	PUNCT
cjfa-35471	59	12	has	have	AUX
cjfa-35471	59	13	shown	show	VERB
cjfa-35471	59	14	that	that	SCONJ
cjfa-35471	59	15	monetary	monetary	ADJ
cjfa-35471	59	16	policies	policy	NOUN
cjfa-35471	59	17	were	be	AUX
cjfa-35471	59	18	less	less	ADV
cjfa-35471	59	19	effective	effective	ADJ
cjfa-35471	59	20	than	than	ADP
cjfa-35471	59	21	fiscal	fiscal	ADJ
cjfa-35471	59	22	policies	policy	NOUN
cjfa-35471	59	23	in	in	ADP
cjfa-35471	59	24	the	the	DET
cjfa-35471	59	25	long	long	ADJ
cjfa-35471	59	26	run	run	NOUN
cjfa-35471	59	27	and	and	CCONJ
cjfa-35471	59	28	ineffective	ineffective	ADJ
cjfa-35471	59	29	in	in	ADP
cjfa-35471	59	30	the	the	DET
cjfa-35471	59	31	short	short	ADJ
cjfa-35471	59	32	run	run	NOUN
cjfa-35471	59	33	in	in	ADP
cjfa-35471	59	34	ethiopia	ethiopia	PROPN
cjfa-35471	59	35	.	.	PUNCT
cjfa-35471	60	1	the	the	DET
cjfa-35471	60	2	review	review	NOUN
cjfa-35471	60	3	of	of	ADP
cjfa-35471	60	4	literature	literature	NOUN
cjfa-35471	60	5	above	above	ADV
cjfa-35471	60	6	on	on	ADP
cjfa-35471	60	7	the	the	DET
cjfa-35471	60	8	impact	impact	NOUN
cjfa-35471	60	9	of	of	ADP
cjfa-35471	60	10	government	government	NOUN
cjfa-35471	60	11	incentives	incentive	NOUN
cjfa-35471	60	12	are	be	AUX
cjfa-35471	60	13	,	,	PUNCT
cjfa-35471	60	14	by	by	ADP
cjfa-35471	60	15	no	no	DET
cjfa-35471	60	16	means	mean	NOUN
cjfa-35471	60	17	,	,	PUNCT
cjfa-35471	60	18	exhaustive	exhaustive	ADJ
cjfa-35471	60	19	,	,	PUNCT
cjfa-35471	60	20	shows	show	VERB
cjfa-35471	60	21	that	that	SCONJ
cjfa-35471	60	22	they	they	PRON
cjfa-35471	60	23	are	be	AUX
cjfa-35471	60	24	largely	largely	ADV
cjfa-35471	60	25	ineffective	ineffective	ADJ
cjfa-35471	60	26	,	,	PUNCT
cjfa-35471	60	27	in	in	ADP
cjfa-35471	60	28	some	some	DET
cjfa-35471	60	29	cases	case	NOUN
cjfa-35471	60	30	detrimental	detrimental	ADJ
cjfa-35471	60	31	to	to	ADP
cjfa-35471	60	32	proper	proper	ADJ
cjfa-35471	60	33	functioning	functioning	NOUN
cjfa-35471	60	34	of	of	ADP
cjfa-35471	60	35	the	the	DET
cjfa-35471	60	36	economy	economy	NOUN
cjfa-35471	60	37	.	.	PUNCT
cjfa-35471	61	1	in	in	ADP
cjfa-35471	61	2	any	any	DET
cjfa-35471	61	3	case	case	NOUN
cjfa-35471	61	4	,	,	PUNCT
cjfa-35471	61	5	there	there	PRON
cjfa-35471	61	6	is	be	VERB
cjfa-35471	61	7	not	not	PART
cjfa-35471	61	8	a	a	DET
cjfa-35471	61	9	consensus	consensus	NOUN
cjfa-35471	61	10	on	on	ADP
cjfa-35471	61	11	the	the	DET
cjfa-35471	61	12	effectiveness	effectiveness	NOUN
cjfa-35471	61	13	of	of	ADP
cjfa-35471	61	14	such	such	ADJ
cjfa-35471	61	15	measures	measure	NOUN
cjfa-35471	61	16	.	.	PUNCT
cjfa-35471	62	1	some	some	DET
cjfa-35471	62	2	studies	study	NOUN
cjfa-35471	62	3	show	show	VERB
cjfa-35471	62	4	,	,	PUNCT
cjfa-35471	62	5	properly	properly	ADV
cjfa-35471	62	6	structured	structure	VERB
cjfa-35471	62	7	,	,	PUNCT
cjfa-35471	62	8	incentives	incentive	NOUN
cjfa-35471	62	9	may	may	AUX
cjfa-35471	62	10	have	have	VERB
cjfa-35471	62	11	positive	positive	ADJ
cjfa-35471	62	12	impacts	impact	NOUN
cjfa-35471	62	13	.	.	PUNCT
cjfa-35471	63	1	one	one	NUM
cjfa-35471	63	2	purpose	purpose	NOUN
cjfa-35471	63	3	of	of	ADP
cjfa-35471	63	4	this	this	DET
cjfa-35471	63	5	paper	paper	NOUN
cjfa-35471	63	6	is	be	AUX
cjfa-35471	63	7	to	to	PART
cjfa-35471	63	8	contribute	contribute	VERB
cjfa-35471	63	9	to	to	ADP
cjfa-35471	63	10	this	this	DET
cjfa-35471	63	11	search	search	NOUN
cjfa-35471	63	12	for	for	ADP
cjfa-35471	63	13	proper	proper	ADJ
cjfa-35471	63	14	incentives	incentive	NOUN
cjfa-35471	63	15	by	by	ADP
cjfa-35471	63	16	studying	study	VERB
cjfa-35471	63	17	the	the	DET
cjfa-35471	63	18	dynamic	dynamic	ADJ
cjfa-35471	63	19	behavior	behavior	NOUN
cjfa-35471	63	20	of	of	ADP
cjfa-35471	63	21	real	real	ADJ
cjfa-35471	63	22	sector	sector	NOUN
cjfa-35471	63	23	companies	company	NOUN
cjfa-35471	63	24	from	from	ADP
cjfa-35471	63	25	a	a	DET
cjfa-35471	63	26	micro	micro	ADJ
cjfa-35471	63	27	point	point	NOUN
cjfa-35471	63	28	of	of	ADP
cjfa-35471	63	29	view	view	NOUN
cjfa-35471	63	30	to	to	PART
cjfa-35471	63	31	determine	determine	VERB
cjfa-35471	63	32	the	the	DET
cjfa-35471	63	33	conditions	condition	NOUN
cjfa-35471	63	34	under	under	ADP
cjfa-35471	63	35	which	which	PRON
cjfa-35471	63	36	they	they	PRON
cjfa-35471	63	37	will	will	AUX
cjfa-35471	63	38	produce	produce	VERB
cjfa-35471	63	39	more	more	ADJ
cjfa-35471	63	40	under	under	ADP
cjfa-35471	63	41	various	various	ADJ
cjfa-35471	63	42	demand	demand	NOUN
cjfa-35471	63	43	expectations	expectation	NOUN
cjfa-35471	63	44	.	.	PUNCT
cjfa-35471	64	1	another	another	DET
cjfa-35471	64	2	purpose	purpose	NOUN
cjfa-35471	64	3	of	of	ADP
cjfa-35471	64	4	the	the	DET
cjfa-35471	64	5	paper	paper	NOUN
cjfa-35471	64	6	is	be	AUX
cjfa-35471	64	7	to	to	PART
cjfa-35471	64	8	analyze	analyze	VERB
cjfa-35471	64	9	the	the	DET
cjfa-35471	64	10	factors	factor	NOUN
cjfa-35471	64	11	that	that	PRON
cjfa-35471	64	12	affect	affect	VERB
cjfa-35471	64	13	the	the	DET
cjfa-35471	64	14	production	production	NOUN
cjfa-35471	64	15	behavior	behavior	NOUN
cjfa-35471	64	16	of	of	ADP
cjfa-35471	64	17	the	the	DET
cjfa-35471	64	18	firms	firm	NOUN
cjfa-35471	64	19	and	and	CCONJ
cjfa-35471	64	20	suggest	suggest	VERB
cjfa-35471	64	21	more	more	ADV
cjfa-35471	64	22	realistic	realistic	ADJ
cjfa-35471	64	23	macro	macro	ADJ
cjfa-35471	64	24	policies	policy	NOUN
cjfa-35471	64	25	to	to	PART
cjfa-35471	64	26	increase	increase	VERB
cjfa-35471	64	27	growth	growth	NOUN
cjfa-35471	64	28	other	other	ADJ
cjfa-35471	64	29	than	than	ADP
cjfa-35471	64	30	reduction	reduction	NOUN
cjfa-35471	64	31	of	of	ADP
cjfa-35471	64	32	borrowing	borrowing	NOUN
cjfa-35471	64	33	costs	cost	NOUN
cjfa-35471	64	34	(	(	PUNCT
cjfa-35471	64	35	interest	interest	NOUN
cjfa-35471	64	36	rates	rate	NOUN
cjfa-35471	64	37	)	)	PUNCT
cjfa-35471	64	38	.	.	PUNCT
cjfa-35471	65	1	it	it	PRON
cjfa-35471	65	2	is	be	AUX
cjfa-35471	65	3	not	not	PART
cjfa-35471	65	4	the	the	DET
cjfa-35471	65	5	purpose	purpose	NOUN
cjfa-35471	65	6	of	of	ADP
cjfa-35471	65	7	this	this	DET
cjfa-35471	65	8	paper	paper	NOUN
cjfa-35471	65	9	to	to	PART
cjfa-35471	65	10	compare	compare	VERB
cjfa-35471	65	11	the	the	DET
cjfa-35471	65	12	effectiveness	effectiveness	NOUN
cjfa-35471	65	13	of	of	ADP
cjfa-35471	65	14	micro	micro	ADJ
cjfa-35471	65	15	and	and	CCONJ
cjfa-35471	65	16	macro	macro	ADJ
cjfa-35471	65	17	policies	policy	NOUN
cjfa-35471	65	18	or	or	CCONJ
cjfa-35471	65	19	to	to	PART
cjfa-35471	65	20	search	search	VERB
cjfa-35471	65	21	for	for	ADP
cjfa-35471	65	22	incentives	incentive	NOUN
cjfa-35471	65	23	to	to	PART
cjfa-35471	65	24	increase	increase	VERB
cjfa-35471	65	25	consumption	consumption	NOUN
cjfa-35471	65	26	.	.	PUNCT
cjfa-35471	66	1	in	in	ADP
cjfa-35471	66	2	the	the	DET
cjfa-35471	66	3	next	next	ADJ
cjfa-35471	66	4	section	section	NOUN
cjfa-35471	66	5	,	,	PUNCT
cjfa-35471	66	6	a	a	DET
cjfa-35471	66	7	brief	brief	ADJ
cjfa-35471	66	8	review	review	NOUN
cjfa-35471	66	9	on	on	ADP
cjfa-35471	66	10	incentives	incentive	NOUN
cjfa-35471	66	11	for	for	ADP
cjfa-35471	66	12	firms	firm	NOUN
cjfa-35471	66	13	will	will	AUX
cjfa-35471	66	14	be	be	AUX
cjfa-35471	66	15	provided	provide	VERB
cjfa-35471	66	16	.	.	PUNCT
cjfa-35471	67	1	in	in	ADP
cjfa-35471	67	2	section	section	PROPN
cjfa-35471	67	3	iii	iii	PROPN
cjfa-35471	67	4	.	.	PUNCT
cjfa-35471	68	1	a	a	DET
cjfa-35471	68	2	general	general	ADJ
cjfa-35471	68	3	dynamic	dynamic	ADJ
cjfa-35471	68	4	model	model	NOUN
cjfa-35471	68	5	of	of	ADP
cjfa-35471	68	6	a	a	DET
cjfa-35471	68	7	real	real	ADJ
cjfa-35471	68	8	sector	sector	NOUN
cjfa-35471	68	9	company	company	NOUN
cjfa-35471	68	10	(	(	PUNCT
cjfa-35471	68	11	nonservice	nonservice	NOUN
cjfa-35471	68	12	)	)	PUNCT
cjfa-35471	68	13	operating	operate	VERB
cjfa-35471	68	14	in	in	ADP
cjfa-35471	68	15	a	a	DET
cjfa-35471	68	16	competitive	competitive	ADJ
cjfa-35471	68	17	environment	environment	NOUN
cjfa-35471	68	18	facing	face	VERB
cjfa-35471	68	19	oscillating	oscillate	VERB
cjfa-35471	68	20	demand	demand	NOUN
cjfa-35471	68	21	and	and	CCONJ
cjfa-35471	68	22	different	different	ADJ
cjfa-35471	68	23	interest	interest	NOUN
cjfa-35471	68	24	rate	rate	NOUN
cjfa-35471	68	25	expectations	expectation	NOUN
cjfa-35471	68	26	will	will	AUX
cjfa-35471	68	27	be	be	AUX
cjfa-35471	68	28	developed	develop	VERB
cjfa-35471	68	29	using	use	VERB
cjfa-35471	68	30	an	an	DET
cjfa-35471	68	31	optimal	optimal	ADJ
cjfa-35471	68	32	control	control	NOUN
cjfa-35471	68	33	theoretic	theoretic	NOUN
cjfa-35471	68	34	model	model	NOUN
cjfa-35471	68	35	will	will	AUX
cjfa-35471	68	36	be	be	AUX
cjfa-35471	68	37	presented	present	VERB
cjfa-35471	68	38	.	.	PUNCT
cjfa-35471	69	1	the	the	DET
cjfa-35471	69	2	examples	example	NOUN
cjfa-35471	69	3	of	of	ADP
cjfa-35471	69	4	solutions	solution	NOUN
cjfa-35471	69	5	under	under	ADP
cjfa-35471	69	6	different	different	ADJ
cjfa-35471	69	7	assumptions	assumption	NOUN
cjfa-35471	69	8	will	will	AUX
cjfa-35471	69	9	be	be	AUX
cjfa-35471	69	10	solved	solve	VERB
cjfa-35471	69	11	in	in	ADP
cjfa-35471	69	12	the	the	DET
cjfa-35471	69	13	section	section	NOUN
cjfa-35471	69	14	iv	iv	NUM
cjfa-35471	69	15	to	to	PART
cjfa-35471	69	16	observe	observe	VERB
cjfa-35471	69	17	the	the	DET
cjfa-35471	69	18	effects	effect	NOUN
cjfa-35471	69	19	of	of	ADP
cjfa-35471	69	20	changes	change	NOUN
cjfa-35471	69	21	in	in	ADP
cjfa-35471	69	22	some	some	DET
cjfa-35471	69	23	parameters	parameter	NOUN
cjfa-35471	69	24	such	such	ADJ
cjfa-35471	69	25	as	as	ADP
cjfa-35471	69	26	interest	interest	NOUN
cjfa-35471	69	27	rates	rate	NOUN
cjfa-35471	69	28	,	,	PUNCT
cjfa-35471	69	29	costs	cost	NOUN
cjfa-35471	69	30	,	,	PUNCT
cjfa-35471	69	31	and	and	CCONJ
cjfa-35471	69	32	changes	change	NOUN
cjfa-35471	69	33	in	in	ADP
cjfa-35471	69	34	demand	demand	NOUN
cjfa-35471	69	35	structure	structure	NOUN
cjfa-35471	69	36	.	.	PUNCT
cjfa-35471	70	1	results	result	NOUN
cjfa-35471	70	2	,	,	PUNCT
cjfa-35471	70	3	conclusions	conclusion	NOUN
cjfa-35471	70	4	,	,	PUNCT
cjfa-35471	70	5	and	and	CCONJ
cjfa-35471	70	6	policy	policy	NOUN
cjfa-35471	70	7	implications	implication	NOUN
cjfa-35471	70	8	of	of	ADP
cjfa-35471	70	9	the	the	DET
cjfa-35471	70	10	results	result	NOUN
cjfa-35471	70	11	will	will	AUX
cjfa-35471	70	12	follow	follow	VERB
cjfa-35471	70	13	in	in	ADP
cjfa-35471	70	14	subsequent	subsequent	ADJ
cjfa-35471	70	15	sections	section	NOUN
cjfa-35471	70	16	.	.	PUNCT
cjfa-35471	71	1	some	some	DET
cjfa-35471	71	2	further	further	ADJ
cjfa-35471	71	3	research	research	NOUN
cjfa-35471	71	4	will	will	AUX
cjfa-35471	71	5	be	be	AUX
cjfa-35471	71	6	suggested	suggest	VERB
cjfa-35471	71	7	in	in	ADP
cjfa-35471	71	8	the	the	DET
cjfa-35471	71	9	last	last	ADJ
cjfa-35471	71	10	section	section	NOUN
cjfa-35471	71	11	.	.	PUNCT
cjfa-35471	72	1	optimal	optimal	ADJ
cjfa-35471	72	2	incentives	incentive	NOUN
cjfa-35471	72	3	for	for	ADP
cjfa-35471	72	4	economic	economic	ADJ
cjfa-35471	72	5	growth	growth	NOUN
cjfa-35471	72	6	…	…	PUNCT
cjfa-35471	72	7	13	13	NUM
cjfa-35471	72	8	research	research	NOUN
cjfa-35471	72	9	methodology	methodology	NOUN
cjfa-35471	72	10	the	the	DET
cjfa-35471	72	11	general	general	ADJ
cjfa-35471	72	12	scheduling	scheduling	NOUN
cjfa-35471	72	13	production	production	NOUN
cjfa-35471	72	14	planning	planning	NOUN
cjfa-35471	72	15	problem	problem	NOUN
cjfa-35471	72	16	of	of	ADP
cjfa-35471	72	17	a	a	DET
cjfa-35471	72	18	firm	firm	NOUN
cjfa-35471	72	19	operating	operate	VERB
cjfa-35471	72	20	in	in	ADP
cjfa-35471	72	21	a	a	DET
cjfa-35471	72	22	perfectly	perfectly	ADV
cjfa-35471	72	23	competitive	competitive	ADJ
cjfa-35471	72	24	market	market	NOUN
cjfa-35471	72	25	(	(	PUNCT
cjfa-35471	72	26	where	where	SCONJ
cjfa-35471	72	27	price	price	NOUN
cjfa-35471	72	28	is	be	AUX
cjfa-35471	72	29	constant	constant	ADJ
cjfa-35471	72	30	)	)	PUNCT
cjfa-35471	72	31	can	can	AUX
cjfa-35471	72	32	be	be	AUX
cjfa-35471	72	33	modelled	model	VERB
cjfa-35471	72	34	as	as	ADP
cjfa-35471	72	35	a	a	DET
cjfa-35471	72	36	cost	cost	NOUN
cjfa-35471	72	37	minimization	minimization	NOUN
cjfa-35471	72	38	(	(	PUNCT
cjfa-35471	72	39	sum	sum	NOUN
cjfa-35471	72	40	of	of	ADP
cjfa-35471	72	41	cost	cost	NOUN
cjfa-35471	72	42	of	of	ADP
cjfa-35471	72	43	production	production	NOUN
cjfa-35471	72	44	and	and	CCONJ
cjfa-35471	72	45	inventory	inventory	NOUN
cjfa-35471	72	46	holding	hold	VERB
cjfa-35471	72	47	cost	cost	NOUN
cjfa-35471	72	48	)	)	PUNCT
cjfa-35471	72	49	where	where	SCONJ
cjfa-35471	72	50	:	:	PUNCT
cjfa-35471	72	51	u(t	u(t	NOUN
cjfa-35471	72	52	):	):	PUNCT
cjfa-35471	72	53	the	the	DET
cjfa-35471	72	54	level	level	NOUN
cjfa-35471	72	55	of	of	ADP
cjfa-35471	72	56	production	production	NOUN
cjfa-35471	72	57	at	at	ADP
cjfa-35471	72	58	time	time	NOUN
cjfa-35471	72	59	t	t	PROPN
cjfa-35471	72	60	,	,	PUNCT
cjfa-35471	72	61	c(u	c(u	PROPN
cjfa-35471	72	62	):	):	PUNCT
cjfa-35471	72	63	strictly	strictly	ADV
cjfa-35471	72	64	convex	convex	VERB
cjfa-35471	72	65	cost	cost	NOUN
cjfa-35471	72	66	function	function	NOUN
cjfa-35471	72	67	h	h	NOUN
cjfa-35471	72	68	:	:	PUNCT
cjfa-35471	72	69	unit	unit	NOUN
cjfa-35471	72	70	holding	hold	VERB
cjfa-35471	72	71	cost	cost	NOUN
cjfa-35471	72	72	,	,	PUNCT
cjfa-35471	72	73	a	a	DET
cjfa-35471	72	74	constant	constant	ADJ
cjfa-35471	72	75	.	.	PUNCT
cjfa-35471	73	1	these	these	DET
cjfa-35471	73	2	costs	cost	NOUN
cjfa-35471	73	3	include	include	VERB
cjfa-35471	73	4	many	many	ADJ
cjfa-35471	73	5	cost	cost	NOUN
cjfa-35471	73	6	items	item	NOUN
cjfa-35471	73	7	such	such	ADJ
cjfa-35471	73	8	as	as	ADP
cjfa-35471	73	9	rent	rent	NOUN
cjfa-35471	73	10	,	,	PUNCT
cjfa-35471	73	11	cost	cost	NOUN
cjfa-35471	73	12	of	of	ADP
cjfa-35471	73	13	relevant	relevant	ADJ
cjfa-35471	73	14	equipment	equipment	NOUN
cjfa-35471	73	15	necessary	necessary	ADJ
cjfa-35471	73	16	to	to	PART
cjfa-35471	73	17	keep	keep	VERB
cjfa-35471	73	18	the	the	DET
cjfa-35471	73	19	products	product	NOUN
cjfa-35471	73	20	in	in	ADP
cjfa-35471	73	21	the	the	DET
cjfa-35471	73	22	inventory	inventory	NOUN
cjfa-35471	73	23	,	,	PUNCT
cjfa-35471	73	24	and	and	CCONJ
cjfa-35471	73	25	insurance	insurance	NOUN
cjfa-35471	73	26	premiums	premium	NOUN
cjfa-35471	73	27	.	.	PUNCT
cjfa-35471	74	1	r(t	r(t	NOUN
cjfa-35471	74	2	):	):	PUNCT
cjfa-35471	74	3	level	level	NOUN
cjfa-35471	74	4	of	of	ADP
cjfa-35471	74	5	demand	demand	NOUN
cjfa-35471	74	6	that	that	PRON
cjfa-35471	74	7	is	be	AUX
cjfa-35471	74	8	an	an	DET
cjfa-35471	74	9	exogenously	exogenously	ADV
cjfa-35471	74	10	determined	determine	VERB
cjfa-35471	74	11	function	function	NOUN
cjfa-35471	74	12	of	of	ADP
cjfa-35471	74	13	time	time	NOUN
cjfa-35471	74	14	l(t	l(t	PROPN
cjfa-35471	74	15	):	):	PUNCT
cjfa-35471	74	16	the	the	DET
cjfa-35471	74	17	level	level	NOUN
cjfa-35471	74	18	of	of	ADP
cjfa-35471	74	19	inventory	inventory	NOUN
cjfa-35471	74	20	at	at	ADP
cjfa-35471	74	21	time	time	NOUN
cjfa-35471	74	22	t	t	PROPN
cjfa-35471	74	23	,	,	PUNCT
cjfa-35471	74	24	which	which	PRON
cjfa-35471	74	25	increases	increase	VERB
cjfa-35471	74	26	by	by	ADP
cjfa-35471	74	27	production	production	NOUN
cjfa-35471	74	28	(	(	PUNCT
cjfa-35471	74	29	u(t	u(t	NOUN
cjfa-35471	74	30	)	)	PUNCT
cjfa-35471	74	31	and	and	CCONJ
cjfa-35471	74	32	decreases	decrease	NOUN
cjfa-35471	74	33	by	by	ADP
cjfa-35471	74	34	sales	sale	NOUN
cjfa-35471	74	35	r(t	r(t	NOUN
cjfa-35471	74	36	)	)	PUNCT
cjfa-35471	74	37	.	.	PUNCT
cjfa-35471	75	1	therefore	therefore	ADV
cjfa-35471	75	2	,	,	PUNCT
cjfa-35471	75	3	the	the	DET
cjfa-35471	75	4	model	model	NOUN
cjfa-35471	75	5	,	,	PUNCT
cjfa-35471	75	6	is	be	AUX
cjfa-35471	75	7	ℎ	ℎ	PROPN
cjfa-35471	75	8	:	:	PUNCT
cjfa-35471	75	9	unit	unit	NOUN
cjfa-35471	75	10	holding	hold	VERB
cjfa-35471	75	11	cost	cost	NOUN
cjfa-35471	75	12	,	,	PUNCT
cjfa-35471	75	13	a	a	DET
cjfa-35471	75	14	constant	constant	ADJ
cjfa-35471	75	15	.	.	PUNCT
cjfa-35471	76	1	these	these	DET
cjfa-35471	76	2	costs	cost	NOUN
cjfa-35471	76	3	include	include	VERB
cjfa-35471	76	4	many	many	ADJ
cjfa-35471	76	5	cost	cost	NOUN
cjfa-35471	76	6	items	item	NOUN
cjfa-35471	76	7	such	such	ADJ
cjfa-35471	76	8	as	as	ADP
cjfa-35471	76	9	rent	rent	NOUN
cjfa-35471	76	10	,	,	PUNCT
cjfa-35471	76	11	cost	cost	NOUN
cjfa-35471	76	12	of	of	ADP
cjfa-35471	76	13	relevant	relevant	ADJ
cjfa-35471	76	14	equipment	equipment	NOUN
cjfa-35471	76	15	necessary	necessary	ADJ
cjfa-35471	76	16	to	to	PART
cjfa-35471	76	17	keep	keep	VERB
cjfa-35471	76	18	the	the	DET
cjfa-35471	76	19	products	product	NOUN
cjfa-35471	76	20	in	in	ADP
cjfa-35471	76	21	the	the	DET
cjfa-35471	76	22	inventory	inventory	NOUN
cjfa-35471	76	23	,	,	PUNCT
cjfa-35471	76	24	and	and	CCONJ
cjfa-35471	76	25	insurance	insurance	NOUN
cjfa-35471	76	26	premiums	premium	NOUN
cjfa-35471	76	27	.	.	PUNCT
cjfa-35471	77	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	77	2	:	:	PUNCT
cjfa-35471	77	3	level	level	NOUN
cjfa-35471	77	4	of	of	ADP
cjfa-35471	77	5	demand	demand	NOUN
cjfa-35471	77	6	that	that	PRON
cjfa-35471	77	7	is	be	AUX
cjfa-35471	77	8	an	an	DET
cjfa-35471	77	9	exogenously	exogenously	ADV
cjfa-35471	77	10	determined	determine	VERB
cjfa-35471	77	11	function	function	NOUN
cjfa-35471	77	12	of	of	ADP
cjfa-35471	77	13	time	time	NOUN
cjfa-35471	77	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	77	15	:	:	PUNCT
cjfa-35471	77	16	the	the	DET
cjfa-35471	77	17	level	level	NOUN
cjfa-35471	77	18	of	of	ADP
cjfa-35471	77	19	inventory	inventory	NOUN
cjfa-35471	77	20	at	at	ADP
cjfa-35471	77	21	time	time	NOUN
cjfa-35471	77	22	t	t	PROPN
cjfa-35471	77	23	,	,	PUNCT
cjfa-35471	77	24	which	which	PRON
cjfa-35471	77	25	increases	increase	VERB
cjfa-35471	77	26	by	by	ADP
cjfa-35471	77	27	production	production	NOUN
cjfa-35471	77	28	(	(	PUNCT
cjfa-35471	77	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	77	30	and	and	CCONJ
cjfa-35471	77	31	decreases	decrease	NOUN
cjfa-35471	77	32	by	by	ADP
cjfa-35471	77	33	sales	sale	NOUN
cjfa-35471	77	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	77	35	therefore	therefore	ADV
cjfa-35471	77	36	,	,	PUNCT
cjfa-35471	77	37	the	the	DET
cjfa-35471	77	38	model	model	NOUN
cjfa-35471	77	39	,	,	PUNCT
cjfa-35471	77	40	is	be	AUX
cjfa-35471	77	41	(	(	PUNCT
cjfa-35471	77	42	)	)	PUNCT
cjfa-35471	77	43	0	0	NUM
cjfa-35471	78	1	max	max	PROPN
cjfa-35471	78	2	[	[	PUNCT
cjfa-35471	78	3	(	(	PUNCT
cjfa-35471	78	4	(	(	PUNCT
cjfa-35471	78	5	)	)	PUNCT
cjfa-35471	78	6	)	)	PUNCT
cjfa-35471	78	7	(	(	PUNCT
cjfa-35471	78	8	)	)	PUNCT
cjfa-35471	78	9	]	]	PUNCT
cjfa-35471	79	1	t	t	X
cjfa-35471	79	2	u	u	NOUN
cjfa-35471	79	3	t	t	X
cjfa-35471	79	4	c	c	NOUN
cjfa-35471	79	5	u	u	NOUN
cjfa-35471	79	6	t	t	X
cjfa-35471	79	7	hi	hi	INTJ
cjfa-35471	79	8	t	t	PROPN
cjfa-35471	79	9	dt	dt	NOUN
cjfa-35471	79	10	subject	subject	NOUN
cjfa-35471	79	11	to	to	ADP
cjfa-35471	79	12	the	the	DET
cjfa-35471	79	13	constraints	constraint	NOUN
cjfa-35471	79	14	:	:	PUNCT
cjfa-35471	79	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	79	16	�	�	PROPN
cjfa-35471	79	17	=	=	PUNCT
cjfa-35471	79	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	79	19	−	−	X
cjfa-35471	79	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	79	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	80	1	=	=	SYM
cjfa-35471	80	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	80	3	�	�	PROPN
cjfa-35471	80	4	given	give	VERB
cjfa-35471	80	5	and	and	CCONJ
cjfa-35471	80	6	the	the	DET
cjfa-35471	80	7	non	non	ADJ
cjfa-35471	80	8	-	-	ADJ
cjfa-35471	80	9	negativity	negativity	ADJ
cjfa-35471	80	10	constraints	constraint	NOUN
cjfa-35471	80	11	.	.	PUNCT
cjfa-35471	81	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	81	2	≥	≥	PROPN
cjfa-35471	81	3	0	0	NUM
cjfa-35471	81	4	,	,	PUNCT
cjfa-35471	81	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	81	6	≥	≥	NOUN
cjfa-35471	81	7	0	0	NUM
cjfa-35471	81	8	cost	cost	NOUN
cjfa-35471	81	9	minimization	minimization	NOUN
cjfa-35471	81	10	is	be	AUX
cjfa-35471	81	11	considered	consider	VERB
cjfa-35471	81	12	since	since	SCONJ
cjfa-35471	81	13	the	the	DET
cjfa-35471	81	14	price	price	NOUN
cjfa-35471	81	15	is	be	AUX
cjfa-35471	81	16	assumed	assume	VERB
cjfa-35471	81	17	to	to	PART
cjfa-35471	81	18	be	be	AUX
cjfa-35471	81	19	constant	constant	ADJ
cjfa-35471	81	20	and	and	CCONJ
cjfa-35471	81	21	the	the	DET
cjfa-35471	81	22	demand	demand	NOUN
cjfa-35471	81	23	,	,	PUNCT
cjfa-35471	81	24	r(t	r(t	NOUN
cjfa-35471	81	25	)	)	PUNCT
cjfa-35471	81	26	,	,	PUNCT
cjfa-35471	81	27	is	be	AUX
cjfa-35471	81	28	an	an	DET
cjfa-35471	81	29	exogenous	exogenous	ADJ
cjfa-35471	81	30	time	time	NOUN
cjfa-35471	81	31	dependent	dependent	ADJ
cjfa-35471	81	32	function	function	NOUN
cjfa-35471	81	33	making	make	VERB
cjfa-35471	81	34	the	the	DET
cjfa-35471	81	35	revenues	revenue	NOUN
cjfa-35471	81	36	an	an	DET
cjfa-35471	81	37	exogenous	exogenous	ADJ
cjfa-35471	81	38	function	function	NOUN
cjfa-35471	81	39	also	also	ADV
cjfa-35471	81	40	thus	thus	ADV
cjfa-35471	81	41	irrelevant	irrelevant	ADJ
cjfa-35471	81	42	in	in	ADP
cjfa-35471	81	43	decision	decision	NOUN
cjfa-35471	81	44	making	making	NOUN
cjfa-35471	81	45	.	.	PUNCT
cjfa-35471	82	1	the	the	DET
cjfa-35471	82	2	last	last	ADJ
cjfa-35471	82	3	constraint	constraint	NOUN
cjfa-35471	82	4	is	be	AUX
cjfa-35471	82	5	a	a	DET
cjfa-35471	82	6	state	state	NOUN
cjfa-35471	82	7	variable	variable	ADJ
cjfa-35471	82	8	inequality	inequality	NOUN
cjfa-35471	82	9	constraint	constraint	NOUN
cjfa-35471	82	10	which	which	PRON
cjfa-35471	82	11	has	have	AUX
cjfa-35471	82	12	been	be	AUX
cjfa-35471	82	13	studied	study	VERB
cjfa-35471	82	14	by	by	ADP
cjfa-35471	82	15	many	many	ADJ
cjfa-35471	82	16	authors	author	NOUN
cjfa-35471	82	17	including	include	VERB
cjfa-35471	82	18	bryson	bryson	PROPN
cjfa-35471	82	19	and	and	CCONJ
cjfa-35471	82	20	ho	ho	PROPN
cjfa-35471	82	21	(	(	PUNCT
cjfa-35471	82	22	1975	1975	NUM
cjfa-35471	82	23	)	)	PUNCT
cjfa-35471	82	24	,	,	PUNCT
cjfa-35471	82	25	bryson	bryson	PROPN
cjfa-35471	82	26	,	,	PUNCT
cjfa-35471	82	27	denham	denham	PROPN
cjfa-35471	82	28	and	and	CCONJ
cjfa-35471	82	29	dreyfus	dreyfus	PROPN
cjfa-35471	82	30	(	(	PUNCT
cjfa-35471	82	31	1963	1963	NUM
cjfa-35471	82	32	)	)	PUNCT
cjfa-35471	82	33	,	,	PUNCT
cjfa-35471	82	34	jacobson	jacobson	PROPN
cjfa-35471	82	35	and	and	CCONJ
cjfa-35471	82	36	lele	lele	PROPN
cjfa-35471	82	37	(	(	PUNCT
cjfa-35471	82	38	1969	1969	NUM
cjfa-35471	82	39	)	)	PUNCT
cjfa-35471	82	40	,	,	PUNCT
cjfa-35471	82	41	jacobson	jacobson	PROPN
cjfa-35471	82	42	,	,	PUNCT
cjfa-35471	82	43	lele	lele	PROPN
cjfa-35471	82	44	and	and	CCONJ
cjfa-35471	82	45	speyer	speyer	PROPN
cjfa-35471	82	46	(	(	PUNCT
cjfa-35471	82	47	1971	1971	NUM
cjfa-35471	82	48	)	)	PUNCT
cjfa-35471	82	49	,	,	PUNCT
cjfa-35471	82	50	mcintyre	mcintyre	PROPN
cjfa-35471	82	51	and	and	CCONJ
cjfa-35471	82	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	82	53	(	(	PUNCT
cjfa-35471	82	54	1967	1967	NUM
cjfa-35471	82	55	)	)	PUNCT
cjfa-35471	82	56	,	,	PUNCT
cjfa-35471	82	57	and	and	CCONJ
cjfa-35471	82	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	82	59	(	(	PUNCT
cjfa-35471	82	60	1967	1967	NUM
cjfa-35471	82	61	)	)	PUNCT
cjfa-35471	82	62	.	.	PUNCT
cjfa-35471	83	1	taylor	taylor	PROPN
cjfa-35471	83	2	(	(	PUNCT
cjfa-35471	83	3	1972	1972	NUM
cjfa-35471	83	4	)	)	PUNCT
cjfa-35471	83	5	studied	study	VERB
cjfa-35471	83	6	the	the	DET
cjfa-35471	83	7	problem	problem	NOUN
cjfa-35471	83	8	stated	state	VERB
cjfa-35471	83	9	above	above	ADV
cjfa-35471	83	10	with	with	ADP
cjfa-35471	83	11	no	no	DET
cjfa-35471	83	12	interest	interest	NOUN
cjfa-35471	83	13	rate	rate	NOUN
cjfa-35471	83	14	consideration	consideration	NOUN
cjfa-35471	83	15	and	and	CCONJ
cjfa-35471	83	16	has	have	AUX
cjfa-35471	83	17	found	find	VERB
cjfa-35471	83	18	that	that	SCONJ
cjfa-35471	83	19	;	;	PUNCT
cjfa-35471	84	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	84	2	�	�	PROPN
cjfa-35471	84	3	�	�	PROPN
cjfa-35471	84	4	�	�	PROPN
cjfa-35471	84	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	84	6	�	�	PROPN
cjfa-35471	84	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	84	8	�	�	PROPN
cjfa-35471	84	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	84	10	𝑡	𝑡	NOUN
cjfa-35471	84	11	ℎ	ℎ	PROPN
cjfa-35471	84	12	is	be	AUX
cjfa-35471	84	13	the	the	DET
cjfa-35471	84	14	condition	condition	NOUN
cjfa-35471	84	15	which	which	PRON
cjfa-35471	84	16	has	have	VERB
cjfa-35471	84	17	to	to	PART
cjfa-35471	84	18	hold	hold	VERB
cjfa-35471	84	19	for	for	ADP
cjfa-35471	84	20	the	the	DET
cjfa-35471	84	21	firm	firm	NOUN
cjfa-35471	84	22	to	to	PART
cjfa-35471	84	23	keep	keep	VERB
cjfa-35471	84	24	i	i	PRON
cjfa-35471	84	25	(	(	PUNCT
cjfa-35471	84	26	t	t	NOUN
cjfa-35471	84	27	)	)	PUNCT
cjfa-35471	84	28	=	=	NOUN
cjfa-35471	84	29	0	0	NUM
cjfa-35471	84	30	which	which	PRON
cjfa-35471	84	31	implies	imply	VERB
cjfa-35471	84	32	that	that	SCONJ
cjfa-35471	84	33	the	the	DET
cjfa-35471	84	34	firm	firm	NOUN
cjfa-35471	84	35	will	will	AUX
cjfa-35471	84	36	produce	produce	VERB
cjfa-35471	84	37	just	just	ADV
cjfa-35471	84	38	to	to	PART
cjfa-35471	84	39	meet	meet	VERB
cjfa-35471	84	40	the	the	DET
cjfa-35471	84	41	demand	demand	NOUN
cjfa-35471	84	42	.	.	PUNCT
cjfa-35471	85	1	the	the	DET
cjfa-35471	85	2	firm	firm	NOUN
cjfa-35471	85	3	will	will	AUX
cjfa-35471	85	4	start	start	VERB
cjfa-35471	85	5	producing	produce	VERB
cjfa-35471	85	6	not	not	PART
cjfa-35471	85	7	only	only	ADV
cjfa-35471	85	8	to	to	PART
cjfa-35471	85	9	meet	meet	VERB
cjfa-35471	85	10	the	the	DET
cjfa-35471	85	11	demand	demand	NOUN
cjfa-35471	85	12	but	but	CCONJ
cjfa-35471	85	13	also	also	ADV
cjfa-35471	85	14	to	to	PART
cjfa-35471	85	15	build	build	VERB
cjfa-35471	85	16	up	up	ADP
cjfa-35471	85	17	inventories	inventory	NOUN
cjfa-35471	85	18	when	when	SCONJ
cjfa-35471	85	19	the	the	DET
cjfa-35471	85	20	change	change	NOUN
cjfa-35471	85	21	in	in	ADP
cjfa-35471	85	22	demand	demand	NOUN
cjfa-35471	85	23	is	be	AUX
cjfa-35471	85	24	such	such	ADJ
cjfa-35471	85	25	that	that	SCONJ
cjfa-35471	85	26	the	the	DET
cjfa-35471	85	27	above	above	ADJ
cjfa-35471	85	28	inequality	inequality	NOUN
cjfa-35471	85	29	will	will	AUX
cjfa-35471	85	30	be	be	AUX
cjfa-35471	85	31	violated	violate	VERB
cjfa-35471	85	32	.	.	PUNCT
cjfa-35471	86	1	in	in	ADP
cjfa-35471	86	2	this	this	DET
cjfa-35471	86	3	paper	paper	NOUN
cjfa-35471	86	4	,	,	PUNCT
cjfa-35471	86	5	we	we	PRON
cjfa-35471	86	6	will	will	AUX
cjfa-35471	86	7	study	study	VERB
cjfa-35471	86	8	the	the	DET
cjfa-35471	86	9	same	same	ADJ
cjfa-35471	86	10	problem	problem	NOUN
cjfa-35471	86	11	introducing	introduce	VERB
cjfa-35471	86	12	present	present	ADJ
cjfa-35471	86	13	value	value	NOUN
cjfa-35471	86	14	factor	factor	NOUN
cjfa-35471	86	15	and	and	CCONJ
cjfa-35471	86	16	fluctuating	fluctuating	NOUN
cjfa-35471	86	17	time	time	NOUN
cjfa-35471	86	18	dependent	dependent	ADJ
cjfa-35471	86	19	demand	demand	NOUN
cjfa-35471	86	20	function	function	NOUN
cjfa-35471	86	21	.	.	PUNCT
cjfa-35471	87	1	then	then	ADV
cjfa-35471	87	2	,	,	PUNCT
cjfa-35471	87	3	the	the	DET
cjfa-35471	87	4	problem	problem	NOUN
cjfa-35471	87	5	becomes	become	VERB
cjfa-35471	87	6	:	:	PUNCT
cjfa-35471	87	7	(	(	PUNCT
cjfa-35471	87	8	)	)	PUNCT
cjfa-35471	87	9	0	0	PUNCT
cjfa-35471	88	1	[	[	PUNCT
cjfa-35471	88	2	(	(	PUNCT
cjfa-35471	88	3	(	(	PUNCT
cjfa-35471	88	4	)	)	PUNCT
cjfa-35471	88	5	(	(	PUNCT
cjfa-35471	88	6	)	)	PUNCT
cjfa-35471	88	7	]	]	PUNCT
cjfa-35471	88	8	t	t	X
cjfa-35471	88	9	i	i	PRON
cjfa-35471	88	10	tmin	tmin	VERB
cjfa-35471	88	11	e	e	PROPN
cjfa-35471	88	12	c	c	NOUN
cjfa-35471	88	13	u	u	X
cjfa-35471	89	1	t	t	X
cjfa-35471	89	2	hi	hi	INTJ
cjfa-35471	89	3	t	t	PROPN
cjfa-35471	89	4	dt	dt	X
cjfa-35471	89	5			NOUN
cjfa-35471	89	6	subject	subject	ADJ
cjfa-35471	89	7	to	to	ADP
cjfa-35471	89	8	the	the	DET
cjfa-35471	89	9	constraints	constraint	NOUN
cjfa-35471	89	10	:	:	PUNCT
cjfa-35471	89	11	subject	subject	ADJ
cjfa-35471	89	12	to	to	ADP
cjfa-35471	89	13	the	the	DET
cjfa-35471	89	14	constraints	constraint	NOUN
cjfa-35471	89	15	:	:	PUNCT
cjfa-35471	89	16	ℎ	ℎ	PROPN
cjfa-35471	89	17	:	:	PUNCT
cjfa-35471	89	18	unit	unit	NOUN
cjfa-35471	89	19	holding	hold	VERB
cjfa-35471	89	20	cost	cost	NOUN
cjfa-35471	89	21	,	,	PUNCT
cjfa-35471	89	22	a	a	DET
cjfa-35471	89	23	constant	constant	ADJ
cjfa-35471	89	24	.	.	PUNCT
cjfa-35471	90	1	these	these	DET
cjfa-35471	90	2	costs	cost	NOUN
cjfa-35471	90	3	include	include	VERB
cjfa-35471	90	4	many	many	ADJ
cjfa-35471	90	5	cost	cost	NOUN
cjfa-35471	90	6	items	item	NOUN
cjfa-35471	90	7	such	such	ADJ
cjfa-35471	90	8	as	as	ADP
cjfa-35471	90	9	rent	rent	NOUN
cjfa-35471	90	10	,	,	PUNCT
cjfa-35471	90	11	cost	cost	NOUN
cjfa-35471	90	12	of	of	ADP
cjfa-35471	90	13	relevant	relevant	ADJ
cjfa-35471	90	14	equipment	equipment	NOUN
cjfa-35471	90	15	necessary	necessary	ADJ
cjfa-35471	90	16	to	to	PART
cjfa-35471	90	17	keep	keep	VERB
cjfa-35471	90	18	the	the	DET
cjfa-35471	90	19	products	product	NOUN
cjfa-35471	90	20	in	in	ADP
cjfa-35471	90	21	the	the	DET
cjfa-35471	90	22	inventory	inventory	NOUN
cjfa-35471	90	23	,	,	PUNCT
cjfa-35471	90	24	and	and	CCONJ
cjfa-35471	90	25	insurance	insurance	NOUN
cjfa-35471	90	26	premiums	premium	NOUN
cjfa-35471	90	27	.	.	PUNCT
cjfa-35471	91	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	91	2	:	:	PUNCT
cjfa-35471	91	3	level	level	NOUN
cjfa-35471	91	4	of	of	ADP
cjfa-35471	91	5	demand	demand	NOUN
cjfa-35471	91	6	that	that	PRON
cjfa-35471	91	7	is	be	AUX
cjfa-35471	91	8	an	an	DET
cjfa-35471	91	9	exogenously	exogenously	ADV
cjfa-35471	91	10	determined	determine	VERB
cjfa-35471	91	11	function	function	NOUN
cjfa-35471	91	12	of	of	ADP
cjfa-35471	91	13	time	time	NOUN
cjfa-35471	91	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	91	15	:	:	PUNCT
cjfa-35471	91	16	the	the	DET
cjfa-35471	91	17	level	level	NOUN
cjfa-35471	91	18	of	of	ADP
cjfa-35471	91	19	inventory	inventory	NOUN
cjfa-35471	91	20	at	at	ADP
cjfa-35471	91	21	time	time	NOUN
cjfa-35471	91	22	t	t	PROPN
cjfa-35471	91	23	,	,	PUNCT
cjfa-35471	91	24	which	which	PRON
cjfa-35471	91	25	increases	increase	VERB
cjfa-35471	91	26	by	by	ADP
cjfa-35471	91	27	production	production	NOUN
cjfa-35471	91	28	(	(	PUNCT
cjfa-35471	91	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	91	30	and	and	CCONJ
cjfa-35471	91	31	decreases	decrease	NOUN
cjfa-35471	91	32	by	by	ADP
cjfa-35471	91	33	sales	sale	NOUN
cjfa-35471	91	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	91	35	therefore	therefore	ADV
cjfa-35471	91	36	,	,	PUNCT
cjfa-35471	91	37	the	the	DET
cjfa-35471	91	38	model	model	NOUN
cjfa-35471	91	39	,	,	PUNCT
cjfa-35471	91	40	is	be	AUX
cjfa-35471	91	41	(	(	PUNCT
cjfa-35471	91	42	)	)	PUNCT
cjfa-35471	91	43	0	0	NUM
cjfa-35471	92	1	max	max	PROPN
cjfa-35471	92	2	[	[	PUNCT
cjfa-35471	92	3	(	(	PUNCT
cjfa-35471	92	4	(	(	PUNCT
cjfa-35471	92	5	)	)	PUNCT
cjfa-35471	92	6	)	)	PUNCT
cjfa-35471	92	7	(	(	PUNCT
cjfa-35471	92	8	)	)	PUNCT
cjfa-35471	92	9	]	]	PUNCT
cjfa-35471	93	1	t	t	X
cjfa-35471	93	2	u	u	NOUN
cjfa-35471	93	3	t	t	X
cjfa-35471	93	4	c	c	NOUN
cjfa-35471	93	5	u	u	NOUN
cjfa-35471	93	6	t	t	X
cjfa-35471	93	7	hi	hi	INTJ
cjfa-35471	93	8	t	t	PROPN
cjfa-35471	93	9	dt	dt	NOUN
cjfa-35471	93	10	subject	subject	NOUN
cjfa-35471	93	11	to	to	ADP
cjfa-35471	93	12	the	the	DET
cjfa-35471	93	13	constraints	constraint	NOUN
cjfa-35471	93	14	:	:	PUNCT
cjfa-35471	93	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	93	16	�	�	PROPN
cjfa-35471	93	17	=	=	PUNCT
cjfa-35471	93	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	93	19	−	−	X
cjfa-35471	93	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	93	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	94	1	=	=	SYM
cjfa-35471	94	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	94	3	�	�	PROPN
cjfa-35471	94	4	given	give	VERB
cjfa-35471	94	5	and	and	CCONJ
cjfa-35471	94	6	the	the	DET
cjfa-35471	94	7	non	non	ADJ
cjfa-35471	94	8	-	-	ADJ
cjfa-35471	94	9	negativity	negativity	ADJ
cjfa-35471	94	10	constraints	constraint	NOUN
cjfa-35471	94	11	.	.	PUNCT
cjfa-35471	95	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	95	2	≥	≥	PROPN
cjfa-35471	95	3	0	0	NUM
cjfa-35471	95	4	,	,	PUNCT
cjfa-35471	95	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	95	6	≥	≥	NOUN
cjfa-35471	95	7	0	0	NUM
cjfa-35471	95	8	cost	cost	NOUN
cjfa-35471	95	9	minimization	minimization	NOUN
cjfa-35471	95	10	is	be	AUX
cjfa-35471	95	11	considered	consider	VERB
cjfa-35471	95	12	since	since	SCONJ
cjfa-35471	95	13	the	the	DET
cjfa-35471	95	14	price	price	NOUN
cjfa-35471	95	15	is	be	AUX
cjfa-35471	95	16	assumed	assume	VERB
cjfa-35471	95	17	to	to	PART
cjfa-35471	95	18	be	be	AUX
cjfa-35471	95	19	constant	constant	ADJ
cjfa-35471	95	20	and	and	CCONJ
cjfa-35471	95	21	the	the	DET
cjfa-35471	95	22	demand	demand	NOUN
cjfa-35471	95	23	,	,	PUNCT
cjfa-35471	95	24	r(t	r(t	NOUN
cjfa-35471	95	25	)	)	PUNCT
cjfa-35471	95	26	,	,	PUNCT
cjfa-35471	95	27	is	be	AUX
cjfa-35471	95	28	an	an	DET
cjfa-35471	95	29	exogenous	exogenous	ADJ
cjfa-35471	95	30	time	time	NOUN
cjfa-35471	95	31	dependent	dependent	ADJ
cjfa-35471	95	32	function	function	NOUN
cjfa-35471	95	33	making	make	VERB
cjfa-35471	95	34	the	the	DET
cjfa-35471	95	35	revenues	revenue	NOUN
cjfa-35471	95	36	an	an	DET
cjfa-35471	95	37	exogenous	exogenous	ADJ
cjfa-35471	95	38	function	function	NOUN
cjfa-35471	95	39	also	also	ADV
cjfa-35471	95	40	thus	thus	ADV
cjfa-35471	95	41	irrelevant	irrelevant	ADJ
cjfa-35471	95	42	in	in	ADP
cjfa-35471	95	43	decision	decision	NOUN
cjfa-35471	95	44	making	making	NOUN
cjfa-35471	95	45	.	.	PUNCT
cjfa-35471	96	1	the	the	DET
cjfa-35471	96	2	last	last	ADJ
cjfa-35471	96	3	constraint	constraint	NOUN
cjfa-35471	96	4	is	be	AUX
cjfa-35471	96	5	a	a	DET
cjfa-35471	96	6	state	state	NOUN
cjfa-35471	96	7	variable	variable	ADJ
cjfa-35471	96	8	inequality	inequality	NOUN
cjfa-35471	96	9	constraint	constraint	NOUN
cjfa-35471	96	10	which	which	PRON
cjfa-35471	96	11	has	have	AUX
cjfa-35471	96	12	been	be	AUX
cjfa-35471	96	13	studied	study	VERB
cjfa-35471	96	14	by	by	ADP
cjfa-35471	96	15	many	many	ADJ
cjfa-35471	96	16	authors	author	NOUN
cjfa-35471	96	17	including	include	VERB
cjfa-35471	96	18	bryson	bryson	PROPN
cjfa-35471	96	19	and	and	CCONJ
cjfa-35471	96	20	ho	ho	PROPN
cjfa-35471	96	21	(	(	PUNCT
cjfa-35471	96	22	1975	1975	NUM
cjfa-35471	96	23	)	)	PUNCT
cjfa-35471	96	24	,	,	PUNCT
cjfa-35471	96	25	bryson	bryson	PROPN
cjfa-35471	96	26	,	,	PUNCT
cjfa-35471	96	27	denham	denham	PROPN
cjfa-35471	96	28	and	and	CCONJ
cjfa-35471	96	29	dreyfus	dreyfus	PROPN
cjfa-35471	96	30	(	(	PUNCT
cjfa-35471	96	31	1963	1963	NUM
cjfa-35471	96	32	)	)	PUNCT
cjfa-35471	96	33	,	,	PUNCT
cjfa-35471	96	34	jacobson	jacobson	PROPN
cjfa-35471	96	35	and	and	CCONJ
cjfa-35471	96	36	lele	lele	PROPN
cjfa-35471	96	37	(	(	PUNCT
cjfa-35471	96	38	1969	1969	NUM
cjfa-35471	96	39	)	)	PUNCT
cjfa-35471	96	40	,	,	PUNCT
cjfa-35471	96	41	jacobson	jacobson	PROPN
cjfa-35471	96	42	,	,	PUNCT
cjfa-35471	96	43	lele	lele	PROPN
cjfa-35471	96	44	and	and	CCONJ
cjfa-35471	96	45	speyer	speyer	PROPN
cjfa-35471	96	46	(	(	PUNCT
cjfa-35471	96	47	1971	1971	NUM
cjfa-35471	96	48	)	)	PUNCT
cjfa-35471	96	49	,	,	PUNCT
cjfa-35471	96	50	mcintyre	mcintyre	PROPN
cjfa-35471	96	51	and	and	CCONJ
cjfa-35471	96	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	96	53	(	(	PUNCT
cjfa-35471	96	54	1967	1967	NUM
cjfa-35471	96	55	)	)	PUNCT
cjfa-35471	96	56	,	,	PUNCT
cjfa-35471	96	57	and	and	CCONJ
cjfa-35471	96	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	96	59	(	(	PUNCT
cjfa-35471	96	60	1967	1967	NUM
cjfa-35471	96	61	)	)	PUNCT
cjfa-35471	96	62	.	.	PUNCT
cjfa-35471	97	1	taylor	taylor	PROPN
cjfa-35471	97	2	(	(	PUNCT
cjfa-35471	97	3	1972	1972	NUM
cjfa-35471	97	4	)	)	PUNCT
cjfa-35471	97	5	studied	study	VERB
cjfa-35471	97	6	the	the	DET
cjfa-35471	97	7	problem	problem	NOUN
cjfa-35471	97	8	stated	state	VERB
cjfa-35471	97	9	above	above	ADV
cjfa-35471	97	10	with	with	ADP
cjfa-35471	97	11	no	no	DET
cjfa-35471	97	12	interest	interest	NOUN
cjfa-35471	97	13	rate	rate	NOUN
cjfa-35471	97	14	consideration	consideration	NOUN
cjfa-35471	97	15	and	and	CCONJ
cjfa-35471	97	16	has	have	AUX
cjfa-35471	97	17	found	find	VERB
cjfa-35471	97	18	that	that	SCONJ
cjfa-35471	97	19	;	;	PUNCT
cjfa-35471	98	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	98	2	�	�	PROPN
cjfa-35471	98	3	�	�	PROPN
cjfa-35471	98	4	�	�	PROPN
cjfa-35471	98	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	98	6	�	�	PROPN
cjfa-35471	98	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	98	8	�	�	PROPN
cjfa-35471	98	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	98	10	𝑡	𝑡	NOUN
cjfa-35471	98	11	ℎ	ℎ	PROPN
cjfa-35471	98	12	is	be	AUX
cjfa-35471	98	13	the	the	DET
cjfa-35471	98	14	condition	condition	NOUN
cjfa-35471	98	15	which	which	PRON
cjfa-35471	98	16	has	have	VERB
cjfa-35471	98	17	to	to	PART
cjfa-35471	98	18	hold	hold	VERB
cjfa-35471	98	19	for	for	ADP
cjfa-35471	98	20	the	the	DET
cjfa-35471	98	21	firm	firm	NOUN
cjfa-35471	98	22	to	to	PART
cjfa-35471	98	23	keep	keep	VERB
cjfa-35471	98	24	i	i	PRON
cjfa-35471	98	25	(	(	PUNCT
cjfa-35471	98	26	t	t	NOUN
cjfa-35471	98	27	)	)	PUNCT
cjfa-35471	98	28	=	=	NOUN
cjfa-35471	98	29	0	0	NUM
cjfa-35471	98	30	which	which	PRON
cjfa-35471	98	31	implies	imply	VERB
cjfa-35471	98	32	that	that	SCONJ
cjfa-35471	98	33	the	the	DET
cjfa-35471	98	34	firm	firm	NOUN
cjfa-35471	98	35	will	will	AUX
cjfa-35471	98	36	produce	produce	VERB
cjfa-35471	98	37	just	just	ADV
cjfa-35471	98	38	to	to	PART
cjfa-35471	98	39	meet	meet	VERB
cjfa-35471	98	40	the	the	DET
cjfa-35471	98	41	demand	demand	NOUN
cjfa-35471	98	42	.	.	PUNCT
cjfa-35471	99	1	the	the	DET
cjfa-35471	99	2	firm	firm	NOUN
cjfa-35471	99	3	will	will	AUX
cjfa-35471	99	4	start	start	VERB
cjfa-35471	99	5	producing	produce	VERB
cjfa-35471	99	6	not	not	PART
cjfa-35471	99	7	only	only	ADV
cjfa-35471	99	8	to	to	PART
cjfa-35471	99	9	meet	meet	VERB
cjfa-35471	99	10	the	the	DET
cjfa-35471	99	11	demand	demand	NOUN
cjfa-35471	99	12	but	but	CCONJ
cjfa-35471	99	13	also	also	ADV
cjfa-35471	99	14	to	to	PART
cjfa-35471	99	15	build	build	VERB
cjfa-35471	99	16	up	up	ADP
cjfa-35471	99	17	inventories	inventory	NOUN
cjfa-35471	99	18	when	when	SCONJ
cjfa-35471	99	19	the	the	DET
cjfa-35471	99	20	change	change	NOUN
cjfa-35471	99	21	in	in	ADP
cjfa-35471	99	22	demand	demand	NOUN
cjfa-35471	99	23	is	be	AUX
cjfa-35471	99	24	such	such	ADJ
cjfa-35471	99	25	that	that	SCONJ
cjfa-35471	99	26	the	the	DET
cjfa-35471	99	27	above	above	ADJ
cjfa-35471	99	28	inequality	inequality	NOUN
cjfa-35471	99	29	will	will	AUX
cjfa-35471	99	30	be	be	AUX
cjfa-35471	99	31	violated	violate	VERB
cjfa-35471	99	32	.	.	PUNCT
cjfa-35471	100	1	in	in	ADP
cjfa-35471	100	2	this	this	DET
cjfa-35471	100	3	paper	paper	NOUN
cjfa-35471	100	4	,	,	PUNCT
cjfa-35471	100	5	we	we	PRON
cjfa-35471	100	6	will	will	AUX
cjfa-35471	100	7	study	study	VERB
cjfa-35471	100	8	the	the	DET
cjfa-35471	100	9	same	same	ADJ
cjfa-35471	100	10	problem	problem	NOUN
cjfa-35471	100	11	introducing	introduce	VERB
cjfa-35471	100	12	present	present	ADJ
cjfa-35471	100	13	value	value	NOUN
cjfa-35471	100	14	factor	factor	NOUN
cjfa-35471	100	15	and	and	CCONJ
cjfa-35471	100	16	fluctuating	fluctuating	NOUN
cjfa-35471	100	17	time	time	NOUN
cjfa-35471	100	18	dependent	dependent	ADJ
cjfa-35471	100	19	demand	demand	NOUN
cjfa-35471	100	20	function	function	NOUN
cjfa-35471	100	21	.	.	PUNCT
cjfa-35471	101	1	then	then	ADV
cjfa-35471	101	2	,	,	PUNCT
cjfa-35471	101	3	the	the	DET
cjfa-35471	101	4	problem	problem	NOUN
cjfa-35471	101	5	becomes	become	VERB
cjfa-35471	101	6	:	:	PUNCT
cjfa-35471	101	7	(	(	PUNCT
cjfa-35471	101	8	)	)	PUNCT
cjfa-35471	101	9	0	0	PUNCT
cjfa-35471	102	1	[	[	PUNCT
cjfa-35471	102	2	(	(	PUNCT
cjfa-35471	102	3	(	(	PUNCT
cjfa-35471	102	4	)	)	PUNCT
cjfa-35471	102	5	(	(	PUNCT
cjfa-35471	102	6	)	)	PUNCT
cjfa-35471	102	7	]	]	PUNCT
cjfa-35471	102	8	t	t	X
cjfa-35471	102	9	i	i	PRON
cjfa-35471	102	10	tmin	tmin	VERB
cjfa-35471	102	11	e	e	PROPN
cjfa-35471	102	12	c	c	NOUN
cjfa-35471	102	13	u	u	X
cjfa-35471	103	1	t	t	X
cjfa-35471	103	2	hi	hi	INTJ
cjfa-35471	103	3	t	t	PROPN
cjfa-35471	103	4	dt	dt	X
cjfa-35471	103	5			NOUN
cjfa-35471	103	6	subject	subject	ADJ
cjfa-35471	103	7	to	to	ADP
cjfa-35471	103	8	the	the	DET
cjfa-35471	103	9	constraints	constraint	NOUN
cjfa-35471	103	10	:	:	PUNCT
cjfa-35471	103	11	ℎ	ℎ	PROPN
cjfa-35471	103	12	:	:	PUNCT
cjfa-35471	103	13	unit	unit	NOUN
cjfa-35471	103	14	holding	hold	VERB
cjfa-35471	103	15	cost	cost	NOUN
cjfa-35471	103	16	,	,	PUNCT
cjfa-35471	103	17	a	a	DET
cjfa-35471	103	18	constant	constant	ADJ
cjfa-35471	103	19	.	.	PUNCT
cjfa-35471	104	1	these	these	DET
cjfa-35471	104	2	costs	cost	NOUN
cjfa-35471	104	3	include	include	VERB
cjfa-35471	104	4	many	many	ADJ
cjfa-35471	104	5	cost	cost	NOUN
cjfa-35471	104	6	items	item	NOUN
cjfa-35471	104	7	such	such	ADJ
cjfa-35471	104	8	as	as	ADP
cjfa-35471	104	9	rent	rent	NOUN
cjfa-35471	104	10	,	,	PUNCT
cjfa-35471	104	11	cost	cost	NOUN
cjfa-35471	104	12	of	of	ADP
cjfa-35471	104	13	relevant	relevant	ADJ
cjfa-35471	104	14	equipment	equipment	NOUN
cjfa-35471	104	15	necessary	necessary	ADJ
cjfa-35471	104	16	to	to	PART
cjfa-35471	104	17	keep	keep	VERB
cjfa-35471	104	18	the	the	DET
cjfa-35471	104	19	products	product	NOUN
cjfa-35471	104	20	in	in	ADP
cjfa-35471	104	21	the	the	DET
cjfa-35471	104	22	inventory	inventory	NOUN
cjfa-35471	104	23	,	,	PUNCT
cjfa-35471	104	24	and	and	CCONJ
cjfa-35471	104	25	insurance	insurance	NOUN
cjfa-35471	104	26	premiums	premium	NOUN
cjfa-35471	104	27	.	.	PUNCT
cjfa-35471	105	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	105	2	:	:	PUNCT
cjfa-35471	105	3	level	level	NOUN
cjfa-35471	105	4	of	of	ADP
cjfa-35471	105	5	demand	demand	NOUN
cjfa-35471	105	6	that	that	PRON
cjfa-35471	105	7	is	be	AUX
cjfa-35471	105	8	an	an	DET
cjfa-35471	105	9	exogenously	exogenously	ADV
cjfa-35471	105	10	determined	determine	VERB
cjfa-35471	105	11	function	function	NOUN
cjfa-35471	105	12	of	of	ADP
cjfa-35471	105	13	time	time	NOUN
cjfa-35471	105	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	105	15	:	:	PUNCT
cjfa-35471	105	16	the	the	DET
cjfa-35471	105	17	level	level	NOUN
cjfa-35471	105	18	of	of	ADP
cjfa-35471	105	19	inventory	inventory	NOUN
cjfa-35471	105	20	at	at	ADP
cjfa-35471	105	21	time	time	NOUN
cjfa-35471	105	22	t	t	PROPN
cjfa-35471	105	23	,	,	PUNCT
cjfa-35471	105	24	which	which	PRON
cjfa-35471	105	25	increases	increase	VERB
cjfa-35471	105	26	by	by	ADP
cjfa-35471	105	27	production	production	NOUN
cjfa-35471	105	28	(	(	PUNCT
cjfa-35471	105	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	105	30	and	and	CCONJ
cjfa-35471	105	31	decreases	decrease	NOUN
cjfa-35471	105	32	by	by	ADP
cjfa-35471	105	33	sales	sale	NOUN
cjfa-35471	105	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	105	35	therefore	therefore	ADV
cjfa-35471	105	36	,	,	PUNCT
cjfa-35471	105	37	the	the	DET
cjfa-35471	105	38	model	model	NOUN
cjfa-35471	105	39	,	,	PUNCT
cjfa-35471	105	40	is	be	AUX
cjfa-35471	105	41	(	(	PUNCT
cjfa-35471	105	42	)	)	PUNCT
cjfa-35471	105	43	0	0	NUM
cjfa-35471	106	1	max	max	PROPN
cjfa-35471	106	2	[	[	PUNCT
cjfa-35471	106	3	(	(	PUNCT
cjfa-35471	106	4	(	(	PUNCT
cjfa-35471	106	5	)	)	PUNCT
cjfa-35471	106	6	)	)	PUNCT
cjfa-35471	106	7	(	(	PUNCT
cjfa-35471	106	8	)	)	PUNCT
cjfa-35471	106	9	]	]	PUNCT
cjfa-35471	107	1	t	t	X
cjfa-35471	107	2	u	u	NOUN
cjfa-35471	107	3	t	t	X
cjfa-35471	107	4	c	c	NOUN
cjfa-35471	107	5	u	u	NOUN
cjfa-35471	107	6	t	t	X
cjfa-35471	107	7	hi	hi	INTJ
cjfa-35471	107	8	t	t	PROPN
cjfa-35471	107	9	dt	dt	NOUN
cjfa-35471	107	10	subject	subject	NOUN
cjfa-35471	107	11	to	to	ADP
cjfa-35471	107	12	the	the	DET
cjfa-35471	107	13	constraints	constraint	NOUN
cjfa-35471	107	14	:	:	PUNCT
cjfa-35471	107	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	107	16	�	�	PROPN
cjfa-35471	107	17	=	=	PUNCT
cjfa-35471	107	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	107	19	−	−	X
cjfa-35471	107	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	107	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	108	1	=	=	SYM
cjfa-35471	108	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	108	3	�	�	PROPN
cjfa-35471	108	4	given	give	VERB
cjfa-35471	108	5	and	and	CCONJ
cjfa-35471	108	6	the	the	DET
cjfa-35471	108	7	non	non	ADJ
cjfa-35471	108	8	-	-	ADJ
cjfa-35471	108	9	negativity	negativity	ADJ
cjfa-35471	108	10	constraints	constraint	NOUN
cjfa-35471	108	11	.	.	PUNCT
cjfa-35471	109	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	109	2	≥	≥	PROPN
cjfa-35471	109	3	0	0	NUM
cjfa-35471	109	4	,	,	PUNCT
cjfa-35471	109	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	109	6	≥	≥	NOUN
cjfa-35471	109	7	0	0	NUM
cjfa-35471	109	8	cost	cost	NOUN
cjfa-35471	109	9	minimization	minimization	NOUN
cjfa-35471	109	10	is	be	AUX
cjfa-35471	109	11	considered	consider	VERB
cjfa-35471	109	12	since	since	SCONJ
cjfa-35471	109	13	the	the	DET
cjfa-35471	109	14	price	price	NOUN
cjfa-35471	109	15	is	be	AUX
cjfa-35471	109	16	assumed	assume	VERB
cjfa-35471	109	17	to	to	PART
cjfa-35471	109	18	be	be	AUX
cjfa-35471	109	19	constant	constant	ADJ
cjfa-35471	109	20	and	and	CCONJ
cjfa-35471	109	21	the	the	DET
cjfa-35471	109	22	demand	demand	NOUN
cjfa-35471	109	23	,	,	PUNCT
cjfa-35471	109	24	r(t	r(t	NOUN
cjfa-35471	109	25	)	)	PUNCT
cjfa-35471	109	26	,	,	PUNCT
cjfa-35471	109	27	is	be	AUX
cjfa-35471	109	28	an	an	DET
cjfa-35471	109	29	exogenous	exogenous	ADJ
cjfa-35471	109	30	time	time	NOUN
cjfa-35471	109	31	dependent	dependent	ADJ
cjfa-35471	109	32	function	function	NOUN
cjfa-35471	109	33	making	make	VERB
cjfa-35471	109	34	the	the	DET
cjfa-35471	109	35	revenues	revenue	NOUN
cjfa-35471	109	36	an	an	DET
cjfa-35471	109	37	exogenous	exogenous	ADJ
cjfa-35471	109	38	function	function	NOUN
cjfa-35471	109	39	also	also	ADV
cjfa-35471	109	40	thus	thus	ADV
cjfa-35471	109	41	irrelevant	irrelevant	ADJ
cjfa-35471	109	42	in	in	ADP
cjfa-35471	109	43	decision	decision	NOUN
cjfa-35471	109	44	making	making	NOUN
cjfa-35471	109	45	.	.	PUNCT
cjfa-35471	110	1	the	the	DET
cjfa-35471	110	2	last	last	ADJ
cjfa-35471	110	3	constraint	constraint	NOUN
cjfa-35471	110	4	is	be	AUX
cjfa-35471	110	5	a	a	DET
cjfa-35471	110	6	state	state	NOUN
cjfa-35471	110	7	variable	variable	ADJ
cjfa-35471	110	8	inequality	inequality	NOUN
cjfa-35471	110	9	constraint	constraint	NOUN
cjfa-35471	110	10	which	which	PRON
cjfa-35471	110	11	has	have	AUX
cjfa-35471	110	12	been	be	AUX
cjfa-35471	110	13	studied	study	VERB
cjfa-35471	110	14	by	by	ADP
cjfa-35471	110	15	many	many	ADJ
cjfa-35471	110	16	authors	author	NOUN
cjfa-35471	110	17	including	include	VERB
cjfa-35471	110	18	bryson	bryson	PROPN
cjfa-35471	110	19	and	and	CCONJ
cjfa-35471	110	20	ho	ho	PROPN
cjfa-35471	110	21	(	(	PUNCT
cjfa-35471	110	22	1975	1975	NUM
cjfa-35471	110	23	)	)	PUNCT
cjfa-35471	110	24	,	,	PUNCT
cjfa-35471	110	25	bryson	bryson	PROPN
cjfa-35471	110	26	,	,	PUNCT
cjfa-35471	110	27	denham	denham	PROPN
cjfa-35471	110	28	and	and	CCONJ
cjfa-35471	110	29	dreyfus	dreyfus	PROPN
cjfa-35471	110	30	(	(	PUNCT
cjfa-35471	110	31	1963	1963	NUM
cjfa-35471	110	32	)	)	PUNCT
cjfa-35471	110	33	,	,	PUNCT
cjfa-35471	110	34	jacobson	jacobson	PROPN
cjfa-35471	110	35	and	and	CCONJ
cjfa-35471	110	36	lele	lele	PROPN
cjfa-35471	110	37	(	(	PUNCT
cjfa-35471	110	38	1969	1969	NUM
cjfa-35471	110	39	)	)	PUNCT
cjfa-35471	110	40	,	,	PUNCT
cjfa-35471	110	41	jacobson	jacobson	PROPN
cjfa-35471	110	42	,	,	PUNCT
cjfa-35471	110	43	lele	lele	PROPN
cjfa-35471	110	44	and	and	CCONJ
cjfa-35471	110	45	speyer	speyer	PROPN
cjfa-35471	110	46	(	(	PUNCT
cjfa-35471	110	47	1971	1971	NUM
cjfa-35471	110	48	)	)	PUNCT
cjfa-35471	110	49	,	,	PUNCT
cjfa-35471	110	50	mcintyre	mcintyre	PROPN
cjfa-35471	110	51	and	and	CCONJ
cjfa-35471	110	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	110	53	(	(	PUNCT
cjfa-35471	110	54	1967	1967	NUM
cjfa-35471	110	55	)	)	PUNCT
cjfa-35471	110	56	,	,	PUNCT
cjfa-35471	110	57	and	and	CCONJ
cjfa-35471	110	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	110	59	(	(	PUNCT
cjfa-35471	110	60	1967	1967	NUM
cjfa-35471	110	61	)	)	PUNCT
cjfa-35471	110	62	.	.	PUNCT
cjfa-35471	111	1	taylor	taylor	PROPN
cjfa-35471	111	2	(	(	PUNCT
cjfa-35471	111	3	1972	1972	NUM
cjfa-35471	111	4	)	)	PUNCT
cjfa-35471	111	5	studied	study	VERB
cjfa-35471	111	6	the	the	DET
cjfa-35471	111	7	problem	problem	NOUN
cjfa-35471	111	8	stated	state	VERB
cjfa-35471	111	9	above	above	ADV
cjfa-35471	111	10	with	with	ADP
cjfa-35471	111	11	no	no	DET
cjfa-35471	111	12	interest	interest	NOUN
cjfa-35471	111	13	rate	rate	NOUN
cjfa-35471	111	14	consideration	consideration	NOUN
cjfa-35471	111	15	and	and	CCONJ
cjfa-35471	111	16	has	have	AUX
cjfa-35471	111	17	found	find	VERB
cjfa-35471	111	18	that	that	SCONJ
cjfa-35471	111	19	;	;	PUNCT
cjfa-35471	112	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	112	2	�	�	PROPN
cjfa-35471	112	3	�	�	PROPN
cjfa-35471	112	4	�	�	PROPN
cjfa-35471	112	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	112	6	�	�	PROPN
cjfa-35471	112	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	112	8	�	�	PROPN
cjfa-35471	112	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	112	10	𝑡	𝑡	NOUN
cjfa-35471	112	11	ℎ	ℎ	PROPN
cjfa-35471	112	12	is	be	AUX
cjfa-35471	112	13	the	the	DET
cjfa-35471	112	14	condition	condition	NOUN
cjfa-35471	112	15	which	which	PRON
cjfa-35471	112	16	has	have	VERB
cjfa-35471	112	17	to	to	PART
cjfa-35471	112	18	hold	hold	VERB
cjfa-35471	112	19	for	for	ADP
cjfa-35471	112	20	the	the	DET
cjfa-35471	112	21	firm	firm	NOUN
cjfa-35471	112	22	to	to	PART
cjfa-35471	112	23	keep	keep	VERB
cjfa-35471	112	24	i	i	PRON
cjfa-35471	112	25	(	(	PUNCT
cjfa-35471	112	26	t	t	NOUN
cjfa-35471	112	27	)	)	PUNCT
cjfa-35471	112	28	=	=	NOUN
cjfa-35471	112	29	0	0	NUM
cjfa-35471	112	30	which	which	PRON
cjfa-35471	112	31	implies	imply	VERB
cjfa-35471	112	32	that	that	SCONJ
cjfa-35471	112	33	the	the	DET
cjfa-35471	112	34	firm	firm	NOUN
cjfa-35471	112	35	will	will	AUX
cjfa-35471	112	36	produce	produce	VERB
cjfa-35471	112	37	just	just	ADV
cjfa-35471	112	38	to	to	PART
cjfa-35471	112	39	meet	meet	VERB
cjfa-35471	112	40	the	the	DET
cjfa-35471	112	41	demand	demand	NOUN
cjfa-35471	112	42	.	.	PUNCT
cjfa-35471	113	1	the	the	DET
cjfa-35471	113	2	firm	firm	NOUN
cjfa-35471	113	3	will	will	AUX
cjfa-35471	113	4	start	start	VERB
cjfa-35471	113	5	producing	produce	VERB
cjfa-35471	113	6	not	not	PART
cjfa-35471	113	7	only	only	ADV
cjfa-35471	113	8	to	to	PART
cjfa-35471	113	9	meet	meet	VERB
cjfa-35471	113	10	the	the	DET
cjfa-35471	113	11	demand	demand	NOUN
cjfa-35471	113	12	but	but	CCONJ
cjfa-35471	113	13	also	also	ADV
cjfa-35471	113	14	to	to	PART
cjfa-35471	113	15	build	build	VERB
cjfa-35471	113	16	up	up	ADP
cjfa-35471	113	17	inventories	inventory	NOUN
cjfa-35471	113	18	when	when	SCONJ
cjfa-35471	113	19	the	the	DET
cjfa-35471	113	20	change	change	NOUN
cjfa-35471	113	21	in	in	ADP
cjfa-35471	113	22	demand	demand	NOUN
cjfa-35471	113	23	is	be	AUX
cjfa-35471	113	24	such	such	ADJ
cjfa-35471	113	25	that	that	SCONJ
cjfa-35471	113	26	the	the	DET
cjfa-35471	113	27	above	above	ADJ
cjfa-35471	113	28	inequality	inequality	NOUN
cjfa-35471	113	29	will	will	AUX
cjfa-35471	113	30	be	be	AUX
cjfa-35471	113	31	violated	violate	VERB
cjfa-35471	113	32	.	.	PUNCT
cjfa-35471	114	1	in	in	ADP
cjfa-35471	114	2	this	this	DET
cjfa-35471	114	3	paper	paper	NOUN
cjfa-35471	114	4	,	,	PUNCT
cjfa-35471	114	5	we	we	PRON
cjfa-35471	114	6	will	will	AUX
cjfa-35471	114	7	study	study	VERB
cjfa-35471	114	8	the	the	DET
cjfa-35471	114	9	same	same	ADJ
cjfa-35471	114	10	problem	problem	NOUN
cjfa-35471	114	11	introducing	introduce	VERB
cjfa-35471	114	12	present	present	ADJ
cjfa-35471	114	13	value	value	NOUN
cjfa-35471	114	14	factor	factor	NOUN
cjfa-35471	114	15	and	and	CCONJ
cjfa-35471	114	16	fluctuating	fluctuating	NOUN
cjfa-35471	114	17	time	time	NOUN
cjfa-35471	114	18	dependent	dependent	ADJ
cjfa-35471	114	19	demand	demand	NOUN
cjfa-35471	114	20	function	function	NOUN
cjfa-35471	114	21	.	.	PUNCT
cjfa-35471	115	1	then	then	ADV
cjfa-35471	115	2	,	,	PUNCT
cjfa-35471	115	3	the	the	DET
cjfa-35471	115	4	problem	problem	NOUN
cjfa-35471	115	5	becomes	become	VERB
cjfa-35471	115	6	:	:	PUNCT
cjfa-35471	115	7	(	(	PUNCT
cjfa-35471	115	8	)	)	PUNCT
cjfa-35471	115	9	0	0	PUNCT
cjfa-35471	116	1	[	[	PUNCT
cjfa-35471	116	2	(	(	PUNCT
cjfa-35471	116	3	(	(	PUNCT
cjfa-35471	116	4	)	)	PUNCT
cjfa-35471	116	5	(	(	PUNCT
cjfa-35471	116	6	)	)	PUNCT
cjfa-35471	116	7	]	]	PUNCT
cjfa-35471	116	8	t	t	X
cjfa-35471	116	9	i	i	PRON
cjfa-35471	116	10	tmin	tmin	VERB
cjfa-35471	116	11	e	e	PROPN
cjfa-35471	116	12	c	c	NOUN
cjfa-35471	116	13	u	u	X
cjfa-35471	117	1	t	t	X
cjfa-35471	117	2	hi	hi	INTJ
cjfa-35471	117	3	t	t	PROPN
cjfa-35471	117	4	dt	dt	X
cjfa-35471	117	5			NOUN
cjfa-35471	117	6	subject	subject	ADJ
cjfa-35471	117	7	to	to	ADP
cjfa-35471	117	8	the	the	DET
cjfa-35471	117	9	constraints	constraint	NOUN
cjfa-35471	117	10	:	:	PUNCT
cjfa-35471	117	11	given	give	VERB
cjfa-35471	117	12	and	and	CCONJ
cjfa-35471	117	13	the	the	DET
cjfa-35471	117	14	non	non	ADJ
cjfa-35471	117	15	-	-	ADJ
cjfa-35471	117	16	negativity	negativity	ADJ
cjfa-35471	117	17	constraints	constraint	NOUN
cjfa-35471	117	18	.	.	PUNCT
cjfa-35471	118	1	ℎ	ℎ	PROPN
cjfa-35471	118	2	:	:	PUNCT
cjfa-35471	118	3	unit	unit	NOUN
cjfa-35471	118	4	holding	hold	VERB
cjfa-35471	118	5	cost	cost	NOUN
cjfa-35471	118	6	,	,	PUNCT
cjfa-35471	118	7	a	a	DET
cjfa-35471	118	8	constant	constant	ADJ
cjfa-35471	118	9	.	.	PUNCT
cjfa-35471	119	1	these	these	DET
cjfa-35471	119	2	costs	cost	NOUN
cjfa-35471	119	3	include	include	VERB
cjfa-35471	119	4	many	many	ADJ
cjfa-35471	119	5	cost	cost	NOUN
cjfa-35471	119	6	items	item	NOUN
cjfa-35471	119	7	such	such	ADJ
cjfa-35471	119	8	as	as	ADP
cjfa-35471	119	9	rent	rent	NOUN
cjfa-35471	119	10	,	,	PUNCT
cjfa-35471	119	11	cost	cost	NOUN
cjfa-35471	119	12	of	of	ADP
cjfa-35471	119	13	relevant	relevant	ADJ
cjfa-35471	119	14	equipment	equipment	NOUN
cjfa-35471	119	15	necessary	necessary	ADJ
cjfa-35471	119	16	to	to	PART
cjfa-35471	119	17	keep	keep	VERB
cjfa-35471	119	18	the	the	DET
cjfa-35471	119	19	products	product	NOUN
cjfa-35471	119	20	in	in	ADP
cjfa-35471	119	21	the	the	DET
cjfa-35471	119	22	inventory	inventory	NOUN
cjfa-35471	119	23	,	,	PUNCT
cjfa-35471	119	24	and	and	CCONJ
cjfa-35471	119	25	insurance	insurance	NOUN
cjfa-35471	119	26	premiums	premium	NOUN
cjfa-35471	119	27	.	.	PUNCT
cjfa-35471	120	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	120	2	:	:	PUNCT
cjfa-35471	120	3	level	level	NOUN
cjfa-35471	120	4	of	of	ADP
cjfa-35471	120	5	demand	demand	NOUN
cjfa-35471	120	6	that	that	PRON
cjfa-35471	120	7	is	be	AUX
cjfa-35471	120	8	an	an	DET
cjfa-35471	120	9	exogenously	exogenously	ADV
cjfa-35471	120	10	determined	determine	VERB
cjfa-35471	120	11	function	function	NOUN
cjfa-35471	120	12	of	of	ADP
cjfa-35471	120	13	time	time	NOUN
cjfa-35471	120	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	120	15	:	:	PUNCT
cjfa-35471	120	16	the	the	DET
cjfa-35471	120	17	level	level	NOUN
cjfa-35471	120	18	of	of	ADP
cjfa-35471	120	19	inventory	inventory	NOUN
cjfa-35471	120	20	at	at	ADP
cjfa-35471	120	21	time	time	NOUN
cjfa-35471	120	22	t	t	PROPN
cjfa-35471	120	23	,	,	PUNCT
cjfa-35471	120	24	which	which	PRON
cjfa-35471	120	25	increases	increase	VERB
cjfa-35471	120	26	by	by	ADP
cjfa-35471	120	27	production	production	NOUN
cjfa-35471	120	28	(	(	PUNCT
cjfa-35471	120	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	120	30	and	and	CCONJ
cjfa-35471	120	31	decreases	decrease	NOUN
cjfa-35471	120	32	by	by	ADP
cjfa-35471	120	33	sales	sale	NOUN
cjfa-35471	120	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	120	35	therefore	therefore	ADV
cjfa-35471	120	36	,	,	PUNCT
cjfa-35471	120	37	the	the	DET
cjfa-35471	120	38	model	model	NOUN
cjfa-35471	120	39	,	,	PUNCT
cjfa-35471	120	40	is	be	AUX
cjfa-35471	120	41	(	(	PUNCT
cjfa-35471	120	42	)	)	PUNCT
cjfa-35471	120	43	0	0	NUM
cjfa-35471	121	1	max	max	PROPN
cjfa-35471	121	2	[	[	PUNCT
cjfa-35471	121	3	(	(	PUNCT
cjfa-35471	121	4	(	(	PUNCT
cjfa-35471	121	5	)	)	PUNCT
cjfa-35471	121	6	)	)	PUNCT
cjfa-35471	121	7	(	(	PUNCT
cjfa-35471	121	8	)	)	PUNCT
cjfa-35471	121	9	]	]	PUNCT
cjfa-35471	122	1	t	t	X
cjfa-35471	122	2	u	u	NOUN
cjfa-35471	122	3	t	t	X
cjfa-35471	122	4	c	c	NOUN
cjfa-35471	122	5	u	u	NOUN
cjfa-35471	122	6	t	t	X
cjfa-35471	122	7	hi	hi	INTJ
cjfa-35471	122	8	t	t	PROPN
cjfa-35471	122	9	dt	dt	NOUN
cjfa-35471	122	10	subject	subject	NOUN
cjfa-35471	122	11	to	to	ADP
cjfa-35471	122	12	the	the	DET
cjfa-35471	122	13	constraints	constraint	NOUN
cjfa-35471	122	14	:	:	PUNCT
cjfa-35471	122	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	122	16	�	�	PROPN
cjfa-35471	122	17	=	=	PUNCT
cjfa-35471	122	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	122	19	−	−	X
cjfa-35471	122	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	122	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	123	1	=	=	SYM
cjfa-35471	123	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	123	3	�	�	PROPN
cjfa-35471	123	4	given	give	VERB
cjfa-35471	123	5	and	and	CCONJ
cjfa-35471	123	6	the	the	DET
cjfa-35471	123	7	non	non	ADJ
cjfa-35471	123	8	-	-	ADJ
cjfa-35471	123	9	negativity	negativity	ADJ
cjfa-35471	123	10	constraints	constraint	NOUN
cjfa-35471	123	11	.	.	PUNCT
cjfa-35471	124	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	124	2	≥	≥	PROPN
cjfa-35471	124	3	0	0	NUM
cjfa-35471	124	4	,	,	PUNCT
cjfa-35471	124	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	124	6	≥	≥	NOUN
cjfa-35471	124	7	0	0	NUM
cjfa-35471	124	8	cost	cost	NOUN
cjfa-35471	124	9	minimization	minimization	NOUN
cjfa-35471	124	10	is	be	AUX
cjfa-35471	124	11	considered	consider	VERB
cjfa-35471	124	12	since	since	SCONJ
cjfa-35471	124	13	the	the	DET
cjfa-35471	124	14	price	price	NOUN
cjfa-35471	124	15	is	be	AUX
cjfa-35471	124	16	assumed	assume	VERB
cjfa-35471	124	17	to	to	PART
cjfa-35471	124	18	be	be	AUX
cjfa-35471	124	19	constant	constant	ADJ
cjfa-35471	124	20	and	and	CCONJ
cjfa-35471	124	21	the	the	DET
cjfa-35471	124	22	demand	demand	NOUN
cjfa-35471	124	23	,	,	PUNCT
cjfa-35471	124	24	r(t	r(t	NOUN
cjfa-35471	124	25	)	)	PUNCT
cjfa-35471	124	26	,	,	PUNCT
cjfa-35471	124	27	is	be	AUX
cjfa-35471	124	28	an	an	DET
cjfa-35471	124	29	exogenous	exogenous	ADJ
cjfa-35471	124	30	time	time	NOUN
cjfa-35471	124	31	dependent	dependent	ADJ
cjfa-35471	124	32	function	function	NOUN
cjfa-35471	124	33	making	make	VERB
cjfa-35471	124	34	the	the	DET
cjfa-35471	124	35	revenues	revenue	NOUN
cjfa-35471	124	36	an	an	DET
cjfa-35471	124	37	exogenous	exogenous	ADJ
cjfa-35471	124	38	function	function	NOUN
cjfa-35471	124	39	also	also	ADV
cjfa-35471	124	40	thus	thus	ADV
cjfa-35471	124	41	irrelevant	irrelevant	ADJ
cjfa-35471	124	42	in	in	ADP
cjfa-35471	124	43	decision	decision	NOUN
cjfa-35471	124	44	making	making	NOUN
cjfa-35471	124	45	.	.	PUNCT
cjfa-35471	125	1	the	the	DET
cjfa-35471	125	2	last	last	ADJ
cjfa-35471	125	3	constraint	constraint	NOUN
cjfa-35471	125	4	is	be	AUX
cjfa-35471	125	5	a	a	DET
cjfa-35471	125	6	state	state	NOUN
cjfa-35471	125	7	variable	variable	ADJ
cjfa-35471	125	8	inequality	inequality	NOUN
cjfa-35471	125	9	constraint	constraint	NOUN
cjfa-35471	125	10	which	which	PRON
cjfa-35471	125	11	has	have	AUX
cjfa-35471	125	12	been	be	AUX
cjfa-35471	125	13	studied	study	VERB
cjfa-35471	125	14	by	by	ADP
cjfa-35471	125	15	many	many	ADJ
cjfa-35471	125	16	authors	author	NOUN
cjfa-35471	125	17	including	include	VERB
cjfa-35471	125	18	bryson	bryson	PROPN
cjfa-35471	125	19	and	and	CCONJ
cjfa-35471	125	20	ho	ho	PROPN
cjfa-35471	125	21	(	(	PUNCT
cjfa-35471	125	22	1975	1975	NUM
cjfa-35471	125	23	)	)	PUNCT
cjfa-35471	125	24	,	,	PUNCT
cjfa-35471	125	25	bryson	bryson	PROPN
cjfa-35471	125	26	,	,	PUNCT
cjfa-35471	125	27	denham	denham	PROPN
cjfa-35471	125	28	and	and	CCONJ
cjfa-35471	125	29	dreyfus	dreyfus	PROPN
cjfa-35471	125	30	(	(	PUNCT
cjfa-35471	125	31	1963	1963	NUM
cjfa-35471	125	32	)	)	PUNCT
cjfa-35471	125	33	,	,	PUNCT
cjfa-35471	125	34	jacobson	jacobson	PROPN
cjfa-35471	125	35	and	and	CCONJ
cjfa-35471	125	36	lele	lele	PROPN
cjfa-35471	125	37	(	(	PUNCT
cjfa-35471	125	38	1969	1969	NUM
cjfa-35471	125	39	)	)	PUNCT
cjfa-35471	125	40	,	,	PUNCT
cjfa-35471	125	41	jacobson	jacobson	PROPN
cjfa-35471	125	42	,	,	PUNCT
cjfa-35471	125	43	lele	lele	PROPN
cjfa-35471	125	44	and	and	CCONJ
cjfa-35471	125	45	speyer	speyer	PROPN
cjfa-35471	125	46	(	(	PUNCT
cjfa-35471	125	47	1971	1971	NUM
cjfa-35471	125	48	)	)	PUNCT
cjfa-35471	125	49	,	,	PUNCT
cjfa-35471	125	50	mcintyre	mcintyre	PROPN
cjfa-35471	125	51	and	and	CCONJ
cjfa-35471	125	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	125	53	(	(	PUNCT
cjfa-35471	125	54	1967	1967	NUM
cjfa-35471	125	55	)	)	PUNCT
cjfa-35471	125	56	,	,	PUNCT
cjfa-35471	125	57	and	and	CCONJ
cjfa-35471	125	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	125	59	(	(	PUNCT
cjfa-35471	125	60	1967	1967	NUM
cjfa-35471	125	61	)	)	PUNCT
cjfa-35471	125	62	.	.	PUNCT
cjfa-35471	126	1	taylor	taylor	PROPN
cjfa-35471	126	2	(	(	PUNCT
cjfa-35471	126	3	1972	1972	NUM
cjfa-35471	126	4	)	)	PUNCT
cjfa-35471	126	5	studied	study	VERB
cjfa-35471	126	6	the	the	DET
cjfa-35471	126	7	problem	problem	NOUN
cjfa-35471	126	8	stated	state	VERB
cjfa-35471	126	9	above	above	ADV
cjfa-35471	126	10	with	with	ADP
cjfa-35471	126	11	no	no	DET
cjfa-35471	126	12	interest	interest	NOUN
cjfa-35471	126	13	rate	rate	NOUN
cjfa-35471	126	14	consideration	consideration	NOUN
cjfa-35471	126	15	and	and	CCONJ
cjfa-35471	126	16	has	have	AUX
cjfa-35471	126	17	found	find	VERB
cjfa-35471	126	18	that	that	SCONJ
cjfa-35471	126	19	;	;	PUNCT
cjfa-35471	127	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	127	2	�	�	PROPN
cjfa-35471	127	3	�	�	PROPN
cjfa-35471	127	4	�	�	PROPN
cjfa-35471	127	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	127	6	�	�	PROPN
cjfa-35471	127	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	127	8	�	�	PROPN
cjfa-35471	127	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	127	10	𝑡	𝑡	NOUN
cjfa-35471	127	11	ℎ	ℎ	PROPN
cjfa-35471	127	12	is	be	AUX
cjfa-35471	127	13	the	the	DET
cjfa-35471	127	14	condition	condition	NOUN
cjfa-35471	127	15	which	which	PRON
cjfa-35471	127	16	has	have	VERB
cjfa-35471	127	17	to	to	PART
cjfa-35471	127	18	hold	hold	VERB
cjfa-35471	127	19	for	for	ADP
cjfa-35471	127	20	the	the	DET
cjfa-35471	127	21	firm	firm	NOUN
cjfa-35471	127	22	to	to	PART
cjfa-35471	127	23	keep	keep	VERB
cjfa-35471	127	24	i	i	PRON
cjfa-35471	127	25	(	(	PUNCT
cjfa-35471	127	26	t	t	NOUN
cjfa-35471	127	27	)	)	PUNCT
cjfa-35471	127	28	=	=	NOUN
cjfa-35471	127	29	0	0	NUM
cjfa-35471	127	30	which	which	PRON
cjfa-35471	127	31	implies	imply	VERB
cjfa-35471	127	32	that	that	SCONJ
cjfa-35471	127	33	the	the	DET
cjfa-35471	127	34	firm	firm	NOUN
cjfa-35471	127	35	will	will	AUX
cjfa-35471	127	36	produce	produce	VERB
cjfa-35471	127	37	just	just	ADV
cjfa-35471	127	38	to	to	PART
cjfa-35471	127	39	meet	meet	VERB
cjfa-35471	127	40	the	the	DET
cjfa-35471	127	41	demand	demand	NOUN
cjfa-35471	127	42	.	.	PUNCT
cjfa-35471	128	1	the	the	DET
cjfa-35471	128	2	firm	firm	NOUN
cjfa-35471	128	3	will	will	AUX
cjfa-35471	128	4	start	start	VERB
cjfa-35471	128	5	producing	produce	VERB
cjfa-35471	128	6	not	not	PART
cjfa-35471	128	7	only	only	ADV
cjfa-35471	128	8	to	to	PART
cjfa-35471	128	9	meet	meet	VERB
cjfa-35471	128	10	the	the	DET
cjfa-35471	128	11	demand	demand	NOUN
cjfa-35471	128	12	but	but	CCONJ
cjfa-35471	128	13	also	also	ADV
cjfa-35471	128	14	to	to	PART
cjfa-35471	128	15	build	build	VERB
cjfa-35471	128	16	up	up	ADP
cjfa-35471	128	17	inventories	inventory	NOUN
cjfa-35471	128	18	when	when	SCONJ
cjfa-35471	128	19	the	the	DET
cjfa-35471	128	20	change	change	NOUN
cjfa-35471	128	21	in	in	ADP
cjfa-35471	128	22	demand	demand	NOUN
cjfa-35471	128	23	is	be	AUX
cjfa-35471	128	24	such	such	ADJ
cjfa-35471	128	25	that	that	SCONJ
cjfa-35471	128	26	the	the	DET
cjfa-35471	128	27	above	above	ADJ
cjfa-35471	128	28	inequality	inequality	NOUN
cjfa-35471	128	29	will	will	AUX
cjfa-35471	128	30	be	be	AUX
cjfa-35471	128	31	violated	violate	VERB
cjfa-35471	128	32	.	.	PUNCT
cjfa-35471	129	1	in	in	ADP
cjfa-35471	129	2	this	this	DET
cjfa-35471	129	3	paper	paper	NOUN
cjfa-35471	129	4	,	,	PUNCT
cjfa-35471	129	5	we	we	PRON
cjfa-35471	129	6	will	will	AUX
cjfa-35471	129	7	study	study	VERB
cjfa-35471	129	8	the	the	DET
cjfa-35471	129	9	same	same	ADJ
cjfa-35471	129	10	problem	problem	NOUN
cjfa-35471	129	11	introducing	introduce	VERB
cjfa-35471	129	12	present	present	ADJ
cjfa-35471	129	13	value	value	NOUN
cjfa-35471	129	14	factor	factor	NOUN
cjfa-35471	129	15	and	and	CCONJ
cjfa-35471	129	16	fluctuating	fluctuating	NOUN
cjfa-35471	129	17	time	time	NOUN
cjfa-35471	129	18	dependent	dependent	ADJ
cjfa-35471	129	19	demand	demand	NOUN
cjfa-35471	129	20	function	function	NOUN
cjfa-35471	129	21	.	.	PUNCT
cjfa-35471	130	1	then	then	ADV
cjfa-35471	130	2	,	,	PUNCT
cjfa-35471	130	3	the	the	DET
cjfa-35471	130	4	problem	problem	NOUN
cjfa-35471	130	5	becomes	become	VERB
cjfa-35471	130	6	:	:	PUNCT
cjfa-35471	130	7	(	(	PUNCT
cjfa-35471	130	8	)	)	PUNCT
cjfa-35471	130	9	0	0	PUNCT
cjfa-35471	131	1	[	[	PUNCT
cjfa-35471	131	2	(	(	PUNCT
cjfa-35471	131	3	(	(	PUNCT
cjfa-35471	131	4	)	)	PUNCT
cjfa-35471	131	5	(	(	PUNCT
cjfa-35471	131	6	)	)	PUNCT
cjfa-35471	131	7	]	]	PUNCT
cjfa-35471	131	8	t	t	X
cjfa-35471	131	9	i	i	PRON
cjfa-35471	131	10	tmin	tmin	VERB
cjfa-35471	131	11	e	e	PROPN
cjfa-35471	131	12	c	c	NOUN
cjfa-35471	131	13	u	u	X
cjfa-35471	132	1	t	t	X
cjfa-35471	132	2	hi	hi	INTJ
cjfa-35471	132	3	t	t	PROPN
cjfa-35471	132	4	dt	dt	X
cjfa-35471	132	5			NOUN
cjfa-35471	132	6	subject	subject	ADJ
cjfa-35471	132	7	to	to	ADP
cjfa-35471	132	8	the	the	DET
cjfa-35471	132	9	constraints	constraint	NOUN
cjfa-35471	132	10	:	:	PUNCT
cjfa-35471	132	11	cost	cost	NOUN
cjfa-35471	132	12	minimization	minimization	NOUN
cjfa-35471	132	13	is	be	AUX
cjfa-35471	132	14	considered	consider	VERB
cjfa-35471	132	15	since	since	SCONJ
cjfa-35471	132	16	the	the	DET
cjfa-35471	132	17	price	price	NOUN
cjfa-35471	132	18	is	be	AUX
cjfa-35471	132	19	assumed	assume	VERB
cjfa-35471	132	20	to	to	PART
cjfa-35471	132	21	be	be	AUX
cjfa-35471	132	22	constant	constant	ADJ
cjfa-35471	132	23	and	and	CCONJ
cjfa-35471	132	24	the	the	DET
cjfa-35471	132	25	demand	demand	NOUN
cjfa-35471	132	26	,	,	PUNCT
cjfa-35471	132	27	r(t	r(t	NOUN
cjfa-35471	132	28	)	)	PUNCT
cjfa-35471	132	29	,	,	PUNCT
cjfa-35471	132	30	is	be	AUX
cjfa-35471	132	31	an	an	DET
cjfa-35471	132	32	exogenous	exogenous	ADJ
cjfa-35471	132	33	time	time	NOUN
cjfa-35471	132	34	dependent	dependent	ADJ
cjfa-35471	132	35	function	function	NOUN
cjfa-35471	132	36	making	make	VERB
cjfa-35471	132	37	the	the	DET
cjfa-35471	132	38	revenues	revenue	NOUN
cjfa-35471	132	39	an	an	DET
cjfa-35471	132	40	exogenous	exogenous	ADJ
cjfa-35471	132	41	function	function	NOUN
cjfa-35471	132	42	also	also	ADV
cjfa-35471	132	43	thus	thus	ADV
cjfa-35471	132	44	irrelevant	irrelevant	ADJ
cjfa-35471	132	45	in	in	ADP
cjfa-35471	132	46	decision	decision	NOUN
cjfa-35471	132	47	making	making	NOUN
cjfa-35471	132	48	.	.	PUNCT
cjfa-35471	133	1	the	the	DET
cjfa-35471	133	2	last	last	ADJ
cjfa-35471	133	3	constraint	constraint	NOUN
cjfa-35471	133	4	is	be	AUX
cjfa-35471	133	5	a	a	DET
cjfa-35471	133	6	state	state	NOUN
cjfa-35471	133	7	variable	variable	ADJ
cjfa-35471	133	8	inequality	inequality	NOUN
cjfa-35471	133	9	constraint	constraint	NOUN
cjfa-35471	133	10	which	which	PRON
cjfa-35471	133	11	has	have	AUX
cjfa-35471	133	12	been	be	AUX
cjfa-35471	133	13	studied	study	VERB
cjfa-35471	133	14	by	by	ADP
cjfa-35471	133	15	many	many	ADJ
cjfa-35471	133	16	authors	author	NOUN
cjfa-35471	133	17	including	include	VERB
cjfa-35471	133	18	bryson	bryson	PROPN
cjfa-35471	133	19	and	and	CCONJ
cjfa-35471	133	20	ho	ho	PROPN
cjfa-35471	133	21	(	(	PUNCT
cjfa-35471	133	22	1975	1975	NUM
cjfa-35471	133	23	)	)	PUNCT
cjfa-35471	133	24	,	,	PUNCT
cjfa-35471	133	25	bryson	bryson	PROPN
cjfa-35471	133	26	,	,	PUNCT
cjfa-35471	133	27	denham	denham	PROPN
cjfa-35471	133	28	and	and	CCONJ
cjfa-35471	133	29	dreyfus	dreyfus	PROPN
cjfa-35471	133	30	(	(	PUNCT
cjfa-35471	133	31	1963	1963	NUM
cjfa-35471	133	32	)	)	PUNCT
cjfa-35471	133	33	,	,	PUNCT
cjfa-35471	133	34	jacobson	jacobson	PROPN
cjfa-35471	133	35	and	and	CCONJ
cjfa-35471	133	36	lele	lele	PROPN
cjfa-35471	133	37	(	(	PUNCT
cjfa-35471	133	38	1969	1969	NUM
cjfa-35471	133	39	)	)	PUNCT
cjfa-35471	133	40	,	,	PUNCT
cjfa-35471	133	41	jacobson	jacobson	PROPN
cjfa-35471	133	42	,	,	PUNCT
cjfa-35471	133	43	lele	lele	PROPN
cjfa-35471	133	44	and	and	CCONJ
cjfa-35471	133	45	speyer	speyer	PROPN
cjfa-35471	133	46	(	(	PUNCT
cjfa-35471	133	47	1971	1971	NUM
cjfa-35471	133	48	)	)	PUNCT
cjfa-35471	133	49	,	,	PUNCT
cjfa-35471	133	50	mcintyre	mcintyre	PROPN
cjfa-35471	133	51	and	and	CCONJ
cjfa-35471	133	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	133	53	(	(	PUNCT
cjfa-35471	133	54	1967	1967	NUM
cjfa-35471	133	55	)	)	PUNCT
cjfa-35471	133	56	,	,	PUNCT
cjfa-35471	133	57	and	and	CCONJ
cjfa-35471	133	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	133	59	(	(	PUNCT
cjfa-35471	133	60	1967	1967	NUM
cjfa-35471	133	61	)	)	PUNCT
cjfa-35471	133	62	.	.	PUNCT
cjfa-35471	134	1	taylor	taylor	PROPN
cjfa-35471	134	2	(	(	PUNCT
cjfa-35471	134	3	1972	1972	NUM
cjfa-35471	134	4	)	)	PUNCT
cjfa-35471	134	5	studied	study	VERB
cjfa-35471	134	6	the	the	DET
cjfa-35471	134	7	problem	problem	NOUN
cjfa-35471	134	8	stated	state	VERB
cjfa-35471	134	9	above	above	ADV
cjfa-35471	134	10	with	with	ADP
cjfa-35471	134	11	no	no	DET
cjfa-35471	134	12	interest	interest	NOUN
cjfa-35471	134	13	rate	rate	NOUN
cjfa-35471	134	14	consideration	consideration	NOUN
cjfa-35471	134	15	and	and	CCONJ
cjfa-35471	134	16	has	have	AUX
cjfa-35471	134	17	found	find	VERB
cjfa-35471	134	18	that	that	SCONJ
cjfa-35471	134	19	;	;	PUNCT
cjfa-35471	134	20	mustafa	mustafa	PROPN
cjfa-35471	134	21	akan	akan	PROPN
cjfa-35471	134	22	,	,	PUNCT
cjfa-35471	134	23	natalia	natalia	PROPN
cjfa-35471	134	24	konovalova14	konovalova14	PROPN
cjfa-35471	134	25	ℎ	ℎ	PROPN
cjfa-35471	134	26	:	:	PUNCT
cjfa-35471	134	27	unit	unit	NOUN
cjfa-35471	134	28	holding	hold	VERB
cjfa-35471	134	29	cost	cost	NOUN
cjfa-35471	134	30	,	,	PUNCT
cjfa-35471	134	31	a	a	DET
cjfa-35471	134	32	constant	constant	ADJ
cjfa-35471	134	33	.	.	PUNCT
cjfa-35471	135	1	these	these	DET
cjfa-35471	135	2	costs	cost	NOUN
cjfa-35471	135	3	include	include	VERB
cjfa-35471	135	4	many	many	ADJ
cjfa-35471	135	5	cost	cost	NOUN
cjfa-35471	135	6	items	item	NOUN
cjfa-35471	135	7	such	such	ADJ
cjfa-35471	135	8	as	as	ADP
cjfa-35471	135	9	rent	rent	NOUN
cjfa-35471	135	10	,	,	PUNCT
cjfa-35471	135	11	cost	cost	NOUN
cjfa-35471	135	12	of	of	ADP
cjfa-35471	135	13	relevant	relevant	ADJ
cjfa-35471	135	14	equipment	equipment	NOUN
cjfa-35471	135	15	necessary	necessary	ADJ
cjfa-35471	135	16	to	to	PART
cjfa-35471	135	17	keep	keep	VERB
cjfa-35471	135	18	the	the	DET
cjfa-35471	135	19	products	product	NOUN
cjfa-35471	135	20	in	in	ADP
cjfa-35471	135	21	the	the	DET
cjfa-35471	135	22	inventory	inventory	NOUN
cjfa-35471	135	23	,	,	PUNCT
cjfa-35471	135	24	and	and	CCONJ
cjfa-35471	135	25	insurance	insurance	NOUN
cjfa-35471	135	26	premiums	premium	NOUN
cjfa-35471	135	27	.	.	PUNCT
cjfa-35471	136	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	136	2	:	:	PUNCT
cjfa-35471	136	3	level	level	NOUN
cjfa-35471	136	4	of	of	ADP
cjfa-35471	136	5	demand	demand	NOUN
cjfa-35471	136	6	that	that	PRON
cjfa-35471	136	7	is	be	AUX
cjfa-35471	136	8	an	an	DET
cjfa-35471	136	9	exogenously	exogenously	ADV
cjfa-35471	136	10	determined	determine	VERB
cjfa-35471	136	11	function	function	NOUN
cjfa-35471	136	12	of	of	ADP
cjfa-35471	136	13	time	time	NOUN
cjfa-35471	136	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	136	15	:	:	PUNCT
cjfa-35471	136	16	the	the	DET
cjfa-35471	136	17	level	level	NOUN
cjfa-35471	136	18	of	of	ADP
cjfa-35471	136	19	inventory	inventory	NOUN
cjfa-35471	136	20	at	at	ADP
cjfa-35471	136	21	time	time	NOUN
cjfa-35471	136	22	t	t	PROPN
cjfa-35471	136	23	,	,	PUNCT
cjfa-35471	136	24	which	which	PRON
cjfa-35471	136	25	increases	increase	VERB
cjfa-35471	136	26	by	by	ADP
cjfa-35471	136	27	production	production	NOUN
cjfa-35471	136	28	(	(	PUNCT
cjfa-35471	136	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	136	30	and	and	CCONJ
cjfa-35471	136	31	decreases	decrease	NOUN
cjfa-35471	136	32	by	by	ADP
cjfa-35471	136	33	sales	sale	NOUN
cjfa-35471	136	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	136	35	therefore	therefore	ADV
cjfa-35471	136	36	,	,	PUNCT
cjfa-35471	136	37	the	the	DET
cjfa-35471	136	38	model	model	NOUN
cjfa-35471	136	39	,	,	PUNCT
cjfa-35471	136	40	is	be	AUX
cjfa-35471	136	41	(	(	PUNCT
cjfa-35471	136	42	)	)	PUNCT
cjfa-35471	136	43	0	0	NUM
cjfa-35471	137	1	max	max	PROPN
cjfa-35471	137	2	[	[	PUNCT
cjfa-35471	137	3	(	(	PUNCT
cjfa-35471	137	4	(	(	PUNCT
cjfa-35471	137	5	)	)	PUNCT
cjfa-35471	137	6	)	)	PUNCT
cjfa-35471	137	7	(	(	PUNCT
cjfa-35471	137	8	)	)	PUNCT
cjfa-35471	137	9	]	]	PUNCT
cjfa-35471	138	1	t	t	X
cjfa-35471	138	2	u	u	NOUN
cjfa-35471	138	3	t	t	X
cjfa-35471	138	4	c	c	NOUN
cjfa-35471	138	5	u	u	NOUN
cjfa-35471	138	6	t	t	X
cjfa-35471	138	7	hi	hi	INTJ
cjfa-35471	138	8	t	t	PROPN
cjfa-35471	138	9	dt	dt	NOUN
cjfa-35471	138	10	subject	subject	NOUN
cjfa-35471	138	11	to	to	ADP
cjfa-35471	138	12	the	the	DET
cjfa-35471	138	13	constraints	constraint	NOUN
cjfa-35471	138	14	:	:	PUNCT
cjfa-35471	138	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	138	16	�	�	PROPN
cjfa-35471	138	17	=	=	PUNCT
cjfa-35471	138	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	138	19	−	−	X
cjfa-35471	138	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	138	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	139	1	=	=	SYM
cjfa-35471	139	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	139	3	�	�	PROPN
cjfa-35471	139	4	given	give	VERB
cjfa-35471	139	5	and	and	CCONJ
cjfa-35471	139	6	the	the	DET
cjfa-35471	139	7	non	non	ADJ
cjfa-35471	139	8	-	-	ADJ
cjfa-35471	139	9	negativity	negativity	ADJ
cjfa-35471	139	10	constraints	constraint	NOUN
cjfa-35471	139	11	.	.	PUNCT
cjfa-35471	140	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	140	2	≥	≥	PROPN
cjfa-35471	140	3	0	0	NUM
cjfa-35471	140	4	,	,	PUNCT
cjfa-35471	140	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	140	6	≥	≥	NOUN
cjfa-35471	140	7	0	0	NUM
cjfa-35471	140	8	cost	cost	NOUN
cjfa-35471	140	9	minimization	minimization	NOUN
cjfa-35471	140	10	is	be	AUX
cjfa-35471	140	11	considered	consider	VERB
cjfa-35471	140	12	since	since	SCONJ
cjfa-35471	140	13	the	the	DET
cjfa-35471	140	14	price	price	NOUN
cjfa-35471	140	15	is	be	AUX
cjfa-35471	140	16	assumed	assume	VERB
cjfa-35471	140	17	to	to	PART
cjfa-35471	140	18	be	be	AUX
cjfa-35471	140	19	constant	constant	ADJ
cjfa-35471	140	20	and	and	CCONJ
cjfa-35471	140	21	the	the	DET
cjfa-35471	140	22	demand	demand	NOUN
cjfa-35471	140	23	,	,	PUNCT
cjfa-35471	140	24	r(t	r(t	NOUN
cjfa-35471	140	25	)	)	PUNCT
cjfa-35471	140	26	,	,	PUNCT
cjfa-35471	140	27	is	be	AUX
cjfa-35471	140	28	an	an	DET
cjfa-35471	140	29	exogenous	exogenous	ADJ
cjfa-35471	140	30	time	time	NOUN
cjfa-35471	140	31	dependent	dependent	ADJ
cjfa-35471	140	32	function	function	NOUN
cjfa-35471	140	33	making	make	VERB
cjfa-35471	140	34	the	the	DET
cjfa-35471	140	35	revenues	revenue	NOUN
cjfa-35471	140	36	an	an	DET
cjfa-35471	140	37	exogenous	exogenous	ADJ
cjfa-35471	140	38	function	function	NOUN
cjfa-35471	140	39	also	also	ADV
cjfa-35471	140	40	thus	thus	ADV
cjfa-35471	140	41	irrelevant	irrelevant	ADJ
cjfa-35471	140	42	in	in	ADP
cjfa-35471	140	43	decision	decision	NOUN
cjfa-35471	140	44	making	making	NOUN
cjfa-35471	140	45	.	.	PUNCT
cjfa-35471	141	1	the	the	DET
cjfa-35471	141	2	last	last	ADJ
cjfa-35471	141	3	constraint	constraint	NOUN
cjfa-35471	141	4	is	be	AUX
cjfa-35471	141	5	a	a	DET
cjfa-35471	141	6	state	state	NOUN
cjfa-35471	141	7	variable	variable	ADJ
cjfa-35471	141	8	inequality	inequality	NOUN
cjfa-35471	141	9	constraint	constraint	NOUN
cjfa-35471	141	10	which	which	PRON
cjfa-35471	141	11	has	have	AUX
cjfa-35471	141	12	been	be	AUX
cjfa-35471	141	13	studied	study	VERB
cjfa-35471	141	14	by	by	ADP
cjfa-35471	141	15	many	many	ADJ
cjfa-35471	141	16	authors	author	NOUN
cjfa-35471	141	17	including	include	VERB
cjfa-35471	141	18	bryson	bryson	PROPN
cjfa-35471	141	19	and	and	CCONJ
cjfa-35471	141	20	ho	ho	PROPN
cjfa-35471	141	21	(	(	PUNCT
cjfa-35471	141	22	1975	1975	NUM
cjfa-35471	141	23	)	)	PUNCT
cjfa-35471	141	24	,	,	PUNCT
cjfa-35471	141	25	bryson	bryson	PROPN
cjfa-35471	141	26	,	,	PUNCT
cjfa-35471	141	27	denham	denham	PROPN
cjfa-35471	141	28	and	and	CCONJ
cjfa-35471	141	29	dreyfus	dreyfus	PROPN
cjfa-35471	141	30	(	(	PUNCT
cjfa-35471	141	31	1963	1963	NUM
cjfa-35471	141	32	)	)	PUNCT
cjfa-35471	141	33	,	,	PUNCT
cjfa-35471	141	34	jacobson	jacobson	PROPN
cjfa-35471	141	35	and	and	CCONJ
cjfa-35471	141	36	lele	lele	PROPN
cjfa-35471	141	37	(	(	PUNCT
cjfa-35471	141	38	1969	1969	NUM
cjfa-35471	141	39	)	)	PUNCT
cjfa-35471	141	40	,	,	PUNCT
cjfa-35471	141	41	jacobson	jacobson	PROPN
cjfa-35471	141	42	,	,	PUNCT
cjfa-35471	141	43	lele	lele	PROPN
cjfa-35471	141	44	and	and	CCONJ
cjfa-35471	141	45	speyer	speyer	PROPN
cjfa-35471	141	46	(	(	PUNCT
cjfa-35471	141	47	1971	1971	NUM
cjfa-35471	141	48	)	)	PUNCT
cjfa-35471	141	49	,	,	PUNCT
cjfa-35471	141	50	mcintyre	mcintyre	PROPN
cjfa-35471	141	51	and	and	CCONJ
cjfa-35471	141	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	141	53	(	(	PUNCT
cjfa-35471	141	54	1967	1967	NUM
cjfa-35471	141	55	)	)	PUNCT
cjfa-35471	141	56	,	,	PUNCT
cjfa-35471	141	57	and	and	CCONJ
cjfa-35471	141	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	141	59	(	(	PUNCT
cjfa-35471	141	60	1967	1967	NUM
cjfa-35471	141	61	)	)	PUNCT
cjfa-35471	141	62	.	.	PUNCT
cjfa-35471	142	1	taylor	taylor	PROPN
cjfa-35471	142	2	(	(	PUNCT
cjfa-35471	142	3	1972	1972	NUM
cjfa-35471	142	4	)	)	PUNCT
cjfa-35471	142	5	studied	study	VERB
cjfa-35471	142	6	the	the	DET
cjfa-35471	142	7	problem	problem	NOUN
cjfa-35471	142	8	stated	state	VERB
cjfa-35471	142	9	above	above	ADV
cjfa-35471	142	10	with	with	ADP
cjfa-35471	142	11	no	no	DET
cjfa-35471	142	12	interest	interest	NOUN
cjfa-35471	142	13	rate	rate	NOUN
cjfa-35471	142	14	consideration	consideration	NOUN
cjfa-35471	142	15	and	and	CCONJ
cjfa-35471	142	16	has	have	AUX
cjfa-35471	142	17	found	find	VERB
cjfa-35471	142	18	that	that	SCONJ
cjfa-35471	142	19	;	;	PUNCT
cjfa-35471	143	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	143	2	�	�	PROPN
cjfa-35471	143	3	�	�	PROPN
cjfa-35471	143	4	�	�	PROPN
cjfa-35471	143	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	143	6	�	�	PROPN
cjfa-35471	143	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	143	8	�	�	PROPN
cjfa-35471	143	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	143	10	𝑡	𝑡	NOUN
cjfa-35471	143	11	ℎ	ℎ	PROPN
cjfa-35471	143	12	is	be	AUX
cjfa-35471	143	13	the	the	DET
cjfa-35471	143	14	condition	condition	NOUN
cjfa-35471	143	15	which	which	PRON
cjfa-35471	143	16	has	have	VERB
cjfa-35471	143	17	to	to	PART
cjfa-35471	143	18	hold	hold	VERB
cjfa-35471	143	19	for	for	ADP
cjfa-35471	143	20	the	the	DET
cjfa-35471	143	21	firm	firm	NOUN
cjfa-35471	143	22	to	to	PART
cjfa-35471	143	23	keep	keep	VERB
cjfa-35471	143	24	i	i	PRON
cjfa-35471	143	25	(	(	PUNCT
cjfa-35471	143	26	t	t	NOUN
cjfa-35471	143	27	)	)	PUNCT
cjfa-35471	143	28	=	=	NOUN
cjfa-35471	143	29	0	0	NUM
cjfa-35471	143	30	which	which	PRON
cjfa-35471	143	31	implies	imply	VERB
cjfa-35471	143	32	that	that	SCONJ
cjfa-35471	143	33	the	the	DET
cjfa-35471	143	34	firm	firm	NOUN
cjfa-35471	143	35	will	will	AUX
cjfa-35471	143	36	produce	produce	VERB
cjfa-35471	143	37	just	just	ADV
cjfa-35471	143	38	to	to	PART
cjfa-35471	143	39	meet	meet	VERB
cjfa-35471	143	40	the	the	DET
cjfa-35471	143	41	demand	demand	NOUN
cjfa-35471	143	42	.	.	PUNCT
cjfa-35471	144	1	the	the	DET
cjfa-35471	144	2	firm	firm	NOUN
cjfa-35471	144	3	will	will	AUX
cjfa-35471	144	4	start	start	VERB
cjfa-35471	144	5	producing	produce	VERB
cjfa-35471	144	6	not	not	PART
cjfa-35471	144	7	only	only	ADV
cjfa-35471	144	8	to	to	PART
cjfa-35471	144	9	meet	meet	VERB
cjfa-35471	144	10	the	the	DET
cjfa-35471	144	11	demand	demand	NOUN
cjfa-35471	144	12	but	but	CCONJ
cjfa-35471	144	13	also	also	ADV
cjfa-35471	144	14	to	to	PART
cjfa-35471	144	15	build	build	VERB
cjfa-35471	144	16	up	up	ADP
cjfa-35471	144	17	inventories	inventory	NOUN
cjfa-35471	144	18	when	when	SCONJ
cjfa-35471	144	19	the	the	DET
cjfa-35471	144	20	change	change	NOUN
cjfa-35471	144	21	in	in	ADP
cjfa-35471	144	22	demand	demand	NOUN
cjfa-35471	144	23	is	be	AUX
cjfa-35471	144	24	such	such	ADJ
cjfa-35471	144	25	that	that	SCONJ
cjfa-35471	144	26	the	the	DET
cjfa-35471	144	27	above	above	ADJ
cjfa-35471	144	28	inequality	inequality	NOUN
cjfa-35471	144	29	will	will	AUX
cjfa-35471	144	30	be	be	AUX
cjfa-35471	144	31	violated	violate	VERB
cjfa-35471	144	32	.	.	PUNCT
cjfa-35471	145	1	in	in	ADP
cjfa-35471	145	2	this	this	DET
cjfa-35471	145	3	paper	paper	NOUN
cjfa-35471	145	4	,	,	PUNCT
cjfa-35471	145	5	we	we	PRON
cjfa-35471	145	6	will	will	AUX
cjfa-35471	145	7	study	study	VERB
cjfa-35471	145	8	the	the	DET
cjfa-35471	145	9	same	same	ADJ
cjfa-35471	145	10	problem	problem	NOUN
cjfa-35471	145	11	introducing	introduce	VERB
cjfa-35471	145	12	present	present	ADJ
cjfa-35471	145	13	value	value	NOUN
cjfa-35471	145	14	factor	factor	NOUN
cjfa-35471	145	15	and	and	CCONJ
cjfa-35471	145	16	fluctuating	fluctuating	NOUN
cjfa-35471	145	17	time	time	NOUN
cjfa-35471	145	18	dependent	dependent	ADJ
cjfa-35471	145	19	demand	demand	NOUN
cjfa-35471	145	20	function	function	NOUN
cjfa-35471	145	21	.	.	PUNCT
cjfa-35471	146	1	then	then	ADV
cjfa-35471	146	2	,	,	PUNCT
cjfa-35471	146	3	the	the	DET
cjfa-35471	146	4	problem	problem	NOUN
cjfa-35471	146	5	becomes	become	VERB
cjfa-35471	146	6	:	:	PUNCT
cjfa-35471	146	7	(	(	PUNCT
cjfa-35471	146	8	)	)	PUNCT
cjfa-35471	146	9	0	0	PUNCT
cjfa-35471	147	1	[	[	PUNCT
cjfa-35471	147	2	(	(	PUNCT
cjfa-35471	147	3	(	(	PUNCT
cjfa-35471	147	4	)	)	PUNCT
cjfa-35471	147	5	(	(	PUNCT
cjfa-35471	147	6	)	)	PUNCT
cjfa-35471	147	7	]	]	PUNCT
cjfa-35471	147	8	t	t	X
cjfa-35471	147	9	i	i	PRON
cjfa-35471	147	10	tmin	tmin	VERB
cjfa-35471	147	11	e	e	PROPN
cjfa-35471	147	12	c	c	NOUN
cjfa-35471	147	13	u	u	X
cjfa-35471	148	1	t	t	X
cjfa-35471	148	2	hi	hi	INTJ
cjfa-35471	148	3	t	t	PROPN
cjfa-35471	148	4	dt	dt	X
cjfa-35471	148	5			NOUN
cjfa-35471	148	6	subject	subject	ADJ
cjfa-35471	148	7	to	to	ADP
cjfa-35471	148	8	the	the	DET
cjfa-35471	148	9	constraints	constraint	NOUN
cjfa-35471	148	10	:	:	PUNCT
cjfa-35471	148	11	is	be	AUX
cjfa-35471	148	12	the	the	DET
cjfa-35471	148	13	condition	condition	NOUN
cjfa-35471	148	14	which	which	PRON
cjfa-35471	148	15	has	have	VERB
cjfa-35471	148	16	to	to	PART
cjfa-35471	148	17	hold	hold	VERB
cjfa-35471	148	18	for	for	ADP
cjfa-35471	148	19	the	the	DET
cjfa-35471	148	20	firm	firm	NOUN
cjfa-35471	148	21	to	to	PART
cjfa-35471	148	22	keep	keep	VERB
cjfa-35471	148	23	i	i	PRON
cjfa-35471	148	24	(	(	PUNCT
cjfa-35471	148	25	t	t	NOUN
cjfa-35471	148	26	)	)	PUNCT
cjfa-35471	148	27	=	=	NOUN
cjfa-35471	148	28	0	0	NUM
cjfa-35471	148	29	which	which	PRON
cjfa-35471	148	30	implies	imply	VERB
cjfa-35471	148	31	that	that	SCONJ
cjfa-35471	148	32	the	the	DET
cjfa-35471	148	33	firm	firm	NOUN
cjfa-35471	148	34	will	will	AUX
cjfa-35471	148	35	produce	produce	VERB
cjfa-35471	148	36	just	just	ADV
cjfa-35471	148	37	to	to	PART
cjfa-35471	148	38	meet	meet	VERB
cjfa-35471	148	39	the	the	DET
cjfa-35471	148	40	demand	demand	NOUN
cjfa-35471	148	41	.	.	PUNCT
cjfa-35471	149	1	the	the	DET
cjfa-35471	149	2	firm	firm	NOUN
cjfa-35471	149	3	will	will	AUX
cjfa-35471	149	4	start	start	VERB
cjfa-35471	149	5	producing	produce	VERB
cjfa-35471	149	6	not	not	PART
cjfa-35471	149	7	only	only	ADV
cjfa-35471	149	8	to	to	PART
cjfa-35471	149	9	meet	meet	VERB
cjfa-35471	149	10	the	the	DET
cjfa-35471	149	11	demand	demand	NOUN
cjfa-35471	149	12	but	but	CCONJ
cjfa-35471	149	13	also	also	ADV
cjfa-35471	149	14	to	to	PART
cjfa-35471	149	15	build	build	VERB
cjfa-35471	149	16	up	up	ADP
cjfa-35471	149	17	inventories	inventory	NOUN
cjfa-35471	149	18	when	when	SCONJ
cjfa-35471	149	19	the	the	DET
cjfa-35471	149	20	change	change	NOUN
cjfa-35471	149	21	in	in	ADP
cjfa-35471	149	22	demand	demand	NOUN
cjfa-35471	149	23	is	be	AUX
cjfa-35471	149	24	such	such	ADJ
cjfa-35471	149	25	that	that	SCONJ
cjfa-35471	149	26	the	the	DET
cjfa-35471	149	27	above	above	ADJ
cjfa-35471	149	28	inequality	inequality	NOUN
cjfa-35471	149	29	will	will	AUX
cjfa-35471	149	30	be	be	AUX
cjfa-35471	149	31	violated	violate	VERB
cjfa-35471	149	32	.	.	PUNCT
cjfa-35471	150	1	in	in	ADP
cjfa-35471	150	2	this	this	DET
cjfa-35471	150	3	paper	paper	NOUN
cjfa-35471	150	4	,	,	PUNCT
cjfa-35471	150	5	we	we	PRON
cjfa-35471	150	6	will	will	AUX
cjfa-35471	150	7	study	study	VERB
cjfa-35471	150	8	the	the	DET
cjfa-35471	150	9	same	same	ADJ
cjfa-35471	150	10	problem	problem	NOUN
cjfa-35471	150	11	introducing	introduce	VERB
cjfa-35471	150	12	present	present	ADJ
cjfa-35471	150	13	value	value	NOUN
cjfa-35471	150	14	factor	factor	NOUN
cjfa-35471	150	15	and	and	CCONJ
cjfa-35471	150	16	fluctuating	fluctuating	NOUN
cjfa-35471	150	17	time	time	NOUN
cjfa-35471	150	18	dependent	dependent	ADJ
cjfa-35471	150	19	demand	demand	NOUN
cjfa-35471	150	20	function	function	NOUN
cjfa-35471	150	21	.	.	PUNCT
cjfa-35471	151	1	then	then	ADV
cjfa-35471	151	2	,	,	PUNCT
cjfa-35471	151	3	the	the	DET
cjfa-35471	151	4	problem	problem	NOUN
cjfa-35471	151	5	becomes	become	VERB
cjfa-35471	151	6	:	:	PUNCT
cjfa-35471	151	7	ℎ	ℎ	PROPN
cjfa-35471	151	8	:	:	PUNCT
cjfa-35471	151	9	unit	unit	NOUN
cjfa-35471	151	10	holding	hold	VERB
cjfa-35471	151	11	cost	cost	NOUN
cjfa-35471	151	12	,	,	PUNCT
cjfa-35471	151	13	a	a	DET
cjfa-35471	151	14	constant	constant	ADJ
cjfa-35471	151	15	.	.	PUNCT
cjfa-35471	152	1	these	these	DET
cjfa-35471	152	2	costs	cost	NOUN
cjfa-35471	152	3	include	include	VERB
cjfa-35471	152	4	many	many	ADJ
cjfa-35471	152	5	cost	cost	NOUN
cjfa-35471	152	6	items	item	NOUN
cjfa-35471	152	7	such	such	ADJ
cjfa-35471	152	8	as	as	ADP
cjfa-35471	152	9	rent	rent	NOUN
cjfa-35471	152	10	,	,	PUNCT
cjfa-35471	152	11	cost	cost	NOUN
cjfa-35471	152	12	of	of	ADP
cjfa-35471	152	13	relevant	relevant	ADJ
cjfa-35471	152	14	equipment	equipment	NOUN
cjfa-35471	152	15	necessary	necessary	ADJ
cjfa-35471	152	16	to	to	PART
cjfa-35471	152	17	keep	keep	VERB
cjfa-35471	152	18	the	the	DET
cjfa-35471	152	19	products	product	NOUN
cjfa-35471	152	20	in	in	ADP
cjfa-35471	152	21	the	the	DET
cjfa-35471	152	22	inventory	inventory	NOUN
cjfa-35471	152	23	,	,	PUNCT
cjfa-35471	152	24	and	and	CCONJ
cjfa-35471	152	25	insurance	insurance	NOUN
cjfa-35471	152	26	premiums	premium	NOUN
cjfa-35471	152	27	.	.	PUNCT
cjfa-35471	153	1	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	153	2	:	:	PUNCT
cjfa-35471	153	3	level	level	NOUN
cjfa-35471	153	4	of	of	ADP
cjfa-35471	153	5	demand	demand	NOUN
cjfa-35471	153	6	that	that	PRON
cjfa-35471	153	7	is	be	AUX
cjfa-35471	153	8	an	an	DET
cjfa-35471	153	9	exogenously	exogenously	ADV
cjfa-35471	153	10	determined	determine	VERB
cjfa-35471	153	11	function	function	NOUN
cjfa-35471	153	12	of	of	ADP
cjfa-35471	153	13	time	time	NOUN
cjfa-35471	153	14	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	153	15	:	:	PUNCT
cjfa-35471	153	16	the	the	DET
cjfa-35471	153	17	level	level	NOUN
cjfa-35471	153	18	of	of	ADP
cjfa-35471	153	19	inventory	inventory	NOUN
cjfa-35471	153	20	at	at	ADP
cjfa-35471	153	21	time	time	NOUN
cjfa-35471	153	22	t	t	PROPN
cjfa-35471	153	23	,	,	PUNCT
cjfa-35471	153	24	which	which	PRON
cjfa-35471	153	25	increases	increase	VERB
cjfa-35471	153	26	by	by	ADP
cjfa-35471	153	27	production	production	NOUN
cjfa-35471	153	28	(	(	PUNCT
cjfa-35471	153	29	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	153	30	and	and	CCONJ
cjfa-35471	153	31	decreases	decrease	NOUN
cjfa-35471	153	32	by	by	ADP
cjfa-35471	153	33	sales	sale	NOUN
cjfa-35471	153	34	𝑟𝑟𝑟𝑟𝑟𝑟.	𝑟𝑟𝑟𝑟𝑟𝑟.	PROPN
cjfa-35471	153	35	therefore	therefore	ADV
cjfa-35471	153	36	,	,	PUNCT
cjfa-35471	153	37	the	the	DET
cjfa-35471	153	38	model	model	NOUN
cjfa-35471	153	39	,	,	PUNCT
cjfa-35471	153	40	is	be	AUX
cjfa-35471	153	41	(	(	PUNCT
cjfa-35471	153	42	)	)	PUNCT
cjfa-35471	153	43	0	0	NUM
cjfa-35471	154	1	max	max	PROPN
cjfa-35471	154	2	[	[	PUNCT
cjfa-35471	154	3	(	(	PUNCT
cjfa-35471	154	4	(	(	PUNCT
cjfa-35471	154	5	)	)	PUNCT
cjfa-35471	154	6	)	)	PUNCT
cjfa-35471	154	7	(	(	PUNCT
cjfa-35471	154	8	)	)	PUNCT
cjfa-35471	154	9	]	]	PUNCT
cjfa-35471	155	1	t	t	X
cjfa-35471	155	2	u	u	NOUN
cjfa-35471	155	3	t	t	X
cjfa-35471	155	4	c	c	NOUN
cjfa-35471	155	5	u	u	NOUN
cjfa-35471	155	6	t	t	X
cjfa-35471	155	7	hi	hi	INTJ
cjfa-35471	155	8	t	t	PROPN
cjfa-35471	155	9	dt	dt	NOUN
cjfa-35471	155	10	subject	subject	NOUN
cjfa-35471	155	11	to	to	ADP
cjfa-35471	155	12	the	the	DET
cjfa-35471	155	13	constraints	constraint	NOUN
cjfa-35471	155	14	:	:	PUNCT
cjfa-35471	155	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	155	16	�	�	PROPN
cjfa-35471	155	17	=	=	PUNCT
cjfa-35471	155	18	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	155	19	−	−	X
cjfa-35471	155	20	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	X
cjfa-35471	155	21	𝐼𝐼𝑟0𝑟	𝐼𝐼𝑟0𝑟	PUNCT
cjfa-35471	156	1	=	=	SYM
cjfa-35471	156	2	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	156	3	�	�	PROPN
cjfa-35471	156	4	given	give	VERB
cjfa-35471	156	5	and	and	CCONJ
cjfa-35471	156	6	the	the	DET
cjfa-35471	156	7	non	non	ADJ
cjfa-35471	156	8	-	-	ADJ
cjfa-35471	156	9	negativity	negativity	ADJ
cjfa-35471	156	10	constraints	constraint	NOUN
cjfa-35471	156	11	.	.	PUNCT
cjfa-35471	157	1	𝑢𝑢𝑟𝑟𝑟𝑟	𝑢𝑢𝑟𝑟𝑟𝑟	ADV
cjfa-35471	157	2	≥	≥	PROPN
cjfa-35471	157	3	0	0	NUM
cjfa-35471	157	4	,	,	PUNCT
cjfa-35471	157	5	𝐼𝐼𝑟𝑟𝑟𝑟	𝐼𝐼𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	157	6	≥	≥	NOUN
cjfa-35471	157	7	0	0	NUM
cjfa-35471	157	8	cost	cost	NOUN
cjfa-35471	157	9	minimization	minimization	NOUN
cjfa-35471	157	10	is	be	AUX
cjfa-35471	157	11	considered	consider	VERB
cjfa-35471	157	12	since	since	SCONJ
cjfa-35471	157	13	the	the	DET
cjfa-35471	157	14	price	price	NOUN
cjfa-35471	157	15	is	be	AUX
cjfa-35471	157	16	assumed	assume	VERB
cjfa-35471	157	17	to	to	PART
cjfa-35471	157	18	be	be	AUX
cjfa-35471	157	19	constant	constant	ADJ
cjfa-35471	157	20	and	and	CCONJ
cjfa-35471	157	21	the	the	DET
cjfa-35471	157	22	demand	demand	NOUN
cjfa-35471	157	23	,	,	PUNCT
cjfa-35471	157	24	r(t	r(t	NOUN
cjfa-35471	157	25	)	)	PUNCT
cjfa-35471	157	26	,	,	PUNCT
cjfa-35471	157	27	is	be	AUX
cjfa-35471	157	28	an	an	DET
cjfa-35471	157	29	exogenous	exogenous	ADJ
cjfa-35471	157	30	time	time	NOUN
cjfa-35471	157	31	dependent	dependent	ADJ
cjfa-35471	157	32	function	function	NOUN
cjfa-35471	157	33	making	make	VERB
cjfa-35471	157	34	the	the	DET
cjfa-35471	157	35	revenues	revenue	NOUN
cjfa-35471	157	36	an	an	DET
cjfa-35471	157	37	exogenous	exogenous	ADJ
cjfa-35471	157	38	function	function	NOUN
cjfa-35471	157	39	also	also	ADV
cjfa-35471	157	40	thus	thus	ADV
cjfa-35471	157	41	irrelevant	irrelevant	ADJ
cjfa-35471	157	42	in	in	ADP
cjfa-35471	157	43	decision	decision	NOUN
cjfa-35471	157	44	making	making	NOUN
cjfa-35471	157	45	.	.	PUNCT
cjfa-35471	158	1	the	the	DET
cjfa-35471	158	2	last	last	ADJ
cjfa-35471	158	3	constraint	constraint	NOUN
cjfa-35471	158	4	is	be	AUX
cjfa-35471	158	5	a	a	DET
cjfa-35471	158	6	state	state	NOUN
cjfa-35471	158	7	variable	variable	ADJ
cjfa-35471	158	8	inequality	inequality	NOUN
cjfa-35471	158	9	constraint	constraint	NOUN
cjfa-35471	158	10	which	which	PRON
cjfa-35471	158	11	has	have	AUX
cjfa-35471	158	12	been	be	AUX
cjfa-35471	158	13	studied	study	VERB
cjfa-35471	158	14	by	by	ADP
cjfa-35471	158	15	many	many	ADJ
cjfa-35471	158	16	authors	author	NOUN
cjfa-35471	158	17	including	include	VERB
cjfa-35471	158	18	bryson	bryson	PROPN
cjfa-35471	158	19	and	and	CCONJ
cjfa-35471	158	20	ho	ho	PROPN
cjfa-35471	158	21	(	(	PUNCT
cjfa-35471	158	22	1975	1975	NUM
cjfa-35471	158	23	)	)	PUNCT
cjfa-35471	158	24	,	,	PUNCT
cjfa-35471	158	25	bryson	bryson	PROPN
cjfa-35471	158	26	,	,	PUNCT
cjfa-35471	158	27	denham	denham	PROPN
cjfa-35471	158	28	and	and	CCONJ
cjfa-35471	158	29	dreyfus	dreyfus	PROPN
cjfa-35471	158	30	(	(	PUNCT
cjfa-35471	158	31	1963	1963	NUM
cjfa-35471	158	32	)	)	PUNCT
cjfa-35471	158	33	,	,	PUNCT
cjfa-35471	158	34	jacobson	jacobson	PROPN
cjfa-35471	158	35	and	and	CCONJ
cjfa-35471	158	36	lele	lele	PROPN
cjfa-35471	158	37	(	(	PUNCT
cjfa-35471	158	38	1969	1969	NUM
cjfa-35471	158	39	)	)	PUNCT
cjfa-35471	158	40	,	,	PUNCT
cjfa-35471	158	41	jacobson	jacobson	PROPN
cjfa-35471	158	42	,	,	PUNCT
cjfa-35471	158	43	lele	lele	PROPN
cjfa-35471	158	44	and	and	CCONJ
cjfa-35471	158	45	speyer	speyer	PROPN
cjfa-35471	158	46	(	(	PUNCT
cjfa-35471	158	47	1971	1971	NUM
cjfa-35471	158	48	)	)	PUNCT
cjfa-35471	158	49	,	,	PUNCT
cjfa-35471	158	50	mcintyre	mcintyre	PROPN
cjfa-35471	158	51	and	and	CCONJ
cjfa-35471	158	52	paiewonsky	paiewonsky	PROPN
cjfa-35471	158	53	(	(	PUNCT
cjfa-35471	158	54	1967	1967	NUM
cjfa-35471	158	55	)	)	PUNCT
cjfa-35471	158	56	,	,	PUNCT
cjfa-35471	158	57	and	and	CCONJ
cjfa-35471	158	58	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	158	59	(	(	PUNCT
cjfa-35471	158	60	1967	1967	NUM
cjfa-35471	158	61	)	)	PUNCT
cjfa-35471	158	62	.	.	PUNCT
cjfa-35471	159	1	taylor	taylor	PROPN
cjfa-35471	159	2	(	(	PUNCT
cjfa-35471	159	3	1972	1972	NUM
cjfa-35471	159	4	)	)	PUNCT
cjfa-35471	159	5	studied	study	VERB
cjfa-35471	159	6	the	the	DET
cjfa-35471	159	7	problem	problem	NOUN
cjfa-35471	159	8	stated	state	VERB
cjfa-35471	159	9	above	above	ADV
cjfa-35471	159	10	with	with	ADP
cjfa-35471	159	11	no	no	DET
cjfa-35471	159	12	interest	interest	NOUN
cjfa-35471	159	13	rate	rate	NOUN
cjfa-35471	159	14	consideration	consideration	NOUN
cjfa-35471	159	15	and	and	CCONJ
cjfa-35471	159	16	has	have	AUX
cjfa-35471	159	17	found	find	VERB
cjfa-35471	159	18	that	that	SCONJ
cjfa-35471	159	19	;	;	PUNCT
cjfa-35471	160	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	160	2	�	�	PROPN
cjfa-35471	160	3	�	�	PROPN
cjfa-35471	160	4	�	�	PROPN
cjfa-35471	160	5	𝑟𝑟𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟𝑟𝑟	PROPN
cjfa-35471	160	6	�	�	PROPN
cjfa-35471	160	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	160	8	�	�	PROPN
cjfa-35471	160	9	𝑟𝑟𝑟𝑟	𝑟𝑟𝑟𝑟	NOUN
cjfa-35471	160	10	𝑡	𝑡	NOUN
cjfa-35471	160	11	ℎ	ℎ	PROPN
cjfa-35471	160	12	is	be	AUX
cjfa-35471	160	13	the	the	DET
cjfa-35471	160	14	condition	condition	NOUN
cjfa-35471	160	15	which	which	PRON
cjfa-35471	160	16	has	have	VERB
cjfa-35471	160	17	to	to	PART
cjfa-35471	160	18	hold	hold	VERB
cjfa-35471	160	19	for	for	ADP
cjfa-35471	160	20	the	the	DET
cjfa-35471	160	21	firm	firm	NOUN
cjfa-35471	160	22	to	to	PART
cjfa-35471	160	23	keep	keep	VERB
cjfa-35471	160	24	i	i	PRON
cjfa-35471	160	25	(	(	PUNCT
cjfa-35471	160	26	t	t	NOUN
cjfa-35471	160	27	)	)	PUNCT
cjfa-35471	160	28	=	=	NOUN
cjfa-35471	160	29	0	0	NUM
cjfa-35471	160	30	which	which	PRON
cjfa-35471	160	31	implies	imply	VERB
cjfa-35471	160	32	that	that	SCONJ
cjfa-35471	160	33	the	the	DET
cjfa-35471	160	34	firm	firm	NOUN
cjfa-35471	160	35	will	will	AUX
cjfa-35471	160	36	produce	produce	VERB
cjfa-35471	160	37	just	just	ADV
cjfa-35471	160	38	to	to	PART
cjfa-35471	160	39	meet	meet	VERB
cjfa-35471	160	40	the	the	DET
cjfa-35471	160	41	demand	demand	NOUN
cjfa-35471	160	42	.	.	PUNCT
cjfa-35471	161	1	the	the	DET
cjfa-35471	161	2	firm	firm	NOUN
cjfa-35471	161	3	will	will	AUX
cjfa-35471	161	4	start	start	VERB
cjfa-35471	161	5	producing	produce	VERB
cjfa-35471	161	6	not	not	PART
cjfa-35471	161	7	only	only	ADV
cjfa-35471	161	8	to	to	PART
cjfa-35471	161	9	meet	meet	VERB
cjfa-35471	161	10	the	the	DET
cjfa-35471	161	11	demand	demand	NOUN
cjfa-35471	161	12	but	but	CCONJ
cjfa-35471	161	13	also	also	ADV
cjfa-35471	161	14	to	to	PART
cjfa-35471	161	15	build	build	VERB
cjfa-35471	161	16	up	up	ADP
cjfa-35471	161	17	inventories	inventory	NOUN
cjfa-35471	161	18	when	when	SCONJ
cjfa-35471	161	19	the	the	DET
cjfa-35471	161	20	change	change	NOUN
cjfa-35471	161	21	in	in	ADP
cjfa-35471	161	22	demand	demand	NOUN
cjfa-35471	161	23	is	be	AUX
cjfa-35471	161	24	such	such	ADJ
cjfa-35471	161	25	that	that	SCONJ
cjfa-35471	161	26	the	the	DET
cjfa-35471	161	27	above	above	ADJ
cjfa-35471	161	28	inequality	inequality	NOUN
cjfa-35471	161	29	will	will	AUX
cjfa-35471	161	30	be	be	AUX
cjfa-35471	161	31	violated	violate	VERB
cjfa-35471	161	32	.	.	PUNCT
cjfa-35471	162	1	in	in	ADP
cjfa-35471	162	2	this	this	DET
cjfa-35471	162	3	paper	paper	NOUN
cjfa-35471	162	4	,	,	PUNCT
cjfa-35471	162	5	we	we	PRON
cjfa-35471	162	6	will	will	AUX
cjfa-35471	162	7	study	study	VERB
cjfa-35471	162	8	the	the	DET
cjfa-35471	162	9	same	same	ADJ
cjfa-35471	162	10	problem	problem	NOUN
cjfa-35471	162	11	introducing	introduce	VERB
cjfa-35471	162	12	present	present	ADJ
cjfa-35471	162	13	value	value	NOUN
cjfa-35471	162	14	factor	factor	NOUN
cjfa-35471	162	15	and	and	CCONJ
cjfa-35471	162	16	fluctuating	fluctuating	NOUN
cjfa-35471	162	17	time	time	NOUN
cjfa-35471	162	18	dependent	dependent	ADJ
cjfa-35471	162	19	demand	demand	NOUN
cjfa-35471	162	20	function	function	NOUN
cjfa-35471	162	21	.	.	PUNCT
cjfa-35471	163	1	then	then	ADV
cjfa-35471	163	2	,	,	PUNCT
cjfa-35471	163	3	the	the	DET
cjfa-35471	163	4	problem	problem	NOUN
cjfa-35471	163	5	becomes	become	VERB
cjfa-35471	163	6	:	:	PUNCT
cjfa-35471	163	7	(	(	PUNCT
cjfa-35471	163	8	)	)	PUNCT
cjfa-35471	163	9	0	0	PUNCT
cjfa-35471	164	1	[	[	PUNCT
cjfa-35471	164	2	(	(	PUNCT
cjfa-35471	164	3	(	(	PUNCT
cjfa-35471	164	4	)	)	PUNCT
cjfa-35471	164	5	(	(	PUNCT
cjfa-35471	164	6	)	)	PUNCT
cjfa-35471	164	7	]	]	PUNCT
cjfa-35471	164	8	t	t	X
cjfa-35471	164	9	i	i	PRON
cjfa-35471	164	10	tmin	tmin	VERB
cjfa-35471	164	11	e	e	PROPN
cjfa-35471	164	12	c	c	NOUN
cjfa-35471	164	13	u	u	X
cjfa-35471	165	1	t	t	X
cjfa-35471	165	2	hi	hi	INTJ
cjfa-35471	165	3	t	t	PROPN
cjfa-35471	165	4	dt	dt	X
cjfa-35471	165	5			NOUN
cjfa-35471	165	6	subject	subject	ADJ
cjfa-35471	165	7	to	to	ADP
cjfa-35471	165	8	the	the	DET
cjfa-35471	165	9	constraints	constraint	NOUN
cjfa-35471	165	10	:	:	PUNCT
cjfa-35471	165	11	subject	subject	ADJ
cjfa-35471	165	12	to	to	ADP
cjfa-35471	165	13	the	the	DET
cjfa-35471	165	14	constraints	constraint	NOUN
cjfa-35471	165	15	:	:	PUNCT
cjfa-35471	165	16	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	165	17	�	�	PROPN
cjfa-35471	165	18	=	=	PUNCT
cjfa-35471	165	19	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	165	20	)	)	PUNCT
cjfa-35471	165	21	−	−	PROPN
cjfa-35471	165	22	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	165	23	)	)	PUNCT
cjfa-35471	165	24	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	165	25	)	)	PUNCT
cjfa-35471	165	26	=	=	SYM
cjfa-35471	165	27	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	165	28	�	�	PROPN
cjfa-35471	165	29	a	a	DET
cjfa-35471	165	30	given	give	VERB
cjfa-35471	165	31	number	number	NOUN
cjfa-35471	165	32	.	.	PUNCT
cjfa-35471	166	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	166	2	)	)	PUNCT
cjfa-35471	167	1	𝑢	𝑢	PROPN
cjfa-35471	167	2	0	0	NUM
cjfa-35471	167	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	167	4	)	)	PUNCT
cjfa-35471	167	5	𝑢	𝑢	ADP
cjfa-35471	167	6	0	0	NUM
cjfa-35471	167	7	with	with	ADP
cjfa-35471	167	8	the	the	DET
cjfa-35471	167	9	assumptions	assumption	NOUN
cjfa-35471	167	10	that	that	SCONJ
cjfa-35471	167	11	the	the	DET
cjfa-35471	167	12	demand	demand	NOUN
cjfa-35471	167	13	(	(	PUNCT
cjfa-35471	167	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	167	15	(	(	PUNCT
cjfa-35471	167	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	167	17	)	)	PUNCT
cjfa-35471	167	18	)	)	PUNCT
cjfa-35471	167	19	is	be	AUX
cjfa-35471	167	20	a	a	DET
cjfa-35471	167	21	simple	simple	ADJ
cjfa-35471	167	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	167	23	function	function	NOUN
cjfa-35471	167	24	and	and	CCONJ
cjfa-35471	167	25	the	the	DET
cjfa-35471	167	26	interest	interest	NOUN
cjfa-35471	167	27	rate	rate	NOUN
cjfa-35471	167	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	167	29	)	)	PUNCT
cjfa-35471	167	30	is	be	AUX
cjfa-35471	167	31	time	time	NOUN
cjfa-35471	167	32	dependent	dependent	ADJ
cjfa-35471	167	33	,	,	PUNCT
cjfa-35471	167	34	i.e.	i.e.	X
cjfa-35471	167	35	:	:	PUNCT
cjfa-35471	167	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	167	37	)	)	PUNCT
cjfa-35471	168	1	=	=	SYM
cjfa-35471	168	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	168	3	𝐴	𝐴	PROPN
cjfa-35471	168	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	168	5	)	)	PUNCT
cjfa-35471	168	6	with	with	ADP
cjfa-35471	168	7	no	no	DET
cjfa-35471	168	8	growth	growth	NOUN
cjfa-35471	168	9	,	,	PUNCT
cjfa-35471	168	10	and	and	CCONJ
cjfa-35471	168	11	,	,	PUNCT
cjfa-35471	168	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	168	13	)	)	PUNCT
cjfa-35471	168	14	=	=	SYM
cjfa-35471	168	15	�	�	PROPN
cjfa-35471	168	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	168	17	�	�	PROPN
cjfa-35471	168	18	�	�	PROPN
cjfa-35471	168	19	implying	imply	VERB
cjfa-35471	168	20	that	that	SCONJ
cjfa-35471	168	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	168	22	)	)	PUNCT
cjfa-35471	169	1	=	=	VERB
cjfa-35471	169	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	169	3	if	if	SCONJ
cjfa-35471	169	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	169	5	is	be	AUX
cjfa-35471	169	6	constant	constant	ADJ
cjfa-35471	169	7	.	.	PUNCT
cjfa-35471	170	1	notice	notice	NOUN
cjfa-35471	170	2	also	also	ADV
cjfa-35471	170	3	that	that	SCONJ
cjfa-35471	170	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	170	5	�	�	X
cjfa-35471	170	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	170	7	)	)	PUNCT
cjfa-35471	170	8	=	=	SYM
cjfa-35471	170	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	170	10	)	)	PUNCT
cjfa-35471	170	11	where	where	SCONJ
cjfa-35471	170	12	f	f	PROPN
cjfa-35471	170	13	(	(	PUNCT
cjfa-35471	170	14	t	t	PROPN
cjfa-35471	170	15	)	)	PUNCT
cjfa-35471	170	16	denotes	denote	NOUN
cjfa-35471	170	17	time	time	VERB
cjfa-35471	170	18	dependent	dependent	ADJ
cjfa-35471	170	19	interest	interest	NOUN
cjfa-35471	170	20	rate	rate	NOUN
cjfa-35471	170	21	.	.	PUNCT
cjfa-35471	171	1	for	for	ADP
cjfa-35471	171	2	ease	ease	NOUN
cjfa-35471	171	3	of	of	ADP
cjfa-35471	171	4	analysis	analysis	NOUN
cjfa-35471	171	5	we	we	PRON
cjfa-35471	171	6	will	will	AUX
cjfa-35471	171	7	assume	assume	VERB
cjfa-35471	171	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	171	9	)	)	PUNCT
cjfa-35471	171	10	to	to	PART
cjfa-35471	171	11	be	be	AUX
cjfa-35471	171	12	constant	constant	ADJ
cjfa-35471	171	13	.	.	PUNCT
cjfa-35471	172	1	the	the	DET
cjfa-35471	172	2	letter	letter	NOUN
cjfa-35471	172	3	k	k	PROPN
cjfa-35471	172	4	denotes	denote	VERB
cjfa-35471	172	5	the	the	DET
cjfa-35471	172	6	periodicity	periodicity	NOUN
cjfa-35471	172	7	of	of	ADP
cjfa-35471	172	8	the	the	DET
cjfa-35471	172	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	172	10	demand	demand	NOUN
cjfa-35471	172	11	function	function	NOUN
cjfa-35471	172	12	over	over	ADP
cjfa-35471	172	13	the	the	DET
cjfa-35471	172	14	planning	planning	NOUN
cjfa-35471	172	15	period	period	NOUN
cjfa-35471	172	16	.	.	PUNCT
cjfa-35471	173	1	the	the	DET
cjfa-35471	173	2	only	only	ADJ
cjfa-35471	173	3	reason	reason	NOUN
cjfa-35471	173	4	for	for	ADP
cjfa-35471	173	5	the	the	DET
cjfa-35471	173	6	use	use	NOUN
cjfa-35471	173	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	173	8	demand	demand	NOUN
cjfa-35471	173	9	curve	curve	NOUN
cjfa-35471	173	10	is	be	AUX
cjfa-35471	173	11	that	that	SCONJ
cjfa-35471	173	12	it	it	PRON
cjfa-35471	173	13	represents	represent	VERB
cjfa-35471	173	14	cyclicality	cyclicality	NOUN
cjfa-35471	173	15	(	(	PUNCT
cjfa-35471	173	16	a	a	DET
cjfa-35471	173	17	measure	measure	NOUN
cjfa-35471	173	18	of	of	ADP
cjfa-35471	173	19	risk	risk	NOUN
cjfa-35471	173	20	)	)	PUNCT
cjfa-35471	173	21	and	and	CCONJ
cjfa-35471	173	22	that	that	SCONJ
cjfa-35471	173	23	it	it	PRON
cjfa-35471	173	24	is	be	AUX
cjfa-35471	173	25	easier	easy	ADJ
cjfa-35471	173	26	to	to	PART
cjfa-35471	173	27	work	work	VERB
cjfa-35471	173	28	with	with	ADP
cjfa-35471	173	29	it	it	PRON
cjfa-35471	173	30	.	.	PUNCT
cjfa-35471	174	1	the	the	DET
cjfa-35471	174	2	appropriate	appropriate	ADJ
cjfa-35471	174	3	lagrangian	lagrangian	NOUN
cjfa-35471	174	4	for	for	ADP
cjfa-35471	174	5	this	this	DET
cjfa-35471	174	6	problem	problem	NOUN
cjfa-35471	174	7	is	be	AUX
cjfa-35471	174	8	:	:	PUNCT
cjfa-35471	174	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	174	10	=	=	SYM
cjfa-35471	174	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	174	12	�	�	PROPN
cjfa-35471	174	13	�	�	PROPN
cjfa-35471	174	14	(	(	PUNCT
cjfa-35471	174	15	�	�	PROPN
cjfa-35471	174	16	)	)	PUNCT
cjfa-35471	174	17	�	�	PROPN
cjfa-35471	174	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	174	19	�	�	PROPN
cjfa-35471	174	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	174	21	)	)	PUNCT
cjfa-35471	174	22	�	�	PROPN
cjfa-35471	174	23	𝐴	𝐴	PROPN
cjfa-35471	174	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	174	25	)	)	PUNCT
cjfa-35471	174	26	�	�	PROPN
cjfa-35471	174	27	𝐴	𝐴	PROPN
cjfa-35471	174	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	174	29	�	�	PROPN
cjfa-35471	174	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	174	31	)	)	PUNCT
cjfa-35471	174	32	−	−	PROPN
cjfa-35471	174	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	174	34	)	)	PUNCT
cjfa-35471	174	35	�	�	PROPN
cjfa-35471	174	36	𝐴	𝐴	PROPN
cjfa-35471	174	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	174	38	�	�	PROPN
cjfa-35471	174	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	174	40	)	)	PUNCT
cjfa-35471	174	41	−	−	PROPN
cjfa-35471	174	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	174	43	)	)	PUNCT
cjfa-35471	174	44	�	�	PROPN
cjfa-35471	174	45	then	then	ADV
cjfa-35471	174	46	the	the	DET
cjfa-35471	174	47	necessary	necessary	ADJ
cjfa-35471	174	48	conditions	condition	NOUN
cjfa-35471	174	49	are	be	AUX
cjfa-35471	174	50	:	:	PUNCT
cjfa-35471	174	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	174	52	�	�	PROPN
cjfa-35471	174	53	�	�	PROPN
cjfa-35471	174	54	(	(	PUNCT
cjfa-35471	174	55	�	�	NOUN
cjfa-35471	174	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	174	57	�	�	PROPN
cjfa-35471	174	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	174	59	)	)	PUNCT
cjfa-35471	174	60	𝐴	𝐴	PROPN
cjfa-35471	174	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	174	62	)	)	PUNCT
cjfa-35471	174	63	−	−	PROPN
cjfa-35471	174	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	174	65	)	)	PUNCT
cjfa-35471	175	1	=	=	SYM
cjfa-35471	175	2	0	0	PUNCT
cjfa-35471	175	3	(	(	PUNCT
cjfa-35471	175	4	1	1	NUM
cjfa-35471	175	5	)	)	PUNCT
cjfa-35471	175	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	175	7	�	�	PROPN
cjfa-35471	175	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	175	9	)	)	PUNCT
cjfa-35471	175	10	=	=	SYM
cjfa-35471	175	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	175	12	�	�	PROPN
cjfa-35471	175	13	�	�	PROPN
cjfa-35471	175	14	(	(	PUNCT
cjfa-35471	175	15	�	�	PROPN
cjfa-35471	175	16	)ℎ	)ℎ	PROPN
cjfa-35471	175	17	(	(	PUNCT
cjfa-35471	175	18	2	2	X
cjfa-35471	175	19	)	)	PUNCT
cjfa-35471	175	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	175	21	�	�	PROPN
cjfa-35471	175	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	175	23	)	)	PUNCT
cjfa-35471	175	24	=	=	SYM
cjfa-35471	175	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	175	26	)	)	PUNCT
cjfa-35471	175	27	−	−	PROPN
cjfa-35471	175	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	175	29	)	)	PUNCT
cjfa-35471	175	30	(	(	PUNCT
cjfa-35471	175	31	3	3	X
cjfa-35471	175	32	)	)	PUNCT
cjfa-35471	175	33	necessary	necessary	ADJ
cjfa-35471	175	34	conditions	condition	NOUN
cjfa-35471	175	35	are	be	AUX
cjfa-35471	175	36	also	also	ADV
cjfa-35471	175	37	sufficient	sufficient	ADJ
cjfa-35471	175	38	since	since	SCONJ
cjfa-35471	175	39	the	the	DET
cjfa-35471	175	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	175	41	is	be	AUX
cjfa-35471	175	42	convex	convex	ADJ
cjfa-35471	175	43	in	in	ADP
cjfa-35471	175	44	both	both	CCONJ
cjfa-35471	175	45	the	the	DET
cjfa-35471	175	46	control	control	NOUN
cjfa-35471	175	47	(	(	PUNCT
cjfa-35471	175	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	175	49	)	)	PUNCT
cjfa-35471	175	50	and	and	CCONJ
cjfa-35471	175	51	state	state	NOUN
cjfa-35471	175	52	(	(	PUNCT
cjfa-35471	175	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	175	54	)	)	PUNCT
cjfa-35471	175	55	variables	variable	NOUN
cjfa-35471	175	56	.	.	PUNCT
cjfa-35471	176	1	the	the	DET
cjfa-35471	176	2	planning	planning	NOUN
cjfa-35471	176	3	horizon	horizon	NOUN
cjfa-35471	176	4	(	(	PUNCT
cjfa-35471	176	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	176	6	)	)	PUNCT
cjfa-35471	176	7	will	will	AUX
cjfa-35471	176	8	be	be	AUX
cjfa-35471	176	9	assumed	assume	VERB
cjfa-35471	176	10	one	one	NUM
cjfa-35471	176	11	.	.	PUNCT
cjfa-35471	177	1	on	on	ADP
cjfa-35471	177	2	a	a	DET
cjfa-35471	177	3	constraint	constraint	NOUN
cjfa-35471	177	4	arc	arc	NOUN
cjfa-35471	177	5	on	on	ADP
cjfa-35471	177	6	which	which	PRON
cjfa-35471	177	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	177	8	)	)	PUNCT
cjfa-35471	177	9	=	=	SYM
cjfa-35471	177	10	0	0	NUM
cjfa-35471	177	11	for	for	ADP
cjfa-35471	177	12	a	a	DET
cjfa-35471	177	13	certain	certain	ADJ
cjfa-35471	177	14	period	period	NOUN
cjfa-35471	177	15	in	in	ADP
cjfa-35471	177	16	[	[	X
cjfa-35471	177	17	0	0	NUM
cjfa-35471	177	18	,	,	PUNCT
cjfa-35471	177	19	1	1	NUM
cjfa-35471	177	20	]	]	PUNCT
cjfa-35471	177	21	i.e.	i.e.	X
cjfa-35471	177	22	0	0	X
cjfa-35471	177	23	<	<	X
cjfa-35471	177	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	177	25	�	�	PROPN
cjfa-35471	177	26	≤	≤	X
cjfa-35471	177	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	177	28	≤	≤	PROPN
cjfa-35471	177	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	177	30	�	�	PROPN
cjfa-35471	177	31	<	<	X
cjfa-35471	177	32	1	1	NUM
cjfa-35471	177	33	we	we	PRON
cjfa-35471	177	34	have	have	VERB
cjfa-35471	177	35	;	;	PUNCT
cjfa-35471	177	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	177	37	�	�	PROPN
cjfa-35471	177	38	=	=	SYM
cjfa-35471	177	39	0	0	NUM
cjfa-35471	177	40	=	=	SYM
cjfa-35471	177	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	177	42	)	)	PUNCT
cjfa-35471	178	1	−	−	PROPN
cjfa-35471	178	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	178	3	)	)	PUNCT
cjfa-35471	178	4	implying	imply	VERB
cjfa-35471	178	5	that	that	SCONJ
cjfa-35471	178	6	over	over	ADP
cjfa-35471	178	7	this	this	DET
cjfa-35471	178	8	period	period	NOUN
cjfa-35471	178	9	a	a	DET
cjfa-35471	178	10	firm	firm	NOUN
cjfa-35471	178	11	will	will	AUX
cjfa-35471	178	12	produce	produce	VERB
cjfa-35471	178	13	just	just	ADV
cjfa-35471	178	14	enough	enough	ADJ
cjfa-35471	178	15	to	to	PART
cjfa-35471	178	16	meet	meet	VERB
cjfa-35471	178	17	the	the	DET
cjfa-35471	178	18	demand	demand	NOUN
cjfa-35471	178	19	,	,	PUNCT
cjfa-35471	178	20	which	which	PRON
cjfa-35471	178	21	is	be	AUX
cjfa-35471	178	22	assumed	assume	VERB
cjfa-35471	178	23	to	to	PART
cjfa-35471	178	24	be	be	AUX
cjfa-35471	178	25	nonzero	nonzero	NOUN
cjfa-35471	178	26	during	during	ADP
cjfa-35471	178	27	the	the	DET
cjfa-35471	178	28	planning	planning	NOUN
cjfa-35471	178	29	horizon	horizon	NOUN
cjfa-35471	178	30	.	.	PUNCT
cjfa-35471	179	1	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	179	2	�	�	PROPN
cjfa-35471	179	3	=	=	SYM
cjfa-35471	179	4	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	179	5	)	)	PUNCT
cjfa-35471	179	6	−	−	PROPN
cjfa-35471	179	7	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	179	8	)	)	PUNCT
cjfa-35471	179	9	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	179	10	)	)	PUNCT
cjfa-35471	179	11	=	=	SYM
cjfa-35471	179	12	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	179	13	�	�	PROPN
cjfa-35471	179	14	a	a	DET
cjfa-35471	179	15	given	give	VERB
cjfa-35471	179	16	number	number	NOUN
cjfa-35471	179	17	.	.	PUNCT
cjfa-35471	180	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	180	2	)	)	PUNCT
cjfa-35471	181	1	𝑢	𝑢	PROPN
cjfa-35471	181	2	0	0	NUM
cjfa-35471	181	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	181	4	)	)	PUNCT
cjfa-35471	181	5	𝑢	𝑢	ADP
cjfa-35471	181	6	0	0	NUM
cjfa-35471	181	7	with	with	ADP
cjfa-35471	181	8	the	the	DET
cjfa-35471	181	9	assumptions	assumption	NOUN
cjfa-35471	181	10	that	that	SCONJ
cjfa-35471	181	11	the	the	DET
cjfa-35471	181	12	demand	demand	NOUN
cjfa-35471	181	13	(	(	PUNCT
cjfa-35471	181	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	181	15	(	(	PUNCT
cjfa-35471	181	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	181	17	)	)	PUNCT
cjfa-35471	181	18	)	)	PUNCT
cjfa-35471	181	19	is	be	AUX
cjfa-35471	181	20	a	a	DET
cjfa-35471	181	21	simple	simple	ADJ
cjfa-35471	181	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	181	23	function	function	NOUN
cjfa-35471	181	24	and	and	CCONJ
cjfa-35471	181	25	the	the	DET
cjfa-35471	181	26	interest	interest	NOUN
cjfa-35471	181	27	rate	rate	NOUN
cjfa-35471	181	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	181	29	)	)	PUNCT
cjfa-35471	181	30	is	be	AUX
cjfa-35471	181	31	time	time	NOUN
cjfa-35471	181	32	dependent	dependent	ADJ
cjfa-35471	181	33	,	,	PUNCT
cjfa-35471	181	34	i.e.	i.e.	X
cjfa-35471	181	35	:	:	PUNCT
cjfa-35471	181	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	181	37	)	)	PUNCT
cjfa-35471	182	1	=	=	SYM
cjfa-35471	182	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	182	3	𝐴	𝐴	PROPN
cjfa-35471	182	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	182	5	)	)	PUNCT
cjfa-35471	182	6	with	with	ADP
cjfa-35471	182	7	no	no	DET
cjfa-35471	182	8	growth	growth	NOUN
cjfa-35471	182	9	,	,	PUNCT
cjfa-35471	182	10	and	and	CCONJ
cjfa-35471	182	11	,	,	PUNCT
cjfa-35471	182	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	182	13	)	)	PUNCT
cjfa-35471	182	14	=	=	SYM
cjfa-35471	182	15	�	�	PROPN
cjfa-35471	182	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	182	17	�	�	PROPN
cjfa-35471	182	18	�	�	PROPN
cjfa-35471	182	19	implying	imply	VERB
cjfa-35471	182	20	that	that	SCONJ
cjfa-35471	182	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	182	22	)	)	PUNCT
cjfa-35471	183	1	=	=	VERB
cjfa-35471	183	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	183	3	if	if	SCONJ
cjfa-35471	183	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	183	5	is	be	AUX
cjfa-35471	183	6	constant	constant	ADJ
cjfa-35471	183	7	.	.	PUNCT
cjfa-35471	184	1	notice	notice	NOUN
cjfa-35471	184	2	also	also	ADV
cjfa-35471	184	3	that	that	SCONJ
cjfa-35471	184	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	184	5	�	�	X
cjfa-35471	184	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	184	7	)	)	PUNCT
cjfa-35471	184	8	=	=	SYM
cjfa-35471	184	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	184	10	)	)	PUNCT
cjfa-35471	184	11	where	where	SCONJ
cjfa-35471	184	12	f	f	PROPN
cjfa-35471	184	13	(	(	PUNCT
cjfa-35471	184	14	t	t	PROPN
cjfa-35471	184	15	)	)	PUNCT
cjfa-35471	184	16	denotes	denote	NOUN
cjfa-35471	184	17	time	time	VERB
cjfa-35471	184	18	dependent	dependent	ADJ
cjfa-35471	184	19	interest	interest	NOUN
cjfa-35471	184	20	rate	rate	NOUN
cjfa-35471	184	21	.	.	PUNCT
cjfa-35471	185	1	for	for	ADP
cjfa-35471	185	2	ease	ease	NOUN
cjfa-35471	185	3	of	of	ADP
cjfa-35471	185	4	analysis	analysis	NOUN
cjfa-35471	185	5	we	we	PRON
cjfa-35471	185	6	will	will	AUX
cjfa-35471	185	7	assume	assume	VERB
cjfa-35471	185	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	185	9	)	)	PUNCT
cjfa-35471	185	10	to	to	PART
cjfa-35471	185	11	be	be	AUX
cjfa-35471	185	12	constant	constant	ADJ
cjfa-35471	185	13	.	.	PUNCT
cjfa-35471	186	1	the	the	DET
cjfa-35471	186	2	letter	letter	NOUN
cjfa-35471	186	3	k	k	PROPN
cjfa-35471	186	4	denotes	denote	VERB
cjfa-35471	186	5	the	the	DET
cjfa-35471	186	6	periodicity	periodicity	NOUN
cjfa-35471	186	7	of	of	ADP
cjfa-35471	186	8	the	the	DET
cjfa-35471	186	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	186	10	demand	demand	NOUN
cjfa-35471	186	11	function	function	NOUN
cjfa-35471	186	12	over	over	ADP
cjfa-35471	186	13	the	the	DET
cjfa-35471	186	14	planning	planning	NOUN
cjfa-35471	186	15	period	period	NOUN
cjfa-35471	186	16	.	.	PUNCT
cjfa-35471	187	1	the	the	DET
cjfa-35471	187	2	only	only	ADJ
cjfa-35471	187	3	reason	reason	NOUN
cjfa-35471	187	4	for	for	ADP
cjfa-35471	187	5	the	the	DET
cjfa-35471	187	6	use	use	NOUN
cjfa-35471	187	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	187	8	demand	demand	NOUN
cjfa-35471	187	9	curve	curve	NOUN
cjfa-35471	187	10	is	be	AUX
cjfa-35471	187	11	that	that	SCONJ
cjfa-35471	187	12	it	it	PRON
cjfa-35471	187	13	represents	represent	VERB
cjfa-35471	187	14	cyclicality	cyclicality	NOUN
cjfa-35471	187	15	(	(	PUNCT
cjfa-35471	187	16	a	a	DET
cjfa-35471	187	17	measure	measure	NOUN
cjfa-35471	187	18	of	of	ADP
cjfa-35471	187	19	risk	risk	NOUN
cjfa-35471	187	20	)	)	PUNCT
cjfa-35471	187	21	and	and	CCONJ
cjfa-35471	187	22	that	that	SCONJ
cjfa-35471	187	23	it	it	PRON
cjfa-35471	187	24	is	be	AUX
cjfa-35471	187	25	easier	easy	ADJ
cjfa-35471	187	26	to	to	PART
cjfa-35471	187	27	work	work	VERB
cjfa-35471	187	28	with	with	ADP
cjfa-35471	187	29	it	it	PRON
cjfa-35471	187	30	.	.	PUNCT
cjfa-35471	188	1	the	the	DET
cjfa-35471	188	2	appropriate	appropriate	ADJ
cjfa-35471	188	3	lagrangian	lagrangian	NOUN
cjfa-35471	188	4	for	for	ADP
cjfa-35471	188	5	this	this	DET
cjfa-35471	188	6	problem	problem	NOUN
cjfa-35471	188	7	is	be	AUX
cjfa-35471	188	8	:	:	PUNCT
cjfa-35471	188	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	188	10	=	=	SYM
cjfa-35471	188	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	188	12	�	�	PROPN
cjfa-35471	188	13	�	�	PROPN
cjfa-35471	188	14	(	(	PUNCT
cjfa-35471	188	15	�	�	PROPN
cjfa-35471	188	16	)	)	PUNCT
cjfa-35471	188	17	�	�	PROPN
cjfa-35471	188	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	188	19	�	�	PROPN
cjfa-35471	188	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	188	21	)	)	PUNCT
cjfa-35471	188	22	�	�	PROPN
cjfa-35471	188	23	𝐴	𝐴	PROPN
cjfa-35471	188	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	188	25	)	)	PUNCT
cjfa-35471	188	26	�	�	PROPN
cjfa-35471	188	27	𝐴	𝐴	PROPN
cjfa-35471	188	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	188	29	�	�	PROPN
cjfa-35471	188	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	188	31	)	)	PUNCT
cjfa-35471	188	32	−	−	PROPN
cjfa-35471	188	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	188	34	)	)	PUNCT
cjfa-35471	188	35	�	�	PROPN
cjfa-35471	188	36	𝐴	𝐴	PROPN
cjfa-35471	188	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	188	38	�	�	PROPN
cjfa-35471	188	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	188	40	)	)	PUNCT
cjfa-35471	188	41	−	−	PROPN
cjfa-35471	188	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	188	43	)	)	PUNCT
cjfa-35471	188	44	�	�	PROPN
cjfa-35471	188	45	then	then	ADV
cjfa-35471	188	46	the	the	DET
cjfa-35471	188	47	necessary	necessary	ADJ
cjfa-35471	188	48	conditions	condition	NOUN
cjfa-35471	188	49	are	be	AUX
cjfa-35471	188	50	:	:	PUNCT
cjfa-35471	188	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	188	52	�	�	PROPN
cjfa-35471	188	53	�	�	PROPN
cjfa-35471	188	54	(	(	PUNCT
cjfa-35471	188	55	�	�	NOUN
cjfa-35471	188	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	188	57	�	�	PROPN
cjfa-35471	188	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	188	59	)	)	PUNCT
cjfa-35471	188	60	𝐴	𝐴	PROPN
cjfa-35471	188	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	188	62	)	)	PUNCT
cjfa-35471	188	63	−	−	PROPN
cjfa-35471	188	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	188	65	)	)	PUNCT
cjfa-35471	189	1	=	=	SYM
cjfa-35471	189	2	0	0	PUNCT
cjfa-35471	189	3	(	(	PUNCT
cjfa-35471	189	4	1	1	NUM
cjfa-35471	189	5	)	)	PUNCT
cjfa-35471	189	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	189	7	�	�	PROPN
cjfa-35471	189	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	189	9	)	)	PUNCT
cjfa-35471	189	10	=	=	SYM
cjfa-35471	189	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	189	12	�	�	PROPN
cjfa-35471	189	13	�	�	PROPN
cjfa-35471	189	14	(	(	PUNCT
cjfa-35471	189	15	�	�	PROPN
cjfa-35471	189	16	)ℎ	)ℎ	PROPN
cjfa-35471	189	17	(	(	PUNCT
cjfa-35471	189	18	2	2	X
cjfa-35471	189	19	)	)	PUNCT
cjfa-35471	189	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	189	21	�	�	PROPN
cjfa-35471	189	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	189	23	)	)	PUNCT
cjfa-35471	189	24	=	=	SYM
cjfa-35471	189	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	189	26	)	)	PUNCT
cjfa-35471	189	27	−	−	PROPN
cjfa-35471	189	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	189	29	)	)	PUNCT
cjfa-35471	189	30	(	(	PUNCT
cjfa-35471	189	31	3	3	X
cjfa-35471	189	32	)	)	PUNCT
cjfa-35471	189	33	necessary	necessary	ADJ
cjfa-35471	189	34	conditions	condition	NOUN
cjfa-35471	189	35	are	be	AUX
cjfa-35471	189	36	also	also	ADV
cjfa-35471	189	37	sufficient	sufficient	ADJ
cjfa-35471	189	38	since	since	SCONJ
cjfa-35471	189	39	the	the	DET
cjfa-35471	189	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	189	41	is	be	AUX
cjfa-35471	189	42	convex	convex	ADJ
cjfa-35471	189	43	in	in	ADP
cjfa-35471	189	44	both	both	CCONJ
cjfa-35471	189	45	the	the	DET
cjfa-35471	189	46	control	control	NOUN
cjfa-35471	189	47	(	(	PUNCT
cjfa-35471	189	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	189	49	)	)	PUNCT
cjfa-35471	189	50	and	and	CCONJ
cjfa-35471	189	51	state	state	NOUN
cjfa-35471	189	52	(	(	PUNCT
cjfa-35471	189	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	189	54	)	)	PUNCT
cjfa-35471	189	55	variables	variable	NOUN
cjfa-35471	189	56	.	.	PUNCT
cjfa-35471	190	1	the	the	DET
cjfa-35471	190	2	planning	planning	NOUN
cjfa-35471	190	3	horizon	horizon	NOUN
cjfa-35471	190	4	(	(	PUNCT
cjfa-35471	190	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	190	6	)	)	PUNCT
cjfa-35471	190	7	will	will	AUX
cjfa-35471	190	8	be	be	AUX
cjfa-35471	190	9	assumed	assume	VERB
cjfa-35471	190	10	one	one	NUM
cjfa-35471	190	11	.	.	PUNCT
cjfa-35471	191	1	on	on	ADP
cjfa-35471	191	2	a	a	DET
cjfa-35471	191	3	constraint	constraint	NOUN
cjfa-35471	191	4	arc	arc	NOUN
cjfa-35471	191	5	on	on	ADP
cjfa-35471	191	6	which	which	PRON
cjfa-35471	191	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	191	8	)	)	PUNCT
cjfa-35471	191	9	=	=	SYM
cjfa-35471	191	10	0	0	NUM
cjfa-35471	191	11	for	for	ADP
cjfa-35471	191	12	a	a	DET
cjfa-35471	191	13	certain	certain	ADJ
cjfa-35471	191	14	period	period	NOUN
cjfa-35471	191	15	in	in	ADP
cjfa-35471	191	16	[	[	X
cjfa-35471	191	17	0	0	NUM
cjfa-35471	191	18	,	,	PUNCT
cjfa-35471	191	19	1	1	NUM
cjfa-35471	191	20	]	]	PUNCT
cjfa-35471	191	21	i.e.	i.e.	X
cjfa-35471	191	22	0	0	X
cjfa-35471	191	23	<	<	X
cjfa-35471	191	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	191	25	�	�	PROPN
cjfa-35471	191	26	≤	≤	X
cjfa-35471	191	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	191	28	≤	≤	PROPN
cjfa-35471	191	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	191	30	�	�	PROPN
cjfa-35471	191	31	<	<	X
cjfa-35471	191	32	1	1	NUM
cjfa-35471	191	33	we	we	PRON
cjfa-35471	191	34	have	have	VERB
cjfa-35471	191	35	;	;	PUNCT
cjfa-35471	191	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	191	37	�	�	PROPN
cjfa-35471	191	38	=	=	SYM
cjfa-35471	191	39	0	0	NUM
cjfa-35471	191	40	=	=	SYM
cjfa-35471	191	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	191	42	)	)	PUNCT
cjfa-35471	192	1	−	−	PROPN
cjfa-35471	192	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	192	3	)	)	PUNCT
cjfa-35471	192	4	implying	imply	VERB
cjfa-35471	192	5	that	that	SCONJ
cjfa-35471	192	6	over	over	ADP
cjfa-35471	192	7	this	this	DET
cjfa-35471	192	8	period	period	NOUN
cjfa-35471	192	9	a	a	DET
cjfa-35471	192	10	firm	firm	NOUN
cjfa-35471	192	11	will	will	AUX
cjfa-35471	192	12	produce	produce	VERB
cjfa-35471	192	13	just	just	ADV
cjfa-35471	192	14	enough	enough	ADJ
cjfa-35471	192	15	to	to	PART
cjfa-35471	192	16	meet	meet	VERB
cjfa-35471	192	17	the	the	DET
cjfa-35471	192	18	demand	demand	NOUN
cjfa-35471	192	19	,	,	PUNCT
cjfa-35471	192	20	which	which	PRON
cjfa-35471	192	21	is	be	AUX
cjfa-35471	192	22	assumed	assume	VERB
cjfa-35471	192	23	to	to	PART
cjfa-35471	192	24	be	be	AUX
cjfa-35471	192	25	nonzero	nonzero	NOUN
cjfa-35471	192	26	during	during	ADP
cjfa-35471	192	27	the	the	DET
cjfa-35471	192	28	planning	planning	NOUN
cjfa-35471	192	29	horizon	horizon	NOUN
cjfa-35471	192	30	.	.	PUNCT
cjfa-35471	193	1	a	a	DET
cjfa-35471	193	2	given	give	VERB
cjfa-35471	193	3	number	number	NOUN
cjfa-35471	193	4	.	.	PUNCT
cjfa-35471	194	1	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	194	2	�	�	PROPN
cjfa-35471	194	3	=	=	SYM
cjfa-35471	194	4	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	194	5	)	)	PUNCT
cjfa-35471	194	6	−	−	PROPN
cjfa-35471	194	7	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	194	8	)	)	PUNCT
cjfa-35471	194	9	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	194	10	)	)	PUNCT
cjfa-35471	194	11	=	=	SYM
cjfa-35471	194	12	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	194	13	�	�	PROPN
cjfa-35471	194	14	a	a	DET
cjfa-35471	194	15	given	give	VERB
cjfa-35471	194	16	number	number	NOUN
cjfa-35471	194	17	.	.	PUNCT
cjfa-35471	195	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	195	2	)	)	PUNCT
cjfa-35471	196	1	𝑢	𝑢	PROPN
cjfa-35471	196	2	0	0	NUM
cjfa-35471	196	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	196	4	)	)	PUNCT
cjfa-35471	196	5	𝑢	𝑢	ADP
cjfa-35471	196	6	0	0	NUM
cjfa-35471	196	7	with	with	ADP
cjfa-35471	196	8	the	the	DET
cjfa-35471	196	9	assumptions	assumption	NOUN
cjfa-35471	196	10	that	that	SCONJ
cjfa-35471	196	11	the	the	DET
cjfa-35471	196	12	demand	demand	NOUN
cjfa-35471	196	13	(	(	PUNCT
cjfa-35471	196	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	196	15	(	(	PUNCT
cjfa-35471	196	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	196	17	)	)	PUNCT
cjfa-35471	196	18	)	)	PUNCT
cjfa-35471	196	19	is	be	AUX
cjfa-35471	196	20	a	a	DET
cjfa-35471	196	21	simple	simple	ADJ
cjfa-35471	196	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	196	23	function	function	NOUN
cjfa-35471	196	24	and	and	CCONJ
cjfa-35471	196	25	the	the	DET
cjfa-35471	196	26	interest	interest	NOUN
cjfa-35471	196	27	rate	rate	NOUN
cjfa-35471	196	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	196	29	)	)	PUNCT
cjfa-35471	196	30	is	be	AUX
cjfa-35471	196	31	time	time	NOUN
cjfa-35471	196	32	dependent	dependent	ADJ
cjfa-35471	196	33	,	,	PUNCT
cjfa-35471	196	34	i.e.	i.e.	X
cjfa-35471	196	35	:	:	PUNCT
cjfa-35471	196	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	196	37	)	)	PUNCT
cjfa-35471	197	1	=	=	SYM
cjfa-35471	197	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	197	3	𝐴	𝐴	PROPN
cjfa-35471	197	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	197	5	)	)	PUNCT
cjfa-35471	197	6	with	with	ADP
cjfa-35471	197	7	no	no	DET
cjfa-35471	197	8	growth	growth	NOUN
cjfa-35471	197	9	,	,	PUNCT
cjfa-35471	197	10	and	and	CCONJ
cjfa-35471	197	11	,	,	PUNCT
cjfa-35471	197	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	197	13	)	)	PUNCT
cjfa-35471	197	14	=	=	SYM
cjfa-35471	197	15	�	�	PROPN
cjfa-35471	197	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	197	17	�	�	PROPN
cjfa-35471	197	18	�	�	PROPN
cjfa-35471	197	19	implying	imply	VERB
cjfa-35471	197	20	that	that	SCONJ
cjfa-35471	197	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	197	22	)	)	PUNCT
cjfa-35471	198	1	=	=	VERB
cjfa-35471	198	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	198	3	if	if	SCONJ
cjfa-35471	198	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	198	5	is	be	AUX
cjfa-35471	198	6	constant	constant	ADJ
cjfa-35471	198	7	.	.	PUNCT
cjfa-35471	199	1	notice	notice	NOUN
cjfa-35471	199	2	also	also	ADV
cjfa-35471	199	3	that	that	SCONJ
cjfa-35471	199	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	199	5	�	�	X
cjfa-35471	199	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	199	7	)	)	PUNCT
cjfa-35471	199	8	=	=	SYM
cjfa-35471	199	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	199	10	)	)	PUNCT
cjfa-35471	199	11	where	where	SCONJ
cjfa-35471	199	12	f	f	PROPN
cjfa-35471	199	13	(	(	PUNCT
cjfa-35471	199	14	t	t	PROPN
cjfa-35471	199	15	)	)	PUNCT
cjfa-35471	199	16	denotes	denote	NOUN
cjfa-35471	199	17	time	time	VERB
cjfa-35471	199	18	dependent	dependent	ADJ
cjfa-35471	199	19	interest	interest	NOUN
cjfa-35471	199	20	rate	rate	NOUN
cjfa-35471	199	21	.	.	PUNCT
cjfa-35471	200	1	for	for	ADP
cjfa-35471	200	2	ease	ease	NOUN
cjfa-35471	200	3	of	of	ADP
cjfa-35471	200	4	analysis	analysis	NOUN
cjfa-35471	200	5	we	we	PRON
cjfa-35471	200	6	will	will	AUX
cjfa-35471	200	7	assume	assume	VERB
cjfa-35471	200	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	200	9	)	)	PUNCT
cjfa-35471	200	10	to	to	PART
cjfa-35471	200	11	be	be	AUX
cjfa-35471	200	12	constant	constant	ADJ
cjfa-35471	200	13	.	.	PUNCT
cjfa-35471	201	1	the	the	DET
cjfa-35471	201	2	letter	letter	NOUN
cjfa-35471	201	3	k	k	PROPN
cjfa-35471	201	4	denotes	denote	VERB
cjfa-35471	201	5	the	the	DET
cjfa-35471	201	6	periodicity	periodicity	NOUN
cjfa-35471	201	7	of	of	ADP
cjfa-35471	201	8	the	the	DET
cjfa-35471	201	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	201	10	demand	demand	NOUN
cjfa-35471	201	11	function	function	NOUN
cjfa-35471	201	12	over	over	ADP
cjfa-35471	201	13	the	the	DET
cjfa-35471	201	14	planning	planning	NOUN
cjfa-35471	201	15	period	period	NOUN
cjfa-35471	201	16	.	.	PUNCT
cjfa-35471	202	1	the	the	DET
cjfa-35471	202	2	only	only	ADJ
cjfa-35471	202	3	reason	reason	NOUN
cjfa-35471	202	4	for	for	ADP
cjfa-35471	202	5	the	the	DET
cjfa-35471	202	6	use	use	NOUN
cjfa-35471	202	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	202	8	demand	demand	NOUN
cjfa-35471	202	9	curve	curve	NOUN
cjfa-35471	202	10	is	be	AUX
cjfa-35471	202	11	that	that	SCONJ
cjfa-35471	202	12	it	it	PRON
cjfa-35471	202	13	represents	represent	VERB
cjfa-35471	202	14	cyclicality	cyclicality	NOUN
cjfa-35471	202	15	(	(	PUNCT
cjfa-35471	202	16	a	a	DET
cjfa-35471	202	17	measure	measure	NOUN
cjfa-35471	202	18	of	of	ADP
cjfa-35471	202	19	risk	risk	NOUN
cjfa-35471	202	20	)	)	PUNCT
cjfa-35471	202	21	and	and	CCONJ
cjfa-35471	202	22	that	that	SCONJ
cjfa-35471	202	23	it	it	PRON
cjfa-35471	202	24	is	be	AUX
cjfa-35471	202	25	easier	easy	ADJ
cjfa-35471	202	26	to	to	PART
cjfa-35471	202	27	work	work	VERB
cjfa-35471	202	28	with	with	ADP
cjfa-35471	202	29	it	it	PRON
cjfa-35471	202	30	.	.	PUNCT
cjfa-35471	203	1	the	the	DET
cjfa-35471	203	2	appropriate	appropriate	ADJ
cjfa-35471	203	3	lagrangian	lagrangian	NOUN
cjfa-35471	203	4	for	for	ADP
cjfa-35471	203	5	this	this	DET
cjfa-35471	203	6	problem	problem	NOUN
cjfa-35471	203	7	is	be	AUX
cjfa-35471	203	8	:	:	PUNCT
cjfa-35471	203	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	203	10	=	=	SYM
cjfa-35471	203	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	203	12	�	�	PROPN
cjfa-35471	203	13	�	�	PROPN
cjfa-35471	203	14	(	(	PUNCT
cjfa-35471	203	15	�	�	PROPN
cjfa-35471	203	16	)	)	PUNCT
cjfa-35471	203	17	�	�	PROPN
cjfa-35471	203	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	203	19	�	�	PROPN
cjfa-35471	203	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	203	21	)	)	PUNCT
cjfa-35471	203	22	�	�	PROPN
cjfa-35471	203	23	𝐴	𝐴	PROPN
cjfa-35471	203	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	203	25	)	)	PUNCT
cjfa-35471	203	26	�	�	PROPN
cjfa-35471	203	27	𝐴	𝐴	PROPN
cjfa-35471	203	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	203	29	�	�	PROPN
cjfa-35471	203	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	203	31	)	)	PUNCT
cjfa-35471	203	32	−	−	PROPN
cjfa-35471	203	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	203	34	)	)	PUNCT
cjfa-35471	203	35	�	�	PROPN
cjfa-35471	203	36	𝐴	𝐴	PROPN
cjfa-35471	203	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	203	38	�	�	PROPN
cjfa-35471	203	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	203	40	)	)	PUNCT
cjfa-35471	203	41	−	−	PROPN
cjfa-35471	203	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	203	43	)	)	PUNCT
cjfa-35471	203	44	�	�	PROPN
cjfa-35471	203	45	then	then	ADV
cjfa-35471	203	46	the	the	DET
cjfa-35471	203	47	necessary	necessary	ADJ
cjfa-35471	203	48	conditions	condition	NOUN
cjfa-35471	203	49	are	be	AUX
cjfa-35471	203	50	:	:	PUNCT
cjfa-35471	203	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	203	52	�	�	PROPN
cjfa-35471	203	53	�	�	PROPN
cjfa-35471	203	54	(	(	PUNCT
cjfa-35471	203	55	�	�	NOUN
cjfa-35471	203	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	203	57	�	�	PROPN
cjfa-35471	203	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	203	59	)	)	PUNCT
cjfa-35471	203	60	𝐴	𝐴	PROPN
cjfa-35471	203	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	203	62	)	)	PUNCT
cjfa-35471	203	63	−	−	PROPN
cjfa-35471	203	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	203	65	)	)	PUNCT
cjfa-35471	204	1	=	=	SYM
cjfa-35471	204	2	0	0	PUNCT
cjfa-35471	204	3	(	(	PUNCT
cjfa-35471	204	4	1	1	NUM
cjfa-35471	204	5	)	)	PUNCT
cjfa-35471	204	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	204	7	�	�	PROPN
cjfa-35471	204	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	204	9	)	)	PUNCT
cjfa-35471	204	10	=	=	SYM
cjfa-35471	204	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	204	12	�	�	PROPN
cjfa-35471	204	13	�	�	PROPN
cjfa-35471	204	14	(	(	PUNCT
cjfa-35471	204	15	�	�	PROPN
cjfa-35471	204	16	)ℎ	)ℎ	PROPN
cjfa-35471	204	17	(	(	PUNCT
cjfa-35471	204	18	2	2	X
cjfa-35471	204	19	)	)	PUNCT
cjfa-35471	204	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	204	21	�	�	PROPN
cjfa-35471	204	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	204	23	)	)	PUNCT
cjfa-35471	204	24	=	=	SYM
cjfa-35471	204	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	204	26	)	)	PUNCT
cjfa-35471	204	27	−	−	PROPN
cjfa-35471	204	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	204	29	)	)	PUNCT
cjfa-35471	204	30	(	(	PUNCT
cjfa-35471	204	31	3	3	X
cjfa-35471	204	32	)	)	PUNCT
cjfa-35471	204	33	necessary	necessary	ADJ
cjfa-35471	204	34	conditions	condition	NOUN
cjfa-35471	204	35	are	be	AUX
cjfa-35471	204	36	also	also	ADV
cjfa-35471	204	37	sufficient	sufficient	ADJ
cjfa-35471	204	38	since	since	SCONJ
cjfa-35471	204	39	the	the	DET
cjfa-35471	204	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	204	41	is	be	AUX
cjfa-35471	204	42	convex	convex	ADJ
cjfa-35471	204	43	in	in	ADP
cjfa-35471	204	44	both	both	CCONJ
cjfa-35471	204	45	the	the	DET
cjfa-35471	204	46	control	control	NOUN
cjfa-35471	204	47	(	(	PUNCT
cjfa-35471	204	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	204	49	)	)	PUNCT
cjfa-35471	204	50	and	and	CCONJ
cjfa-35471	204	51	state	state	NOUN
cjfa-35471	204	52	(	(	PUNCT
cjfa-35471	204	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	204	54	)	)	PUNCT
cjfa-35471	204	55	variables	variable	NOUN
cjfa-35471	204	56	.	.	PUNCT
cjfa-35471	205	1	the	the	DET
cjfa-35471	205	2	planning	planning	NOUN
cjfa-35471	205	3	horizon	horizon	NOUN
cjfa-35471	205	4	(	(	PUNCT
cjfa-35471	205	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	205	6	)	)	PUNCT
cjfa-35471	205	7	will	will	AUX
cjfa-35471	205	8	be	be	AUX
cjfa-35471	205	9	assumed	assume	VERB
cjfa-35471	205	10	one	one	NUM
cjfa-35471	205	11	.	.	PUNCT
cjfa-35471	206	1	on	on	ADP
cjfa-35471	206	2	a	a	DET
cjfa-35471	206	3	constraint	constraint	NOUN
cjfa-35471	206	4	arc	arc	NOUN
cjfa-35471	206	5	on	on	ADP
cjfa-35471	206	6	which	which	PRON
cjfa-35471	206	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	206	8	)	)	PUNCT
cjfa-35471	206	9	=	=	SYM
cjfa-35471	206	10	0	0	NUM
cjfa-35471	206	11	for	for	ADP
cjfa-35471	206	12	a	a	DET
cjfa-35471	206	13	certain	certain	ADJ
cjfa-35471	206	14	period	period	NOUN
cjfa-35471	206	15	in	in	ADP
cjfa-35471	206	16	[	[	X
cjfa-35471	206	17	0	0	NUM
cjfa-35471	206	18	,	,	PUNCT
cjfa-35471	206	19	1	1	NUM
cjfa-35471	206	20	]	]	PUNCT
cjfa-35471	206	21	i.e.	i.e.	X
cjfa-35471	206	22	0	0	X
cjfa-35471	206	23	<	<	X
cjfa-35471	206	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	206	25	�	�	PROPN
cjfa-35471	206	26	≤	≤	X
cjfa-35471	206	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	206	28	≤	≤	PROPN
cjfa-35471	206	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	206	30	�	�	PROPN
cjfa-35471	206	31	<	<	X
cjfa-35471	206	32	1	1	NUM
cjfa-35471	206	33	we	we	PRON
cjfa-35471	206	34	have	have	VERB
cjfa-35471	206	35	;	;	PUNCT
cjfa-35471	206	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	206	37	�	�	PROPN
cjfa-35471	206	38	=	=	SYM
cjfa-35471	206	39	0	0	NUM
cjfa-35471	206	40	=	=	SYM
cjfa-35471	206	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	206	42	)	)	PUNCT
cjfa-35471	207	1	−	−	PROPN
cjfa-35471	207	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	207	3	)	)	PUNCT
cjfa-35471	207	4	implying	imply	VERB
cjfa-35471	207	5	that	that	SCONJ
cjfa-35471	207	6	over	over	ADP
cjfa-35471	207	7	this	this	DET
cjfa-35471	207	8	period	period	NOUN
cjfa-35471	207	9	a	a	DET
cjfa-35471	207	10	firm	firm	NOUN
cjfa-35471	207	11	will	will	AUX
cjfa-35471	207	12	produce	produce	VERB
cjfa-35471	207	13	just	just	ADV
cjfa-35471	207	14	enough	enough	ADJ
cjfa-35471	207	15	to	to	PART
cjfa-35471	207	16	meet	meet	VERB
cjfa-35471	207	17	the	the	DET
cjfa-35471	207	18	demand	demand	NOUN
cjfa-35471	207	19	,	,	PUNCT
cjfa-35471	207	20	which	which	PRON
cjfa-35471	207	21	is	be	AUX
cjfa-35471	207	22	assumed	assume	VERB
cjfa-35471	207	23	to	to	PART
cjfa-35471	207	24	be	be	AUX
cjfa-35471	207	25	nonzero	nonzero	NOUN
cjfa-35471	207	26	during	during	ADP
cjfa-35471	207	27	the	the	DET
cjfa-35471	207	28	planning	planning	NOUN
cjfa-35471	207	29	horizon	horizon	NOUN
cjfa-35471	207	30	.	.	PUNCT
cjfa-35471	208	1	with	with	ADP
cjfa-35471	208	2	the	the	DET
cjfa-35471	208	3	assumptions	assumption	NOUN
cjfa-35471	208	4	that	that	SCONJ
cjfa-35471	208	5	the	the	DET
cjfa-35471	208	6	demand	demand	NOUN
cjfa-35471	208	7	(	(	PUNCT
cjfa-35471	208	8	 	 	SPACE
cjfa-35471	208	9	r(t	r(t	NOUN
cjfa-35471	208	10	)	)	PUNCT
cjfa-35471	208	11	 	 	SPACE
cjfa-35471	208	12	)	)	PUNCT
cjfa-35471	208	13	is	be	AUX
cjfa-35471	208	14	a	a	DET
cjfa-35471	208	15	simple	simple	ADJ
cjfa-35471	208	16	sinusoidal	sinusoidal	NOUN
cjfa-35471	208	17	function	function	NOUN
cjfa-35471	208	18	and	and	CCONJ
cjfa-35471	208	19	the	the	DET
cjfa-35471	208	20	interest	interest	NOUN
cjfa-35471	208	21	rate	rate	NOUN
cjfa-35471	208	22	i(t	i(t	PROPN
cjfa-35471	208	23	)	)	PUNCT
cjfa-35471	208	24	is	be	AUX
cjfa-35471	208	25	time	time	NOUN
cjfa-35471	208	26	dependent	dependent	ADJ
cjfa-35471	208	27	,	,	PUNCT
cjfa-35471	208	28	i.e.	i.e.	ADV
cjfa-35471	208	29	:	:	PUNCT
cjfa-35471	208	30	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	208	31	�	�	PROPN
cjfa-35471	208	32	=	=	PUNCT
cjfa-35471	208	33	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	208	34	)	)	PUNCT
cjfa-35471	209	1	−	−	PROPN
cjfa-35471	209	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	209	3	)	)	PUNCT
cjfa-35471	209	4	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	209	5	)	)	PUNCT
cjfa-35471	209	6	=	=	SYM
cjfa-35471	209	7	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	209	8	�	�	PROPN
cjfa-35471	209	9	a	a	DET
cjfa-35471	209	10	given	give	VERB
cjfa-35471	209	11	number	number	NOUN
cjfa-35471	209	12	.	.	PUNCT
cjfa-35471	210	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	210	2	)	)	PUNCT
cjfa-35471	211	1	𝑢	𝑢	PROPN
cjfa-35471	211	2	0	0	NUM
cjfa-35471	211	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	211	4	)	)	PUNCT
cjfa-35471	211	5	𝑢	𝑢	ADP
cjfa-35471	211	6	0	0	NUM
cjfa-35471	211	7	with	with	ADP
cjfa-35471	211	8	the	the	DET
cjfa-35471	211	9	assumptions	assumption	NOUN
cjfa-35471	211	10	that	that	SCONJ
cjfa-35471	211	11	the	the	DET
cjfa-35471	211	12	demand	demand	NOUN
cjfa-35471	211	13	(	(	PUNCT
cjfa-35471	211	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	211	15	(	(	PUNCT
cjfa-35471	211	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	211	17	)	)	PUNCT
cjfa-35471	211	18	)	)	PUNCT
cjfa-35471	211	19	is	be	AUX
cjfa-35471	211	20	a	a	DET
cjfa-35471	211	21	simple	simple	ADJ
cjfa-35471	211	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	211	23	function	function	NOUN
cjfa-35471	211	24	and	and	CCONJ
cjfa-35471	211	25	the	the	DET
cjfa-35471	211	26	interest	interest	NOUN
cjfa-35471	211	27	rate	rate	NOUN
cjfa-35471	211	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	211	29	)	)	PUNCT
cjfa-35471	211	30	is	be	AUX
cjfa-35471	211	31	time	time	NOUN
cjfa-35471	211	32	dependent	dependent	ADJ
cjfa-35471	211	33	,	,	PUNCT
cjfa-35471	211	34	i.e.	i.e.	X
cjfa-35471	211	35	:	:	PUNCT
cjfa-35471	211	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	211	37	)	)	PUNCT
cjfa-35471	212	1	=	=	SYM
cjfa-35471	212	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	212	3	𝐴	𝐴	PROPN
cjfa-35471	212	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	212	5	)	)	PUNCT
cjfa-35471	212	6	with	with	ADP
cjfa-35471	212	7	no	no	DET
cjfa-35471	212	8	growth	growth	NOUN
cjfa-35471	212	9	,	,	PUNCT
cjfa-35471	212	10	and	and	CCONJ
cjfa-35471	212	11	,	,	PUNCT
cjfa-35471	212	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	212	13	)	)	PUNCT
cjfa-35471	212	14	=	=	SYM
cjfa-35471	212	15	�	�	PROPN
cjfa-35471	212	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	212	17	�	�	PROPN
cjfa-35471	212	18	�	�	PROPN
cjfa-35471	212	19	implying	imply	VERB
cjfa-35471	212	20	that	that	SCONJ
cjfa-35471	212	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	212	22	)	)	PUNCT
cjfa-35471	213	1	=	=	VERB
cjfa-35471	213	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	213	3	if	if	SCONJ
cjfa-35471	213	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	213	5	is	be	AUX
cjfa-35471	213	6	constant	constant	ADJ
cjfa-35471	213	7	.	.	PUNCT
cjfa-35471	214	1	notice	notice	NOUN
cjfa-35471	214	2	also	also	ADV
cjfa-35471	214	3	that	that	SCONJ
cjfa-35471	214	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	214	5	�	�	X
cjfa-35471	214	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	214	7	)	)	PUNCT
cjfa-35471	214	8	=	=	SYM
cjfa-35471	214	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	214	10	)	)	PUNCT
cjfa-35471	214	11	where	where	SCONJ
cjfa-35471	214	12	f	f	PROPN
cjfa-35471	214	13	(	(	PUNCT
cjfa-35471	214	14	t	t	PROPN
cjfa-35471	214	15	)	)	PUNCT
cjfa-35471	214	16	denotes	denote	NOUN
cjfa-35471	214	17	time	time	VERB
cjfa-35471	214	18	dependent	dependent	ADJ
cjfa-35471	214	19	interest	interest	NOUN
cjfa-35471	214	20	rate	rate	NOUN
cjfa-35471	214	21	.	.	PUNCT
cjfa-35471	215	1	for	for	ADP
cjfa-35471	215	2	ease	ease	NOUN
cjfa-35471	215	3	of	of	ADP
cjfa-35471	215	4	analysis	analysis	NOUN
cjfa-35471	215	5	we	we	PRON
cjfa-35471	215	6	will	will	AUX
cjfa-35471	215	7	assume	assume	VERB
cjfa-35471	215	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	215	9	)	)	PUNCT
cjfa-35471	215	10	to	to	PART
cjfa-35471	215	11	be	be	AUX
cjfa-35471	215	12	constant	constant	ADJ
cjfa-35471	215	13	.	.	PUNCT
cjfa-35471	216	1	the	the	DET
cjfa-35471	216	2	letter	letter	NOUN
cjfa-35471	216	3	k	k	PROPN
cjfa-35471	216	4	denotes	denote	VERB
cjfa-35471	216	5	the	the	DET
cjfa-35471	216	6	periodicity	periodicity	NOUN
cjfa-35471	216	7	of	of	ADP
cjfa-35471	216	8	the	the	DET
cjfa-35471	216	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	216	10	demand	demand	NOUN
cjfa-35471	216	11	function	function	NOUN
cjfa-35471	216	12	over	over	ADP
cjfa-35471	216	13	the	the	DET
cjfa-35471	216	14	planning	planning	NOUN
cjfa-35471	216	15	period	period	NOUN
cjfa-35471	216	16	.	.	PUNCT
cjfa-35471	217	1	the	the	DET
cjfa-35471	217	2	only	only	ADJ
cjfa-35471	217	3	reason	reason	NOUN
cjfa-35471	217	4	for	for	ADP
cjfa-35471	217	5	the	the	DET
cjfa-35471	217	6	use	use	NOUN
cjfa-35471	217	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	217	8	demand	demand	NOUN
cjfa-35471	217	9	curve	curve	NOUN
cjfa-35471	217	10	is	be	AUX
cjfa-35471	217	11	that	that	SCONJ
cjfa-35471	217	12	it	it	PRON
cjfa-35471	217	13	represents	represent	VERB
cjfa-35471	217	14	cyclicality	cyclicality	NOUN
cjfa-35471	217	15	(	(	PUNCT
cjfa-35471	217	16	a	a	DET
cjfa-35471	217	17	measure	measure	NOUN
cjfa-35471	217	18	of	of	ADP
cjfa-35471	217	19	risk	risk	NOUN
cjfa-35471	217	20	)	)	PUNCT
cjfa-35471	217	21	and	and	CCONJ
cjfa-35471	217	22	that	that	SCONJ
cjfa-35471	217	23	it	it	PRON
cjfa-35471	217	24	is	be	AUX
cjfa-35471	217	25	easier	easy	ADJ
cjfa-35471	217	26	to	to	PART
cjfa-35471	217	27	work	work	VERB
cjfa-35471	217	28	with	with	ADP
cjfa-35471	217	29	it	it	PRON
cjfa-35471	217	30	.	.	PUNCT
cjfa-35471	218	1	the	the	DET
cjfa-35471	218	2	appropriate	appropriate	ADJ
cjfa-35471	218	3	lagrangian	lagrangian	NOUN
cjfa-35471	218	4	for	for	ADP
cjfa-35471	218	5	this	this	DET
cjfa-35471	218	6	problem	problem	NOUN
cjfa-35471	218	7	is	be	AUX
cjfa-35471	218	8	:	:	PUNCT
cjfa-35471	218	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	218	10	=	=	SYM
cjfa-35471	218	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	218	12	�	�	PROPN
cjfa-35471	218	13	�	�	PROPN
cjfa-35471	218	14	(	(	PUNCT
cjfa-35471	218	15	�	�	PROPN
cjfa-35471	218	16	)	)	PUNCT
cjfa-35471	218	17	�	�	PROPN
cjfa-35471	218	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	218	19	�	�	PROPN
cjfa-35471	218	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	218	21	)	)	PUNCT
cjfa-35471	218	22	�	�	PROPN
cjfa-35471	218	23	𝐴	𝐴	PROPN
cjfa-35471	218	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	218	25	)	)	PUNCT
cjfa-35471	218	26	�	�	PROPN
cjfa-35471	218	27	𝐴	𝐴	PROPN
cjfa-35471	218	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	218	29	�	�	PROPN
cjfa-35471	218	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	218	31	)	)	PUNCT
cjfa-35471	218	32	−	−	PROPN
cjfa-35471	218	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	218	34	)	)	PUNCT
cjfa-35471	218	35	�	�	PROPN
cjfa-35471	218	36	𝐴	𝐴	PROPN
cjfa-35471	218	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	218	38	�	�	PROPN
cjfa-35471	218	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	218	40	)	)	PUNCT
cjfa-35471	218	41	−	−	PROPN
cjfa-35471	218	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	218	43	)	)	PUNCT
cjfa-35471	218	44	�	�	PROPN
cjfa-35471	218	45	then	then	ADV
cjfa-35471	218	46	the	the	DET
cjfa-35471	218	47	necessary	necessary	ADJ
cjfa-35471	218	48	conditions	condition	NOUN
cjfa-35471	218	49	are	be	AUX
cjfa-35471	218	50	:	:	PUNCT
cjfa-35471	218	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	218	52	�	�	PROPN
cjfa-35471	218	53	�	�	PROPN
cjfa-35471	218	54	(	(	PUNCT
cjfa-35471	218	55	�	�	NOUN
cjfa-35471	218	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	218	57	�	�	PROPN
cjfa-35471	218	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	218	59	)	)	PUNCT
cjfa-35471	218	60	𝐴	𝐴	PROPN
cjfa-35471	218	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	218	62	)	)	PUNCT
cjfa-35471	218	63	−	−	PROPN
cjfa-35471	218	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	218	65	)	)	PUNCT
cjfa-35471	219	1	=	=	SYM
cjfa-35471	219	2	0	0	PUNCT
cjfa-35471	219	3	(	(	PUNCT
cjfa-35471	219	4	1	1	NUM
cjfa-35471	219	5	)	)	PUNCT
cjfa-35471	219	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	219	7	�	�	PROPN
cjfa-35471	219	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	219	9	)	)	PUNCT
cjfa-35471	219	10	=	=	SYM
cjfa-35471	219	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	219	12	�	�	PROPN
cjfa-35471	219	13	�	�	PROPN
cjfa-35471	219	14	(	(	PUNCT
cjfa-35471	219	15	�	�	PROPN
cjfa-35471	219	16	)ℎ	)ℎ	PROPN
cjfa-35471	219	17	(	(	PUNCT
cjfa-35471	219	18	2	2	X
cjfa-35471	219	19	)	)	PUNCT
cjfa-35471	219	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	219	21	�	�	PROPN
cjfa-35471	219	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	219	23	)	)	PUNCT
cjfa-35471	219	24	=	=	SYM
cjfa-35471	219	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	219	26	)	)	PUNCT
cjfa-35471	219	27	−	−	PROPN
cjfa-35471	219	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	219	29	)	)	PUNCT
cjfa-35471	219	30	(	(	PUNCT
cjfa-35471	219	31	3	3	X
cjfa-35471	219	32	)	)	PUNCT
cjfa-35471	219	33	necessary	necessary	ADJ
cjfa-35471	219	34	conditions	condition	NOUN
cjfa-35471	219	35	are	be	AUX
cjfa-35471	219	36	also	also	ADV
cjfa-35471	219	37	sufficient	sufficient	ADJ
cjfa-35471	219	38	since	since	SCONJ
cjfa-35471	219	39	the	the	DET
cjfa-35471	219	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	219	41	is	be	AUX
cjfa-35471	219	42	convex	convex	ADJ
cjfa-35471	219	43	in	in	ADP
cjfa-35471	219	44	both	both	CCONJ
cjfa-35471	219	45	the	the	DET
cjfa-35471	219	46	control	control	NOUN
cjfa-35471	219	47	(	(	PUNCT
cjfa-35471	219	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	219	49	)	)	PUNCT
cjfa-35471	219	50	and	and	CCONJ
cjfa-35471	219	51	state	state	NOUN
cjfa-35471	219	52	(	(	PUNCT
cjfa-35471	219	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	219	54	)	)	PUNCT
cjfa-35471	219	55	variables	variable	NOUN
cjfa-35471	219	56	.	.	PUNCT
cjfa-35471	220	1	the	the	DET
cjfa-35471	220	2	planning	planning	NOUN
cjfa-35471	220	3	horizon	horizon	NOUN
cjfa-35471	220	4	(	(	PUNCT
cjfa-35471	220	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	220	6	)	)	PUNCT
cjfa-35471	220	7	will	will	AUX
cjfa-35471	220	8	be	be	AUX
cjfa-35471	220	9	assumed	assume	VERB
cjfa-35471	220	10	one	one	NUM
cjfa-35471	220	11	.	.	PUNCT
cjfa-35471	221	1	on	on	ADP
cjfa-35471	221	2	a	a	DET
cjfa-35471	221	3	constraint	constraint	NOUN
cjfa-35471	221	4	arc	arc	NOUN
cjfa-35471	221	5	on	on	ADP
cjfa-35471	221	6	which	which	PRON
cjfa-35471	221	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	221	8	)	)	PUNCT
cjfa-35471	221	9	=	=	SYM
cjfa-35471	221	10	0	0	NUM
cjfa-35471	221	11	for	for	ADP
cjfa-35471	221	12	a	a	DET
cjfa-35471	221	13	certain	certain	ADJ
cjfa-35471	221	14	period	period	NOUN
cjfa-35471	221	15	in	in	ADP
cjfa-35471	221	16	[	[	X
cjfa-35471	221	17	0	0	NUM
cjfa-35471	221	18	,	,	PUNCT
cjfa-35471	221	19	1	1	NUM
cjfa-35471	221	20	]	]	PUNCT
cjfa-35471	221	21	i.e.	i.e.	X
cjfa-35471	221	22	0	0	X
cjfa-35471	221	23	<	<	X
cjfa-35471	221	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	221	25	�	�	PROPN
cjfa-35471	221	26	≤	≤	X
cjfa-35471	221	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	221	28	≤	≤	PROPN
cjfa-35471	221	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	221	30	�	�	PROPN
cjfa-35471	221	31	<	<	X
cjfa-35471	221	32	1	1	NUM
cjfa-35471	221	33	we	we	PRON
cjfa-35471	221	34	have	have	VERB
cjfa-35471	221	35	;	;	PUNCT
cjfa-35471	221	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	221	37	�	�	PROPN
cjfa-35471	221	38	=	=	SYM
cjfa-35471	221	39	0	0	NUM
cjfa-35471	221	40	=	=	SYM
cjfa-35471	221	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	221	42	)	)	PUNCT
cjfa-35471	222	1	−	−	PROPN
cjfa-35471	222	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	222	3	)	)	PUNCT
cjfa-35471	222	4	implying	imply	VERB
cjfa-35471	222	5	that	that	SCONJ
cjfa-35471	222	6	over	over	ADP
cjfa-35471	222	7	this	this	DET
cjfa-35471	222	8	period	period	NOUN
cjfa-35471	222	9	a	a	DET
cjfa-35471	222	10	firm	firm	NOUN
cjfa-35471	222	11	will	will	AUX
cjfa-35471	222	12	produce	produce	VERB
cjfa-35471	222	13	just	just	ADV
cjfa-35471	222	14	enough	enough	ADJ
cjfa-35471	222	15	to	to	PART
cjfa-35471	222	16	meet	meet	VERB
cjfa-35471	222	17	the	the	DET
cjfa-35471	222	18	demand	demand	NOUN
cjfa-35471	222	19	,	,	PUNCT
cjfa-35471	222	20	which	which	PRON
cjfa-35471	222	21	is	be	AUX
cjfa-35471	222	22	assumed	assume	VERB
cjfa-35471	222	23	to	to	PART
cjfa-35471	222	24	be	be	AUX
cjfa-35471	222	25	nonzero	nonzero	NOUN
cjfa-35471	222	26	during	during	ADP
cjfa-35471	222	27	the	the	DET
cjfa-35471	222	28	planning	planning	NOUN
cjfa-35471	222	29	horizon	horizon	NOUN
cjfa-35471	222	30	.	.	PUNCT
cjfa-35471	223	1	with	with	ADP
cjfa-35471	223	2	no	no	DET
cjfa-35471	223	3	growth	growth	NOUN
cjfa-35471	223	4	,	,	PUNCT
cjfa-35471	223	5	and	and	CCONJ
cjfa-35471	223	6	,	,	PUNCT
cjfa-35471	223	7	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	223	8	�	�	PROPN
cjfa-35471	223	9	=	=	PUNCT
cjfa-35471	223	10	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	223	11	)	)	PUNCT
cjfa-35471	224	1	−	−	PROPN
cjfa-35471	224	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	224	3	)	)	PUNCT
cjfa-35471	224	4	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	224	5	)	)	PUNCT
cjfa-35471	224	6	=	=	SYM
cjfa-35471	224	7	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	224	8	�	�	PROPN
cjfa-35471	224	9	a	a	DET
cjfa-35471	224	10	given	give	VERB
cjfa-35471	224	11	number	number	NOUN
cjfa-35471	224	12	.	.	PUNCT
cjfa-35471	225	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	225	2	)	)	PUNCT
cjfa-35471	226	1	𝑢	𝑢	PROPN
cjfa-35471	226	2	0	0	NUM
cjfa-35471	226	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	226	4	)	)	PUNCT
cjfa-35471	226	5	𝑢	𝑢	ADP
cjfa-35471	226	6	0	0	NUM
cjfa-35471	226	7	with	with	ADP
cjfa-35471	226	8	the	the	DET
cjfa-35471	226	9	assumptions	assumption	NOUN
cjfa-35471	226	10	that	that	SCONJ
cjfa-35471	226	11	the	the	DET
cjfa-35471	226	12	demand	demand	NOUN
cjfa-35471	226	13	(	(	PUNCT
cjfa-35471	226	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	226	15	(	(	PUNCT
cjfa-35471	226	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	226	17	)	)	PUNCT
cjfa-35471	226	18	)	)	PUNCT
cjfa-35471	226	19	is	be	AUX
cjfa-35471	226	20	a	a	DET
cjfa-35471	226	21	simple	simple	ADJ
cjfa-35471	226	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	226	23	function	function	NOUN
cjfa-35471	226	24	and	and	CCONJ
cjfa-35471	226	25	the	the	DET
cjfa-35471	226	26	interest	interest	NOUN
cjfa-35471	226	27	rate	rate	NOUN
cjfa-35471	226	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	226	29	)	)	PUNCT
cjfa-35471	226	30	is	be	AUX
cjfa-35471	226	31	time	time	NOUN
cjfa-35471	226	32	dependent	dependent	ADJ
cjfa-35471	226	33	,	,	PUNCT
cjfa-35471	226	34	i.e.	i.e.	X
cjfa-35471	226	35	:	:	PUNCT
cjfa-35471	226	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	226	37	)	)	PUNCT
cjfa-35471	227	1	=	=	SYM
cjfa-35471	227	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	227	3	𝐴	𝐴	PROPN
cjfa-35471	227	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	227	5	)	)	PUNCT
cjfa-35471	227	6	with	with	ADP
cjfa-35471	227	7	no	no	DET
cjfa-35471	227	8	growth	growth	NOUN
cjfa-35471	227	9	,	,	PUNCT
cjfa-35471	227	10	and	and	CCONJ
cjfa-35471	227	11	,	,	PUNCT
cjfa-35471	227	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	227	13	)	)	PUNCT
cjfa-35471	227	14	=	=	SYM
cjfa-35471	227	15	�	�	PROPN
cjfa-35471	227	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	227	17	�	�	PROPN
cjfa-35471	227	18	�	�	PROPN
cjfa-35471	227	19	implying	imply	VERB
cjfa-35471	227	20	that	that	SCONJ
cjfa-35471	227	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	227	22	)	)	PUNCT
cjfa-35471	228	1	=	=	VERB
cjfa-35471	228	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	228	3	if	if	SCONJ
cjfa-35471	228	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	228	5	is	be	AUX
cjfa-35471	228	6	constant	constant	ADJ
cjfa-35471	228	7	.	.	PUNCT
cjfa-35471	229	1	notice	notice	NOUN
cjfa-35471	229	2	also	also	ADV
cjfa-35471	229	3	that	that	SCONJ
cjfa-35471	229	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	229	5	�	�	X
cjfa-35471	229	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	229	7	)	)	PUNCT
cjfa-35471	229	8	=	=	SYM
cjfa-35471	229	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	229	10	)	)	PUNCT
cjfa-35471	229	11	where	where	SCONJ
cjfa-35471	229	12	f	f	PROPN
cjfa-35471	229	13	(	(	PUNCT
cjfa-35471	229	14	t	t	PROPN
cjfa-35471	229	15	)	)	PUNCT
cjfa-35471	229	16	denotes	denote	NOUN
cjfa-35471	229	17	time	time	VERB
cjfa-35471	229	18	dependent	dependent	ADJ
cjfa-35471	229	19	interest	interest	NOUN
cjfa-35471	229	20	rate	rate	NOUN
cjfa-35471	229	21	.	.	PUNCT
cjfa-35471	230	1	for	for	ADP
cjfa-35471	230	2	ease	ease	NOUN
cjfa-35471	230	3	of	of	ADP
cjfa-35471	230	4	analysis	analysis	NOUN
cjfa-35471	230	5	we	we	PRON
cjfa-35471	230	6	will	will	AUX
cjfa-35471	230	7	assume	assume	VERB
cjfa-35471	230	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	230	9	)	)	PUNCT
cjfa-35471	230	10	to	to	PART
cjfa-35471	230	11	be	be	AUX
cjfa-35471	230	12	constant	constant	ADJ
cjfa-35471	230	13	.	.	PUNCT
cjfa-35471	231	1	the	the	DET
cjfa-35471	231	2	letter	letter	NOUN
cjfa-35471	231	3	k	k	PROPN
cjfa-35471	231	4	denotes	denote	VERB
cjfa-35471	231	5	the	the	DET
cjfa-35471	231	6	periodicity	periodicity	NOUN
cjfa-35471	231	7	of	of	ADP
cjfa-35471	231	8	the	the	DET
cjfa-35471	231	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	231	10	demand	demand	NOUN
cjfa-35471	231	11	function	function	NOUN
cjfa-35471	231	12	over	over	ADP
cjfa-35471	231	13	the	the	DET
cjfa-35471	231	14	planning	planning	NOUN
cjfa-35471	231	15	period	period	NOUN
cjfa-35471	231	16	.	.	PUNCT
cjfa-35471	232	1	the	the	DET
cjfa-35471	232	2	only	only	ADJ
cjfa-35471	232	3	reason	reason	NOUN
cjfa-35471	232	4	for	for	ADP
cjfa-35471	232	5	the	the	DET
cjfa-35471	232	6	use	use	NOUN
cjfa-35471	232	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	232	8	demand	demand	NOUN
cjfa-35471	232	9	curve	curve	NOUN
cjfa-35471	232	10	is	be	AUX
cjfa-35471	232	11	that	that	SCONJ
cjfa-35471	232	12	it	it	PRON
cjfa-35471	232	13	represents	represent	VERB
cjfa-35471	232	14	cyclicality	cyclicality	NOUN
cjfa-35471	232	15	(	(	PUNCT
cjfa-35471	232	16	a	a	DET
cjfa-35471	232	17	measure	measure	NOUN
cjfa-35471	232	18	of	of	ADP
cjfa-35471	232	19	risk	risk	NOUN
cjfa-35471	232	20	)	)	PUNCT
cjfa-35471	232	21	and	and	CCONJ
cjfa-35471	232	22	that	that	SCONJ
cjfa-35471	232	23	it	it	PRON
cjfa-35471	232	24	is	be	AUX
cjfa-35471	232	25	easier	easy	ADJ
cjfa-35471	232	26	to	to	PART
cjfa-35471	232	27	work	work	VERB
cjfa-35471	232	28	with	with	ADP
cjfa-35471	232	29	it	it	PRON
cjfa-35471	232	30	.	.	PUNCT
cjfa-35471	233	1	the	the	DET
cjfa-35471	233	2	appropriate	appropriate	ADJ
cjfa-35471	233	3	lagrangian	lagrangian	NOUN
cjfa-35471	233	4	for	for	ADP
cjfa-35471	233	5	this	this	DET
cjfa-35471	233	6	problem	problem	NOUN
cjfa-35471	233	7	is	be	AUX
cjfa-35471	233	8	:	:	PUNCT
cjfa-35471	233	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	233	10	=	=	SYM
cjfa-35471	233	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	233	12	�	�	PROPN
cjfa-35471	233	13	�	�	PROPN
cjfa-35471	233	14	(	(	PUNCT
cjfa-35471	233	15	�	�	PROPN
cjfa-35471	233	16	)	)	PUNCT
cjfa-35471	233	17	�	�	PROPN
cjfa-35471	233	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	233	19	�	�	PROPN
cjfa-35471	233	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	233	21	)	)	PUNCT
cjfa-35471	233	22	�	�	PROPN
cjfa-35471	233	23	𝐴	𝐴	PROPN
cjfa-35471	233	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	233	25	)	)	PUNCT
cjfa-35471	233	26	�	�	PROPN
cjfa-35471	233	27	𝐴	𝐴	PROPN
cjfa-35471	233	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	233	29	�	�	PROPN
cjfa-35471	233	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	233	31	)	)	PUNCT
cjfa-35471	233	32	−	−	PROPN
cjfa-35471	233	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	233	34	)	)	PUNCT
cjfa-35471	233	35	�	�	PROPN
cjfa-35471	233	36	𝐴	𝐴	PROPN
cjfa-35471	233	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	233	38	�	�	PROPN
cjfa-35471	233	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	233	40	)	)	PUNCT
cjfa-35471	233	41	−	−	PROPN
cjfa-35471	233	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	233	43	)	)	PUNCT
cjfa-35471	233	44	�	�	PROPN
cjfa-35471	233	45	then	then	ADV
cjfa-35471	233	46	the	the	DET
cjfa-35471	233	47	necessary	necessary	ADJ
cjfa-35471	233	48	conditions	condition	NOUN
cjfa-35471	233	49	are	be	AUX
cjfa-35471	233	50	:	:	PUNCT
cjfa-35471	233	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	233	52	�	�	PROPN
cjfa-35471	233	53	�	�	PROPN
cjfa-35471	233	54	(	(	PUNCT
cjfa-35471	233	55	�	�	NOUN
cjfa-35471	233	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	233	57	�	�	PROPN
cjfa-35471	233	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	233	59	)	)	PUNCT
cjfa-35471	233	60	𝐴	𝐴	PROPN
cjfa-35471	233	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	233	62	)	)	PUNCT
cjfa-35471	233	63	−	−	PROPN
cjfa-35471	233	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	233	65	)	)	PUNCT
cjfa-35471	234	1	=	=	SYM
cjfa-35471	234	2	0	0	PUNCT
cjfa-35471	234	3	(	(	PUNCT
cjfa-35471	234	4	1	1	NUM
cjfa-35471	234	5	)	)	PUNCT
cjfa-35471	234	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	234	7	�	�	PROPN
cjfa-35471	234	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	234	9	)	)	PUNCT
cjfa-35471	234	10	=	=	SYM
cjfa-35471	234	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	234	12	�	�	PROPN
cjfa-35471	234	13	�	�	PROPN
cjfa-35471	234	14	(	(	PUNCT
cjfa-35471	234	15	�	�	PROPN
cjfa-35471	234	16	)ℎ	)ℎ	PROPN
cjfa-35471	234	17	(	(	PUNCT
cjfa-35471	234	18	2	2	X
cjfa-35471	234	19	)	)	PUNCT
cjfa-35471	234	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	234	21	�	�	PROPN
cjfa-35471	234	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	234	23	)	)	PUNCT
cjfa-35471	234	24	=	=	SYM
cjfa-35471	234	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	234	26	)	)	PUNCT
cjfa-35471	234	27	−	−	PROPN
cjfa-35471	234	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	234	29	)	)	PUNCT
cjfa-35471	234	30	(	(	PUNCT
cjfa-35471	234	31	3	3	X
cjfa-35471	234	32	)	)	PUNCT
cjfa-35471	234	33	necessary	necessary	ADJ
cjfa-35471	234	34	conditions	condition	NOUN
cjfa-35471	234	35	are	be	AUX
cjfa-35471	234	36	also	also	ADV
cjfa-35471	234	37	sufficient	sufficient	ADJ
cjfa-35471	234	38	since	since	SCONJ
cjfa-35471	234	39	the	the	DET
cjfa-35471	234	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	234	41	is	be	AUX
cjfa-35471	234	42	convex	convex	ADJ
cjfa-35471	234	43	in	in	ADP
cjfa-35471	234	44	both	both	CCONJ
cjfa-35471	234	45	the	the	DET
cjfa-35471	234	46	control	control	NOUN
cjfa-35471	234	47	(	(	PUNCT
cjfa-35471	234	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	234	49	)	)	PUNCT
cjfa-35471	234	50	and	and	CCONJ
cjfa-35471	234	51	state	state	NOUN
cjfa-35471	234	52	(	(	PUNCT
cjfa-35471	234	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	234	54	)	)	PUNCT
cjfa-35471	234	55	variables	variable	NOUN
cjfa-35471	234	56	.	.	PUNCT
cjfa-35471	235	1	the	the	DET
cjfa-35471	235	2	planning	planning	NOUN
cjfa-35471	235	3	horizon	horizon	NOUN
cjfa-35471	235	4	(	(	PUNCT
cjfa-35471	235	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	235	6	)	)	PUNCT
cjfa-35471	235	7	will	will	AUX
cjfa-35471	235	8	be	be	AUX
cjfa-35471	235	9	assumed	assume	VERB
cjfa-35471	235	10	one	one	NUM
cjfa-35471	235	11	.	.	PUNCT
cjfa-35471	236	1	on	on	ADP
cjfa-35471	236	2	a	a	DET
cjfa-35471	236	3	constraint	constraint	NOUN
cjfa-35471	236	4	arc	arc	NOUN
cjfa-35471	236	5	on	on	ADP
cjfa-35471	236	6	which	which	PRON
cjfa-35471	236	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	236	8	)	)	PUNCT
cjfa-35471	236	9	=	=	SYM
cjfa-35471	236	10	0	0	NUM
cjfa-35471	236	11	for	for	ADP
cjfa-35471	236	12	a	a	DET
cjfa-35471	236	13	certain	certain	ADJ
cjfa-35471	236	14	period	period	NOUN
cjfa-35471	236	15	in	in	ADP
cjfa-35471	236	16	[	[	X
cjfa-35471	236	17	0	0	NUM
cjfa-35471	236	18	,	,	PUNCT
cjfa-35471	236	19	1	1	NUM
cjfa-35471	236	20	]	]	PUNCT
cjfa-35471	236	21	i.e.	i.e.	X
cjfa-35471	236	22	0	0	X
cjfa-35471	236	23	<	<	X
cjfa-35471	236	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	236	25	�	�	PROPN
cjfa-35471	236	26	≤	≤	X
cjfa-35471	236	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	236	28	≤	≤	PROPN
cjfa-35471	236	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	236	30	�	�	PROPN
cjfa-35471	236	31	<	<	X
cjfa-35471	236	32	1	1	NUM
cjfa-35471	236	33	we	we	PRON
cjfa-35471	236	34	have	have	VERB
cjfa-35471	236	35	;	;	PUNCT
cjfa-35471	236	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	236	37	�	�	PROPN
cjfa-35471	236	38	=	=	SYM
cjfa-35471	236	39	0	0	NUM
cjfa-35471	236	40	=	=	SYM
cjfa-35471	236	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	236	42	)	)	PUNCT
cjfa-35471	237	1	−	−	PROPN
cjfa-35471	237	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	237	3	)	)	PUNCT
cjfa-35471	237	4	implying	imply	VERB
cjfa-35471	237	5	that	that	SCONJ
cjfa-35471	237	6	over	over	ADP
cjfa-35471	237	7	this	this	DET
cjfa-35471	237	8	period	period	NOUN
cjfa-35471	237	9	a	a	DET
cjfa-35471	237	10	firm	firm	NOUN
cjfa-35471	237	11	will	will	AUX
cjfa-35471	237	12	produce	produce	VERB
cjfa-35471	237	13	just	just	ADV
cjfa-35471	237	14	enough	enough	ADJ
cjfa-35471	237	15	to	to	PART
cjfa-35471	237	16	meet	meet	VERB
cjfa-35471	237	17	the	the	DET
cjfa-35471	237	18	demand	demand	NOUN
cjfa-35471	237	19	,	,	PUNCT
cjfa-35471	237	20	which	which	PRON
cjfa-35471	237	21	is	be	AUX
cjfa-35471	237	22	assumed	assume	VERB
cjfa-35471	237	23	to	to	PART
cjfa-35471	237	24	be	be	AUX
cjfa-35471	237	25	nonzero	nonzero	NOUN
cjfa-35471	237	26	during	during	ADP
cjfa-35471	237	27	the	the	DET
cjfa-35471	237	28	planning	planning	NOUN
cjfa-35471	237	29	horizon	horizon	NOUN
cjfa-35471	237	30	.	.	PUNCT
cjfa-35471	238	1	implying	imply	VERB
cjfa-35471	238	2	that	that	SCONJ
cjfa-35471	238	3	i(t	i(t	NOUN
cjfa-35471	238	4	)	)	PUNCT
cjfa-35471	239	1	=	=	PUNCT
cjfa-35471	240	1	f	f	X
cjfa-35471	240	2	 	 	SPACE
cjfa-35471	240	3	t	t	PROPN
cjfa-35471	240	4	if	if	SCONJ
cjfa-35471	240	5	f	f	PROPN
cjfa-35471	240	6	is	be	AUX
cjfa-35471	240	7	constant	constant	ADJ
cjfa-35471	240	8	.	.	PUNCT
cjfa-35471	241	1	notice	notice	NOUN
cjfa-35471	241	2	also	also	ADV
cjfa-35471	241	3	that	that	SCONJ
cjfa-35471	241	4	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	241	5	�	�	PROPN
cjfa-35471	241	6	=	=	SYM
cjfa-35471	241	7	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	241	8	)	)	PUNCT
cjfa-35471	241	9	−	−	PROPN
cjfa-35471	242	1	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	242	2	)	)	PUNCT
cjfa-35471	242	3	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	242	4	)	)	PUNCT
cjfa-35471	242	5	=	=	SYM
cjfa-35471	242	6	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	242	7	�	�	PROPN
cjfa-35471	242	8	a	a	DET
cjfa-35471	242	9	given	give	VERB
cjfa-35471	242	10	number	number	NOUN
cjfa-35471	242	11	.	.	PUNCT
cjfa-35471	243	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	243	2	)	)	PUNCT
cjfa-35471	244	1	𝑢	𝑢	PROPN
cjfa-35471	244	2	0	0	NUM
cjfa-35471	244	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	244	4	)	)	PUNCT
cjfa-35471	244	5	𝑢	𝑢	ADP
cjfa-35471	244	6	0	0	NUM
cjfa-35471	244	7	with	with	ADP
cjfa-35471	244	8	the	the	DET
cjfa-35471	244	9	assumptions	assumption	NOUN
cjfa-35471	244	10	that	that	SCONJ
cjfa-35471	244	11	the	the	DET
cjfa-35471	244	12	demand	demand	NOUN
cjfa-35471	244	13	(	(	PUNCT
cjfa-35471	244	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	244	15	(	(	PUNCT
cjfa-35471	244	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	244	17	)	)	PUNCT
cjfa-35471	244	18	)	)	PUNCT
cjfa-35471	244	19	is	be	AUX
cjfa-35471	244	20	a	a	DET
cjfa-35471	244	21	simple	simple	ADJ
cjfa-35471	244	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	244	23	function	function	NOUN
cjfa-35471	244	24	and	and	CCONJ
cjfa-35471	244	25	the	the	DET
cjfa-35471	244	26	interest	interest	NOUN
cjfa-35471	244	27	rate	rate	NOUN
cjfa-35471	244	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	244	29	)	)	PUNCT
cjfa-35471	244	30	is	be	AUX
cjfa-35471	244	31	time	time	NOUN
cjfa-35471	244	32	dependent	dependent	ADJ
cjfa-35471	244	33	,	,	PUNCT
cjfa-35471	244	34	i.e.	i.e.	X
cjfa-35471	244	35	:	:	PUNCT
cjfa-35471	244	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	244	37	)	)	PUNCT
cjfa-35471	245	1	=	=	SYM
cjfa-35471	245	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	245	3	𝐴	𝐴	PROPN
cjfa-35471	245	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	245	5	)	)	PUNCT
cjfa-35471	245	6	with	with	ADP
cjfa-35471	245	7	no	no	DET
cjfa-35471	245	8	growth	growth	NOUN
cjfa-35471	245	9	,	,	PUNCT
cjfa-35471	245	10	and	and	CCONJ
cjfa-35471	245	11	,	,	PUNCT
cjfa-35471	245	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	245	13	)	)	PUNCT
cjfa-35471	245	14	=	=	SYM
cjfa-35471	245	15	�	�	PROPN
cjfa-35471	245	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	245	17	�	�	PROPN
cjfa-35471	245	18	�	�	PROPN
cjfa-35471	245	19	implying	imply	VERB
cjfa-35471	245	20	that	that	SCONJ
cjfa-35471	245	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	245	22	)	)	PUNCT
cjfa-35471	246	1	=	=	VERB
cjfa-35471	246	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	246	3	if	if	SCONJ
cjfa-35471	246	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	246	5	is	be	AUX
cjfa-35471	246	6	constant	constant	ADJ
cjfa-35471	246	7	.	.	PUNCT
cjfa-35471	247	1	notice	notice	NOUN
cjfa-35471	247	2	also	also	ADV
cjfa-35471	247	3	that	that	SCONJ
cjfa-35471	247	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	247	5	�	�	X
cjfa-35471	247	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	247	7	)	)	PUNCT
cjfa-35471	247	8	=	=	SYM
cjfa-35471	247	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	247	10	)	)	PUNCT
cjfa-35471	247	11	where	where	SCONJ
cjfa-35471	247	12	f	f	PROPN
cjfa-35471	247	13	(	(	PUNCT
cjfa-35471	247	14	t	t	PROPN
cjfa-35471	247	15	)	)	PUNCT
cjfa-35471	247	16	denotes	denote	NOUN
cjfa-35471	247	17	time	time	VERB
cjfa-35471	247	18	dependent	dependent	ADJ
cjfa-35471	247	19	interest	interest	NOUN
cjfa-35471	247	20	rate	rate	NOUN
cjfa-35471	247	21	.	.	PUNCT
cjfa-35471	248	1	for	for	ADP
cjfa-35471	248	2	ease	ease	NOUN
cjfa-35471	248	3	of	of	ADP
cjfa-35471	248	4	analysis	analysis	NOUN
cjfa-35471	248	5	we	we	PRON
cjfa-35471	248	6	will	will	AUX
cjfa-35471	248	7	assume	assume	VERB
cjfa-35471	248	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	248	9	)	)	PUNCT
cjfa-35471	248	10	to	to	PART
cjfa-35471	248	11	be	be	AUX
cjfa-35471	248	12	constant	constant	ADJ
cjfa-35471	248	13	.	.	PUNCT
cjfa-35471	249	1	the	the	DET
cjfa-35471	249	2	letter	letter	NOUN
cjfa-35471	249	3	k	k	PROPN
cjfa-35471	249	4	denotes	denote	VERB
cjfa-35471	249	5	the	the	DET
cjfa-35471	249	6	periodicity	periodicity	NOUN
cjfa-35471	249	7	of	of	ADP
cjfa-35471	249	8	the	the	DET
cjfa-35471	249	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	249	10	demand	demand	NOUN
cjfa-35471	249	11	function	function	NOUN
cjfa-35471	249	12	over	over	ADP
cjfa-35471	249	13	the	the	DET
cjfa-35471	249	14	planning	planning	NOUN
cjfa-35471	249	15	period	period	NOUN
cjfa-35471	249	16	.	.	PUNCT
cjfa-35471	250	1	the	the	DET
cjfa-35471	250	2	only	only	ADJ
cjfa-35471	250	3	reason	reason	NOUN
cjfa-35471	250	4	for	for	ADP
cjfa-35471	250	5	the	the	DET
cjfa-35471	250	6	use	use	NOUN
cjfa-35471	250	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	250	8	demand	demand	NOUN
cjfa-35471	250	9	curve	curve	NOUN
cjfa-35471	250	10	is	be	AUX
cjfa-35471	250	11	that	that	SCONJ
cjfa-35471	250	12	it	it	PRON
cjfa-35471	250	13	represents	represent	VERB
cjfa-35471	250	14	cyclicality	cyclicality	NOUN
cjfa-35471	250	15	(	(	PUNCT
cjfa-35471	250	16	a	a	DET
cjfa-35471	250	17	measure	measure	NOUN
cjfa-35471	250	18	of	of	ADP
cjfa-35471	250	19	risk	risk	NOUN
cjfa-35471	250	20	)	)	PUNCT
cjfa-35471	250	21	and	and	CCONJ
cjfa-35471	250	22	that	that	SCONJ
cjfa-35471	250	23	it	it	PRON
cjfa-35471	250	24	is	be	AUX
cjfa-35471	250	25	easier	easy	ADJ
cjfa-35471	250	26	to	to	PART
cjfa-35471	250	27	work	work	VERB
cjfa-35471	250	28	with	with	ADP
cjfa-35471	250	29	it	it	PRON
cjfa-35471	250	30	.	.	PUNCT
cjfa-35471	251	1	the	the	DET
cjfa-35471	251	2	appropriate	appropriate	ADJ
cjfa-35471	251	3	lagrangian	lagrangian	NOUN
cjfa-35471	251	4	for	for	ADP
cjfa-35471	251	5	this	this	DET
cjfa-35471	251	6	problem	problem	NOUN
cjfa-35471	251	7	is	be	AUX
cjfa-35471	251	8	:	:	PUNCT
cjfa-35471	251	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	251	10	=	=	SYM
cjfa-35471	251	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	251	12	�	�	PROPN
cjfa-35471	251	13	�	�	PROPN
cjfa-35471	251	14	(	(	PUNCT
cjfa-35471	251	15	�	�	PROPN
cjfa-35471	251	16	)	)	PUNCT
cjfa-35471	251	17	�	�	PROPN
cjfa-35471	251	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	251	19	�	�	PROPN
cjfa-35471	251	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	251	21	)	)	PUNCT
cjfa-35471	251	22	�	�	PROPN
cjfa-35471	251	23	𝐴	𝐴	PROPN
cjfa-35471	251	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	251	25	)	)	PUNCT
cjfa-35471	251	26	�	�	PROPN
cjfa-35471	251	27	𝐴	𝐴	PROPN
cjfa-35471	251	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	251	29	�	�	PROPN
cjfa-35471	251	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	251	31	)	)	PUNCT
cjfa-35471	251	32	−	−	PROPN
cjfa-35471	251	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	251	34	)	)	PUNCT
cjfa-35471	251	35	�	�	PROPN
cjfa-35471	251	36	𝐴	𝐴	PROPN
cjfa-35471	251	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	251	38	�	�	PROPN
cjfa-35471	251	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	251	40	)	)	PUNCT
cjfa-35471	251	41	−	−	PROPN
cjfa-35471	251	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	251	43	)	)	PUNCT
cjfa-35471	251	44	�	�	PROPN
cjfa-35471	251	45	then	then	ADV
cjfa-35471	251	46	the	the	DET
cjfa-35471	251	47	necessary	necessary	ADJ
cjfa-35471	251	48	conditions	condition	NOUN
cjfa-35471	251	49	are	be	AUX
cjfa-35471	251	50	:	:	PUNCT
cjfa-35471	251	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	251	52	�	�	PROPN
cjfa-35471	251	53	�	�	PROPN
cjfa-35471	251	54	(	(	PUNCT
cjfa-35471	251	55	�	�	NOUN
cjfa-35471	251	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	251	57	�	�	PROPN
cjfa-35471	251	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	251	59	)	)	PUNCT
cjfa-35471	251	60	𝐴	𝐴	PROPN
cjfa-35471	251	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	251	62	)	)	PUNCT
cjfa-35471	251	63	−	−	PROPN
cjfa-35471	251	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	251	65	)	)	PUNCT
cjfa-35471	252	1	=	=	SYM
cjfa-35471	252	2	0	0	PUNCT
cjfa-35471	252	3	(	(	PUNCT
cjfa-35471	252	4	1	1	NUM
cjfa-35471	252	5	)	)	PUNCT
cjfa-35471	252	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	252	7	�	�	PROPN
cjfa-35471	252	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	252	9	)	)	PUNCT
cjfa-35471	252	10	=	=	SYM
cjfa-35471	252	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	252	12	�	�	PROPN
cjfa-35471	252	13	�	�	PROPN
cjfa-35471	252	14	(	(	PUNCT
cjfa-35471	252	15	�	�	PROPN
cjfa-35471	252	16	)ℎ	)ℎ	PROPN
cjfa-35471	252	17	(	(	PUNCT
cjfa-35471	252	18	2	2	X
cjfa-35471	252	19	)	)	PUNCT
cjfa-35471	252	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	252	21	�	�	PROPN
cjfa-35471	252	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	252	23	)	)	PUNCT
cjfa-35471	252	24	=	=	SYM
cjfa-35471	252	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	252	26	)	)	PUNCT
cjfa-35471	252	27	−	−	PROPN
cjfa-35471	252	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	252	29	)	)	PUNCT
cjfa-35471	252	30	(	(	PUNCT
cjfa-35471	252	31	3	3	X
cjfa-35471	252	32	)	)	PUNCT
cjfa-35471	252	33	necessary	necessary	ADJ
cjfa-35471	252	34	conditions	condition	NOUN
cjfa-35471	252	35	are	be	AUX
cjfa-35471	252	36	also	also	ADV
cjfa-35471	252	37	sufficient	sufficient	ADJ
cjfa-35471	252	38	since	since	SCONJ
cjfa-35471	252	39	the	the	DET
cjfa-35471	252	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	252	41	is	be	AUX
cjfa-35471	252	42	convex	convex	ADJ
cjfa-35471	252	43	in	in	ADP
cjfa-35471	252	44	both	both	CCONJ
cjfa-35471	252	45	the	the	DET
cjfa-35471	252	46	control	control	NOUN
cjfa-35471	252	47	(	(	PUNCT
cjfa-35471	252	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	252	49	)	)	PUNCT
cjfa-35471	252	50	and	and	CCONJ
cjfa-35471	252	51	state	state	NOUN
cjfa-35471	252	52	(	(	PUNCT
cjfa-35471	252	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	252	54	)	)	PUNCT
cjfa-35471	252	55	variables	variable	NOUN
cjfa-35471	252	56	.	.	PUNCT
cjfa-35471	253	1	the	the	DET
cjfa-35471	253	2	planning	planning	NOUN
cjfa-35471	253	3	horizon	horizon	NOUN
cjfa-35471	253	4	(	(	PUNCT
cjfa-35471	253	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	253	6	)	)	PUNCT
cjfa-35471	253	7	will	will	AUX
cjfa-35471	253	8	be	be	AUX
cjfa-35471	253	9	assumed	assume	VERB
cjfa-35471	253	10	one	one	NUM
cjfa-35471	253	11	.	.	PUNCT
cjfa-35471	254	1	on	on	ADP
cjfa-35471	254	2	a	a	DET
cjfa-35471	254	3	constraint	constraint	NOUN
cjfa-35471	254	4	arc	arc	NOUN
cjfa-35471	254	5	on	on	ADP
cjfa-35471	254	6	which	which	PRON
cjfa-35471	254	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	254	8	)	)	PUNCT
cjfa-35471	254	9	=	=	SYM
cjfa-35471	254	10	0	0	NUM
cjfa-35471	254	11	for	for	ADP
cjfa-35471	254	12	a	a	DET
cjfa-35471	254	13	certain	certain	ADJ
cjfa-35471	254	14	period	period	NOUN
cjfa-35471	254	15	in	in	ADP
cjfa-35471	254	16	[	[	X
cjfa-35471	254	17	0	0	NUM
cjfa-35471	254	18	,	,	PUNCT
cjfa-35471	254	19	1	1	NUM
cjfa-35471	254	20	]	]	PUNCT
cjfa-35471	254	21	i.e.	i.e.	X
cjfa-35471	254	22	0	0	X
cjfa-35471	254	23	<	<	X
cjfa-35471	254	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	254	25	�	�	PROPN
cjfa-35471	254	26	≤	≤	X
cjfa-35471	254	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	254	28	≤	≤	PROPN
cjfa-35471	254	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	254	30	�	�	PROPN
cjfa-35471	254	31	<	<	X
cjfa-35471	254	32	1	1	NUM
cjfa-35471	254	33	we	we	PRON
cjfa-35471	254	34	have	have	VERB
cjfa-35471	254	35	;	;	PUNCT
cjfa-35471	254	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	254	37	�	�	PROPN
cjfa-35471	254	38	=	=	SYM
cjfa-35471	254	39	0	0	NUM
cjfa-35471	254	40	=	=	SYM
cjfa-35471	254	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	254	42	)	)	PUNCT
cjfa-35471	255	1	−	−	PROPN
cjfa-35471	255	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	255	3	)	)	PUNCT
cjfa-35471	255	4	implying	imply	VERB
cjfa-35471	255	5	that	that	SCONJ
cjfa-35471	255	6	over	over	ADP
cjfa-35471	255	7	this	this	DET
cjfa-35471	255	8	period	period	NOUN
cjfa-35471	255	9	a	a	DET
cjfa-35471	255	10	firm	firm	NOUN
cjfa-35471	255	11	will	will	AUX
cjfa-35471	255	12	produce	produce	VERB
cjfa-35471	255	13	just	just	ADV
cjfa-35471	255	14	enough	enough	ADJ
cjfa-35471	255	15	to	to	PART
cjfa-35471	255	16	meet	meet	VERB
cjfa-35471	255	17	the	the	DET
cjfa-35471	255	18	demand	demand	NOUN
cjfa-35471	255	19	,	,	PUNCT
cjfa-35471	255	20	which	which	PRON
cjfa-35471	255	21	is	be	AUX
cjfa-35471	255	22	assumed	assume	VERB
cjfa-35471	255	23	to	to	PART
cjfa-35471	255	24	be	be	AUX
cjfa-35471	255	25	nonzero	nonzero	NOUN
cjfa-35471	255	26	during	during	ADP
cjfa-35471	255	27	the	the	DET
cjfa-35471	255	28	planning	planning	NOUN
cjfa-35471	255	29	horizon	horizon	NOUN
cjfa-35471	255	30	.	.	PUNCT
cjfa-35471	256	1	where	where	SCONJ
cjfa-35471	256	2	f	f	PROPN
cjfa-35471	256	3	(	(	PUNCT
cjfa-35471	256	4	t	t	PROPN
cjfa-35471	256	5	)	)	PUNCT
cjfa-35471	256	6	denotes	denote	NOUN
cjfa-35471	256	7	time	time	VERB
cjfa-35471	256	8	dependent	dependent	ADJ
cjfa-35471	256	9	interest	interest	NOUN
cjfa-35471	256	10	rate	rate	NOUN
cjfa-35471	256	11	.	.	PUNCT
cjfa-35471	257	1	for	for	ADP
cjfa-35471	257	2	ease	ease	NOUN
cjfa-35471	257	3	of	of	ADP
cjfa-35471	257	4	analysis	analysis	NOUN
cjfa-35471	257	5	we	we	PRON
cjfa-35471	257	6	will	will	AUX
cjfa-35471	257	7	assume	assume	VERB
cjfa-35471	257	8	f(t	f(t	PROPN
cjfa-35471	257	9	)	)	PUNCT
cjfa-35471	257	10	to	to	PART
cjfa-35471	257	11	be	be	AUX
cjfa-35471	257	12	constant	constant	ADJ
cjfa-35471	257	13	.	.	PUNCT
cjfa-35471	258	1	the	the	DET
cjfa-35471	258	2	letter	letter	NOUN
cjfa-35471	258	3	k	k	PROPN
cjfa-35471	258	4	denotes	denote	VERB
cjfa-35471	258	5	the	the	DET
cjfa-35471	258	6	periodicity	periodicity	NOUN
cjfa-35471	258	7	of	of	ADP
cjfa-35471	258	8	the	the	DET
cjfa-35471	258	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	258	10	demand	demand	NOUN
cjfa-35471	258	11	function	function	NOUN
cjfa-35471	258	12	over	over	ADP
cjfa-35471	258	13	the	the	DET
cjfa-35471	258	14	planning	planning	NOUN
cjfa-35471	258	15	period	period	NOUN
cjfa-35471	258	16	.	.	PUNCT
cjfa-35471	259	1	the	the	DET
cjfa-35471	259	2	only	only	ADJ
cjfa-35471	259	3	reason	reason	NOUN
cjfa-35471	259	4	for	for	ADP
cjfa-35471	259	5	the	the	DET
cjfa-35471	259	6	use	use	NOUN
cjfa-35471	259	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	259	8	demand	demand	NOUN
cjfa-35471	259	9	curve	curve	NOUN
cjfa-35471	259	10	is	be	AUX
cjfa-35471	259	11	that	that	SCONJ
cjfa-35471	259	12	it	it	PRON
cjfa-35471	259	13	represents	represent	VERB
cjfa-35471	259	14	cyclicality	cyclicality	NOUN
cjfa-35471	259	15	(	(	PUNCT
cjfa-35471	259	16	a	a	DET
cjfa-35471	259	17	measure	measure	NOUN
cjfa-35471	259	18	of	of	ADP
cjfa-35471	259	19	risk	risk	NOUN
cjfa-35471	259	20	)	)	PUNCT
cjfa-35471	259	21	and	and	CCONJ
cjfa-35471	259	22	that	that	SCONJ
cjfa-35471	259	23	it	it	PRON
cjfa-35471	259	24	is	be	AUX
cjfa-35471	259	25	easier	easy	ADJ
cjfa-35471	259	26	to	to	PART
cjfa-35471	259	27	work	work	VERB
cjfa-35471	259	28	with	with	ADP
cjfa-35471	259	29	it	it	PRON
cjfa-35471	259	30	.	.	PUNCT
cjfa-35471	260	1	the	the	DET
cjfa-35471	260	2	appropriate	appropriate	ADJ
cjfa-35471	260	3	lagrangian	lagrangian	NOUN
cjfa-35471	260	4	for	for	ADP
cjfa-35471	260	5	this	this	DET
cjfa-35471	260	6	problem	problem	NOUN
cjfa-35471	260	7	is	be	AUX
cjfa-35471	260	8	:	:	PUNCT
cjfa-35471	260	9	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	260	10	�	�	PROPN
cjfa-35471	260	11	=	=	SYM
cjfa-35471	260	12	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	260	13	)	)	PUNCT
cjfa-35471	260	14	−	−	PROPN
cjfa-35471	260	15	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	260	16	)	)	PUNCT
cjfa-35471	260	17	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	260	18	)	)	PUNCT
cjfa-35471	260	19	=	=	SYM
cjfa-35471	260	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	260	21	�	�	PROPN
cjfa-35471	260	22	a	a	DET
cjfa-35471	260	23	given	give	VERB
cjfa-35471	260	24	number	number	NOUN
cjfa-35471	260	25	.	.	PUNCT
cjfa-35471	261	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	261	2	)	)	PUNCT
cjfa-35471	262	1	𝑢	𝑢	PROPN
cjfa-35471	262	2	0	0	NUM
cjfa-35471	262	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	262	4	)	)	PUNCT
cjfa-35471	262	5	𝑢	𝑢	ADP
cjfa-35471	262	6	0	0	NUM
cjfa-35471	262	7	with	with	ADP
cjfa-35471	262	8	the	the	DET
cjfa-35471	262	9	assumptions	assumption	NOUN
cjfa-35471	262	10	that	that	SCONJ
cjfa-35471	262	11	the	the	DET
cjfa-35471	262	12	demand	demand	NOUN
cjfa-35471	262	13	(	(	PUNCT
cjfa-35471	262	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	262	15	(	(	PUNCT
cjfa-35471	262	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	262	17	)	)	PUNCT
cjfa-35471	262	18	)	)	PUNCT
cjfa-35471	262	19	is	be	AUX
cjfa-35471	262	20	a	a	DET
cjfa-35471	262	21	simple	simple	ADJ
cjfa-35471	262	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	262	23	function	function	NOUN
cjfa-35471	262	24	and	and	CCONJ
cjfa-35471	262	25	the	the	DET
cjfa-35471	262	26	interest	interest	NOUN
cjfa-35471	262	27	rate	rate	NOUN
cjfa-35471	262	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	262	29	)	)	PUNCT
cjfa-35471	262	30	is	be	AUX
cjfa-35471	262	31	time	time	NOUN
cjfa-35471	262	32	dependent	dependent	ADJ
cjfa-35471	262	33	,	,	PUNCT
cjfa-35471	262	34	i.e.	i.e.	X
cjfa-35471	262	35	:	:	PUNCT
cjfa-35471	262	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	262	37	)	)	PUNCT
cjfa-35471	263	1	=	=	SYM
cjfa-35471	263	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	263	3	𝐴	𝐴	PROPN
cjfa-35471	263	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	263	5	)	)	PUNCT
cjfa-35471	263	6	with	with	ADP
cjfa-35471	263	7	no	no	DET
cjfa-35471	263	8	growth	growth	NOUN
cjfa-35471	263	9	,	,	PUNCT
cjfa-35471	263	10	and	and	CCONJ
cjfa-35471	263	11	,	,	PUNCT
cjfa-35471	263	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	263	13	)	)	PUNCT
cjfa-35471	263	14	=	=	SYM
cjfa-35471	263	15	�	�	PROPN
cjfa-35471	263	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	263	17	�	�	PROPN
cjfa-35471	263	18	�	�	PROPN
cjfa-35471	263	19	implying	imply	VERB
cjfa-35471	263	20	that	that	SCONJ
cjfa-35471	263	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	263	22	)	)	PUNCT
cjfa-35471	264	1	=	=	VERB
cjfa-35471	264	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	264	3	if	if	SCONJ
cjfa-35471	264	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	264	5	is	be	AUX
cjfa-35471	264	6	constant	constant	ADJ
cjfa-35471	264	7	.	.	PUNCT
cjfa-35471	265	1	notice	notice	NOUN
cjfa-35471	265	2	also	also	ADV
cjfa-35471	265	3	that	that	SCONJ
cjfa-35471	265	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	265	5	�	�	X
cjfa-35471	265	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	265	7	)	)	PUNCT
cjfa-35471	265	8	=	=	SYM
cjfa-35471	265	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	265	10	)	)	PUNCT
cjfa-35471	265	11	where	where	SCONJ
cjfa-35471	265	12	f	f	PROPN
cjfa-35471	265	13	(	(	PUNCT
cjfa-35471	265	14	t	t	PROPN
cjfa-35471	265	15	)	)	PUNCT
cjfa-35471	265	16	denotes	denote	NOUN
cjfa-35471	265	17	time	time	VERB
cjfa-35471	265	18	dependent	dependent	ADJ
cjfa-35471	265	19	interest	interest	NOUN
cjfa-35471	265	20	rate	rate	NOUN
cjfa-35471	265	21	.	.	PUNCT
cjfa-35471	266	1	for	for	ADP
cjfa-35471	266	2	ease	ease	NOUN
cjfa-35471	266	3	of	of	ADP
cjfa-35471	266	4	analysis	analysis	NOUN
cjfa-35471	266	5	we	we	PRON
cjfa-35471	266	6	will	will	AUX
cjfa-35471	266	7	assume	assume	VERB
cjfa-35471	266	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	266	9	)	)	PUNCT
cjfa-35471	266	10	to	to	PART
cjfa-35471	266	11	be	be	AUX
cjfa-35471	266	12	constant	constant	ADJ
cjfa-35471	266	13	.	.	PUNCT
cjfa-35471	267	1	the	the	DET
cjfa-35471	267	2	letter	letter	NOUN
cjfa-35471	267	3	k	k	PROPN
cjfa-35471	267	4	denotes	denote	VERB
cjfa-35471	267	5	the	the	DET
cjfa-35471	267	6	periodicity	periodicity	NOUN
cjfa-35471	267	7	of	of	ADP
cjfa-35471	267	8	the	the	DET
cjfa-35471	267	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	267	10	demand	demand	NOUN
cjfa-35471	267	11	function	function	NOUN
cjfa-35471	267	12	over	over	ADP
cjfa-35471	267	13	the	the	DET
cjfa-35471	267	14	planning	planning	NOUN
cjfa-35471	267	15	period	period	NOUN
cjfa-35471	267	16	.	.	PUNCT
cjfa-35471	268	1	the	the	DET
cjfa-35471	268	2	only	only	ADJ
cjfa-35471	268	3	reason	reason	NOUN
cjfa-35471	268	4	for	for	ADP
cjfa-35471	268	5	the	the	DET
cjfa-35471	268	6	use	use	NOUN
cjfa-35471	268	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	268	8	demand	demand	NOUN
cjfa-35471	268	9	curve	curve	NOUN
cjfa-35471	268	10	is	be	AUX
cjfa-35471	268	11	that	that	SCONJ
cjfa-35471	268	12	it	it	PRON
cjfa-35471	268	13	represents	represent	VERB
cjfa-35471	268	14	cyclicality	cyclicality	NOUN
cjfa-35471	268	15	(	(	PUNCT
cjfa-35471	268	16	a	a	DET
cjfa-35471	268	17	measure	measure	NOUN
cjfa-35471	268	18	of	of	ADP
cjfa-35471	268	19	risk	risk	NOUN
cjfa-35471	268	20	)	)	PUNCT
cjfa-35471	268	21	and	and	CCONJ
cjfa-35471	268	22	that	that	SCONJ
cjfa-35471	268	23	it	it	PRON
cjfa-35471	268	24	is	be	AUX
cjfa-35471	268	25	easier	easy	ADJ
cjfa-35471	268	26	to	to	PART
cjfa-35471	268	27	work	work	VERB
cjfa-35471	268	28	with	with	ADP
cjfa-35471	268	29	it	it	PRON
cjfa-35471	268	30	.	.	PUNCT
cjfa-35471	269	1	the	the	DET
cjfa-35471	269	2	appropriate	appropriate	ADJ
cjfa-35471	269	3	lagrangian	lagrangian	NOUN
cjfa-35471	269	4	for	for	ADP
cjfa-35471	269	5	this	this	DET
cjfa-35471	269	6	problem	problem	NOUN
cjfa-35471	269	7	is	be	AUX
cjfa-35471	269	8	:	:	PUNCT
cjfa-35471	269	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	269	10	=	=	SYM
cjfa-35471	269	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	269	12	�	�	PROPN
cjfa-35471	269	13	�	�	PROPN
cjfa-35471	269	14	(	(	PUNCT
cjfa-35471	269	15	�	�	PROPN
cjfa-35471	269	16	)	)	PUNCT
cjfa-35471	269	17	�	�	PROPN
cjfa-35471	269	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	269	19	�	�	PROPN
cjfa-35471	269	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	269	21	)	)	PUNCT
cjfa-35471	269	22	�	�	PROPN
cjfa-35471	269	23	𝐴	𝐴	PROPN
cjfa-35471	269	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	269	25	)	)	PUNCT
cjfa-35471	269	26	�	�	PROPN
cjfa-35471	269	27	𝐴	𝐴	PROPN
cjfa-35471	269	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	269	29	�	�	PROPN
cjfa-35471	269	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	269	31	)	)	PUNCT
cjfa-35471	269	32	−	−	PROPN
cjfa-35471	269	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	269	34	)	)	PUNCT
cjfa-35471	269	35	�	�	PROPN
cjfa-35471	269	36	𝐴	𝐴	PROPN
cjfa-35471	269	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	269	38	�	�	PROPN
cjfa-35471	269	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	269	40	)	)	PUNCT
cjfa-35471	269	41	−	−	PROPN
cjfa-35471	269	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	269	43	)	)	PUNCT
cjfa-35471	269	44	�	�	PROPN
cjfa-35471	269	45	then	then	ADV
cjfa-35471	269	46	the	the	DET
cjfa-35471	269	47	necessary	necessary	ADJ
cjfa-35471	269	48	conditions	condition	NOUN
cjfa-35471	269	49	are	be	AUX
cjfa-35471	269	50	:	:	PUNCT
cjfa-35471	269	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	269	52	�	�	PROPN
cjfa-35471	269	53	�	�	PROPN
cjfa-35471	269	54	(	(	PUNCT
cjfa-35471	269	55	�	�	NOUN
cjfa-35471	269	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	269	57	�	�	PROPN
cjfa-35471	269	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	269	59	)	)	PUNCT
cjfa-35471	269	60	𝐴	𝐴	PROPN
cjfa-35471	269	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	269	62	)	)	PUNCT
cjfa-35471	269	63	−	−	PROPN
cjfa-35471	269	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	269	65	)	)	PUNCT
cjfa-35471	270	1	=	=	SYM
cjfa-35471	270	2	0	0	PUNCT
cjfa-35471	270	3	(	(	PUNCT
cjfa-35471	270	4	1	1	NUM
cjfa-35471	270	5	)	)	PUNCT
cjfa-35471	270	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	270	7	�	�	PROPN
cjfa-35471	270	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	270	9	)	)	PUNCT
cjfa-35471	270	10	=	=	SYM
cjfa-35471	270	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	270	12	�	�	PROPN
cjfa-35471	270	13	�	�	PROPN
cjfa-35471	270	14	(	(	PUNCT
cjfa-35471	270	15	�	�	PROPN
cjfa-35471	270	16	)ℎ	)ℎ	PROPN
cjfa-35471	270	17	(	(	PUNCT
cjfa-35471	270	18	2	2	X
cjfa-35471	270	19	)	)	PUNCT
cjfa-35471	270	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	270	21	�	�	PROPN
cjfa-35471	270	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	270	23	)	)	PUNCT
cjfa-35471	270	24	=	=	SYM
cjfa-35471	270	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	270	26	)	)	PUNCT
cjfa-35471	270	27	−	−	PROPN
cjfa-35471	270	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	270	29	)	)	PUNCT
cjfa-35471	270	30	(	(	PUNCT
cjfa-35471	270	31	3	3	X
cjfa-35471	270	32	)	)	PUNCT
cjfa-35471	270	33	necessary	necessary	ADJ
cjfa-35471	270	34	conditions	condition	NOUN
cjfa-35471	270	35	are	be	AUX
cjfa-35471	270	36	also	also	ADV
cjfa-35471	270	37	sufficient	sufficient	ADJ
cjfa-35471	270	38	since	since	SCONJ
cjfa-35471	270	39	the	the	DET
cjfa-35471	270	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	270	41	is	be	AUX
cjfa-35471	270	42	convex	convex	ADJ
cjfa-35471	270	43	in	in	ADP
cjfa-35471	270	44	both	both	CCONJ
cjfa-35471	270	45	the	the	DET
cjfa-35471	270	46	control	control	NOUN
cjfa-35471	270	47	(	(	PUNCT
cjfa-35471	270	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	270	49	)	)	PUNCT
cjfa-35471	270	50	and	and	CCONJ
cjfa-35471	270	51	state	state	NOUN
cjfa-35471	270	52	(	(	PUNCT
cjfa-35471	270	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	270	54	)	)	PUNCT
cjfa-35471	270	55	variables	variable	NOUN
cjfa-35471	270	56	.	.	PUNCT
cjfa-35471	271	1	the	the	DET
cjfa-35471	271	2	planning	planning	NOUN
cjfa-35471	271	3	horizon	horizon	NOUN
cjfa-35471	271	4	(	(	PUNCT
cjfa-35471	271	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	271	6	)	)	PUNCT
cjfa-35471	271	7	will	will	AUX
cjfa-35471	271	8	be	be	AUX
cjfa-35471	271	9	assumed	assume	VERB
cjfa-35471	271	10	one	one	NUM
cjfa-35471	271	11	.	.	PUNCT
cjfa-35471	272	1	on	on	ADP
cjfa-35471	272	2	a	a	DET
cjfa-35471	272	3	constraint	constraint	NOUN
cjfa-35471	272	4	arc	arc	NOUN
cjfa-35471	272	5	on	on	ADP
cjfa-35471	272	6	which	which	PRON
cjfa-35471	272	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	272	8	)	)	PUNCT
cjfa-35471	272	9	=	=	SYM
cjfa-35471	272	10	0	0	NUM
cjfa-35471	272	11	for	for	ADP
cjfa-35471	272	12	a	a	DET
cjfa-35471	272	13	certain	certain	ADJ
cjfa-35471	272	14	period	period	NOUN
cjfa-35471	272	15	in	in	ADP
cjfa-35471	272	16	[	[	X
cjfa-35471	272	17	0	0	NUM
cjfa-35471	272	18	,	,	PUNCT
cjfa-35471	272	19	1	1	NUM
cjfa-35471	272	20	]	]	PUNCT
cjfa-35471	272	21	i.e.	i.e.	X
cjfa-35471	272	22	0	0	X
cjfa-35471	272	23	<	<	X
cjfa-35471	272	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	272	25	�	�	PROPN
cjfa-35471	272	26	≤	≤	X
cjfa-35471	272	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	272	28	≤	≤	PROPN
cjfa-35471	272	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	272	30	�	�	PROPN
cjfa-35471	272	31	<	<	X
cjfa-35471	272	32	1	1	NUM
cjfa-35471	272	33	we	we	PRON
cjfa-35471	272	34	have	have	VERB
cjfa-35471	272	35	;	;	PUNCT
cjfa-35471	272	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	272	37	�	�	PROPN
cjfa-35471	272	38	=	=	SYM
cjfa-35471	272	39	0	0	NUM
cjfa-35471	272	40	=	=	SYM
cjfa-35471	272	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	272	42	)	)	PUNCT
cjfa-35471	273	1	−	−	PROPN
cjfa-35471	273	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	273	3	)	)	PUNCT
cjfa-35471	273	4	implying	imply	VERB
cjfa-35471	273	5	that	that	SCONJ
cjfa-35471	273	6	over	over	ADP
cjfa-35471	273	7	this	this	DET
cjfa-35471	273	8	period	period	NOUN
cjfa-35471	273	9	a	a	DET
cjfa-35471	273	10	firm	firm	NOUN
cjfa-35471	273	11	will	will	AUX
cjfa-35471	273	12	produce	produce	VERB
cjfa-35471	273	13	just	just	ADV
cjfa-35471	273	14	enough	enough	ADJ
cjfa-35471	273	15	to	to	PART
cjfa-35471	273	16	meet	meet	VERB
cjfa-35471	273	17	the	the	DET
cjfa-35471	273	18	demand	demand	NOUN
cjfa-35471	273	19	,	,	PUNCT
cjfa-35471	273	20	which	which	PRON
cjfa-35471	273	21	is	be	AUX
cjfa-35471	273	22	assumed	assume	VERB
cjfa-35471	273	23	to	to	PART
cjfa-35471	273	24	be	be	AUX
cjfa-35471	273	25	nonzero	nonzero	NOUN
cjfa-35471	273	26	during	during	ADP
cjfa-35471	273	27	the	the	DET
cjfa-35471	273	28	planning	planning	NOUN
cjfa-35471	273	29	horizon	horizon	NOUN
cjfa-35471	273	30	.	.	PUNCT
cjfa-35471	274	1	optimal	optimal	ADJ
cjfa-35471	274	2	incentives	incentive	NOUN
cjfa-35471	274	3	for	for	ADP
cjfa-35471	274	4	economic	economic	ADJ
cjfa-35471	274	5	growth	growth	NOUN
cjfa-35471	274	6	…	…	PUNCT
cjfa-35471	274	7	15	15	NUM
cjfa-35471	274	8	then	then	ADV
cjfa-35471	274	9	the	the	DET
cjfa-35471	274	10	necessary	necessary	ADJ
cjfa-35471	274	11	conditions	condition	NOUN
cjfa-35471	274	12	are	be	AUX
cjfa-35471	274	13	:	:	PUNCT
cjfa-35471	274	14	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	274	15	�	�	PROPN
cjfa-35471	274	16	=	=	SYM
cjfa-35471	274	17	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	274	18	)	)	PUNCT
cjfa-35471	274	19	−	−	PROPN
cjfa-35471	274	20	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	274	21	)	)	PUNCT
cjfa-35471	274	22	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	274	23	)	)	PUNCT
cjfa-35471	274	24	=	=	SYM
cjfa-35471	274	25	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	274	26	�	�	PROPN
cjfa-35471	274	27	a	a	DET
cjfa-35471	274	28	given	give	VERB
cjfa-35471	274	29	number	number	NOUN
cjfa-35471	274	30	.	.	PUNCT
cjfa-35471	275	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	275	2	)	)	PUNCT
cjfa-35471	276	1	𝑢	𝑢	PROPN
cjfa-35471	276	2	0	0	NUM
cjfa-35471	276	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	276	4	)	)	PUNCT
cjfa-35471	276	5	𝑢	𝑢	ADP
cjfa-35471	276	6	0	0	NUM
cjfa-35471	276	7	with	with	ADP
cjfa-35471	276	8	the	the	DET
cjfa-35471	276	9	assumptions	assumption	NOUN
cjfa-35471	276	10	that	that	SCONJ
cjfa-35471	276	11	the	the	DET
cjfa-35471	276	12	demand	demand	NOUN
cjfa-35471	276	13	(	(	PUNCT
cjfa-35471	276	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	276	15	(	(	PUNCT
cjfa-35471	276	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	276	17	)	)	PUNCT
cjfa-35471	276	18	)	)	PUNCT
cjfa-35471	276	19	is	be	AUX
cjfa-35471	276	20	a	a	DET
cjfa-35471	276	21	simple	simple	ADJ
cjfa-35471	276	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	276	23	function	function	NOUN
cjfa-35471	276	24	and	and	CCONJ
cjfa-35471	276	25	the	the	DET
cjfa-35471	276	26	interest	interest	NOUN
cjfa-35471	276	27	rate	rate	NOUN
cjfa-35471	276	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	276	29	)	)	PUNCT
cjfa-35471	276	30	is	be	AUX
cjfa-35471	276	31	time	time	NOUN
cjfa-35471	276	32	dependent	dependent	ADJ
cjfa-35471	276	33	,	,	PUNCT
cjfa-35471	276	34	i.e.	i.e.	X
cjfa-35471	276	35	:	:	PUNCT
cjfa-35471	276	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	276	37	)	)	PUNCT
cjfa-35471	277	1	=	=	SYM
cjfa-35471	277	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	277	3	𝐴	𝐴	PROPN
cjfa-35471	277	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	277	5	)	)	PUNCT
cjfa-35471	277	6	with	with	ADP
cjfa-35471	277	7	no	no	DET
cjfa-35471	277	8	growth	growth	NOUN
cjfa-35471	277	9	,	,	PUNCT
cjfa-35471	277	10	and	and	CCONJ
cjfa-35471	277	11	,	,	PUNCT
cjfa-35471	277	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	277	13	)	)	PUNCT
cjfa-35471	277	14	=	=	SYM
cjfa-35471	277	15	�	�	PROPN
cjfa-35471	277	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	277	17	�	�	PROPN
cjfa-35471	277	18	�	�	PROPN
cjfa-35471	277	19	implying	imply	VERB
cjfa-35471	277	20	that	that	SCONJ
cjfa-35471	277	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	277	22	)	)	PUNCT
cjfa-35471	278	1	=	=	VERB
cjfa-35471	278	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	278	3	if	if	SCONJ
cjfa-35471	278	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	278	5	is	be	AUX
cjfa-35471	278	6	constant	constant	ADJ
cjfa-35471	278	7	.	.	PUNCT
cjfa-35471	279	1	notice	notice	NOUN
cjfa-35471	279	2	also	also	ADV
cjfa-35471	279	3	that	that	SCONJ
cjfa-35471	279	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	279	5	�	�	X
cjfa-35471	279	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	279	7	)	)	PUNCT
cjfa-35471	279	8	=	=	SYM
cjfa-35471	279	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	279	10	)	)	PUNCT
cjfa-35471	279	11	where	where	SCONJ
cjfa-35471	279	12	f	f	PROPN
cjfa-35471	279	13	(	(	PUNCT
cjfa-35471	279	14	t	t	PROPN
cjfa-35471	279	15	)	)	PUNCT
cjfa-35471	279	16	denotes	denote	NOUN
cjfa-35471	279	17	time	time	VERB
cjfa-35471	279	18	dependent	dependent	ADJ
cjfa-35471	279	19	interest	interest	NOUN
cjfa-35471	279	20	rate	rate	NOUN
cjfa-35471	279	21	.	.	PUNCT
cjfa-35471	280	1	for	for	ADP
cjfa-35471	280	2	ease	ease	NOUN
cjfa-35471	280	3	of	of	ADP
cjfa-35471	280	4	analysis	analysis	NOUN
cjfa-35471	280	5	we	we	PRON
cjfa-35471	280	6	will	will	AUX
cjfa-35471	280	7	assume	assume	VERB
cjfa-35471	280	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	280	9	)	)	PUNCT
cjfa-35471	280	10	to	to	PART
cjfa-35471	280	11	be	be	AUX
cjfa-35471	280	12	constant	constant	ADJ
cjfa-35471	280	13	.	.	PUNCT
cjfa-35471	281	1	the	the	DET
cjfa-35471	281	2	letter	letter	NOUN
cjfa-35471	281	3	k	k	PROPN
cjfa-35471	281	4	denotes	denote	VERB
cjfa-35471	281	5	the	the	DET
cjfa-35471	281	6	periodicity	periodicity	NOUN
cjfa-35471	281	7	of	of	ADP
cjfa-35471	281	8	the	the	DET
cjfa-35471	281	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	281	10	demand	demand	NOUN
cjfa-35471	281	11	function	function	NOUN
cjfa-35471	281	12	over	over	ADP
cjfa-35471	281	13	the	the	DET
cjfa-35471	281	14	planning	planning	NOUN
cjfa-35471	281	15	period	period	NOUN
cjfa-35471	281	16	.	.	PUNCT
cjfa-35471	282	1	the	the	DET
cjfa-35471	282	2	only	only	ADJ
cjfa-35471	282	3	reason	reason	NOUN
cjfa-35471	282	4	for	for	ADP
cjfa-35471	282	5	the	the	DET
cjfa-35471	282	6	use	use	NOUN
cjfa-35471	282	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	282	8	demand	demand	NOUN
cjfa-35471	282	9	curve	curve	NOUN
cjfa-35471	282	10	is	be	AUX
cjfa-35471	282	11	that	that	SCONJ
cjfa-35471	282	12	it	it	PRON
cjfa-35471	282	13	represents	represent	VERB
cjfa-35471	282	14	cyclicality	cyclicality	NOUN
cjfa-35471	282	15	(	(	PUNCT
cjfa-35471	282	16	a	a	DET
cjfa-35471	282	17	measure	measure	NOUN
cjfa-35471	282	18	of	of	ADP
cjfa-35471	282	19	risk	risk	NOUN
cjfa-35471	282	20	)	)	PUNCT
cjfa-35471	282	21	and	and	CCONJ
cjfa-35471	282	22	that	that	SCONJ
cjfa-35471	282	23	it	it	PRON
cjfa-35471	282	24	is	be	AUX
cjfa-35471	282	25	easier	easy	ADJ
cjfa-35471	282	26	to	to	PART
cjfa-35471	282	27	work	work	VERB
cjfa-35471	282	28	with	with	ADP
cjfa-35471	282	29	it	it	PRON
cjfa-35471	282	30	.	.	PUNCT
cjfa-35471	283	1	the	the	DET
cjfa-35471	283	2	appropriate	appropriate	ADJ
cjfa-35471	283	3	lagrangian	lagrangian	NOUN
cjfa-35471	283	4	for	for	ADP
cjfa-35471	283	5	this	this	DET
cjfa-35471	283	6	problem	problem	NOUN
cjfa-35471	283	7	is	be	AUX
cjfa-35471	283	8	:	:	PUNCT
cjfa-35471	283	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	283	10	=	=	SYM
cjfa-35471	283	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	283	12	�	�	PROPN
cjfa-35471	283	13	�	�	PROPN
cjfa-35471	283	14	(	(	PUNCT
cjfa-35471	283	15	�	�	PROPN
cjfa-35471	283	16	)	)	PUNCT
cjfa-35471	283	17	�	�	PROPN
cjfa-35471	283	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	283	19	�	�	PROPN
cjfa-35471	283	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	283	21	)	)	PUNCT
cjfa-35471	283	22	�	�	PROPN
cjfa-35471	283	23	𝐴	𝐴	PROPN
cjfa-35471	283	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	283	25	)	)	PUNCT
cjfa-35471	283	26	�	�	PROPN
cjfa-35471	283	27	𝐴	𝐴	PROPN
cjfa-35471	283	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	283	29	�	�	PROPN
cjfa-35471	283	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	283	31	)	)	PUNCT
cjfa-35471	283	32	−	−	PROPN
cjfa-35471	283	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	283	34	)	)	PUNCT
cjfa-35471	283	35	�	�	PROPN
cjfa-35471	283	36	𝐴	𝐴	PROPN
cjfa-35471	283	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	283	38	�	�	PROPN
cjfa-35471	283	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	283	40	)	)	PUNCT
cjfa-35471	283	41	−	−	PROPN
cjfa-35471	283	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	283	43	)	)	PUNCT
cjfa-35471	283	44	�	�	PROPN
cjfa-35471	283	45	then	then	ADV
cjfa-35471	283	46	the	the	DET
cjfa-35471	283	47	necessary	necessary	ADJ
cjfa-35471	283	48	conditions	condition	NOUN
cjfa-35471	283	49	are	be	AUX
cjfa-35471	283	50	:	:	PUNCT
cjfa-35471	283	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	283	52	�	�	PROPN
cjfa-35471	283	53	�	�	PROPN
cjfa-35471	283	54	(	(	PUNCT
cjfa-35471	283	55	�	�	NOUN
cjfa-35471	283	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	283	57	�	�	PROPN
cjfa-35471	283	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	283	59	)	)	PUNCT
cjfa-35471	283	60	𝐴	𝐴	PROPN
cjfa-35471	283	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	283	62	)	)	PUNCT
cjfa-35471	283	63	−	−	PROPN
cjfa-35471	283	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	283	65	)	)	PUNCT
cjfa-35471	284	1	=	=	SYM
cjfa-35471	284	2	0	0	PUNCT
cjfa-35471	284	3	(	(	PUNCT
cjfa-35471	284	4	1	1	NUM
cjfa-35471	284	5	)	)	PUNCT
cjfa-35471	284	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	284	7	�	�	PROPN
cjfa-35471	284	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	284	9	)	)	PUNCT
cjfa-35471	284	10	=	=	SYM
cjfa-35471	284	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	284	12	�	�	PROPN
cjfa-35471	284	13	�	�	PROPN
cjfa-35471	284	14	(	(	PUNCT
cjfa-35471	284	15	�	�	PROPN
cjfa-35471	284	16	)ℎ	)ℎ	PROPN
cjfa-35471	284	17	(	(	PUNCT
cjfa-35471	284	18	2	2	X
cjfa-35471	284	19	)	)	PUNCT
cjfa-35471	284	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	284	21	�	�	PROPN
cjfa-35471	284	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	284	23	)	)	PUNCT
cjfa-35471	284	24	=	=	SYM
cjfa-35471	284	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	284	26	)	)	PUNCT
cjfa-35471	284	27	−	−	PROPN
cjfa-35471	284	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	284	29	)	)	PUNCT
cjfa-35471	284	30	(	(	PUNCT
cjfa-35471	284	31	3	3	X
cjfa-35471	284	32	)	)	PUNCT
cjfa-35471	284	33	necessary	necessary	ADJ
cjfa-35471	284	34	conditions	condition	NOUN
cjfa-35471	284	35	are	be	AUX
cjfa-35471	284	36	also	also	ADV
cjfa-35471	284	37	sufficient	sufficient	ADJ
cjfa-35471	284	38	since	since	SCONJ
cjfa-35471	284	39	the	the	DET
cjfa-35471	284	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	284	41	is	be	AUX
cjfa-35471	284	42	convex	convex	ADJ
cjfa-35471	284	43	in	in	ADP
cjfa-35471	284	44	both	both	CCONJ
cjfa-35471	284	45	the	the	DET
cjfa-35471	284	46	control	control	NOUN
cjfa-35471	284	47	(	(	PUNCT
cjfa-35471	284	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	284	49	)	)	PUNCT
cjfa-35471	284	50	and	and	CCONJ
cjfa-35471	284	51	state	state	NOUN
cjfa-35471	284	52	(	(	PUNCT
cjfa-35471	284	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	284	54	)	)	PUNCT
cjfa-35471	284	55	variables	variable	NOUN
cjfa-35471	284	56	.	.	PUNCT
cjfa-35471	285	1	the	the	DET
cjfa-35471	285	2	planning	planning	NOUN
cjfa-35471	285	3	horizon	horizon	NOUN
cjfa-35471	285	4	(	(	PUNCT
cjfa-35471	285	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	285	6	)	)	PUNCT
cjfa-35471	285	7	will	will	AUX
cjfa-35471	285	8	be	be	AUX
cjfa-35471	285	9	assumed	assume	VERB
cjfa-35471	285	10	one	one	NUM
cjfa-35471	285	11	.	.	PUNCT
cjfa-35471	286	1	on	on	ADP
cjfa-35471	286	2	a	a	DET
cjfa-35471	286	3	constraint	constraint	NOUN
cjfa-35471	286	4	arc	arc	NOUN
cjfa-35471	286	5	on	on	ADP
cjfa-35471	286	6	which	which	PRON
cjfa-35471	286	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	286	8	)	)	PUNCT
cjfa-35471	286	9	=	=	SYM
cjfa-35471	286	10	0	0	NUM
cjfa-35471	286	11	for	for	ADP
cjfa-35471	286	12	a	a	DET
cjfa-35471	286	13	certain	certain	ADJ
cjfa-35471	286	14	period	period	NOUN
cjfa-35471	286	15	in	in	ADP
cjfa-35471	286	16	[	[	X
cjfa-35471	286	17	0	0	NUM
cjfa-35471	286	18	,	,	PUNCT
cjfa-35471	286	19	1	1	NUM
cjfa-35471	286	20	]	]	PUNCT
cjfa-35471	286	21	i.e.	i.e.	X
cjfa-35471	286	22	0	0	X
cjfa-35471	286	23	<	<	X
cjfa-35471	286	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	286	25	�	�	PROPN
cjfa-35471	286	26	≤	≤	X
cjfa-35471	286	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	286	28	≤	≤	PROPN
cjfa-35471	286	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	286	30	�	�	PROPN
cjfa-35471	286	31	<	<	X
cjfa-35471	286	32	1	1	NUM
cjfa-35471	286	33	we	we	PRON
cjfa-35471	286	34	have	have	VERB
cjfa-35471	286	35	;	;	PUNCT
cjfa-35471	286	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	286	37	�	�	PROPN
cjfa-35471	286	38	=	=	SYM
cjfa-35471	286	39	0	0	NUM
cjfa-35471	286	40	=	=	SYM
cjfa-35471	286	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	286	42	)	)	PUNCT
cjfa-35471	287	1	−	−	PROPN
cjfa-35471	287	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	287	3	)	)	PUNCT
cjfa-35471	287	4	implying	imply	VERB
cjfa-35471	287	5	that	that	SCONJ
cjfa-35471	287	6	over	over	ADP
cjfa-35471	287	7	this	this	DET
cjfa-35471	287	8	period	period	NOUN
cjfa-35471	287	9	a	a	DET
cjfa-35471	287	10	firm	firm	NOUN
cjfa-35471	287	11	will	will	AUX
cjfa-35471	287	12	produce	produce	VERB
cjfa-35471	287	13	just	just	ADV
cjfa-35471	287	14	enough	enough	ADJ
cjfa-35471	287	15	to	to	PART
cjfa-35471	287	16	meet	meet	VERB
cjfa-35471	287	17	the	the	DET
cjfa-35471	287	18	demand	demand	NOUN
cjfa-35471	287	19	,	,	PUNCT
cjfa-35471	287	20	which	which	PRON
cjfa-35471	287	21	is	be	AUX
cjfa-35471	287	22	assumed	assume	VERB
cjfa-35471	287	23	to	to	PART
cjfa-35471	287	24	be	be	AUX
cjfa-35471	287	25	nonzero	nonzero	NOUN
cjfa-35471	287	26	during	during	ADP
cjfa-35471	287	27	the	the	DET
cjfa-35471	287	28	planning	planning	NOUN
cjfa-35471	287	29	horizon	horizon	NOUN
cjfa-35471	287	30	.	.	PUNCT
cjfa-35471	288	1	(	(	PUNCT
cjfa-35471	288	2	1	1	X
cjfa-35471	288	3	)	)	PUNCT
cjfa-35471	288	4	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	288	5	�	�	PROPN
cjfa-35471	288	6	=	=	SYM
cjfa-35471	288	7	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	288	8	)	)	PUNCT
cjfa-35471	288	9	−	−	PROPN
cjfa-35471	288	10	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	288	11	)	)	PUNCT
cjfa-35471	288	12	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	288	13	)	)	PUNCT
cjfa-35471	288	14	=	=	SYM
cjfa-35471	288	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	288	16	�	�	PROPN
cjfa-35471	288	17	a	a	DET
cjfa-35471	288	18	given	give	VERB
cjfa-35471	288	19	number	number	NOUN
cjfa-35471	288	20	.	.	PUNCT
cjfa-35471	289	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	289	2	)	)	PUNCT
cjfa-35471	290	1	𝑢	𝑢	PROPN
cjfa-35471	290	2	0	0	NUM
cjfa-35471	290	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	290	4	)	)	PUNCT
cjfa-35471	290	5	𝑢	𝑢	ADP
cjfa-35471	290	6	0	0	NUM
cjfa-35471	290	7	with	with	ADP
cjfa-35471	290	8	the	the	DET
cjfa-35471	290	9	assumptions	assumption	NOUN
cjfa-35471	290	10	that	that	SCONJ
cjfa-35471	290	11	the	the	DET
cjfa-35471	290	12	demand	demand	NOUN
cjfa-35471	290	13	(	(	PUNCT
cjfa-35471	290	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	290	15	(	(	PUNCT
cjfa-35471	290	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	290	17	)	)	PUNCT
cjfa-35471	290	18	)	)	PUNCT
cjfa-35471	290	19	is	be	AUX
cjfa-35471	290	20	a	a	DET
cjfa-35471	290	21	simple	simple	ADJ
cjfa-35471	290	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	290	23	function	function	NOUN
cjfa-35471	290	24	and	and	CCONJ
cjfa-35471	290	25	the	the	DET
cjfa-35471	290	26	interest	interest	NOUN
cjfa-35471	290	27	rate	rate	NOUN
cjfa-35471	290	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	290	29	)	)	PUNCT
cjfa-35471	290	30	is	be	AUX
cjfa-35471	290	31	time	time	NOUN
cjfa-35471	290	32	dependent	dependent	ADJ
cjfa-35471	290	33	,	,	PUNCT
cjfa-35471	290	34	i.e.	i.e.	X
cjfa-35471	290	35	:	:	PUNCT
cjfa-35471	290	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	290	37	)	)	PUNCT
cjfa-35471	291	1	=	=	SYM
cjfa-35471	291	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	291	3	𝐴	𝐴	PROPN
cjfa-35471	291	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	291	5	)	)	PUNCT
cjfa-35471	291	6	with	with	ADP
cjfa-35471	291	7	no	no	DET
cjfa-35471	291	8	growth	growth	NOUN
cjfa-35471	291	9	,	,	PUNCT
cjfa-35471	291	10	and	and	CCONJ
cjfa-35471	291	11	,	,	PUNCT
cjfa-35471	291	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	291	13	)	)	PUNCT
cjfa-35471	291	14	=	=	SYM
cjfa-35471	291	15	�	�	PROPN
cjfa-35471	291	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	291	17	�	�	PROPN
cjfa-35471	291	18	�	�	PROPN
cjfa-35471	291	19	implying	imply	VERB
cjfa-35471	291	20	that	that	SCONJ
cjfa-35471	291	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	291	22	)	)	PUNCT
cjfa-35471	292	1	=	=	VERB
cjfa-35471	292	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	292	3	if	if	SCONJ
cjfa-35471	292	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	292	5	is	be	AUX
cjfa-35471	292	6	constant	constant	ADJ
cjfa-35471	292	7	.	.	PUNCT
cjfa-35471	293	1	notice	notice	NOUN
cjfa-35471	293	2	also	also	ADV
cjfa-35471	293	3	that	that	SCONJ
cjfa-35471	293	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	293	5	�	�	X
cjfa-35471	293	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	293	7	)	)	PUNCT
cjfa-35471	293	8	=	=	SYM
cjfa-35471	293	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	293	10	)	)	PUNCT
cjfa-35471	293	11	where	where	SCONJ
cjfa-35471	293	12	f	f	PROPN
cjfa-35471	293	13	(	(	PUNCT
cjfa-35471	293	14	t	t	PROPN
cjfa-35471	293	15	)	)	PUNCT
cjfa-35471	293	16	denotes	denote	NOUN
cjfa-35471	293	17	time	time	VERB
cjfa-35471	293	18	dependent	dependent	ADJ
cjfa-35471	293	19	interest	interest	NOUN
cjfa-35471	293	20	rate	rate	NOUN
cjfa-35471	293	21	.	.	PUNCT
cjfa-35471	294	1	for	for	ADP
cjfa-35471	294	2	ease	ease	NOUN
cjfa-35471	294	3	of	of	ADP
cjfa-35471	294	4	analysis	analysis	NOUN
cjfa-35471	294	5	we	we	PRON
cjfa-35471	294	6	will	will	AUX
cjfa-35471	294	7	assume	assume	VERB
cjfa-35471	294	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	294	9	)	)	PUNCT
cjfa-35471	294	10	to	to	PART
cjfa-35471	294	11	be	be	AUX
cjfa-35471	294	12	constant	constant	ADJ
cjfa-35471	294	13	.	.	PUNCT
cjfa-35471	295	1	the	the	DET
cjfa-35471	295	2	letter	letter	NOUN
cjfa-35471	295	3	k	k	PROPN
cjfa-35471	295	4	denotes	denote	VERB
cjfa-35471	295	5	the	the	DET
cjfa-35471	295	6	periodicity	periodicity	NOUN
cjfa-35471	295	7	of	of	ADP
cjfa-35471	295	8	the	the	DET
cjfa-35471	295	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	295	10	demand	demand	NOUN
cjfa-35471	295	11	function	function	NOUN
cjfa-35471	295	12	over	over	ADP
cjfa-35471	295	13	the	the	DET
cjfa-35471	295	14	planning	planning	NOUN
cjfa-35471	295	15	period	period	NOUN
cjfa-35471	295	16	.	.	PUNCT
cjfa-35471	296	1	the	the	DET
cjfa-35471	296	2	only	only	ADJ
cjfa-35471	296	3	reason	reason	NOUN
cjfa-35471	296	4	for	for	ADP
cjfa-35471	296	5	the	the	DET
cjfa-35471	296	6	use	use	NOUN
cjfa-35471	296	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	296	8	demand	demand	NOUN
cjfa-35471	296	9	curve	curve	NOUN
cjfa-35471	296	10	is	be	AUX
cjfa-35471	296	11	that	that	SCONJ
cjfa-35471	296	12	it	it	PRON
cjfa-35471	296	13	represents	represent	VERB
cjfa-35471	296	14	cyclicality	cyclicality	NOUN
cjfa-35471	296	15	(	(	PUNCT
cjfa-35471	296	16	a	a	DET
cjfa-35471	296	17	measure	measure	NOUN
cjfa-35471	296	18	of	of	ADP
cjfa-35471	296	19	risk	risk	NOUN
cjfa-35471	296	20	)	)	PUNCT
cjfa-35471	296	21	and	and	CCONJ
cjfa-35471	296	22	that	that	SCONJ
cjfa-35471	296	23	it	it	PRON
cjfa-35471	296	24	is	be	AUX
cjfa-35471	296	25	easier	easy	ADJ
cjfa-35471	296	26	to	to	PART
cjfa-35471	296	27	work	work	VERB
cjfa-35471	296	28	with	with	ADP
cjfa-35471	296	29	it	it	PRON
cjfa-35471	296	30	.	.	PUNCT
cjfa-35471	297	1	the	the	DET
cjfa-35471	297	2	appropriate	appropriate	ADJ
cjfa-35471	297	3	lagrangian	lagrangian	NOUN
cjfa-35471	297	4	for	for	ADP
cjfa-35471	297	5	this	this	DET
cjfa-35471	297	6	problem	problem	NOUN
cjfa-35471	297	7	is	be	AUX
cjfa-35471	297	8	:	:	PUNCT
cjfa-35471	297	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	297	10	=	=	SYM
cjfa-35471	297	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	297	12	�	�	PROPN
cjfa-35471	297	13	�	�	PROPN
cjfa-35471	297	14	(	(	PUNCT
cjfa-35471	297	15	�	�	PROPN
cjfa-35471	297	16	)	)	PUNCT
cjfa-35471	297	17	�	�	PROPN
cjfa-35471	297	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	297	19	�	�	PROPN
cjfa-35471	297	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	297	21	)	)	PUNCT
cjfa-35471	297	22	�	�	PROPN
cjfa-35471	297	23	𝐴	𝐴	PROPN
cjfa-35471	297	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	297	25	)	)	PUNCT
cjfa-35471	297	26	�	�	PROPN
cjfa-35471	297	27	𝐴	𝐴	PROPN
cjfa-35471	297	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	297	29	�	�	PROPN
cjfa-35471	297	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	297	31	)	)	PUNCT
cjfa-35471	297	32	−	−	PROPN
cjfa-35471	297	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	297	34	)	)	PUNCT
cjfa-35471	297	35	�	�	PROPN
cjfa-35471	297	36	𝐴	𝐴	PROPN
cjfa-35471	297	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	297	38	�	�	PROPN
cjfa-35471	297	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	297	40	)	)	PUNCT
cjfa-35471	297	41	−	−	PROPN
cjfa-35471	297	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	297	43	)	)	PUNCT
cjfa-35471	297	44	�	�	PROPN
cjfa-35471	297	45	then	then	ADV
cjfa-35471	297	46	the	the	DET
cjfa-35471	297	47	necessary	necessary	ADJ
cjfa-35471	297	48	conditions	condition	NOUN
cjfa-35471	297	49	are	be	AUX
cjfa-35471	297	50	:	:	PUNCT
cjfa-35471	297	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	297	52	�	�	PROPN
cjfa-35471	297	53	�	�	PROPN
cjfa-35471	297	54	(	(	PUNCT
cjfa-35471	297	55	�	�	NOUN
cjfa-35471	297	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	297	57	�	�	PROPN
cjfa-35471	297	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	297	59	)	)	PUNCT
cjfa-35471	297	60	𝐴	𝐴	PROPN
cjfa-35471	297	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	297	62	)	)	PUNCT
cjfa-35471	297	63	−	−	PROPN
cjfa-35471	297	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	297	65	)	)	PUNCT
cjfa-35471	298	1	=	=	SYM
cjfa-35471	298	2	0	0	PUNCT
cjfa-35471	298	3	(	(	PUNCT
cjfa-35471	298	4	1	1	NUM
cjfa-35471	298	5	)	)	PUNCT
cjfa-35471	298	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	298	7	�	�	PROPN
cjfa-35471	298	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	298	9	)	)	PUNCT
cjfa-35471	298	10	=	=	SYM
cjfa-35471	298	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	298	12	�	�	PROPN
cjfa-35471	298	13	�	�	PROPN
cjfa-35471	298	14	(	(	PUNCT
cjfa-35471	298	15	�	�	PROPN
cjfa-35471	298	16	)ℎ	)ℎ	PROPN
cjfa-35471	298	17	(	(	PUNCT
cjfa-35471	298	18	2	2	X
cjfa-35471	298	19	)	)	PUNCT
cjfa-35471	298	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	298	21	�	�	PROPN
cjfa-35471	298	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	298	23	)	)	PUNCT
cjfa-35471	298	24	=	=	SYM
cjfa-35471	298	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	298	26	)	)	PUNCT
cjfa-35471	298	27	−	−	PROPN
cjfa-35471	298	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	298	29	)	)	PUNCT
cjfa-35471	298	30	(	(	PUNCT
cjfa-35471	298	31	3	3	X
cjfa-35471	298	32	)	)	PUNCT
cjfa-35471	298	33	necessary	necessary	ADJ
cjfa-35471	298	34	conditions	condition	NOUN
cjfa-35471	298	35	are	be	AUX
cjfa-35471	298	36	also	also	ADV
cjfa-35471	298	37	sufficient	sufficient	ADJ
cjfa-35471	298	38	since	since	SCONJ
cjfa-35471	298	39	the	the	DET
cjfa-35471	298	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	298	41	is	be	AUX
cjfa-35471	298	42	convex	convex	ADJ
cjfa-35471	298	43	in	in	ADP
cjfa-35471	298	44	both	both	CCONJ
cjfa-35471	298	45	the	the	DET
cjfa-35471	298	46	control	control	NOUN
cjfa-35471	298	47	(	(	PUNCT
cjfa-35471	298	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	298	49	)	)	PUNCT
cjfa-35471	298	50	and	and	CCONJ
cjfa-35471	298	51	state	state	NOUN
cjfa-35471	298	52	(	(	PUNCT
cjfa-35471	298	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	298	54	)	)	PUNCT
cjfa-35471	298	55	variables	variable	NOUN
cjfa-35471	298	56	.	.	PUNCT
cjfa-35471	299	1	the	the	DET
cjfa-35471	299	2	planning	planning	NOUN
cjfa-35471	299	3	horizon	horizon	NOUN
cjfa-35471	299	4	(	(	PUNCT
cjfa-35471	299	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	299	6	)	)	PUNCT
cjfa-35471	299	7	will	will	AUX
cjfa-35471	299	8	be	be	AUX
cjfa-35471	299	9	assumed	assume	VERB
cjfa-35471	299	10	one	one	NUM
cjfa-35471	299	11	.	.	PUNCT
cjfa-35471	300	1	on	on	ADP
cjfa-35471	300	2	a	a	DET
cjfa-35471	300	3	constraint	constraint	NOUN
cjfa-35471	300	4	arc	arc	NOUN
cjfa-35471	300	5	on	on	ADP
cjfa-35471	300	6	which	which	PRON
cjfa-35471	300	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	300	8	)	)	PUNCT
cjfa-35471	300	9	=	=	SYM
cjfa-35471	300	10	0	0	NUM
cjfa-35471	300	11	for	for	ADP
cjfa-35471	300	12	a	a	DET
cjfa-35471	300	13	certain	certain	ADJ
cjfa-35471	300	14	period	period	NOUN
cjfa-35471	300	15	in	in	ADP
cjfa-35471	300	16	[	[	X
cjfa-35471	300	17	0	0	NUM
cjfa-35471	300	18	,	,	PUNCT
cjfa-35471	300	19	1	1	NUM
cjfa-35471	300	20	]	]	PUNCT
cjfa-35471	300	21	i.e.	i.e.	X
cjfa-35471	300	22	0	0	X
cjfa-35471	300	23	<	<	X
cjfa-35471	300	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	300	25	�	�	PROPN
cjfa-35471	300	26	≤	≤	X
cjfa-35471	300	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	300	28	≤	≤	PROPN
cjfa-35471	300	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	300	30	�	�	PROPN
cjfa-35471	300	31	<	<	X
cjfa-35471	300	32	1	1	NUM
cjfa-35471	300	33	we	we	PRON
cjfa-35471	300	34	have	have	VERB
cjfa-35471	300	35	;	;	PUNCT
cjfa-35471	300	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	300	37	�	�	PROPN
cjfa-35471	300	38	=	=	SYM
cjfa-35471	300	39	0	0	NUM
cjfa-35471	300	40	=	=	SYM
cjfa-35471	300	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	300	42	)	)	PUNCT
cjfa-35471	301	1	−	−	PROPN
cjfa-35471	301	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	301	3	)	)	PUNCT
cjfa-35471	301	4	implying	imply	VERB
cjfa-35471	301	5	that	that	SCONJ
cjfa-35471	301	6	over	over	ADP
cjfa-35471	301	7	this	this	DET
cjfa-35471	301	8	period	period	NOUN
cjfa-35471	301	9	a	a	DET
cjfa-35471	301	10	firm	firm	NOUN
cjfa-35471	301	11	will	will	AUX
cjfa-35471	301	12	produce	produce	VERB
cjfa-35471	301	13	just	just	ADV
cjfa-35471	301	14	enough	enough	ADJ
cjfa-35471	301	15	to	to	PART
cjfa-35471	301	16	meet	meet	VERB
cjfa-35471	301	17	the	the	DET
cjfa-35471	301	18	demand	demand	NOUN
cjfa-35471	301	19	,	,	PUNCT
cjfa-35471	301	20	which	which	PRON
cjfa-35471	301	21	is	be	AUX
cjfa-35471	301	22	assumed	assume	VERB
cjfa-35471	301	23	to	to	PART
cjfa-35471	301	24	be	be	AUX
cjfa-35471	301	25	nonzero	nonzero	NOUN
cjfa-35471	301	26	during	during	ADP
cjfa-35471	301	27	the	the	DET
cjfa-35471	301	28	planning	planning	NOUN
cjfa-35471	301	29	horizon	horizon	NOUN
cjfa-35471	301	30	.	.	PUNCT
cjfa-35471	302	1	(	(	PUNCT
cjfa-35471	302	2	2	2	X
cjfa-35471	302	3	)	)	PUNCT
cjfa-35471	302	4	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	302	5	�	�	PROPN
cjfa-35471	302	6	=	=	SYM
cjfa-35471	302	7	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	302	8	)	)	PUNCT
cjfa-35471	302	9	−	−	PROPN
cjfa-35471	302	10	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	302	11	)	)	PUNCT
cjfa-35471	302	12	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	302	13	)	)	PUNCT
cjfa-35471	302	14	=	=	SYM
cjfa-35471	302	15	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	302	16	�	�	PROPN
cjfa-35471	302	17	a	a	DET
cjfa-35471	302	18	given	give	VERB
cjfa-35471	302	19	number	number	NOUN
cjfa-35471	302	20	.	.	PUNCT
cjfa-35471	303	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	303	2	)	)	PUNCT
cjfa-35471	304	1	𝑢	𝑢	PROPN
cjfa-35471	304	2	0	0	NUM
cjfa-35471	304	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	304	4	)	)	PUNCT
cjfa-35471	304	5	𝑢	𝑢	ADP
cjfa-35471	304	6	0	0	NUM
cjfa-35471	304	7	with	with	ADP
cjfa-35471	304	8	the	the	DET
cjfa-35471	304	9	assumptions	assumption	NOUN
cjfa-35471	304	10	that	that	SCONJ
cjfa-35471	304	11	the	the	DET
cjfa-35471	304	12	demand	demand	NOUN
cjfa-35471	304	13	(	(	PUNCT
cjfa-35471	304	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	304	15	(	(	PUNCT
cjfa-35471	304	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	304	17	)	)	PUNCT
cjfa-35471	304	18	)	)	PUNCT
cjfa-35471	304	19	is	be	AUX
cjfa-35471	304	20	a	a	DET
cjfa-35471	304	21	simple	simple	ADJ
cjfa-35471	304	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	304	23	function	function	NOUN
cjfa-35471	304	24	and	and	CCONJ
cjfa-35471	304	25	the	the	DET
cjfa-35471	304	26	interest	interest	NOUN
cjfa-35471	304	27	rate	rate	NOUN
cjfa-35471	304	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	304	29	)	)	PUNCT
cjfa-35471	304	30	is	be	AUX
cjfa-35471	304	31	time	time	NOUN
cjfa-35471	304	32	dependent	dependent	ADJ
cjfa-35471	304	33	,	,	PUNCT
cjfa-35471	304	34	i.e.	i.e.	X
cjfa-35471	304	35	:	:	PUNCT
cjfa-35471	304	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	304	37	)	)	PUNCT
cjfa-35471	305	1	=	=	SYM
cjfa-35471	305	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	305	3	𝐴	𝐴	PROPN
cjfa-35471	305	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	305	5	)	)	PUNCT
cjfa-35471	305	6	with	with	ADP
cjfa-35471	305	7	no	no	DET
cjfa-35471	305	8	growth	growth	NOUN
cjfa-35471	305	9	,	,	PUNCT
cjfa-35471	305	10	and	and	CCONJ
cjfa-35471	305	11	,	,	PUNCT
cjfa-35471	305	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	305	13	)	)	PUNCT
cjfa-35471	305	14	=	=	SYM
cjfa-35471	305	15	�	�	PROPN
cjfa-35471	305	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	305	17	�	�	PROPN
cjfa-35471	305	18	�	�	PROPN
cjfa-35471	305	19	implying	imply	VERB
cjfa-35471	305	20	that	that	SCONJ
cjfa-35471	305	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	305	22	)	)	PUNCT
cjfa-35471	306	1	=	=	VERB
cjfa-35471	306	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	306	3	if	if	SCONJ
cjfa-35471	306	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	306	5	is	be	AUX
cjfa-35471	306	6	constant	constant	ADJ
cjfa-35471	306	7	.	.	PUNCT
cjfa-35471	307	1	notice	notice	NOUN
cjfa-35471	307	2	also	also	ADV
cjfa-35471	307	3	that	that	SCONJ
cjfa-35471	307	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	307	5	�	�	X
cjfa-35471	307	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	307	7	)	)	PUNCT
cjfa-35471	307	8	=	=	SYM
cjfa-35471	307	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	307	10	)	)	PUNCT
cjfa-35471	307	11	where	where	SCONJ
cjfa-35471	307	12	f	f	PROPN
cjfa-35471	307	13	(	(	PUNCT
cjfa-35471	307	14	t	t	PROPN
cjfa-35471	307	15	)	)	PUNCT
cjfa-35471	307	16	denotes	denote	NOUN
cjfa-35471	307	17	time	time	VERB
cjfa-35471	307	18	dependent	dependent	ADJ
cjfa-35471	307	19	interest	interest	NOUN
cjfa-35471	307	20	rate	rate	NOUN
cjfa-35471	307	21	.	.	PUNCT
cjfa-35471	308	1	for	for	ADP
cjfa-35471	308	2	ease	ease	NOUN
cjfa-35471	308	3	of	of	ADP
cjfa-35471	308	4	analysis	analysis	NOUN
cjfa-35471	308	5	we	we	PRON
cjfa-35471	308	6	will	will	AUX
cjfa-35471	308	7	assume	assume	VERB
cjfa-35471	308	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	308	9	)	)	PUNCT
cjfa-35471	308	10	to	to	PART
cjfa-35471	308	11	be	be	AUX
cjfa-35471	308	12	constant	constant	ADJ
cjfa-35471	308	13	.	.	PUNCT
cjfa-35471	309	1	the	the	DET
cjfa-35471	309	2	letter	letter	NOUN
cjfa-35471	309	3	k	k	PROPN
cjfa-35471	309	4	denotes	denote	VERB
cjfa-35471	309	5	the	the	DET
cjfa-35471	309	6	periodicity	periodicity	NOUN
cjfa-35471	309	7	of	of	ADP
cjfa-35471	309	8	the	the	DET
cjfa-35471	309	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	309	10	demand	demand	NOUN
cjfa-35471	309	11	function	function	NOUN
cjfa-35471	309	12	over	over	ADP
cjfa-35471	309	13	the	the	DET
cjfa-35471	309	14	planning	planning	NOUN
cjfa-35471	309	15	period	period	NOUN
cjfa-35471	309	16	.	.	PUNCT
cjfa-35471	310	1	the	the	DET
cjfa-35471	310	2	only	only	ADJ
cjfa-35471	310	3	reason	reason	NOUN
cjfa-35471	310	4	for	for	ADP
cjfa-35471	310	5	the	the	DET
cjfa-35471	310	6	use	use	NOUN
cjfa-35471	310	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	310	8	demand	demand	NOUN
cjfa-35471	310	9	curve	curve	NOUN
cjfa-35471	310	10	is	be	AUX
cjfa-35471	310	11	that	that	SCONJ
cjfa-35471	310	12	it	it	PRON
cjfa-35471	310	13	represents	represent	VERB
cjfa-35471	310	14	cyclicality	cyclicality	NOUN
cjfa-35471	310	15	(	(	PUNCT
cjfa-35471	310	16	a	a	DET
cjfa-35471	310	17	measure	measure	NOUN
cjfa-35471	310	18	of	of	ADP
cjfa-35471	310	19	risk	risk	NOUN
cjfa-35471	310	20	)	)	PUNCT
cjfa-35471	310	21	and	and	CCONJ
cjfa-35471	310	22	that	that	SCONJ
cjfa-35471	310	23	it	it	PRON
cjfa-35471	310	24	is	be	AUX
cjfa-35471	310	25	easier	easy	ADJ
cjfa-35471	310	26	to	to	PART
cjfa-35471	310	27	work	work	VERB
cjfa-35471	310	28	with	with	ADP
cjfa-35471	310	29	it	it	PRON
cjfa-35471	310	30	.	.	PUNCT
cjfa-35471	311	1	the	the	DET
cjfa-35471	311	2	appropriate	appropriate	ADJ
cjfa-35471	311	3	lagrangian	lagrangian	NOUN
cjfa-35471	311	4	for	for	ADP
cjfa-35471	311	5	this	this	DET
cjfa-35471	311	6	problem	problem	NOUN
cjfa-35471	311	7	is	be	AUX
cjfa-35471	311	8	:	:	PUNCT
cjfa-35471	311	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	311	10	=	=	SYM
cjfa-35471	311	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	311	12	�	�	PROPN
cjfa-35471	311	13	�	�	PROPN
cjfa-35471	311	14	(	(	PUNCT
cjfa-35471	311	15	�	�	PROPN
cjfa-35471	311	16	)	)	PUNCT
cjfa-35471	311	17	�	�	PROPN
cjfa-35471	311	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	311	19	�	�	PROPN
cjfa-35471	311	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	311	21	)	)	PUNCT
cjfa-35471	311	22	�	�	PROPN
cjfa-35471	311	23	𝐴	𝐴	PROPN
cjfa-35471	311	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	311	25	)	)	PUNCT
cjfa-35471	311	26	�	�	PROPN
cjfa-35471	311	27	𝐴	𝐴	PROPN
cjfa-35471	311	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	311	29	�	�	PROPN
cjfa-35471	311	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	311	31	)	)	PUNCT
cjfa-35471	311	32	−	−	PROPN
cjfa-35471	311	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	311	34	)	)	PUNCT
cjfa-35471	311	35	�	�	PROPN
cjfa-35471	311	36	𝐴	𝐴	PROPN
cjfa-35471	311	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	311	38	�	�	PROPN
cjfa-35471	311	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	311	40	)	)	PUNCT
cjfa-35471	311	41	−	−	PROPN
cjfa-35471	311	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	311	43	)	)	PUNCT
cjfa-35471	311	44	�	�	PROPN
cjfa-35471	311	45	then	then	ADV
cjfa-35471	311	46	the	the	DET
cjfa-35471	311	47	necessary	necessary	ADJ
cjfa-35471	311	48	conditions	condition	NOUN
cjfa-35471	311	49	are	be	AUX
cjfa-35471	311	50	:	:	PUNCT
cjfa-35471	311	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	311	52	�	�	PROPN
cjfa-35471	311	53	�	�	PROPN
cjfa-35471	311	54	(	(	PUNCT
cjfa-35471	311	55	�	�	NOUN
cjfa-35471	311	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	311	57	�	�	PROPN
cjfa-35471	311	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	311	59	)	)	PUNCT
cjfa-35471	311	60	𝐴	𝐴	PROPN
cjfa-35471	311	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	311	62	)	)	PUNCT
cjfa-35471	311	63	−	−	PROPN
cjfa-35471	311	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	311	65	)	)	PUNCT
cjfa-35471	312	1	=	=	SYM
cjfa-35471	312	2	0	0	PUNCT
cjfa-35471	312	3	(	(	PUNCT
cjfa-35471	312	4	1	1	NUM
cjfa-35471	312	5	)	)	PUNCT
cjfa-35471	312	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	312	7	�	�	PROPN
cjfa-35471	312	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	312	9	)	)	PUNCT
cjfa-35471	312	10	=	=	SYM
cjfa-35471	312	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	312	12	�	�	PROPN
cjfa-35471	312	13	�	�	PROPN
cjfa-35471	312	14	(	(	PUNCT
cjfa-35471	312	15	�	�	PROPN
cjfa-35471	312	16	)ℎ	)ℎ	PROPN
cjfa-35471	312	17	(	(	PUNCT
cjfa-35471	312	18	2	2	X
cjfa-35471	312	19	)	)	PUNCT
cjfa-35471	312	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	312	21	�	�	PROPN
cjfa-35471	312	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	312	23	)	)	PUNCT
cjfa-35471	312	24	=	=	SYM
cjfa-35471	312	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	312	26	)	)	PUNCT
cjfa-35471	312	27	−	−	PROPN
cjfa-35471	312	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	312	29	)	)	PUNCT
cjfa-35471	312	30	(	(	PUNCT
cjfa-35471	312	31	3	3	X
cjfa-35471	312	32	)	)	PUNCT
cjfa-35471	312	33	necessary	necessary	ADJ
cjfa-35471	312	34	conditions	condition	NOUN
cjfa-35471	312	35	are	be	AUX
cjfa-35471	312	36	also	also	ADV
cjfa-35471	312	37	sufficient	sufficient	ADJ
cjfa-35471	312	38	since	since	SCONJ
cjfa-35471	312	39	the	the	DET
cjfa-35471	312	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	312	41	is	be	AUX
cjfa-35471	312	42	convex	convex	ADJ
cjfa-35471	312	43	in	in	ADP
cjfa-35471	312	44	both	both	CCONJ
cjfa-35471	312	45	the	the	DET
cjfa-35471	312	46	control	control	NOUN
cjfa-35471	312	47	(	(	PUNCT
cjfa-35471	312	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	312	49	)	)	PUNCT
cjfa-35471	312	50	and	and	CCONJ
cjfa-35471	312	51	state	state	NOUN
cjfa-35471	312	52	(	(	PUNCT
cjfa-35471	312	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	312	54	)	)	PUNCT
cjfa-35471	312	55	variables	variable	NOUN
cjfa-35471	312	56	.	.	PUNCT
cjfa-35471	313	1	the	the	DET
cjfa-35471	313	2	planning	planning	NOUN
cjfa-35471	313	3	horizon	horizon	NOUN
cjfa-35471	313	4	(	(	PUNCT
cjfa-35471	313	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	313	6	)	)	PUNCT
cjfa-35471	313	7	will	will	AUX
cjfa-35471	313	8	be	be	AUX
cjfa-35471	313	9	assumed	assume	VERB
cjfa-35471	313	10	one	one	NUM
cjfa-35471	313	11	.	.	PUNCT
cjfa-35471	314	1	on	on	ADP
cjfa-35471	314	2	a	a	DET
cjfa-35471	314	3	constraint	constraint	NOUN
cjfa-35471	314	4	arc	arc	NOUN
cjfa-35471	314	5	on	on	ADP
cjfa-35471	314	6	which	which	PRON
cjfa-35471	314	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	314	8	)	)	PUNCT
cjfa-35471	314	9	=	=	SYM
cjfa-35471	314	10	0	0	NUM
cjfa-35471	314	11	for	for	ADP
cjfa-35471	314	12	a	a	DET
cjfa-35471	314	13	certain	certain	ADJ
cjfa-35471	314	14	period	period	NOUN
cjfa-35471	314	15	in	in	ADP
cjfa-35471	314	16	[	[	X
cjfa-35471	314	17	0	0	NUM
cjfa-35471	314	18	,	,	PUNCT
cjfa-35471	314	19	1	1	NUM
cjfa-35471	314	20	]	]	PUNCT
cjfa-35471	314	21	i.e.	i.e.	X
cjfa-35471	314	22	0	0	X
cjfa-35471	314	23	<	<	X
cjfa-35471	314	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	314	25	�	�	PROPN
cjfa-35471	314	26	≤	≤	X
cjfa-35471	314	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	314	28	≤	≤	PROPN
cjfa-35471	314	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	314	30	�	�	PROPN
cjfa-35471	314	31	<	<	X
cjfa-35471	314	32	1	1	NUM
cjfa-35471	314	33	we	we	PRON
cjfa-35471	314	34	have	have	VERB
cjfa-35471	314	35	;	;	PUNCT
cjfa-35471	314	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	314	37	�	�	PROPN
cjfa-35471	314	38	=	=	SYM
cjfa-35471	314	39	0	0	NUM
cjfa-35471	314	40	=	=	SYM
cjfa-35471	314	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	314	42	)	)	PUNCT
cjfa-35471	315	1	−	−	PROPN
cjfa-35471	315	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	315	3	)	)	PUNCT
cjfa-35471	315	4	implying	imply	VERB
cjfa-35471	315	5	that	that	SCONJ
cjfa-35471	315	6	over	over	ADP
cjfa-35471	315	7	this	this	DET
cjfa-35471	315	8	period	period	NOUN
cjfa-35471	315	9	a	a	DET
cjfa-35471	315	10	firm	firm	NOUN
cjfa-35471	315	11	will	will	AUX
cjfa-35471	315	12	produce	produce	VERB
cjfa-35471	315	13	just	just	ADV
cjfa-35471	315	14	enough	enough	ADJ
cjfa-35471	315	15	to	to	PART
cjfa-35471	315	16	meet	meet	VERB
cjfa-35471	315	17	the	the	DET
cjfa-35471	315	18	demand	demand	NOUN
cjfa-35471	315	19	,	,	PUNCT
cjfa-35471	315	20	which	which	PRON
cjfa-35471	315	21	is	be	AUX
cjfa-35471	315	22	assumed	assume	VERB
cjfa-35471	315	23	to	to	PART
cjfa-35471	315	24	be	be	AUX
cjfa-35471	315	25	nonzero	nonzero	NOUN
cjfa-35471	315	26	during	during	ADP
cjfa-35471	315	27	the	the	DET
cjfa-35471	315	28	planning	planning	NOUN
cjfa-35471	315	29	horizon	horizon	NOUN
cjfa-35471	315	30	.	.	PUNCT
cjfa-35471	316	1	(	(	PUNCT
cjfa-35471	316	2	3	3	X
cjfa-35471	316	3	)	)	PUNCT
cjfa-35471	316	4	necessary	necessary	ADJ
cjfa-35471	316	5	conditions	condition	NOUN
cjfa-35471	316	6	are	be	AUX
cjfa-35471	316	7	also	also	ADV
cjfa-35471	316	8	sufficient	sufficient	ADJ
cjfa-35471	316	9	since	since	SCONJ
cjfa-35471	316	10	the	the	DET
cjfa-35471	316	11	hamiltonian	hamiltonian	NOUN
cjfa-35471	316	12	is	be	AUX
cjfa-35471	316	13	convex	convex	ADJ
cjfa-35471	316	14	in	in	ADP
cjfa-35471	316	15	both	both	CCONJ
cjfa-35471	316	16	the	the	DET
cjfa-35471	316	17	control	control	NOUN
cjfa-35471	316	18	(	(	PUNCT
cjfa-35471	316	19	u	u	NOUN
cjfa-35471	316	20	)	)	PUNCT
cjfa-35471	316	21	and	and	CCONJ
cjfa-35471	316	22	state	state	NOUN
cjfa-35471	316	23	(	(	PUNCT
cjfa-35471	316	24	l	l	NOUN
cjfa-35471	316	25	)	)	PUNCT
cjfa-35471	316	26	variables	variable	NOUN
cjfa-35471	316	27	.	.	PUNCT
cjfa-35471	317	1	the	the	DET
cjfa-35471	317	2	planning	planning	NOUN
cjfa-35471	317	3	horizon	horizon	NOUN
cjfa-35471	317	4	(	(	PUNCT
cjfa-35471	317	5	t	t	NOUN
cjfa-35471	317	6	)	)	PUNCT
cjfa-35471	317	7	will	will	AUX
cjfa-35471	317	8	be	be	AUX
cjfa-35471	317	9	assumed	assume	VERB
cjfa-35471	317	10	one	one	NUM
cjfa-35471	317	11	.	.	PUNCT
cjfa-35471	318	1	on	on	ADP
cjfa-35471	318	2	a	a	DET
cjfa-35471	318	3	constraint	constraint	NOUN
cjfa-35471	318	4	arc	arc	NOUN
cjfa-35471	318	5	on	on	ADP
cjfa-35471	318	6	which	which	PRON
cjfa-35471	318	7	l(t	l(t	VERB
cjfa-35471	318	8	)	)	PUNCT
cjfa-35471	318	9	=	=	SYM
cjfa-35471	318	10	0	0	NUM
cjfa-35471	318	11	for	for	ADP
cjfa-35471	318	12	a	a	DET
cjfa-35471	318	13	certain	certain	ADJ
cjfa-35471	318	14	period	period	NOUN
cjfa-35471	318	15	in	in	ADP
cjfa-35471	318	16	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	318	17	�	�	PROPN
cjfa-35471	318	18	=	=	SYM
cjfa-35471	318	19	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	318	20	)	)	PUNCT
cjfa-35471	318	21	−	−	PROPN
cjfa-35471	318	22	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	318	23	)	)	PUNCT
cjfa-35471	318	24	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	318	25	)	)	PUNCT
cjfa-35471	318	26	=	=	SYM
cjfa-35471	318	27	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	318	28	�	�	PROPN
cjfa-35471	318	29	a	a	DET
cjfa-35471	318	30	given	give	VERB
cjfa-35471	318	31	number	number	NOUN
cjfa-35471	318	32	.	.	PUNCT
cjfa-35471	319	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	319	2	)	)	PUNCT
cjfa-35471	320	1	𝑢	𝑢	PROPN
cjfa-35471	320	2	0	0	NUM
cjfa-35471	320	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	320	4	)	)	PUNCT
cjfa-35471	320	5	𝑢	𝑢	ADP
cjfa-35471	320	6	0	0	NUM
cjfa-35471	320	7	with	with	ADP
cjfa-35471	320	8	the	the	DET
cjfa-35471	320	9	assumptions	assumption	NOUN
cjfa-35471	320	10	that	that	SCONJ
cjfa-35471	320	11	the	the	DET
cjfa-35471	320	12	demand	demand	NOUN
cjfa-35471	320	13	(	(	PUNCT
cjfa-35471	320	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	320	15	(	(	PUNCT
cjfa-35471	320	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	320	17	)	)	PUNCT
cjfa-35471	320	18	)	)	PUNCT
cjfa-35471	320	19	is	be	AUX
cjfa-35471	320	20	a	a	DET
cjfa-35471	320	21	simple	simple	ADJ
cjfa-35471	320	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	320	23	function	function	NOUN
cjfa-35471	320	24	and	and	CCONJ
cjfa-35471	320	25	the	the	DET
cjfa-35471	320	26	interest	interest	NOUN
cjfa-35471	320	27	rate	rate	NOUN
cjfa-35471	320	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	320	29	)	)	PUNCT
cjfa-35471	320	30	is	be	AUX
cjfa-35471	320	31	time	time	NOUN
cjfa-35471	320	32	dependent	dependent	ADJ
cjfa-35471	320	33	,	,	PUNCT
cjfa-35471	320	34	i.e.	i.e.	X
cjfa-35471	320	35	:	:	PUNCT
cjfa-35471	320	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	320	37	)	)	PUNCT
cjfa-35471	321	1	=	=	SYM
cjfa-35471	321	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	321	3	𝐴	𝐴	PROPN
cjfa-35471	321	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	321	5	)	)	PUNCT
cjfa-35471	321	6	with	with	ADP
cjfa-35471	321	7	no	no	DET
cjfa-35471	321	8	growth	growth	NOUN
cjfa-35471	321	9	,	,	PUNCT
cjfa-35471	321	10	and	and	CCONJ
cjfa-35471	321	11	,	,	PUNCT
cjfa-35471	321	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	321	13	)	)	PUNCT
cjfa-35471	321	14	=	=	SYM
cjfa-35471	321	15	�	�	PROPN
cjfa-35471	321	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	321	17	�	�	PROPN
cjfa-35471	321	18	�	�	PROPN
cjfa-35471	321	19	implying	imply	VERB
cjfa-35471	321	20	that	that	SCONJ
cjfa-35471	321	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	321	22	)	)	PUNCT
cjfa-35471	322	1	=	=	VERB
cjfa-35471	322	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	322	3	if	if	SCONJ
cjfa-35471	322	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	322	5	is	be	AUX
cjfa-35471	322	6	constant	constant	ADJ
cjfa-35471	322	7	.	.	PUNCT
cjfa-35471	323	1	notice	notice	NOUN
cjfa-35471	323	2	also	also	ADV
cjfa-35471	323	3	that	that	SCONJ
cjfa-35471	323	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	323	5	�	�	X
cjfa-35471	323	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	323	7	)	)	PUNCT
cjfa-35471	323	8	=	=	SYM
cjfa-35471	323	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	323	10	)	)	PUNCT
cjfa-35471	323	11	where	where	SCONJ
cjfa-35471	323	12	f	f	PROPN
cjfa-35471	323	13	(	(	PUNCT
cjfa-35471	323	14	t	t	PROPN
cjfa-35471	323	15	)	)	PUNCT
cjfa-35471	323	16	denotes	denote	NOUN
cjfa-35471	323	17	time	time	VERB
cjfa-35471	323	18	dependent	dependent	ADJ
cjfa-35471	323	19	interest	interest	NOUN
cjfa-35471	323	20	rate	rate	NOUN
cjfa-35471	323	21	.	.	PUNCT
cjfa-35471	324	1	for	for	ADP
cjfa-35471	324	2	ease	ease	NOUN
cjfa-35471	324	3	of	of	ADP
cjfa-35471	324	4	analysis	analysis	NOUN
cjfa-35471	324	5	we	we	PRON
cjfa-35471	324	6	will	will	AUX
cjfa-35471	324	7	assume	assume	VERB
cjfa-35471	324	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	324	9	)	)	PUNCT
cjfa-35471	324	10	to	to	PART
cjfa-35471	324	11	be	be	AUX
cjfa-35471	324	12	constant	constant	ADJ
cjfa-35471	324	13	.	.	PUNCT
cjfa-35471	325	1	the	the	DET
cjfa-35471	325	2	letter	letter	NOUN
cjfa-35471	325	3	k	k	PROPN
cjfa-35471	325	4	denotes	denote	VERB
cjfa-35471	325	5	the	the	DET
cjfa-35471	325	6	periodicity	periodicity	NOUN
cjfa-35471	325	7	of	of	ADP
cjfa-35471	325	8	the	the	DET
cjfa-35471	325	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	325	10	demand	demand	NOUN
cjfa-35471	325	11	function	function	NOUN
cjfa-35471	325	12	over	over	ADP
cjfa-35471	325	13	the	the	DET
cjfa-35471	325	14	planning	planning	NOUN
cjfa-35471	325	15	period	period	NOUN
cjfa-35471	325	16	.	.	PUNCT
cjfa-35471	326	1	the	the	DET
cjfa-35471	326	2	only	only	ADJ
cjfa-35471	326	3	reason	reason	NOUN
cjfa-35471	326	4	for	for	ADP
cjfa-35471	326	5	the	the	DET
cjfa-35471	326	6	use	use	NOUN
cjfa-35471	326	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	326	8	demand	demand	NOUN
cjfa-35471	326	9	curve	curve	NOUN
cjfa-35471	326	10	is	be	AUX
cjfa-35471	326	11	that	that	SCONJ
cjfa-35471	326	12	it	it	PRON
cjfa-35471	326	13	represents	represent	VERB
cjfa-35471	326	14	cyclicality	cyclicality	NOUN
cjfa-35471	326	15	(	(	PUNCT
cjfa-35471	326	16	a	a	DET
cjfa-35471	326	17	measure	measure	NOUN
cjfa-35471	326	18	of	of	ADP
cjfa-35471	326	19	risk	risk	NOUN
cjfa-35471	326	20	)	)	PUNCT
cjfa-35471	326	21	and	and	CCONJ
cjfa-35471	326	22	that	that	SCONJ
cjfa-35471	326	23	it	it	PRON
cjfa-35471	326	24	is	be	AUX
cjfa-35471	326	25	easier	easy	ADJ
cjfa-35471	326	26	to	to	PART
cjfa-35471	326	27	work	work	VERB
cjfa-35471	326	28	with	with	ADP
cjfa-35471	326	29	it	it	PRON
cjfa-35471	326	30	.	.	PUNCT
cjfa-35471	327	1	the	the	DET
cjfa-35471	327	2	appropriate	appropriate	ADJ
cjfa-35471	327	3	lagrangian	lagrangian	NOUN
cjfa-35471	327	4	for	for	ADP
cjfa-35471	327	5	this	this	DET
cjfa-35471	327	6	problem	problem	NOUN
cjfa-35471	327	7	is	be	AUX
cjfa-35471	327	8	:	:	PUNCT
cjfa-35471	327	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	327	10	=	=	SYM
cjfa-35471	327	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	327	12	�	�	PROPN
cjfa-35471	327	13	�	�	PROPN
cjfa-35471	327	14	(	(	PUNCT
cjfa-35471	327	15	�	�	PROPN
cjfa-35471	327	16	)	)	PUNCT
cjfa-35471	327	17	�	�	PROPN
cjfa-35471	327	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	327	19	�	�	PROPN
cjfa-35471	327	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	327	21	)	)	PUNCT
cjfa-35471	327	22	�	�	PROPN
cjfa-35471	327	23	𝐴	𝐴	PROPN
cjfa-35471	327	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	327	25	)	)	PUNCT
cjfa-35471	327	26	�	�	PROPN
cjfa-35471	327	27	𝐴	𝐴	PROPN
cjfa-35471	327	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	327	29	�	�	PROPN
cjfa-35471	327	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	327	31	)	)	PUNCT
cjfa-35471	327	32	−	−	PROPN
cjfa-35471	327	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	327	34	)	)	PUNCT
cjfa-35471	327	35	�	�	PROPN
cjfa-35471	327	36	𝐴	𝐴	PROPN
cjfa-35471	327	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	327	38	�	�	PROPN
cjfa-35471	327	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	327	40	)	)	PUNCT
cjfa-35471	327	41	−	−	PROPN
cjfa-35471	327	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	327	43	)	)	PUNCT
cjfa-35471	327	44	�	�	PROPN
cjfa-35471	327	45	then	then	ADV
cjfa-35471	327	46	the	the	DET
cjfa-35471	327	47	necessary	necessary	ADJ
cjfa-35471	327	48	conditions	condition	NOUN
cjfa-35471	327	49	are	be	AUX
cjfa-35471	327	50	:	:	PUNCT
cjfa-35471	327	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	327	52	�	�	PROPN
cjfa-35471	327	53	�	�	PROPN
cjfa-35471	327	54	(	(	PUNCT
cjfa-35471	327	55	�	�	NOUN
cjfa-35471	327	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	327	57	�	�	PROPN
cjfa-35471	327	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	327	59	)	)	PUNCT
cjfa-35471	327	60	𝐴	𝐴	PROPN
cjfa-35471	327	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	327	62	)	)	PUNCT
cjfa-35471	327	63	−	−	PROPN
cjfa-35471	327	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	327	65	)	)	PUNCT
cjfa-35471	328	1	=	=	SYM
cjfa-35471	328	2	0	0	PUNCT
cjfa-35471	328	3	(	(	PUNCT
cjfa-35471	328	4	1	1	NUM
cjfa-35471	328	5	)	)	PUNCT
cjfa-35471	328	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	328	7	�	�	PROPN
cjfa-35471	328	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	328	9	)	)	PUNCT
cjfa-35471	328	10	=	=	SYM
cjfa-35471	328	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	328	12	�	�	PROPN
cjfa-35471	328	13	�	�	PROPN
cjfa-35471	328	14	(	(	PUNCT
cjfa-35471	328	15	�	�	PROPN
cjfa-35471	328	16	)ℎ	)ℎ	PROPN
cjfa-35471	328	17	(	(	PUNCT
cjfa-35471	328	18	2	2	X
cjfa-35471	328	19	)	)	PUNCT
cjfa-35471	328	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	328	21	�	�	PROPN
cjfa-35471	328	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	328	23	)	)	PUNCT
cjfa-35471	328	24	=	=	SYM
cjfa-35471	328	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	328	26	)	)	PUNCT
cjfa-35471	328	27	−	−	PROPN
cjfa-35471	328	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	328	29	)	)	PUNCT
cjfa-35471	328	30	(	(	PUNCT
cjfa-35471	328	31	3	3	X
cjfa-35471	328	32	)	)	PUNCT
cjfa-35471	328	33	necessary	necessary	ADJ
cjfa-35471	328	34	conditions	condition	NOUN
cjfa-35471	328	35	are	be	AUX
cjfa-35471	328	36	also	also	ADV
cjfa-35471	328	37	sufficient	sufficient	ADJ
cjfa-35471	328	38	since	since	SCONJ
cjfa-35471	328	39	the	the	DET
cjfa-35471	328	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	328	41	is	be	AUX
cjfa-35471	328	42	convex	convex	ADJ
cjfa-35471	328	43	in	in	ADP
cjfa-35471	328	44	both	both	CCONJ
cjfa-35471	328	45	the	the	DET
cjfa-35471	328	46	control	control	NOUN
cjfa-35471	328	47	(	(	PUNCT
cjfa-35471	328	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	328	49	)	)	PUNCT
cjfa-35471	328	50	and	and	CCONJ
cjfa-35471	328	51	state	state	NOUN
cjfa-35471	328	52	(	(	PUNCT
cjfa-35471	328	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	328	54	)	)	PUNCT
cjfa-35471	328	55	variables	variable	NOUN
cjfa-35471	328	56	.	.	PUNCT
cjfa-35471	329	1	the	the	DET
cjfa-35471	329	2	planning	planning	NOUN
cjfa-35471	329	3	horizon	horizon	NOUN
cjfa-35471	329	4	(	(	PUNCT
cjfa-35471	329	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	329	6	)	)	PUNCT
cjfa-35471	329	7	will	will	AUX
cjfa-35471	329	8	be	be	AUX
cjfa-35471	329	9	assumed	assume	VERB
cjfa-35471	329	10	one	one	NUM
cjfa-35471	329	11	.	.	PUNCT
cjfa-35471	330	1	on	on	ADP
cjfa-35471	330	2	a	a	DET
cjfa-35471	330	3	constraint	constraint	NOUN
cjfa-35471	330	4	arc	arc	NOUN
cjfa-35471	330	5	on	on	ADP
cjfa-35471	330	6	which	which	PRON
cjfa-35471	330	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	330	8	)	)	PUNCT
cjfa-35471	330	9	=	=	SYM
cjfa-35471	330	10	0	0	NUM
cjfa-35471	330	11	for	for	ADP
cjfa-35471	330	12	a	a	DET
cjfa-35471	330	13	certain	certain	ADJ
cjfa-35471	330	14	period	period	NOUN
cjfa-35471	330	15	in	in	ADP
cjfa-35471	330	16	[	[	X
cjfa-35471	330	17	0	0	NUM
cjfa-35471	330	18	,	,	PUNCT
cjfa-35471	330	19	1	1	NUM
cjfa-35471	330	20	]	]	PUNCT
cjfa-35471	330	21	i.e.	i.e.	X
cjfa-35471	330	22	0	0	X
cjfa-35471	330	23	<	<	X
cjfa-35471	330	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	330	25	�	�	PROPN
cjfa-35471	330	26	≤	≤	X
cjfa-35471	330	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	330	28	≤	≤	PROPN
cjfa-35471	330	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	330	30	�	�	PROPN
cjfa-35471	330	31	<	<	X
cjfa-35471	330	32	1	1	NUM
cjfa-35471	330	33	we	we	PRON
cjfa-35471	330	34	have	have	VERB
cjfa-35471	330	35	;	;	PUNCT
cjfa-35471	330	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	330	37	�	�	PROPN
cjfa-35471	330	38	=	=	SYM
cjfa-35471	330	39	0	0	NUM
cjfa-35471	330	40	=	=	SYM
cjfa-35471	330	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	330	42	)	)	PUNCT
cjfa-35471	331	1	−	−	PROPN
cjfa-35471	331	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	331	3	)	)	PUNCT
cjfa-35471	331	4	implying	imply	VERB
cjfa-35471	331	5	that	that	SCONJ
cjfa-35471	331	6	over	over	ADP
cjfa-35471	331	7	this	this	DET
cjfa-35471	331	8	period	period	NOUN
cjfa-35471	331	9	a	a	DET
cjfa-35471	331	10	firm	firm	NOUN
cjfa-35471	331	11	will	will	AUX
cjfa-35471	331	12	produce	produce	VERB
cjfa-35471	331	13	just	just	ADV
cjfa-35471	331	14	enough	enough	ADJ
cjfa-35471	331	15	to	to	PART
cjfa-35471	331	16	meet	meet	VERB
cjfa-35471	331	17	the	the	DET
cjfa-35471	331	18	demand	demand	NOUN
cjfa-35471	331	19	,	,	PUNCT
cjfa-35471	331	20	which	which	PRON
cjfa-35471	331	21	is	be	AUX
cjfa-35471	331	22	assumed	assume	VERB
cjfa-35471	331	23	to	to	PART
cjfa-35471	331	24	be	be	AUX
cjfa-35471	331	25	nonzero	nonzero	NOUN
cjfa-35471	331	26	during	during	ADP
cjfa-35471	331	27	the	the	DET
cjfa-35471	331	28	planning	planning	NOUN
cjfa-35471	331	29	horizon	horizon	NOUN
cjfa-35471	331	30	.	.	PUNCT
cjfa-35471	332	1	then	then	ADV
cjfa-35471	332	2	using	use	VERB
cjfa-35471	332	3	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	332	4	)	)	PUNCT
cjfa-35471	332	5	=	=	SYM
cjfa-35471	332	6	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	332	7	)	)	PUNCT
cjfa-35471	332	8	,	,	PUNCT
cjfa-35471	332	9	equation	equation	NOUN
cjfa-35471	332	10	(	(	PUNCT
cjfa-35471	332	11	1	1	NUM
cjfa-35471	332	12	)	)	PUNCT
cjfa-35471	332	13	,	,	PUNCT
cjfa-35471	332	14	and	and	CCONJ
cjfa-35471	332	15	the	the	DET
cjfa-35471	332	16	conditions	condition	NOUN
cjfa-35471	332	17	(	(	PUNCT
cjfa-35471	332	18	the	the	DET
cjfa-35471	332	19	necessary	necessary	ADJ
cjfa-35471	332	20	condition	condition	NOUN
cjfa-35471	332	21	to	to	PART
cjfa-35471	332	22	keep	keep	VERB
cjfa-35471	332	23	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	332	24	)	)	PUNCT
cjfa-35471	332	25	=	=	SYM
cjfa-35471	332	26	0	0	NUM
cjfa-35471	332	27	optimal	optimal	ADJ
cjfa-35471	332	28	)	)	PUNCT
cjfa-35471	332	29	developed	develop	VERB
cjfa-35471	332	30	by	by	ADP
cjfa-35471	332	31	pontryagin	pontryagin	NOUN
cjfa-35471	332	32	,	,	PUNCT
cjfa-35471	332	33	boltyanskii	boltyanskii	ADJ
cjfa-35471	332	34	,	,	PUNCT
cjfa-35471	332	35	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	332	36	and	and	CCONJ
cjfa-35471	332	37	mishechenko	mishechenko	NOUN
cjfa-35471	332	38	(	(	PUNCT
cjfa-35471	332	39	1962	1962	NUM
cjfa-35471	332	40	)	)	PUNCT
cjfa-35471	332	41	,	,	PUNCT
cjfa-35471	332	42	hestenes	hestene	NOUN
cjfa-35471	332	43	(	(	PUNCT
cjfa-35471	332	44	1966	1966	NUM
cjfa-35471	332	45	)	)	PUNCT
cjfa-35471	332	46	,	,	PUNCT
cjfa-35471	332	47	kamien	kamien	NOUN
cjfa-35471	332	48	and	and	CCONJ
cjfa-35471	332	49	schwartz	schwartz	PROPN
cjfa-35471	332	50	(	(	PUNCT
cjfa-35471	332	51	2012	2012	NUM
cjfa-35471	332	52	)	)	PUNCT
cjfa-35471	332	53	among	among	ADP
cjfa-35471	332	54	many	many	ADJ
cjfa-35471	332	55	others	other	NOUN
cjfa-35471	332	56	,	,	PUNCT
cjfa-35471	332	57	we	we	PRON
cjfa-35471	332	58	have	have	VERB
cjfa-35471	332	59	;	;	PUNCT
cjfa-35471	332	60	𝜇𝜇	𝜇𝜇	ADP
cjfa-35471	332	61	�	�	PROPN
cjfa-35471	332	62	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	332	63	)	)	PUNCT
cjfa-35471	332	64	≤	≤	NOUN
cjfa-35471	332	65	0	0	NUM
cjfa-35471	332	66	for	for	ADP
cjfa-35471	332	67	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	332	68	�	�	PROPN
cjfa-35471	332	69	≤	≤	NOUN
cjfa-35471	332	70	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	332	71	≤	≤	PROPN
cjfa-35471	332	72	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	332	73	�	�	PROPN
cjfa-35471	332	74	implies	imply	VERB
cjfa-35471	332	75	:	:	PUNCT
cjfa-35471	333	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	333	2	�	�	PROPN
cjfa-35471	333	3	�	�	PROPN
cjfa-35471	333	4	�	�	PROPN
cjfa-35471	333	5	𝑟𝑟(𝑡𝑡)	𝑟𝑟(𝑡𝑡)	PROPN
cjfa-35471	333	6	�	�	PROPN
cjfa-35471	333	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	333	8	�	�	PROPN
cjfa-35471	333	9	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	333	10	)	)	PUNCT
cjfa-35471	333	11	≤	≤	NOUN
cjfa-35471	333	12	ℎ	ℎ	PROPN
cjfa-35471	333	13	𝐴	𝐴	PROPN
cjfa-35471	333	14	𝑓𝑓(𝑡𝑡)𝑐𝑐	𝑓𝑓(𝑡𝑡)𝑐𝑐	VERB
cjfa-35471	333	15	�	�	PROPN
cjfa-35471	333	16	�	�	NOUN
cjfa-35471	333	17	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	333	18	)	)	PUNCT
cjfa-35471	333	19	�	�	PROPN
cjfa-35471	333	20	(	(	PUNCT
cjfa-35471	333	21	4	4	NUM
cjfa-35471	333	22	)	)	PUNCT
cjfa-35471	333	23	we	we	PRON
cjfa-35471	333	24	have	have	VERB
cjfa-35471	333	25	;	;	PUNCT
cjfa-35471	333	26	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	333	27	�	�	PROPN
cjfa-35471	333	28	=	=	SYM
cjfa-35471	333	29	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	333	30	)	)	PUNCT
cjfa-35471	334	1	−	−	PROPN
cjfa-35471	334	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	334	3	)	)	PUNCT
cjfa-35471	334	4	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	334	5	)	)	PUNCT
cjfa-35471	334	6	=	=	SYM
cjfa-35471	334	7	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	334	8	�	�	PROPN
cjfa-35471	334	9	a	a	DET
cjfa-35471	334	10	given	give	VERB
cjfa-35471	334	11	number	number	NOUN
cjfa-35471	334	12	.	.	PUNCT
cjfa-35471	335	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	335	2	)	)	PUNCT
cjfa-35471	336	1	𝑢	𝑢	PROPN
cjfa-35471	336	2	0	0	NUM
cjfa-35471	336	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	336	4	)	)	PUNCT
cjfa-35471	336	5	𝑢	𝑢	ADP
cjfa-35471	336	6	0	0	NUM
cjfa-35471	336	7	with	with	ADP
cjfa-35471	336	8	the	the	DET
cjfa-35471	336	9	assumptions	assumption	NOUN
cjfa-35471	336	10	that	that	SCONJ
cjfa-35471	336	11	the	the	DET
cjfa-35471	336	12	demand	demand	NOUN
cjfa-35471	336	13	(	(	PUNCT
cjfa-35471	336	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	336	15	(	(	PUNCT
cjfa-35471	336	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	336	17	)	)	PUNCT
cjfa-35471	336	18	)	)	PUNCT
cjfa-35471	336	19	is	be	AUX
cjfa-35471	336	20	a	a	DET
cjfa-35471	336	21	simple	simple	ADJ
cjfa-35471	336	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	336	23	function	function	NOUN
cjfa-35471	336	24	and	and	CCONJ
cjfa-35471	336	25	the	the	DET
cjfa-35471	336	26	interest	interest	NOUN
cjfa-35471	336	27	rate	rate	NOUN
cjfa-35471	336	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	336	29	)	)	PUNCT
cjfa-35471	336	30	is	be	AUX
cjfa-35471	336	31	time	time	NOUN
cjfa-35471	336	32	dependent	dependent	ADJ
cjfa-35471	336	33	,	,	PUNCT
cjfa-35471	336	34	i.e.	i.e.	X
cjfa-35471	336	35	:	:	PUNCT
cjfa-35471	336	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	336	37	)	)	PUNCT
cjfa-35471	337	1	=	=	SYM
cjfa-35471	337	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	337	3	𝐴	𝐴	PROPN
cjfa-35471	337	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	337	5	)	)	PUNCT
cjfa-35471	337	6	with	with	ADP
cjfa-35471	337	7	no	no	DET
cjfa-35471	337	8	growth	growth	NOUN
cjfa-35471	337	9	,	,	PUNCT
cjfa-35471	337	10	and	and	CCONJ
cjfa-35471	337	11	,	,	PUNCT
cjfa-35471	337	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	337	13	)	)	PUNCT
cjfa-35471	337	14	=	=	SYM
cjfa-35471	337	15	�	�	PROPN
cjfa-35471	337	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	337	17	�	�	PROPN
cjfa-35471	337	18	�	�	PROPN
cjfa-35471	337	19	implying	imply	VERB
cjfa-35471	337	20	that	that	SCONJ
cjfa-35471	337	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	337	22	)	)	PUNCT
cjfa-35471	338	1	=	=	VERB
cjfa-35471	338	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	338	3	if	if	SCONJ
cjfa-35471	338	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	338	5	is	be	AUX
cjfa-35471	338	6	constant	constant	ADJ
cjfa-35471	338	7	.	.	PUNCT
cjfa-35471	339	1	notice	notice	NOUN
cjfa-35471	339	2	also	also	ADV
cjfa-35471	339	3	that	that	SCONJ
cjfa-35471	339	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	339	5	�	�	X
cjfa-35471	339	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	339	7	)	)	PUNCT
cjfa-35471	339	8	=	=	SYM
cjfa-35471	339	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	339	10	)	)	PUNCT
cjfa-35471	339	11	where	where	SCONJ
cjfa-35471	339	12	f	f	PROPN
cjfa-35471	339	13	(	(	PUNCT
cjfa-35471	339	14	t	t	PROPN
cjfa-35471	339	15	)	)	PUNCT
cjfa-35471	339	16	denotes	denote	NOUN
cjfa-35471	339	17	time	time	VERB
cjfa-35471	339	18	dependent	dependent	ADJ
cjfa-35471	339	19	interest	interest	NOUN
cjfa-35471	339	20	rate	rate	NOUN
cjfa-35471	339	21	.	.	PUNCT
cjfa-35471	340	1	for	for	ADP
cjfa-35471	340	2	ease	ease	NOUN
cjfa-35471	340	3	of	of	ADP
cjfa-35471	340	4	analysis	analysis	NOUN
cjfa-35471	340	5	we	we	PRON
cjfa-35471	340	6	will	will	AUX
cjfa-35471	340	7	assume	assume	VERB
cjfa-35471	340	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	340	9	)	)	PUNCT
cjfa-35471	340	10	to	to	PART
cjfa-35471	340	11	be	be	AUX
cjfa-35471	340	12	constant	constant	ADJ
cjfa-35471	340	13	.	.	PUNCT
cjfa-35471	341	1	the	the	DET
cjfa-35471	341	2	letter	letter	NOUN
cjfa-35471	341	3	k	k	PROPN
cjfa-35471	341	4	denotes	denote	VERB
cjfa-35471	341	5	the	the	DET
cjfa-35471	341	6	periodicity	periodicity	NOUN
cjfa-35471	341	7	of	of	ADP
cjfa-35471	341	8	the	the	DET
cjfa-35471	341	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	341	10	demand	demand	NOUN
cjfa-35471	341	11	function	function	NOUN
cjfa-35471	341	12	over	over	ADP
cjfa-35471	341	13	the	the	DET
cjfa-35471	341	14	planning	planning	NOUN
cjfa-35471	341	15	period	period	NOUN
cjfa-35471	341	16	.	.	PUNCT
cjfa-35471	342	1	the	the	DET
cjfa-35471	342	2	only	only	ADJ
cjfa-35471	342	3	reason	reason	NOUN
cjfa-35471	342	4	for	for	ADP
cjfa-35471	342	5	the	the	DET
cjfa-35471	342	6	use	use	NOUN
cjfa-35471	342	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	342	8	demand	demand	NOUN
cjfa-35471	342	9	curve	curve	NOUN
cjfa-35471	342	10	is	be	AUX
cjfa-35471	342	11	that	that	SCONJ
cjfa-35471	342	12	it	it	PRON
cjfa-35471	342	13	represents	represent	VERB
cjfa-35471	342	14	cyclicality	cyclicality	NOUN
cjfa-35471	342	15	(	(	PUNCT
cjfa-35471	342	16	a	a	DET
cjfa-35471	342	17	measure	measure	NOUN
cjfa-35471	342	18	of	of	ADP
cjfa-35471	342	19	risk	risk	NOUN
cjfa-35471	342	20	)	)	PUNCT
cjfa-35471	342	21	and	and	CCONJ
cjfa-35471	342	22	that	that	SCONJ
cjfa-35471	342	23	it	it	PRON
cjfa-35471	342	24	is	be	AUX
cjfa-35471	342	25	easier	easy	ADJ
cjfa-35471	342	26	to	to	PART
cjfa-35471	342	27	work	work	VERB
cjfa-35471	342	28	with	with	ADP
cjfa-35471	342	29	it	it	PRON
cjfa-35471	342	30	.	.	PUNCT
cjfa-35471	343	1	the	the	DET
cjfa-35471	343	2	appropriate	appropriate	ADJ
cjfa-35471	343	3	lagrangian	lagrangian	NOUN
cjfa-35471	343	4	for	for	ADP
cjfa-35471	343	5	this	this	DET
cjfa-35471	343	6	problem	problem	NOUN
cjfa-35471	343	7	is	be	AUX
cjfa-35471	343	8	:	:	PUNCT
cjfa-35471	343	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	343	10	=	=	SYM
cjfa-35471	343	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	343	12	�	�	PROPN
cjfa-35471	343	13	�	�	PROPN
cjfa-35471	343	14	(	(	PUNCT
cjfa-35471	343	15	�	�	PROPN
cjfa-35471	343	16	)	)	PUNCT
cjfa-35471	343	17	�	�	PROPN
cjfa-35471	343	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	343	19	�	�	PROPN
cjfa-35471	343	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	343	21	)	)	PUNCT
cjfa-35471	343	22	�	�	PROPN
cjfa-35471	343	23	𝐴	𝐴	PROPN
cjfa-35471	343	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	343	25	)	)	PUNCT
cjfa-35471	343	26	�	�	PROPN
cjfa-35471	343	27	𝐴	𝐴	PROPN
cjfa-35471	343	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	343	29	�	�	PROPN
cjfa-35471	343	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	343	31	)	)	PUNCT
cjfa-35471	343	32	−	−	PROPN
cjfa-35471	343	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	343	34	)	)	PUNCT
cjfa-35471	343	35	�	�	PROPN
cjfa-35471	343	36	𝐴	𝐴	PROPN
cjfa-35471	343	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	343	38	�	�	PROPN
cjfa-35471	343	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	343	40	)	)	PUNCT
cjfa-35471	343	41	−	−	PROPN
cjfa-35471	343	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	343	43	)	)	PUNCT
cjfa-35471	343	44	�	�	PROPN
cjfa-35471	343	45	then	then	ADV
cjfa-35471	343	46	the	the	DET
cjfa-35471	343	47	necessary	necessary	ADJ
cjfa-35471	343	48	conditions	condition	NOUN
cjfa-35471	343	49	are	be	AUX
cjfa-35471	343	50	:	:	PUNCT
cjfa-35471	343	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	343	52	�	�	PROPN
cjfa-35471	343	53	�	�	PROPN
cjfa-35471	343	54	(	(	PUNCT
cjfa-35471	343	55	�	�	NOUN
cjfa-35471	343	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	343	57	�	�	PROPN
cjfa-35471	343	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	343	59	)	)	PUNCT
cjfa-35471	343	60	𝐴	𝐴	PROPN
cjfa-35471	343	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	343	62	)	)	PUNCT
cjfa-35471	343	63	−	−	PROPN
cjfa-35471	343	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	343	65	)	)	PUNCT
cjfa-35471	344	1	=	=	SYM
cjfa-35471	344	2	0	0	PUNCT
cjfa-35471	344	3	(	(	PUNCT
cjfa-35471	344	4	1	1	NUM
cjfa-35471	344	5	)	)	PUNCT
cjfa-35471	344	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	344	7	�	�	PROPN
cjfa-35471	344	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	344	9	)	)	PUNCT
cjfa-35471	344	10	=	=	SYM
cjfa-35471	344	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	344	12	�	�	PROPN
cjfa-35471	344	13	�	�	PROPN
cjfa-35471	344	14	(	(	PUNCT
cjfa-35471	344	15	�	�	PROPN
cjfa-35471	344	16	)ℎ	)ℎ	PROPN
cjfa-35471	344	17	(	(	PUNCT
cjfa-35471	344	18	2	2	X
cjfa-35471	344	19	)	)	PUNCT
cjfa-35471	344	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	344	21	�	�	PROPN
cjfa-35471	344	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	344	23	)	)	PUNCT
cjfa-35471	344	24	=	=	SYM
cjfa-35471	344	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	344	26	)	)	PUNCT
cjfa-35471	344	27	−	−	PROPN
cjfa-35471	344	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	344	29	)	)	PUNCT
cjfa-35471	344	30	(	(	PUNCT
cjfa-35471	344	31	3	3	X
cjfa-35471	344	32	)	)	PUNCT
cjfa-35471	344	33	necessary	necessary	ADJ
cjfa-35471	344	34	conditions	condition	NOUN
cjfa-35471	344	35	are	be	AUX
cjfa-35471	344	36	also	also	ADV
cjfa-35471	344	37	sufficient	sufficient	ADJ
cjfa-35471	344	38	since	since	SCONJ
cjfa-35471	344	39	the	the	DET
cjfa-35471	344	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	344	41	is	be	AUX
cjfa-35471	344	42	convex	convex	ADJ
cjfa-35471	344	43	in	in	ADP
cjfa-35471	344	44	both	both	CCONJ
cjfa-35471	344	45	the	the	DET
cjfa-35471	344	46	control	control	NOUN
cjfa-35471	344	47	(	(	PUNCT
cjfa-35471	344	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	344	49	)	)	PUNCT
cjfa-35471	344	50	and	and	CCONJ
cjfa-35471	344	51	state	state	NOUN
cjfa-35471	344	52	(	(	PUNCT
cjfa-35471	344	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	344	54	)	)	PUNCT
cjfa-35471	344	55	variables	variable	NOUN
cjfa-35471	344	56	.	.	PUNCT
cjfa-35471	345	1	the	the	DET
cjfa-35471	345	2	planning	planning	NOUN
cjfa-35471	345	3	horizon	horizon	NOUN
cjfa-35471	345	4	(	(	PUNCT
cjfa-35471	345	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	345	6	)	)	PUNCT
cjfa-35471	345	7	will	will	AUX
cjfa-35471	345	8	be	be	AUX
cjfa-35471	345	9	assumed	assume	VERB
cjfa-35471	345	10	one	one	NUM
cjfa-35471	345	11	.	.	PUNCT
cjfa-35471	346	1	on	on	ADP
cjfa-35471	346	2	a	a	DET
cjfa-35471	346	3	constraint	constraint	NOUN
cjfa-35471	346	4	arc	arc	NOUN
cjfa-35471	346	5	on	on	ADP
cjfa-35471	346	6	which	which	PRON
cjfa-35471	346	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	346	8	)	)	PUNCT
cjfa-35471	346	9	=	=	SYM
cjfa-35471	346	10	0	0	NUM
cjfa-35471	346	11	for	for	ADP
cjfa-35471	346	12	a	a	DET
cjfa-35471	346	13	certain	certain	ADJ
cjfa-35471	346	14	period	period	NOUN
cjfa-35471	346	15	in	in	ADP
cjfa-35471	346	16	[	[	X
cjfa-35471	346	17	0	0	NUM
cjfa-35471	346	18	,	,	PUNCT
cjfa-35471	346	19	1	1	NUM
cjfa-35471	346	20	]	]	PUNCT
cjfa-35471	346	21	i.e.	i.e.	X
cjfa-35471	346	22	0	0	X
cjfa-35471	346	23	<	<	X
cjfa-35471	346	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	346	25	�	�	PROPN
cjfa-35471	346	26	≤	≤	X
cjfa-35471	346	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	346	28	≤	≤	PROPN
cjfa-35471	346	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	346	30	�	�	PROPN
cjfa-35471	346	31	<	<	X
cjfa-35471	346	32	1	1	NUM
cjfa-35471	346	33	we	we	PRON
cjfa-35471	346	34	have	have	VERB
cjfa-35471	346	35	;	;	PUNCT
cjfa-35471	346	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	346	37	�	�	PROPN
cjfa-35471	346	38	=	=	SYM
cjfa-35471	346	39	0	0	NUM
cjfa-35471	346	40	=	=	SYM
cjfa-35471	346	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	346	42	)	)	PUNCT
cjfa-35471	347	1	−	−	PROPN
cjfa-35471	347	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	347	3	)	)	PUNCT
cjfa-35471	347	4	implying	imply	VERB
cjfa-35471	347	5	that	that	SCONJ
cjfa-35471	347	6	over	over	ADP
cjfa-35471	347	7	this	this	DET
cjfa-35471	347	8	period	period	NOUN
cjfa-35471	347	9	a	a	DET
cjfa-35471	347	10	firm	firm	NOUN
cjfa-35471	347	11	will	will	AUX
cjfa-35471	347	12	produce	produce	VERB
cjfa-35471	347	13	just	just	ADV
cjfa-35471	347	14	enough	enough	ADJ
cjfa-35471	347	15	to	to	PART
cjfa-35471	347	16	meet	meet	VERB
cjfa-35471	347	17	the	the	DET
cjfa-35471	347	18	demand	demand	NOUN
cjfa-35471	347	19	,	,	PUNCT
cjfa-35471	347	20	which	which	PRON
cjfa-35471	347	21	is	be	AUX
cjfa-35471	347	22	assumed	assume	VERB
cjfa-35471	347	23	to	to	PART
cjfa-35471	347	24	be	be	AUX
cjfa-35471	347	25	nonzero	nonzero	NOUN
cjfa-35471	347	26	during	during	ADP
cjfa-35471	347	27	the	the	DET
cjfa-35471	347	28	planning	planning	NOUN
cjfa-35471	347	29	horizon	horizon	NOUN
cjfa-35471	347	30	.	.	PUNCT
cjfa-35471	348	1	implying	imply	VERB
cjfa-35471	348	2	that	that	SCONJ
cjfa-35471	348	3	over	over	ADP
cjfa-35471	348	4	this	this	DET
cjfa-35471	348	5	period	period	NOUN
cjfa-35471	348	6	a	a	DET
cjfa-35471	348	7	firm	firm	NOUN
cjfa-35471	348	8	will	will	AUX
cjfa-35471	348	9	produce	produce	VERB
cjfa-35471	348	10	just	just	ADV
cjfa-35471	348	11	enough	enough	ADJ
cjfa-35471	348	12	to	to	PART
cjfa-35471	348	13	meet	meet	VERB
cjfa-35471	348	14	the	the	DET
cjfa-35471	348	15	demand	demand	NOUN
cjfa-35471	348	16	,	,	PUNCT
cjfa-35471	348	17	which	which	PRON
cjfa-35471	348	18	is	be	AUX
cjfa-35471	348	19	assumed	assume	VERB
cjfa-35471	348	20	to	to	PART
cjfa-35471	348	21	be	be	AUX
cjfa-35471	348	22	nonzero	nonzero	NOUN
cjfa-35471	348	23	during	during	ADP
cjfa-35471	348	24	the	the	DET
cjfa-35471	348	25	planning	planning	NOUN
cjfa-35471	348	26	horizon	horizon	NOUN
cjfa-35471	348	27	.	.	PUNCT
cjfa-35471	349	1	then	then	ADV
cjfa-35471	349	2	using	use	VERB
cjfa-35471	349	3	u(t	u(t	NOUN
cjfa-35471	349	4	)	)	PUNCT
cjfa-35471	349	5	=	=	SYM
cjfa-35471	349	6	r(t	r(t	NOUN
cjfa-35471	349	7	)	)	PUNCT
cjfa-35471	349	8	,	,	PUNCT
cjfa-35471	349	9	equation	equation	NOUN
cjfa-35471	349	10	(	(	PUNCT
cjfa-35471	349	11	1	1	NUM
cjfa-35471	349	12	)	)	PUNCT
cjfa-35471	349	13	,	,	PUNCT
cjfa-35471	349	14	and	and	CCONJ
cjfa-35471	349	15	the	the	DET
cjfa-35471	349	16	conditions	condition	NOUN
cjfa-35471	349	17	(	(	PUNCT
cjfa-35471	349	18	the	the	DET
cjfa-35471	349	19	necessary	necessary	ADJ
cjfa-35471	349	20	condition	condition	NOUN
cjfa-35471	349	21	to	to	PART
cjfa-35471	349	22	keep	keep	VERB
cjfa-35471	349	23	i(t	i(t	NOUN
cjfa-35471	349	24	)	)	PUNCT
cjfa-35471	349	25	=	=	SYM
cjfa-35471	349	26	0	0	NUM
cjfa-35471	349	27	optimal	optimal	ADJ
cjfa-35471	349	28	)	)	PUNCT
cjfa-35471	349	29	developed	develop	VERB
cjfa-35471	349	30	by	by	ADP
cjfa-35471	349	31	pontryagin	pontryagin	NOUN
cjfa-35471	349	32	,	,	PUNCT
cjfa-35471	349	33	boltyanskii	boltyanskii	ADJ
cjfa-35471	349	34	,	,	PUNCT
cjfa-35471	349	35	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	349	36	and	and	CCONJ
cjfa-35471	349	37	mishechenko	mishechenko	NOUN
cjfa-35471	349	38	(	(	PUNCT
cjfa-35471	349	39	1962	1962	NUM
cjfa-35471	349	40	)	)	PUNCT
cjfa-35471	349	41	,	,	PUNCT
cjfa-35471	349	42	hestenes	hestene	NOUN
cjfa-35471	349	43	(	(	PUNCT
cjfa-35471	349	44	1966	1966	NUM
cjfa-35471	349	45	)	)	PUNCT
cjfa-35471	349	46	,	,	PUNCT
cjfa-35471	349	47	kamien	kamien	NOUN
cjfa-35471	349	48	and	and	CCONJ
cjfa-35471	349	49	schwartz	schwartz	PROPN
cjfa-35471	349	50	(	(	PUNCT
cjfa-35471	349	51	2012	2012	NUM
cjfa-35471	349	52	)	)	PUNCT
cjfa-35471	349	53	among	among	ADP
cjfa-35471	349	54	many	many	ADJ
cjfa-35471	349	55	others	other	NOUN
cjfa-35471	349	56	,	,	PUNCT
cjfa-35471	349	57	we	we	PRON
cjfa-35471	349	58	have	have	VERB
cjfa-35471	349	59	;	;	PUNCT
cjfa-35471	349	60	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	349	61	�	�	PROPN
cjfa-35471	349	62	=	=	SYM
cjfa-35471	349	63	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	349	64	)	)	PUNCT
cjfa-35471	350	1	−	−	PROPN
cjfa-35471	350	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	350	3	)	)	PUNCT
cjfa-35471	350	4	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	350	5	)	)	PUNCT
cjfa-35471	350	6	=	=	SYM
cjfa-35471	350	7	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	350	8	�	�	PROPN
cjfa-35471	350	9	a	a	DET
cjfa-35471	350	10	given	give	VERB
cjfa-35471	350	11	number	number	NOUN
cjfa-35471	350	12	.	.	PUNCT
cjfa-35471	351	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	351	2	)	)	PUNCT
cjfa-35471	352	1	𝑢	𝑢	PROPN
cjfa-35471	352	2	0	0	NUM
cjfa-35471	352	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	352	4	)	)	PUNCT
cjfa-35471	352	5	𝑢	𝑢	ADP
cjfa-35471	352	6	0	0	NUM
cjfa-35471	352	7	with	with	ADP
cjfa-35471	352	8	the	the	DET
cjfa-35471	352	9	assumptions	assumption	NOUN
cjfa-35471	352	10	that	that	SCONJ
cjfa-35471	352	11	the	the	DET
cjfa-35471	352	12	demand	demand	NOUN
cjfa-35471	352	13	(	(	PUNCT
cjfa-35471	352	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	352	15	(	(	PUNCT
cjfa-35471	352	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	352	17	)	)	PUNCT
cjfa-35471	352	18	)	)	PUNCT
cjfa-35471	352	19	is	be	AUX
cjfa-35471	352	20	a	a	DET
cjfa-35471	352	21	simple	simple	ADJ
cjfa-35471	352	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	352	23	function	function	NOUN
cjfa-35471	352	24	and	and	CCONJ
cjfa-35471	352	25	the	the	DET
cjfa-35471	352	26	interest	interest	NOUN
cjfa-35471	352	27	rate	rate	NOUN
cjfa-35471	352	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	352	29	)	)	PUNCT
cjfa-35471	352	30	is	be	AUX
cjfa-35471	352	31	time	time	NOUN
cjfa-35471	352	32	dependent	dependent	ADJ
cjfa-35471	352	33	,	,	PUNCT
cjfa-35471	352	34	i.e.	i.e.	X
cjfa-35471	352	35	:	:	PUNCT
cjfa-35471	352	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	352	37	)	)	PUNCT
cjfa-35471	353	1	=	=	SYM
cjfa-35471	353	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	353	3	𝐴	𝐴	PROPN
cjfa-35471	353	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	353	5	)	)	PUNCT
cjfa-35471	353	6	with	with	ADP
cjfa-35471	353	7	no	no	DET
cjfa-35471	353	8	growth	growth	NOUN
cjfa-35471	353	9	,	,	PUNCT
cjfa-35471	353	10	and	and	CCONJ
cjfa-35471	353	11	,	,	PUNCT
cjfa-35471	353	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	353	13	)	)	PUNCT
cjfa-35471	353	14	=	=	SYM
cjfa-35471	353	15	�	�	PROPN
cjfa-35471	353	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	353	17	�	�	PROPN
cjfa-35471	353	18	�	�	PROPN
cjfa-35471	353	19	implying	imply	VERB
cjfa-35471	353	20	that	that	SCONJ
cjfa-35471	353	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	353	22	)	)	PUNCT
cjfa-35471	354	1	=	=	VERB
cjfa-35471	354	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	354	3	if	if	SCONJ
cjfa-35471	354	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	354	5	is	be	AUX
cjfa-35471	354	6	constant	constant	ADJ
cjfa-35471	354	7	.	.	PUNCT
cjfa-35471	355	1	notice	notice	NOUN
cjfa-35471	355	2	also	also	ADV
cjfa-35471	355	3	that	that	SCONJ
cjfa-35471	355	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	355	5	�	�	X
cjfa-35471	355	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	355	7	)	)	PUNCT
cjfa-35471	355	8	=	=	SYM
cjfa-35471	355	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	355	10	)	)	PUNCT
cjfa-35471	355	11	where	where	SCONJ
cjfa-35471	355	12	f	f	PROPN
cjfa-35471	355	13	(	(	PUNCT
cjfa-35471	355	14	t	t	PROPN
cjfa-35471	355	15	)	)	PUNCT
cjfa-35471	355	16	denotes	denote	NOUN
cjfa-35471	355	17	time	time	VERB
cjfa-35471	355	18	dependent	dependent	ADJ
cjfa-35471	355	19	interest	interest	NOUN
cjfa-35471	355	20	rate	rate	NOUN
cjfa-35471	355	21	.	.	PUNCT
cjfa-35471	356	1	for	for	ADP
cjfa-35471	356	2	ease	ease	NOUN
cjfa-35471	356	3	of	of	ADP
cjfa-35471	356	4	analysis	analysis	NOUN
cjfa-35471	356	5	we	we	PRON
cjfa-35471	356	6	will	will	AUX
cjfa-35471	356	7	assume	assume	VERB
cjfa-35471	356	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	356	9	)	)	PUNCT
cjfa-35471	356	10	to	to	PART
cjfa-35471	356	11	be	be	AUX
cjfa-35471	356	12	constant	constant	ADJ
cjfa-35471	356	13	.	.	PUNCT
cjfa-35471	357	1	the	the	DET
cjfa-35471	357	2	letter	letter	NOUN
cjfa-35471	357	3	k	k	PROPN
cjfa-35471	357	4	denotes	denote	VERB
cjfa-35471	357	5	the	the	DET
cjfa-35471	357	6	periodicity	periodicity	NOUN
cjfa-35471	357	7	of	of	ADP
cjfa-35471	357	8	the	the	DET
cjfa-35471	357	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	357	10	demand	demand	NOUN
cjfa-35471	357	11	function	function	NOUN
cjfa-35471	357	12	over	over	ADP
cjfa-35471	357	13	the	the	DET
cjfa-35471	357	14	planning	planning	NOUN
cjfa-35471	357	15	period	period	NOUN
cjfa-35471	357	16	.	.	PUNCT
cjfa-35471	358	1	the	the	DET
cjfa-35471	358	2	only	only	ADJ
cjfa-35471	358	3	reason	reason	NOUN
cjfa-35471	358	4	for	for	ADP
cjfa-35471	358	5	the	the	DET
cjfa-35471	358	6	use	use	NOUN
cjfa-35471	358	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	358	8	demand	demand	NOUN
cjfa-35471	358	9	curve	curve	NOUN
cjfa-35471	358	10	is	be	AUX
cjfa-35471	358	11	that	that	SCONJ
cjfa-35471	358	12	it	it	PRON
cjfa-35471	358	13	represents	represent	VERB
cjfa-35471	358	14	cyclicality	cyclicality	NOUN
cjfa-35471	358	15	(	(	PUNCT
cjfa-35471	358	16	a	a	DET
cjfa-35471	358	17	measure	measure	NOUN
cjfa-35471	358	18	of	of	ADP
cjfa-35471	358	19	risk	risk	NOUN
cjfa-35471	358	20	)	)	PUNCT
cjfa-35471	358	21	and	and	CCONJ
cjfa-35471	358	22	that	that	SCONJ
cjfa-35471	358	23	it	it	PRON
cjfa-35471	358	24	is	be	AUX
cjfa-35471	358	25	easier	easy	ADJ
cjfa-35471	358	26	to	to	PART
cjfa-35471	358	27	work	work	VERB
cjfa-35471	358	28	with	with	ADP
cjfa-35471	358	29	it	it	PRON
cjfa-35471	358	30	.	.	PUNCT
cjfa-35471	359	1	the	the	DET
cjfa-35471	359	2	appropriate	appropriate	ADJ
cjfa-35471	359	3	lagrangian	lagrangian	NOUN
cjfa-35471	359	4	for	for	ADP
cjfa-35471	359	5	this	this	DET
cjfa-35471	359	6	problem	problem	NOUN
cjfa-35471	359	7	is	be	AUX
cjfa-35471	359	8	:	:	PUNCT
cjfa-35471	359	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	359	10	=	=	SYM
cjfa-35471	359	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	359	12	�	�	PROPN
cjfa-35471	359	13	�	�	PROPN
cjfa-35471	359	14	(	(	PUNCT
cjfa-35471	359	15	�	�	PROPN
cjfa-35471	359	16	)	)	PUNCT
cjfa-35471	359	17	�	�	PROPN
cjfa-35471	359	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	359	19	�	�	PROPN
cjfa-35471	359	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	359	21	)	)	PUNCT
cjfa-35471	359	22	�	�	PROPN
cjfa-35471	359	23	𝐴	𝐴	PROPN
cjfa-35471	359	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	359	25	)	)	PUNCT
cjfa-35471	359	26	�	�	PROPN
cjfa-35471	359	27	𝐴	𝐴	PROPN
cjfa-35471	359	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	359	29	�	�	PROPN
cjfa-35471	359	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	359	31	)	)	PUNCT
cjfa-35471	359	32	−	−	PROPN
cjfa-35471	359	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	359	34	)	)	PUNCT
cjfa-35471	359	35	�	�	PROPN
cjfa-35471	359	36	𝐴	𝐴	PROPN
cjfa-35471	359	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	359	38	�	�	PROPN
cjfa-35471	359	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	359	40	)	)	PUNCT
cjfa-35471	359	41	−	−	PROPN
cjfa-35471	359	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	359	43	)	)	PUNCT
cjfa-35471	359	44	�	�	PROPN
cjfa-35471	359	45	then	then	ADV
cjfa-35471	359	46	the	the	DET
cjfa-35471	359	47	necessary	necessary	ADJ
cjfa-35471	359	48	conditions	condition	NOUN
cjfa-35471	359	49	are	be	AUX
cjfa-35471	359	50	:	:	PUNCT
cjfa-35471	359	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	359	52	�	�	PROPN
cjfa-35471	359	53	�	�	PROPN
cjfa-35471	359	54	(	(	PUNCT
cjfa-35471	359	55	�	�	NOUN
cjfa-35471	359	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	359	57	�	�	PROPN
cjfa-35471	359	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	359	59	)	)	PUNCT
cjfa-35471	359	60	𝐴	𝐴	PROPN
cjfa-35471	359	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	359	62	)	)	PUNCT
cjfa-35471	359	63	−	−	PROPN
cjfa-35471	359	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	359	65	)	)	PUNCT
cjfa-35471	360	1	=	=	SYM
cjfa-35471	360	2	0	0	PUNCT
cjfa-35471	360	3	(	(	PUNCT
cjfa-35471	360	4	1	1	NUM
cjfa-35471	360	5	)	)	PUNCT
cjfa-35471	360	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	360	7	�	�	PROPN
cjfa-35471	360	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	360	9	)	)	PUNCT
cjfa-35471	360	10	=	=	SYM
cjfa-35471	360	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	360	12	�	�	PROPN
cjfa-35471	360	13	�	�	PROPN
cjfa-35471	360	14	(	(	PUNCT
cjfa-35471	360	15	�	�	PROPN
cjfa-35471	360	16	)ℎ	)ℎ	PROPN
cjfa-35471	360	17	(	(	PUNCT
cjfa-35471	360	18	2	2	X
cjfa-35471	360	19	)	)	PUNCT
cjfa-35471	360	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	360	21	�	�	PROPN
cjfa-35471	360	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	360	23	)	)	PUNCT
cjfa-35471	360	24	=	=	SYM
cjfa-35471	360	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	360	26	)	)	PUNCT
cjfa-35471	360	27	−	−	PROPN
cjfa-35471	360	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	360	29	)	)	PUNCT
cjfa-35471	360	30	(	(	PUNCT
cjfa-35471	360	31	3	3	X
cjfa-35471	360	32	)	)	PUNCT
cjfa-35471	360	33	necessary	necessary	ADJ
cjfa-35471	360	34	conditions	condition	NOUN
cjfa-35471	360	35	are	be	AUX
cjfa-35471	360	36	also	also	ADV
cjfa-35471	360	37	sufficient	sufficient	ADJ
cjfa-35471	360	38	since	since	SCONJ
cjfa-35471	360	39	the	the	DET
cjfa-35471	360	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	360	41	is	be	AUX
cjfa-35471	360	42	convex	convex	ADJ
cjfa-35471	360	43	in	in	ADP
cjfa-35471	360	44	both	both	CCONJ
cjfa-35471	360	45	the	the	DET
cjfa-35471	360	46	control	control	NOUN
cjfa-35471	360	47	(	(	PUNCT
cjfa-35471	360	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	360	49	)	)	PUNCT
cjfa-35471	360	50	and	and	CCONJ
cjfa-35471	360	51	state	state	NOUN
cjfa-35471	360	52	(	(	PUNCT
cjfa-35471	360	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	360	54	)	)	PUNCT
cjfa-35471	360	55	variables	variable	NOUN
cjfa-35471	360	56	.	.	PUNCT
cjfa-35471	361	1	the	the	DET
cjfa-35471	361	2	planning	planning	NOUN
cjfa-35471	361	3	horizon	horizon	NOUN
cjfa-35471	361	4	(	(	PUNCT
cjfa-35471	361	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	361	6	)	)	PUNCT
cjfa-35471	361	7	will	will	AUX
cjfa-35471	361	8	be	be	AUX
cjfa-35471	361	9	assumed	assume	VERB
cjfa-35471	361	10	one	one	NUM
cjfa-35471	361	11	.	.	PUNCT
cjfa-35471	362	1	on	on	ADP
cjfa-35471	362	2	a	a	DET
cjfa-35471	362	3	constraint	constraint	NOUN
cjfa-35471	362	4	arc	arc	NOUN
cjfa-35471	362	5	on	on	ADP
cjfa-35471	362	6	which	which	PRON
cjfa-35471	362	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	362	8	)	)	PUNCT
cjfa-35471	362	9	=	=	SYM
cjfa-35471	362	10	0	0	NUM
cjfa-35471	362	11	for	for	ADP
cjfa-35471	362	12	a	a	DET
cjfa-35471	362	13	certain	certain	ADJ
cjfa-35471	362	14	period	period	NOUN
cjfa-35471	362	15	in	in	ADP
cjfa-35471	362	16	[	[	X
cjfa-35471	362	17	0	0	NUM
cjfa-35471	362	18	,	,	PUNCT
cjfa-35471	362	19	1	1	NUM
cjfa-35471	362	20	]	]	PUNCT
cjfa-35471	362	21	i.e.	i.e.	X
cjfa-35471	362	22	0	0	X
cjfa-35471	362	23	<	<	X
cjfa-35471	362	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	362	25	�	�	PROPN
cjfa-35471	362	26	≤	≤	X
cjfa-35471	362	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	362	28	≤	≤	PROPN
cjfa-35471	362	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	362	30	�	�	PROPN
cjfa-35471	362	31	<	<	X
cjfa-35471	362	32	1	1	NUM
cjfa-35471	362	33	we	we	PRON
cjfa-35471	362	34	have	have	VERB
cjfa-35471	362	35	;	;	PUNCT
cjfa-35471	362	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	362	37	�	�	PROPN
cjfa-35471	362	38	=	=	SYM
cjfa-35471	362	39	0	0	NUM
cjfa-35471	362	40	=	=	SYM
cjfa-35471	362	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	362	42	)	)	PUNCT
cjfa-35471	363	1	−	−	PROPN
cjfa-35471	363	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	363	3	)	)	PUNCT
cjfa-35471	363	4	implying	imply	VERB
cjfa-35471	363	5	that	that	SCONJ
cjfa-35471	363	6	over	over	ADP
cjfa-35471	363	7	this	this	DET
cjfa-35471	363	8	period	period	NOUN
cjfa-35471	363	9	a	a	DET
cjfa-35471	363	10	firm	firm	NOUN
cjfa-35471	363	11	will	will	AUX
cjfa-35471	363	12	produce	produce	VERB
cjfa-35471	363	13	just	just	ADV
cjfa-35471	363	14	enough	enough	ADJ
cjfa-35471	363	15	to	to	PART
cjfa-35471	363	16	meet	meet	VERB
cjfa-35471	363	17	the	the	DET
cjfa-35471	363	18	demand	demand	NOUN
cjfa-35471	363	19	,	,	PUNCT
cjfa-35471	363	20	which	which	PRON
cjfa-35471	363	21	is	be	AUX
cjfa-35471	363	22	assumed	assume	VERB
cjfa-35471	363	23	to	to	PART
cjfa-35471	363	24	be	be	AUX
cjfa-35471	363	25	nonzero	nonzero	NOUN
cjfa-35471	363	26	during	during	ADP
cjfa-35471	363	27	the	the	DET
cjfa-35471	363	28	planning	planning	NOUN
cjfa-35471	363	29	horizon	horizon	NOUN
cjfa-35471	363	30	.	.	PUNCT
cjfa-35471	364	1	then	then	ADV
cjfa-35471	364	2	using	use	VERB
cjfa-35471	364	3	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	364	4	)	)	PUNCT
cjfa-35471	364	5	=	=	SYM
cjfa-35471	364	6	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	364	7	)	)	PUNCT
cjfa-35471	364	8	,	,	PUNCT
cjfa-35471	364	9	equation	equation	NOUN
cjfa-35471	364	10	(	(	PUNCT
cjfa-35471	364	11	1	1	NUM
cjfa-35471	364	12	)	)	PUNCT
cjfa-35471	364	13	,	,	PUNCT
cjfa-35471	364	14	and	and	CCONJ
cjfa-35471	364	15	the	the	DET
cjfa-35471	364	16	conditions	condition	NOUN
cjfa-35471	364	17	(	(	PUNCT
cjfa-35471	364	18	the	the	DET
cjfa-35471	364	19	necessary	necessary	ADJ
cjfa-35471	364	20	condition	condition	NOUN
cjfa-35471	364	21	to	to	PART
cjfa-35471	364	22	keep	keep	VERB
cjfa-35471	364	23	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	364	24	)	)	PUNCT
cjfa-35471	364	25	=	=	SYM
cjfa-35471	364	26	0	0	NUM
cjfa-35471	364	27	optimal	optimal	ADJ
cjfa-35471	364	28	)	)	PUNCT
cjfa-35471	364	29	developed	develop	VERB
cjfa-35471	364	30	by	by	ADP
cjfa-35471	364	31	pontryagin	pontryagin	NOUN
cjfa-35471	364	32	,	,	PUNCT
cjfa-35471	364	33	boltyanskii	boltyanskii	ADJ
cjfa-35471	364	34	,	,	PUNCT
cjfa-35471	364	35	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	364	36	and	and	CCONJ
cjfa-35471	364	37	mishechenko	mishechenko	NOUN
cjfa-35471	364	38	(	(	PUNCT
cjfa-35471	364	39	1962	1962	NUM
cjfa-35471	364	40	)	)	PUNCT
cjfa-35471	364	41	,	,	PUNCT
cjfa-35471	364	42	hestenes	hestene	NOUN
cjfa-35471	364	43	(	(	PUNCT
cjfa-35471	364	44	1966	1966	NUM
cjfa-35471	364	45	)	)	PUNCT
cjfa-35471	364	46	,	,	PUNCT
cjfa-35471	364	47	kamien	kamien	NOUN
cjfa-35471	364	48	and	and	CCONJ
cjfa-35471	364	49	schwartz	schwartz	PROPN
cjfa-35471	364	50	(	(	PUNCT
cjfa-35471	364	51	2012	2012	NUM
cjfa-35471	364	52	)	)	PUNCT
cjfa-35471	364	53	among	among	ADP
cjfa-35471	364	54	many	many	ADJ
cjfa-35471	364	55	others	other	NOUN
cjfa-35471	364	56	,	,	PUNCT
cjfa-35471	364	57	we	we	PRON
cjfa-35471	364	58	have	have	VERB
cjfa-35471	364	59	;	;	PUNCT
cjfa-35471	364	60	𝜇𝜇	𝜇𝜇	ADP
cjfa-35471	364	61	�	�	PROPN
cjfa-35471	364	62	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	364	63	)	)	PUNCT
cjfa-35471	364	64	≤	≤	NOUN
cjfa-35471	364	65	0	0	NUM
cjfa-35471	364	66	for	for	ADP
cjfa-35471	364	67	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	364	68	�	�	PROPN
cjfa-35471	364	69	≤	≤	NOUN
cjfa-35471	364	70	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	364	71	≤	≤	PROPN
cjfa-35471	364	72	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	364	73	�	�	PROPN
cjfa-35471	364	74	implies	imply	VERB
cjfa-35471	364	75	:	:	PUNCT
cjfa-35471	365	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	365	2	�	�	PROPN
cjfa-35471	365	3	�	�	PROPN
cjfa-35471	365	4	�	�	PROPN
cjfa-35471	365	5	𝑟𝑟(𝑡𝑡)	𝑟𝑟(𝑡𝑡)	PROPN
cjfa-35471	365	6	�	�	PROPN
cjfa-35471	365	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	365	8	�	�	PROPN
cjfa-35471	365	9	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	365	10	)	)	PUNCT
cjfa-35471	365	11	≤	≤	NOUN
cjfa-35471	365	12	ℎ	ℎ	PROPN
cjfa-35471	365	13	𝐴	𝐴	PROPN
cjfa-35471	365	14	𝑓𝑓(𝑡𝑡)𝑐𝑐	𝑓𝑓(𝑡𝑡)𝑐𝑐	VERB
cjfa-35471	365	15	�	�	PROPN
cjfa-35471	365	16	�	�	NOUN
cjfa-35471	365	17	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	365	18	)	)	PUNCT
cjfa-35471	365	19	�	�	PROPN
cjfa-35471	365	20	(	(	PUNCT
cjfa-35471	365	21	4	4	NUM
cjfa-35471	365	22	)	)	PUNCT
cjfa-35471	365	23	implies	imply	VERB
cjfa-35471	365	24	:	:	PUNCT
cjfa-35471	365	25	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	365	26	�	�	PROPN
cjfa-35471	365	27	=	=	PUNCT
cjfa-35471	365	28	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	365	29	)	)	PUNCT
cjfa-35471	365	30	−	−	PROPN
cjfa-35471	365	31	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	365	32	)	)	PUNCT
cjfa-35471	365	33	𝐼𝐼(0	𝐼𝐼(0	PROPN
cjfa-35471	365	34	)	)	PUNCT
cjfa-35471	365	35	=	=	SYM
cjfa-35471	365	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	365	37	�	�	PROPN
cjfa-35471	365	38	a	a	DET
cjfa-35471	365	39	given	give	VERB
cjfa-35471	365	40	number	number	NOUN
cjfa-35471	365	41	.	.	PUNCT
cjfa-35471	366	1	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	NOUN
cjfa-35471	366	2	)	)	PUNCT
cjfa-35471	367	1	𝑢	𝑢	PROPN
cjfa-35471	367	2	0	0	NUM
cjfa-35471	367	3	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	367	4	)	)	PUNCT
cjfa-35471	367	5	𝑢	𝑢	ADP
cjfa-35471	367	6	0	0	NUM
cjfa-35471	367	7	with	with	ADP
cjfa-35471	367	8	the	the	DET
cjfa-35471	367	9	assumptions	assumption	NOUN
cjfa-35471	367	10	that	that	SCONJ
cjfa-35471	367	11	the	the	DET
cjfa-35471	367	12	demand	demand	NOUN
cjfa-35471	367	13	(	(	PUNCT
cjfa-35471	367	14	𝑟𝑟	𝑟𝑟	INTJ
cjfa-35471	367	15	(	(	PUNCT
cjfa-35471	367	16	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	367	17	)	)	PUNCT
cjfa-35471	367	18	)	)	PUNCT
cjfa-35471	367	19	is	be	AUX
cjfa-35471	367	20	a	a	DET
cjfa-35471	367	21	simple	simple	ADJ
cjfa-35471	367	22	sinusoidal	sinusoidal	NOUN
cjfa-35471	367	23	function	function	NOUN
cjfa-35471	367	24	and	and	CCONJ
cjfa-35471	367	25	the	the	DET
cjfa-35471	367	26	interest	interest	NOUN
cjfa-35471	367	27	rate	rate	NOUN
cjfa-35471	367	28	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PROPN
cjfa-35471	367	29	)	)	PUNCT
cjfa-35471	367	30	is	be	AUX
cjfa-35471	367	31	time	time	NOUN
cjfa-35471	367	32	dependent	dependent	ADJ
cjfa-35471	367	33	,	,	PUNCT
cjfa-35471	367	34	i.e.	i.e.	X
cjfa-35471	367	35	:	:	PUNCT
cjfa-35471	367	36	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	367	37	)	)	PUNCT
cjfa-35471	368	1	=	=	SYM
cjfa-35471	368	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	368	3	𝐴	𝐴	PROPN
cjfa-35471	368	4	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	𝐴𝐴𝐴𝐴𝑖𝑖𝐴𝐴(𝐴𝐴𝐴𝐴𝐴𝑡𝑡	NOUN
cjfa-35471	368	5	)	)	PUNCT
cjfa-35471	368	6	with	with	ADP
cjfa-35471	368	7	no	no	DET
cjfa-35471	368	8	growth	growth	NOUN
cjfa-35471	368	9	,	,	PUNCT
cjfa-35471	368	10	and	and	CCONJ
cjfa-35471	368	11	,	,	PUNCT
cjfa-35471	368	12	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	NUM
cjfa-35471	368	13	)	)	PUNCT
cjfa-35471	368	14	=	=	SYM
cjfa-35471	368	15	�	�	PROPN
cjfa-35471	368	16	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	𝑓𝑓(𝐴𝐴)𝑑𝑑𝐴𝐴	PROPN
cjfa-35471	368	17	�	�	PROPN
cjfa-35471	368	18	�	�	PROPN
cjfa-35471	368	19	implying	imply	VERB
cjfa-35471	368	20	that	that	SCONJ
cjfa-35471	368	21	𝑖𝑖(𝑡𝑡	𝑖𝑖(𝑡𝑡	PUNCT
cjfa-35471	368	22	)	)	PUNCT
cjfa-35471	369	1	=	=	VERB
cjfa-35471	369	2	𝑓𝑓𝑡𝑡	𝑓𝑓𝑡𝑡	VERB
cjfa-35471	369	3	if	if	SCONJ
cjfa-35471	369	4	𝑓𝑓	𝑓𝑓	NOUN
cjfa-35471	369	5	is	be	AUX
cjfa-35471	369	6	constant	constant	ADJ
cjfa-35471	369	7	.	.	PUNCT
cjfa-35471	370	1	notice	notice	NOUN
cjfa-35471	370	2	also	also	ADV
cjfa-35471	370	3	that	that	SCONJ
cjfa-35471	370	4	𝑖𝑖	𝑖𝑖	VERB
cjfa-35471	370	5	�	�	X
cjfa-35471	370	6	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	370	7	)	)	PUNCT
cjfa-35471	370	8	=	=	SYM
cjfa-35471	370	9	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	370	10	)	)	PUNCT
cjfa-35471	370	11	where	where	SCONJ
cjfa-35471	370	12	f	f	PROPN
cjfa-35471	370	13	(	(	PUNCT
cjfa-35471	370	14	t	t	PROPN
cjfa-35471	370	15	)	)	PUNCT
cjfa-35471	370	16	denotes	denote	NOUN
cjfa-35471	370	17	time	time	VERB
cjfa-35471	370	18	dependent	dependent	ADJ
cjfa-35471	370	19	interest	interest	NOUN
cjfa-35471	370	20	rate	rate	NOUN
cjfa-35471	370	21	.	.	PUNCT
cjfa-35471	371	1	for	for	ADP
cjfa-35471	371	2	ease	ease	NOUN
cjfa-35471	371	3	of	of	ADP
cjfa-35471	371	4	analysis	analysis	NOUN
cjfa-35471	371	5	we	we	PRON
cjfa-35471	371	6	will	will	AUX
cjfa-35471	371	7	assume	assume	VERB
cjfa-35471	371	8	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	PROPN
cjfa-35471	371	9	)	)	PUNCT
cjfa-35471	371	10	to	to	PART
cjfa-35471	371	11	be	be	AUX
cjfa-35471	371	12	constant	constant	ADJ
cjfa-35471	371	13	.	.	PUNCT
cjfa-35471	372	1	the	the	DET
cjfa-35471	372	2	letter	letter	NOUN
cjfa-35471	372	3	k	k	PROPN
cjfa-35471	372	4	denotes	denote	VERB
cjfa-35471	372	5	the	the	DET
cjfa-35471	372	6	periodicity	periodicity	NOUN
cjfa-35471	372	7	of	of	ADP
cjfa-35471	372	8	the	the	DET
cjfa-35471	372	9	sinusoidal	sinusoidal	ADJ
cjfa-35471	372	10	demand	demand	NOUN
cjfa-35471	372	11	function	function	NOUN
cjfa-35471	372	12	over	over	ADP
cjfa-35471	372	13	the	the	DET
cjfa-35471	372	14	planning	planning	NOUN
cjfa-35471	372	15	period	period	NOUN
cjfa-35471	372	16	.	.	PUNCT
cjfa-35471	373	1	the	the	DET
cjfa-35471	373	2	only	only	ADJ
cjfa-35471	373	3	reason	reason	NOUN
cjfa-35471	373	4	for	for	ADP
cjfa-35471	373	5	the	the	DET
cjfa-35471	373	6	use	use	NOUN
cjfa-35471	373	7	sinusoidal	sinusoidal	NOUN
cjfa-35471	373	8	demand	demand	NOUN
cjfa-35471	373	9	curve	curve	NOUN
cjfa-35471	373	10	is	be	AUX
cjfa-35471	373	11	that	that	SCONJ
cjfa-35471	373	12	it	it	PRON
cjfa-35471	373	13	represents	represent	VERB
cjfa-35471	373	14	cyclicality	cyclicality	NOUN
cjfa-35471	373	15	(	(	PUNCT
cjfa-35471	373	16	a	a	DET
cjfa-35471	373	17	measure	measure	NOUN
cjfa-35471	373	18	of	of	ADP
cjfa-35471	373	19	risk	risk	NOUN
cjfa-35471	373	20	)	)	PUNCT
cjfa-35471	373	21	and	and	CCONJ
cjfa-35471	373	22	that	that	SCONJ
cjfa-35471	373	23	it	it	PRON
cjfa-35471	373	24	is	be	AUX
cjfa-35471	373	25	easier	easy	ADJ
cjfa-35471	373	26	to	to	PART
cjfa-35471	373	27	work	work	VERB
cjfa-35471	373	28	with	with	ADP
cjfa-35471	373	29	it	it	PRON
cjfa-35471	373	30	.	.	PUNCT
cjfa-35471	374	1	the	the	DET
cjfa-35471	374	2	appropriate	appropriate	ADJ
cjfa-35471	374	3	lagrangian	lagrangian	NOUN
cjfa-35471	374	4	for	for	ADP
cjfa-35471	374	5	this	this	DET
cjfa-35471	374	6	problem	problem	NOUN
cjfa-35471	374	7	is	be	AUX
cjfa-35471	374	8	:	:	PUNCT
cjfa-35471	374	9	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	374	10	=	=	SYM
cjfa-35471	374	11	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	374	12	�	�	PROPN
cjfa-35471	374	13	�	�	PROPN
cjfa-35471	374	14	(	(	PUNCT
cjfa-35471	374	15	�	�	PROPN
cjfa-35471	374	16	)	)	PUNCT
cjfa-35471	374	17	�	�	PROPN
cjfa-35471	374	18	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	374	19	�	�	PROPN
cjfa-35471	374	20	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	374	21	)	)	PUNCT
cjfa-35471	374	22	�	�	PROPN
cjfa-35471	374	23	𝐴	𝐴	PROPN
cjfa-35471	374	24	ℎ𝐼𝐼(𝑡𝑡	ℎ𝐼𝐼(𝑡𝑡	PROPN
cjfa-35471	374	25	)	)	PUNCT
cjfa-35471	374	26	�	�	PROPN
cjfa-35471	374	27	𝐴	𝐴	PROPN
cjfa-35471	374	28	𝜌𝜌(𝑡𝑡)	𝜌𝜌(𝑡𝑡)	PROPN
cjfa-35471	374	29	�	�	PROPN
cjfa-35471	374	30	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	374	31	)	)	PUNCT
cjfa-35471	374	32	−	−	PROPN
cjfa-35471	374	33	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	374	34	)	)	PUNCT
cjfa-35471	374	35	�	�	PROPN
cjfa-35471	374	36	𝐴	𝐴	PROPN
cjfa-35471	374	37	𝜇𝜇(𝑡𝑡)	𝜇𝜇(𝑡𝑡)	PROPN
cjfa-35471	374	38	�	�	PROPN
cjfa-35471	374	39	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	374	40	)	)	PUNCT
cjfa-35471	374	41	−	−	PROPN
cjfa-35471	374	42	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	374	43	)	)	PUNCT
cjfa-35471	374	44	�	�	PROPN
cjfa-35471	374	45	then	then	ADV
cjfa-35471	374	46	the	the	DET
cjfa-35471	374	47	necessary	necessary	ADJ
cjfa-35471	374	48	conditions	condition	NOUN
cjfa-35471	374	49	are	be	AUX
cjfa-35471	374	50	:	:	PUNCT
cjfa-35471	374	51	𝐻𝐻	𝐻𝐻	PROPN
cjfa-35471	374	52	�	�	PROPN
cjfa-35471	374	53	�	�	PROPN
cjfa-35471	374	54	(	(	PUNCT
cjfa-35471	374	55	�	�	NOUN
cjfa-35471	374	56	)𝑐𝑐	)𝑐𝑐	NOUN
cjfa-35471	374	57	�	�	PROPN
cjfa-35471	374	58	(𝑡𝑡	(𝑡𝑡	SYM
cjfa-35471	374	59	)	)	PUNCT
cjfa-35471	374	60	𝐴	𝐴	PROPN
cjfa-35471	374	61	𝜌𝜌(𝑡𝑡	𝜌𝜌(𝑡𝑡	PROPN
cjfa-35471	374	62	)	)	PUNCT
cjfa-35471	374	63	−	−	PROPN
cjfa-35471	374	64	𝜇𝜇(𝑡𝑡	𝜇𝜇(𝑡𝑡	NOUN
cjfa-35471	374	65	)	)	PUNCT
cjfa-35471	375	1	=	=	SYM
cjfa-35471	375	2	0	0	PUNCT
cjfa-35471	375	3	(	(	PUNCT
cjfa-35471	375	4	1	1	NUM
cjfa-35471	375	5	)	)	PUNCT
cjfa-35471	375	6	𝜌𝜌	𝜌𝜌	ADP
cjfa-35471	375	7	�	�	PROPN
cjfa-35471	375	8	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	375	9	)	)	PUNCT
cjfa-35471	375	10	=	=	SYM
cjfa-35471	375	11	−𝐻𝐻	−𝐻𝐻	PROPN
cjfa-35471	375	12	�	�	PROPN
cjfa-35471	375	13	�	�	PROPN
cjfa-35471	375	14	(	(	PUNCT
cjfa-35471	375	15	�	�	PROPN
cjfa-35471	375	16	)ℎ	)ℎ	PROPN
cjfa-35471	375	17	(	(	PUNCT
cjfa-35471	375	18	2	2	X
cjfa-35471	375	19	)	)	PUNCT
cjfa-35471	375	20	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	375	21	�	�	PROPN
cjfa-35471	375	22	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	375	23	)	)	PUNCT
cjfa-35471	375	24	=	=	SYM
cjfa-35471	375	25	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	375	26	)	)	PUNCT
cjfa-35471	375	27	−	−	PROPN
cjfa-35471	375	28	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	PROPN
cjfa-35471	375	29	)	)	PUNCT
cjfa-35471	375	30	(	(	PUNCT
cjfa-35471	375	31	3	3	X
cjfa-35471	375	32	)	)	PUNCT
cjfa-35471	375	33	necessary	necessary	ADJ
cjfa-35471	375	34	conditions	condition	NOUN
cjfa-35471	375	35	are	be	AUX
cjfa-35471	375	36	also	also	ADV
cjfa-35471	375	37	sufficient	sufficient	ADJ
cjfa-35471	375	38	since	since	SCONJ
cjfa-35471	375	39	the	the	DET
cjfa-35471	375	40	hamiltonian	hamiltonian	NOUN
cjfa-35471	375	41	is	be	AUX
cjfa-35471	375	42	convex	convex	ADJ
cjfa-35471	375	43	in	in	ADP
cjfa-35471	375	44	both	both	CCONJ
cjfa-35471	375	45	the	the	DET
cjfa-35471	375	46	control	control	NOUN
cjfa-35471	375	47	(	(	PUNCT
cjfa-35471	375	48	𝑢𝑢	𝑢𝑢	NUM
cjfa-35471	375	49	)	)	PUNCT
cjfa-35471	375	50	and	and	CCONJ
cjfa-35471	375	51	state	state	NOUN
cjfa-35471	375	52	(	(	PUNCT
cjfa-35471	375	53	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	375	54	)	)	PUNCT
cjfa-35471	375	55	variables	variable	NOUN
cjfa-35471	375	56	.	.	PUNCT
cjfa-35471	376	1	the	the	DET
cjfa-35471	376	2	planning	planning	NOUN
cjfa-35471	376	3	horizon	horizon	NOUN
cjfa-35471	376	4	(	(	PUNCT
cjfa-35471	376	5	𝑇𝑇	𝑇𝑇	PROPN
cjfa-35471	376	6	)	)	PUNCT
cjfa-35471	376	7	will	will	AUX
cjfa-35471	376	8	be	be	AUX
cjfa-35471	376	9	assumed	assume	VERB
cjfa-35471	376	10	one	one	NUM
cjfa-35471	376	11	.	.	PUNCT
cjfa-35471	377	1	on	on	ADP
cjfa-35471	377	2	a	a	DET
cjfa-35471	377	3	constraint	constraint	NOUN
cjfa-35471	377	4	arc	arc	NOUN
cjfa-35471	377	5	on	on	ADP
cjfa-35471	377	6	which	which	PRON
cjfa-35471	377	7	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	377	8	)	)	PUNCT
cjfa-35471	377	9	=	=	SYM
cjfa-35471	377	10	0	0	NUM
cjfa-35471	377	11	for	for	ADP
cjfa-35471	377	12	a	a	DET
cjfa-35471	377	13	certain	certain	ADJ
cjfa-35471	377	14	period	period	NOUN
cjfa-35471	377	15	in	in	ADP
cjfa-35471	377	16	[	[	X
cjfa-35471	377	17	0	0	NUM
cjfa-35471	377	18	,	,	PUNCT
cjfa-35471	377	19	1	1	NUM
cjfa-35471	377	20	]	]	PUNCT
cjfa-35471	377	21	i.e.	i.e.	X
cjfa-35471	377	22	0	0	X
cjfa-35471	377	23	<	<	X
cjfa-35471	377	24	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	377	25	�	�	PROPN
cjfa-35471	377	26	≤	≤	X
cjfa-35471	377	27	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	377	28	≤	≤	PROPN
cjfa-35471	377	29	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	377	30	�	�	PROPN
cjfa-35471	377	31	<	<	X
cjfa-35471	377	32	1	1	NUM
cjfa-35471	377	33	we	we	PRON
cjfa-35471	377	34	have	have	VERB
cjfa-35471	377	35	;	;	PUNCT
cjfa-35471	377	36	𝐼𝐼	𝐼𝐼	PROPN
cjfa-35471	377	37	�	�	PROPN
cjfa-35471	377	38	=	=	SYM
cjfa-35471	377	39	0	0	NUM
cjfa-35471	377	40	=	=	SYM
cjfa-35471	377	41	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	377	42	)	)	PUNCT
cjfa-35471	378	1	−	−	PROPN
cjfa-35471	378	2	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	378	3	)	)	PUNCT
cjfa-35471	378	4	implying	imply	VERB
cjfa-35471	378	5	that	that	SCONJ
cjfa-35471	378	6	over	over	ADP
cjfa-35471	378	7	this	this	DET
cjfa-35471	378	8	period	period	NOUN
cjfa-35471	378	9	a	a	DET
cjfa-35471	378	10	firm	firm	NOUN
cjfa-35471	378	11	will	will	AUX
cjfa-35471	378	12	produce	produce	VERB
cjfa-35471	378	13	just	just	ADV
cjfa-35471	378	14	enough	enough	ADJ
cjfa-35471	378	15	to	to	PART
cjfa-35471	378	16	meet	meet	VERB
cjfa-35471	378	17	the	the	DET
cjfa-35471	378	18	demand	demand	NOUN
cjfa-35471	378	19	,	,	PUNCT
cjfa-35471	378	20	which	which	PRON
cjfa-35471	378	21	is	be	AUX
cjfa-35471	378	22	assumed	assume	VERB
cjfa-35471	378	23	to	to	PART
cjfa-35471	378	24	be	be	AUX
cjfa-35471	378	25	nonzero	nonzero	NOUN
cjfa-35471	378	26	during	during	ADP
cjfa-35471	378	27	the	the	DET
cjfa-35471	378	28	planning	planning	NOUN
cjfa-35471	378	29	horizon	horizon	NOUN
cjfa-35471	378	30	.	.	PUNCT
cjfa-35471	379	1	then	then	ADV
cjfa-35471	379	2	using	use	VERB
cjfa-35471	379	3	𝑢𝑢(𝑡𝑡	𝑢𝑢(𝑡𝑡	PROPN
cjfa-35471	379	4	)	)	PUNCT
cjfa-35471	379	5	=	=	SYM
cjfa-35471	379	6	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	379	7	)	)	PUNCT
cjfa-35471	379	8	,	,	PUNCT
cjfa-35471	379	9	equation	equation	NOUN
cjfa-35471	379	10	(	(	PUNCT
cjfa-35471	379	11	1	1	NUM
cjfa-35471	379	12	)	)	PUNCT
cjfa-35471	379	13	,	,	PUNCT
cjfa-35471	379	14	and	and	CCONJ
cjfa-35471	379	15	the	the	DET
cjfa-35471	379	16	conditions	condition	NOUN
cjfa-35471	379	17	(	(	PUNCT
cjfa-35471	379	18	the	the	DET
cjfa-35471	379	19	necessary	necessary	ADJ
cjfa-35471	379	20	condition	condition	NOUN
cjfa-35471	379	21	to	to	PART
cjfa-35471	379	22	keep	keep	VERB
cjfa-35471	379	23	𝐼𝐼(𝑡𝑡	𝐼𝐼(𝑡𝑡	NOUN
cjfa-35471	379	24	)	)	PUNCT
cjfa-35471	379	25	=	=	SYM
cjfa-35471	379	26	0	0	NUM
cjfa-35471	379	27	optimal	optimal	ADJ
cjfa-35471	379	28	)	)	PUNCT
cjfa-35471	379	29	developed	develop	VERB
cjfa-35471	379	30	by	by	ADP
cjfa-35471	379	31	pontryagin	pontryagin	NOUN
cjfa-35471	379	32	,	,	PUNCT
cjfa-35471	379	33	boltyanskii	boltyanskii	ADJ
cjfa-35471	379	34	,	,	PUNCT
cjfa-35471	379	35	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	379	36	and	and	CCONJ
cjfa-35471	379	37	mishechenko	mishechenko	NOUN
cjfa-35471	379	38	(	(	PUNCT
cjfa-35471	379	39	1962	1962	NUM
cjfa-35471	379	40	)	)	PUNCT
cjfa-35471	379	41	,	,	PUNCT
cjfa-35471	379	42	hestenes	hestene	NOUN
cjfa-35471	379	43	(	(	PUNCT
cjfa-35471	379	44	1966	1966	NUM
cjfa-35471	379	45	)	)	PUNCT
cjfa-35471	379	46	,	,	PUNCT
cjfa-35471	379	47	kamien	kamien	NOUN
cjfa-35471	379	48	and	and	CCONJ
cjfa-35471	379	49	schwartz	schwartz	PROPN
cjfa-35471	379	50	(	(	PUNCT
cjfa-35471	379	51	2012	2012	NUM
cjfa-35471	379	52	)	)	PUNCT
cjfa-35471	379	53	among	among	ADP
cjfa-35471	379	54	many	many	ADJ
cjfa-35471	379	55	others	other	NOUN
cjfa-35471	379	56	,	,	PUNCT
cjfa-35471	379	57	we	we	PRON
cjfa-35471	379	58	have	have	VERB
cjfa-35471	379	59	;	;	PUNCT
cjfa-35471	379	60	𝜇𝜇	𝜇𝜇	ADP
cjfa-35471	379	61	�	�	PROPN
cjfa-35471	379	62	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	379	63	)	)	PUNCT
cjfa-35471	379	64	≤	≤	NOUN
cjfa-35471	379	65	0	0	NUM
cjfa-35471	379	66	for	for	ADP
cjfa-35471	379	67	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	379	68	�	�	PROPN
cjfa-35471	379	69	≤	≤	NOUN
cjfa-35471	379	70	𝑡𝑡	𝑡𝑡	ADJ
cjfa-35471	379	71	≤	≤	PROPN
cjfa-35471	379	72	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	379	73	�	�	PROPN
cjfa-35471	379	74	implies	imply	VERB
cjfa-35471	379	75	:	:	PUNCT
cjfa-35471	380	1	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	380	2	�	�	PROPN
cjfa-35471	380	3	�	�	PROPN
cjfa-35471	380	4	�	�	PROPN
cjfa-35471	380	5	𝑟𝑟(𝑡𝑡)	𝑟𝑟(𝑡𝑡)	PROPN
cjfa-35471	380	6	�	�	PROPN
cjfa-35471	380	7	𝑟𝑟	𝑟𝑟	NOUN
cjfa-35471	380	8	�	�	PROPN
cjfa-35471	380	9	(𝑡𝑡	(𝑡𝑡	NUM
cjfa-35471	380	10	)	)	PUNCT
cjfa-35471	380	11	≤	≤	NOUN
cjfa-35471	380	12	ℎ	ℎ	PROPN
cjfa-35471	380	13	𝐴	𝐴	PROPN
cjfa-35471	380	14	𝑓𝑓(𝑡𝑡)𝑐𝑐	𝑓𝑓(𝑡𝑡)𝑐𝑐	VERB
cjfa-35471	380	15	�	�	PROPN
cjfa-35471	380	16	�	�	NOUN
cjfa-35471	380	17	𝑟𝑟(𝑡𝑡	𝑟𝑟(𝑡𝑡	NOUN
cjfa-35471	380	18	)	)	PUNCT
cjfa-35471	380	19	�	�	PROPN
cjfa-35471	380	20	(	(	PUNCT
cjfa-35471	380	21	4	4	NUM
cjfa-35471	380	22	)	)	PUNCT
cjfa-35471	380	23	(	(	PUNCT
cjfa-35471	380	24	4	4	X
cjfa-35471	380	25	)	)	PUNCT
cjfa-35471	380	26	where	where	SCONJ
cjfa-35471	380	27	then	then	ADV
cjfa-35471	380	28	using	use	VERB
cjfa-35471	380	29	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	380	30	𝑢	𝑢	PROPN
cjfa-35471	380	31	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	380	32	,	,	PUNCT
cjfa-35471	380	33	equation	equation	NOUN
cjfa-35471	380	34	(	(	PUNCT
cjfa-35471	380	35	1	1	NUM
cjfa-35471	380	36	)	)	PUNCT
cjfa-35471	380	37	,	,	PUNCT
cjfa-35471	380	38	and	and	CCONJ
cjfa-35471	380	39	the	the	DET
cjfa-35471	380	40	conditions	condition	NOUN
cjfa-35471	380	41	(	(	PUNCT
cjfa-35471	380	42	the	the	DET
cjfa-35471	380	43	necessary	necessary	ADJ
cjfa-35471	380	44	condition	condition	NOUN
cjfa-35471	380	45	to	to	PART
cjfa-35471	380	46	keep	keep	VERB
cjfa-35471	380	47	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	380	48	𝑢	𝑢	ADP
cjfa-35471	380	49	𝐼	𝐼	PROPN
cjfa-35471	380	50	optimal	optimal	ADJ
cjfa-35471	380	51	)	)	PUNCT
cjfa-35471	380	52	developed	develop	VERB
cjfa-35471	380	53	by	by	ADP
cjfa-35471	380	54	pontryagin	pontryagin	NOUN
cjfa-35471	380	55	,	,	PUNCT
cjfa-35471	380	56	boltyanskii	boltyanskii	ADJ
cjfa-35471	380	57	,	,	PUNCT
cjfa-35471	380	58	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	380	59	and	and	CCONJ
cjfa-35471	380	60	mishechenko	mishechenko	NOUN
cjfa-35471	380	61	(	(	PUNCT
cjfa-35471	380	62	1962	1962	NUM
cjfa-35471	380	63	)	)	PUNCT
cjfa-35471	380	64	,	,	PUNCT
cjfa-35471	380	65	hestenes	hestene	NOUN
cjfa-35471	380	66	(	(	PUNCT
cjfa-35471	380	67	1966	1966	NUM
cjfa-35471	380	68	)	)	PUNCT
cjfa-35471	380	69	,	,	PUNCT
cjfa-35471	380	70	kamien	kamien	NOUN
cjfa-35471	380	71	and	and	CCONJ
cjfa-35471	380	72	schwartz	schwartz	PROPN
cjfa-35471	380	73	(	(	PUNCT
cjfa-35471	380	74	2012	2012	NUM
cjfa-35471	380	75	)	)	PUNCT
cjfa-35471	380	76	among	among	ADP
cjfa-35471	380	77	many	many	ADJ
cjfa-35471	380	78	others	other	NOUN
cjfa-35471	380	79	,	,	PUNCT
cjfa-35471	380	80	we	we	PRON
cjfa-35471	380	81	have	have	AUX
cjfa-35471	380	82	;	;	PUNCT
cjfa-35471	380	83	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	380	84	�	�	NOUN
cjfa-35471	380	85	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	380	86	≤	≤	PUNCT
cjfa-35471	380	87	𝐼	𝐼	PROPN
cjfa-35471	380	88	for	for	ADP
cjfa-35471	380	89	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	380	90	�	�	PROPN
cjfa-35471	380	91	≤	≤	NUM
cjfa-35471	381	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	381	2	≤	≤	NUM
cjfa-35471	381	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	381	4	�	�	PROPN
cjfa-35471	381	5	implies	imply	VERB
cjfa-35471	381	6	:	:	PUNCT
cjfa-35471	381	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	381	8	�	�	PROPN
cjfa-35471	381	9	�	�	PROPN
cjfa-35471	381	10	�	�	PROPN
cjfa-35471	381	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	381	12	�	�	PROPN
cjfa-35471	381	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	381	14	�	�	PROPN
cjfa-35471	381	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	381	16	≤	≤	PUNCT
cjfa-35471	381	17	ℎ	ℎ	PROPN
cjfa-35471	381	18	+	+	PROPN
cjfa-35471	381	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	381	20	�	�	PROPN
cjfa-35471	381	21	�	�	PROPN
cjfa-35471	381	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	381	23	�	�	PROPN
cjfa-35471	381	24	(	(	PUNCT
cjfa-35471	381	25	4	4	NUM
cjfa-35471	381	26	)	)	PUNCT
cjfa-35471	381	27	where	where	SCONJ
cjfa-35471	381	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	381	29	𝑢	𝑢	PROPN
cjfa-35471	381	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	381	31	�	�	NOUN
cjfa-35471	381	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	381	33	denotes	denote	VERB
cjfa-35471	381	34	the	the	DET
cjfa-35471	381	35	interest	interest	NOUN
cjfa-35471	381	36	rate	rate	NOUN
cjfa-35471	381	37	.	.	PUNCT
cjfa-35471	382	1	as	as	ADV
cjfa-35471	382	2	long	long	ADV
cjfa-35471	382	3	as	as	SCONJ
cjfa-35471	382	4	the	the	DET
cjfa-35471	382	5	condition	condition	NOUN
cjfa-35471	382	6	specified	specify	VERB
cjfa-35471	382	7	by	by	ADP
cjfa-35471	382	8	this	this	DET
cjfa-35471	382	9	inequality	inequality	NOUN
cjfa-35471	382	10	is	be	AUX
cjfa-35471	382	11	satisfied	satisfied	ADJ
cjfa-35471	382	12	it	it	PRON
cjfa-35471	382	13	will	will	AUX
cjfa-35471	382	14	be	be	AUX
cjfa-35471	382	15	optimal	optimal	ADJ
cjfa-35471	382	16	to	to	PART
cjfa-35471	382	17	keep	keep	VERB
cjfa-35471	382	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	382	19	𝑢	𝑢	ADP
cjfa-35471	382	20	𝐼	𝐼	ADP
cjfa-35471	382	21	implying	imply	VERB
cjfa-35471	382	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	382	23	𝑢	𝑢	PRON
cjfa-35471	382	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	382	25	this	this	PRON
cjfa-35471	382	26	means	mean	VERB
cjfa-35471	382	27	that	that	SCONJ
cjfa-35471	382	28	during	during	ADP
cjfa-35471	382	29	the	the	DET
cjfa-35471	382	30	intervals	interval	NOUN
cjfa-35471	382	31	where	where	SCONJ
cjfa-35471	382	32	this	this	DET
cjfa-35471	382	33	inequality	inequality	NOUN
cjfa-35471	382	34	is	be	AUX
cjfa-35471	382	35	satisfied	satisfied	ADJ
cjfa-35471	382	36	the	the	DET
cjfa-35471	382	37	firm	firm	NOUN
cjfa-35471	382	38	will	will	AUX
cjfa-35471	382	39	produce	produce	VERB
cjfa-35471	382	40	just	just	ADV
cjfa-35471	382	41	enough	enough	ADJ
cjfa-35471	382	42	to	to	PART
cjfa-35471	382	43	satisfy	satisfy	VERB
cjfa-35471	382	44	the	the	DET
cjfa-35471	382	45	demand	demand	NOUN
cjfa-35471	382	46	.	.	PUNCT
cjfa-35471	383	1	so	so	ADV
cjfa-35471	383	2	,	,	PUNCT
cjfa-35471	383	3	the	the	DET
cjfa-35471	383	4	condition	condition	NOUN
cjfa-35471	383	5	above	above	ADV
cjfa-35471	383	6	will	will	AUX
cjfa-35471	383	7	synthesize	synthesize	VERB
cjfa-35471	383	8	the	the	DET
cjfa-35471	383	9	periods	period	NOUN
cjfa-35471	383	10	where	where	SCONJ
cjfa-35471	383	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	383	12	𝑢	𝑢	PRON
cjfa-35471	383	13	𝐼	𝐼	PROPN
cjfa-35471	383	14	or	or	CCONJ
cjfa-35471	383	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	383	16	𝑢	𝑢	PROPN
cjfa-35471	383	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	383	18	and	and	CCONJ
cjfa-35471	383	19	the	the	DET
cjfa-35471	383	20	periods	period	NOUN
cjfa-35471	383	21	where	where	SCONJ
cjfa-35471	383	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	383	23	𝐼	𝐼	ADP
cjfa-35471	383	24	𝐼.	𝐼.	PROPN
cjfa-35471	383	25	notice	notice	VERB
cjfa-35471	383	26	that	that	SCONJ
cjfa-35471	383	27	for	for	ADP
cjfa-35471	383	28	the	the	DET
cjfa-35471	383	29	condition	condition	NOUN
cjfa-35471	383	30	above	above	ADV
cjfa-35471	383	31	(	(	PUNCT
cjfa-35471	383	32	equation	equation	NOUN
cjfa-35471	383	33	4	4	NUM
cjfa-35471	383	34	)	)	PUNCT
cjfa-35471	383	35	to	to	PART
cjfa-35471	383	36	be	be	AUX
cjfa-35471	383	37	kept	keep	VERB
cjfa-35471	383	38	satisfied	satisfied	ADJ
cjfa-35471	383	39	depends	depend	VERB
cjfa-35471	383	40	on	on	ADP
cjfa-35471	383	41	ℎ	ℎ	PROPN
cjfa-35471	383	42	(	(	PUNCT
cjfa-35471	383	43	inventory	inventory	NOUN
cjfa-35471	383	44	holding	hold	VERB
cjfa-35471	383	45	cost	cost	NOUN
cjfa-35471	383	46	)	)	PUNCT
cjfa-35471	383	47	,	,	PUNCT
cjfa-35471	383	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	383	49	the	the	DET
cjfa-35471	383	50	interest	interest	NOUN
cjfa-35471	383	51	rates	rate	NOUN
cjfa-35471	383	52	,	,	PUNCT
cjfa-35471	383	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	383	54	,	,	PUNCT
cjfa-35471	383	55	the	the	DET
cjfa-35471	383	56	marginal	marginal	ADJ
cjfa-35471	383	57	cost	cost	NOUN
cjfa-35471	383	58	of	of	ADP
cjfa-35471	383	59	production	production	NOUN
cjfa-35471	383	60	,	,	PUNCT
cjfa-35471	383	61	and	and	CCONJ
cjfa-35471	383	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	383	63	change	change	NOUN
cjfa-35471	383	64	in	in	ADP
cjfa-35471	383	65	the	the	DET
cjfa-35471	383	66	marginal	marginal	ADJ
cjfa-35471	383	67	cost	cost	NOUN
cjfa-35471	383	68	.	.	PUNCT
cjfa-35471	384	1	following	follow	VERB
cjfa-35471	384	2	conclusions	conclusion	NOUN
cjfa-35471	384	3	can	can	AUX
cjfa-35471	384	4	be	be	AUX
cjfa-35471	384	5	made	make	VERB
cjfa-35471	384	6	even	even	ADV
cjfa-35471	384	7	without	without	ADP
cjfa-35471	384	8	specific	specific	ADJ
cjfa-35471	384	9	forms	form	NOUN
cjfa-35471	384	10	of	of	ADP
cjfa-35471	384	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	384	12	,	,	PUNCT
cjfa-35471	384	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	384	14	,	,	PUNCT
cjfa-35471	384	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	384	16	and	and	CCONJ
cjfa-35471	384	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	384	18	on	on	ADP
cjfa-35471	384	19	the	the	DET
cjfa-35471	384	20	basis	basis	NOUN
cjfa-35471	384	21	of	of	ADP
cjfa-35471	384	22	equation	equation	NOUN
cjfa-35471	384	23	(	(	PUNCT
cjfa-35471	384	24	4	4	NUM
cjfa-35471	384	25	):	):	PUNCT
cjfa-35471	384	26	1	1	NUM
cjfa-35471	384	27	.	.	PUNCT
cjfa-35471	385	1	the	the	DET
cjfa-35471	385	2	firm	firm	NOUN
cjfa-35471	385	3	will	will	AUX
cjfa-35471	385	4	keep	keep	VERB
cjfa-35471	385	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	385	6	𝑢	𝑢	ADP
cjfa-35471	385	7	𝐼	𝐼	PROPN
cjfa-35471	385	8	as	as	ADV
cjfa-35471	385	9	long	long	ADV
cjfa-35471	385	10	as	as	SCONJ
cjfa-35471	385	11	demand	demand	NOUN
cjfa-35471	385	12	is	be	AUX
cjfa-35471	385	13	falling	fall	VERB
cjfa-35471	385	14	or	or	CCONJ
cjfa-35471	385	15	constant	constant	ADJ
cjfa-35471	385	16	i.e.	i.e.	X
cjfa-35471	385	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	385	18	0	0	NOUN
cjfa-35471	385	19	implying	imply	VERB
cjfa-35471	385	20	that	that	SCONJ
cjfa-35471	385	21	the	the	DET
cjfa-35471	385	22	firm	firm	NOUN
cjfa-35471	385	23	will	will	AUX
cjfa-35471	385	24	choose	choose	VERB
cjfa-35471	385	25	to	to	PART
cjfa-35471	385	26	produce	produce	VERB
cjfa-35471	385	27	just	just	ADV
cjfa-35471	385	28	enough	enough	ADJ
cjfa-35471	385	29	to	to	PART
cjfa-35471	385	30	meet	meet	VERB
cjfa-35471	385	31	the	the	DET
cjfa-35471	385	32	demand	demand	NOUN
cjfa-35471	385	33	if	if	SCONJ
cjfa-35471	385	34	demand	demand	NOUN
cjfa-35471	385	35	is	be	AUX
cjfa-35471	385	36	falling	fall	VERB
cjfa-35471	385	37	since	since	SCONJ
cjfa-35471	385	38	both	both	PRON
cjfa-35471	385	39	ℎ	ℎ	NOUN
cjfa-35471	385	40	and	and	CCONJ
cjfa-35471	385	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	385	42	are	be	AUX
cjfa-35471	385	43	positive	positive	ADJ
cjfa-35471	385	44	.	.	PUNCT
cjfa-35471	386	1	2	2	X
cjfa-35471	386	2	.	.	X
cjfa-35471	386	3	the	the	DET
cjfa-35471	386	4	firm	firm	NOUN
cjfa-35471	386	5	will	will	AUX
cjfa-35471	386	6	keep	keep	VERB
cjfa-35471	386	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	386	8	𝑢	𝑢	ADP
cjfa-35471	386	9	𝐼	𝐼	NOUN
cjfa-35471	386	10	even	even	ADV
cjfa-35471	386	11	if	if	SCONJ
cjfa-35471	386	12	demand	demand	NOUN
cjfa-35471	386	13	is	be	AUX
cjfa-35471	386	14	increasing	increase	VERB
cjfa-35471	386	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	386	16	𝑟	𝑟	X
cjfa-35471	386	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	386	18	but	but	CCONJ
cjfa-35471	386	19	the	the	DET
cjfa-35471	386	20	term	term	NOUN
cjfa-35471	386	21	ℎ	ℎ	PROPN
cjfa-35471	386	22	+	+	CCONJ
cjfa-35471	386	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	386	24	�	�	PROPN
cjfa-35471	386	25	�	�	PROPN
cjfa-35471	386	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	386	27	�	�	PROPN
cjfa-35471	386	28	is	be	AUX
cjfa-35471	386	29	large	large	ADJ
cjfa-35471	386	30	enough	enough	ADV
cjfa-35471	386	31	to	to	PART
cjfa-35471	386	32	keep	keep	VERB
cjfa-35471	386	33	inequality	inequality	NOUN
cjfa-35471	386	34	(	(	PUNCT
cjfa-35471	386	35	4	4	NUM
cjfa-35471	386	36	)	)	PUNCT
cjfa-35471	386	37	satisfied	satisfied	ADJ
cjfa-35471	386	38	.	.	PUNCT
cjfa-35471	387	1	decreasing	decrease	VERB
cjfa-35471	387	2	interest	interest	NOUN
cjfa-35471	387	3	rates	rate	NOUN
cjfa-35471	387	4	will	will	AUX
cjfa-35471	387	5	not	not	PART
cjfa-35471	387	6	be	be	AUX
cjfa-35471	387	7	a	a	DET
cjfa-35471	387	8	remedy	remedy	NOUN
cjfa-35471	387	9	in	in	ADP
cjfa-35471	387	10	this	this	DET
cjfa-35471	387	11	case	case	NOUN
cjfa-35471	387	12	if	if	SCONJ
cjfa-35471	387	13	they	they	PRON
cjfa-35471	387	14	are	be	AUX
cjfa-35471	387	15	already	already	ADV
cjfa-35471	387	16	low	low	ADJ
cjfa-35471	387	17	.	.	PUNCT
cjfa-35471	388	1	firms	firm	NOUN
cjfa-35471	388	2	where	where	SCONJ
cjfa-35471	388	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	388	4	�	�	PROPN
cjfa-35471	388	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	388	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	388	7	�	�	PROPN
cjfa-35471	388	8	is	be	AUX
cjfa-35471	388	9	low	low	ADJ
cjfa-35471	388	10	(	(	PUNCT
cjfa-35471	388	11	large	large	ADJ
cjfa-35471	388	12	and	and	CCONJ
cjfa-35471	388	13	already	already	ADV
cjfa-35471	388	14	very	very	ADV
cjfa-35471	388	15	efficient	efficient	ADJ
cjfa-35471	388	16	firms	firm	NOUN
cjfa-35471	388	17	)	)	PUNCT
cjfa-35471	388	18	will	will	AUX
cjfa-35471	388	19	have	have	VERB
cjfa-35471	388	20	more	more	ADJ
cjfa-35471	388	21	difficulty	difficulty	NOUN
cjfa-35471	388	22	to	to	PART
cjfa-35471	388	23	produce	produce	VERB
cjfa-35471	388	24	to	to	PART
cjfa-35471	388	25	build	build	VERB
cjfa-35471	388	26	up	up	ADP
cjfa-35471	388	27	inventories	inventory	NOUN
cjfa-35471	388	28	.	.	PUNCT
cjfa-35471	389	1	currently	currently	ADV
cjfa-35471	389	2	,	,	PUNCT
cjfa-35471	389	3	this	this	PRON
cjfa-35471	389	4	seems	seem	VERB
cjfa-35471	389	5	to	to	PART
cjfa-35471	389	6	be	be	AUX
cjfa-35471	389	7	the	the	DET
cjfa-35471	389	8	case	case	NOUN
cjfa-35471	389	9	in	in	ADP
cjfa-35471	389	10	major	major	ADJ
cjfa-35471	389	11	economies	economy	NOUN
cjfa-35471	389	12	.	.	PUNCT
cjfa-35471	390	1	3	3	X
cjfa-35471	390	2	.	.	X
cjfa-35471	390	3	higher	high	ADJ
cjfa-35471	390	4	interest	interest	NOUN
cjfa-35471	390	5	rates	rate	NOUN
cjfa-35471	390	6	and	and	CCONJ
cjfa-35471	390	7	the	the	DET
cjfa-35471	390	8	use	use	NOUN
cjfa-35471	390	9	of	of	ADP
cjfa-35471	390	10	inefficient	inefficient	ADJ
cjfa-35471	390	11	technologies	technology	NOUN
cjfa-35471	390	12	(	(	PUNCT
cjfa-35471	390	13	large	large	ADJ
cjfa-35471	390	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	390	15	)	)	PUNCT
cjfa-35471	390	16	implies	imply	VERB
cjfa-35471	390	17	high	high	ADJ
cjfa-35471	390	18	marginal	marginal	ADJ
cjfa-35471	390	19	cost	cost	NOUN
cjfa-35471	390	20	)	)	PUNCT
cjfa-35471	390	21	will	will	AUX
cjfa-35471	390	22	induce	induce	VERB
cjfa-35471	390	23	firms	firm	NOUN
cjfa-35471	390	24	to	to	PART
cjfa-35471	390	25	wait	wait	VERB
cjfa-35471	390	26	longer	long	ADV
cjfa-35471	390	27	for	for	ADP
cjfa-35471	390	28	inventory	inventory	NOUN
cjfa-35471	390	29	build	build	NOUN
cjfa-35471	390	30	-	-	PUNCT
cjfa-35471	390	31	up	up	NOUN
cjfa-35471	390	32	even	even	ADV
cjfa-35471	390	33	if	if	SCONJ
cjfa-35471	390	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	390	35	is	be	AUX
cjfa-35471	390	36	positive	positive	ADJ
cjfa-35471	390	37	.	.	PUNCT
cjfa-35471	391	1	4	4	X
cjfa-35471	391	2	.	.	X
cjfa-35471	391	3	the	the	DET
cjfa-35471	391	4	level	level	NOUN
cjfa-35471	391	5	of	of	ADP
cjfa-35471	391	6	technology	technology	NOUN
cjfa-35471	391	7	used	use	VERB
cjfa-35471	391	8	will	will	AUX
cjfa-35471	391	9	not	not	PART
cjfa-35471	391	10	affect	affect	VERB
cjfa-35471	391	11	the	the	DET
cjfa-35471	391	12	behavior	behavior	NOUN
cjfa-35471	391	13	of	of	ADP
cjfa-35471	391	14	the	the	DET
cjfa-35471	391	15	firms	firm	NOUN
cjfa-35471	391	16	if	if	SCONJ
cjfa-35471	391	17	the	the	DET
cjfa-35471	391	18	interest	interest	NOUN
cjfa-35471	391	19	rates	rate	NOUN
cjfa-35471	391	20	are	be	AUX
cjfa-35471	391	21	very	very	ADV
cjfa-35471	391	22	low	low	ADJ
cjfa-35471	391	23	as	as	SCONJ
cjfa-35471	391	24	they	they	PRON
cjfa-35471	391	25	are	be	AUX
cjfa-35471	391	26	now	now	ADV
cjfa-35471	391	27	in	in	ADP
cjfa-35471	391	28	many	many	ADJ
cjfa-35471	391	29	developed	develop	VERB
cjfa-35471	391	30	nations	nation	NOUN
cjfa-35471	391	31	since	since	SCONJ
cjfa-35471	391	32	the	the	DET
cjfa-35471	391	33	term	term	NOUN
cjfa-35471	391	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	391	35	in	in	ADP
cjfa-35471	391	36	denotes	denote	NOUN
cjfa-35471	391	37	the	the	DET
cjfa-35471	391	38	interest	interest	NOUN
cjfa-35471	391	39	rate	rate	NOUN
cjfa-35471	391	40	.	.	PUNCT
cjfa-35471	392	1	as	as	ADV
cjfa-35471	392	2	long	long	ADV
cjfa-35471	392	3	as	as	SCONJ
cjfa-35471	392	4	the	the	DET
cjfa-35471	392	5	condition	condition	NOUN
cjfa-35471	392	6	specified	specify	VERB
cjfa-35471	392	7	by	by	ADP
cjfa-35471	392	8	this	this	DET
cjfa-35471	392	9	inequality	inequality	NOUN
cjfa-35471	392	10	is	be	AUX
cjfa-35471	392	11	satisfied	satisfied	ADJ
cjfa-35471	392	12	it	it	PRON
cjfa-35471	392	13	will	will	AUX
cjfa-35471	392	14	be	be	AUX
cjfa-35471	392	15	optimal	optimal	ADJ
cjfa-35471	392	16	to	to	PART
cjfa-35471	392	17	keep	keep	VERB
cjfa-35471	392	18	i(t	i(t	NOUN
cjfa-35471	392	19	)	)	PUNCT
cjfa-35471	393	1	=	=	SYM
cjfa-35471	393	2	0	0	NUM
cjfa-35471	393	3	implying	imply	VERB
cjfa-35471	393	4	u(t	u(t	NOUN
cjfa-35471	393	5	)	)	PUNCT
cjfa-35471	393	6	=	=	SYM
cjfa-35471	393	7	r(t	r(t	NOUN
cjfa-35471	393	8	)	)	PUNCT
cjfa-35471	393	9	.	.	PUNCT
cjfa-35471	394	1	this	this	PRON
cjfa-35471	394	2	means	mean	VERB
cjfa-35471	394	3	that	that	SCONJ
cjfa-35471	394	4	during	during	ADP
cjfa-35471	394	5	the	the	DET
cjfa-35471	394	6	intervals	interval	NOUN
cjfa-35471	394	7	where	where	SCONJ
cjfa-35471	394	8	this	this	DET
cjfa-35471	394	9	inequality	inequality	NOUN
cjfa-35471	394	10	is	be	AUX
cjfa-35471	394	11	satisfied	satisfied	ADJ
cjfa-35471	394	12	the	the	DET
cjfa-35471	394	13	firm	firm	NOUN
cjfa-35471	394	14	will	will	AUX
cjfa-35471	394	15	produce	produce	VERB
cjfa-35471	394	16	just	just	ADV
cjfa-35471	394	17	enough	enough	ADJ
cjfa-35471	394	18	to	to	PART
cjfa-35471	394	19	satisfy	satisfy	VERB
cjfa-35471	394	20	the	the	DET
cjfa-35471	394	21	demand	demand	NOUN
cjfa-35471	394	22	.	.	PUNCT
cjfa-35471	395	1	so	so	ADV
cjfa-35471	395	2	,	,	PUNCT
cjfa-35471	395	3	the	the	DET
cjfa-35471	395	4	condition	condition	NOUN
cjfa-35471	395	5	above	above	ADV
cjfa-35471	395	6	will	will	AUX
cjfa-35471	395	7	synthesize	synthesize	VERB
cjfa-35471	395	8	the	the	DET
cjfa-35471	395	9	periods	period	NOUN
cjfa-35471	395	10	where	where	SCONJ
cjfa-35471	395	11	then	then	ADV
cjfa-35471	395	12	using	use	VERB
cjfa-35471	395	13	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	395	14	𝑢	𝑢	PROPN
cjfa-35471	395	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	395	16	,	,	PUNCT
cjfa-35471	395	17	equation	equation	NOUN
cjfa-35471	395	18	(	(	PUNCT
cjfa-35471	395	19	1	1	NUM
cjfa-35471	395	20	)	)	PUNCT
cjfa-35471	395	21	,	,	PUNCT
cjfa-35471	395	22	and	and	CCONJ
cjfa-35471	395	23	the	the	DET
cjfa-35471	395	24	conditions	condition	NOUN
cjfa-35471	395	25	(	(	PUNCT
cjfa-35471	395	26	the	the	DET
cjfa-35471	395	27	necessary	necessary	ADJ
cjfa-35471	395	28	condition	condition	NOUN
cjfa-35471	395	29	to	to	PART
cjfa-35471	395	30	keep	keep	VERB
cjfa-35471	395	31	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	395	32	𝑢	𝑢	ADP
cjfa-35471	395	33	𝐼	𝐼	PROPN
cjfa-35471	395	34	optimal	optimal	ADJ
cjfa-35471	395	35	)	)	PUNCT
cjfa-35471	395	36	developed	develop	VERB
cjfa-35471	395	37	by	by	ADP
cjfa-35471	395	38	pontryagin	pontryagin	NOUN
cjfa-35471	395	39	,	,	PUNCT
cjfa-35471	395	40	boltyanskii	boltyanskii	ADJ
cjfa-35471	395	41	,	,	PUNCT
cjfa-35471	395	42	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	395	43	and	and	CCONJ
cjfa-35471	395	44	mishechenko	mishechenko	NOUN
cjfa-35471	395	45	(	(	PUNCT
cjfa-35471	395	46	1962	1962	NUM
cjfa-35471	395	47	)	)	PUNCT
cjfa-35471	395	48	,	,	PUNCT
cjfa-35471	395	49	hestenes	hestene	NOUN
cjfa-35471	395	50	(	(	PUNCT
cjfa-35471	395	51	1966	1966	NUM
cjfa-35471	395	52	)	)	PUNCT
cjfa-35471	395	53	,	,	PUNCT
cjfa-35471	395	54	kamien	kamien	NOUN
cjfa-35471	395	55	and	and	CCONJ
cjfa-35471	395	56	schwartz	schwartz	PROPN
cjfa-35471	395	57	(	(	PUNCT
cjfa-35471	395	58	2012	2012	NUM
cjfa-35471	395	59	)	)	PUNCT
cjfa-35471	395	60	among	among	ADP
cjfa-35471	395	61	many	many	ADJ
cjfa-35471	395	62	others	other	NOUN
cjfa-35471	395	63	,	,	PUNCT
cjfa-35471	395	64	we	we	PRON
cjfa-35471	395	65	have	have	AUX
cjfa-35471	395	66	;	;	PUNCT
cjfa-35471	395	67	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	395	68	�	�	NOUN
cjfa-35471	395	69	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	395	70	≤	≤	PUNCT
cjfa-35471	395	71	𝐼	𝐼	PROPN
cjfa-35471	395	72	for	for	ADP
cjfa-35471	395	73	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	395	74	�	�	PROPN
cjfa-35471	395	75	≤	≤	NUM
cjfa-35471	396	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	396	2	≤	≤	NUM
cjfa-35471	396	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	396	4	�	�	PROPN
cjfa-35471	396	5	implies	imply	VERB
cjfa-35471	396	6	:	:	PUNCT
cjfa-35471	396	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	396	8	�	�	PROPN
cjfa-35471	396	9	�	�	PROPN
cjfa-35471	396	10	�	�	PROPN
cjfa-35471	396	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	396	12	�	�	PROPN
cjfa-35471	396	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	396	14	�	�	PROPN
cjfa-35471	396	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	396	16	≤	≤	PUNCT
cjfa-35471	396	17	ℎ	ℎ	PROPN
cjfa-35471	396	18	+	+	PROPN
cjfa-35471	396	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	396	20	�	�	PROPN
cjfa-35471	396	21	�	�	PROPN
cjfa-35471	396	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	396	23	�	�	PROPN
cjfa-35471	396	24	(	(	PUNCT
cjfa-35471	396	25	4	4	NUM
cjfa-35471	396	26	)	)	PUNCT
cjfa-35471	396	27	where	where	SCONJ
cjfa-35471	396	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	396	29	𝑢	𝑢	PROPN
cjfa-35471	396	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	396	31	�	�	NOUN
cjfa-35471	396	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	396	33	denotes	denote	VERB
cjfa-35471	396	34	the	the	DET
cjfa-35471	396	35	interest	interest	NOUN
cjfa-35471	396	36	rate	rate	NOUN
cjfa-35471	396	37	.	.	PUNCT
cjfa-35471	397	1	as	as	ADV
cjfa-35471	397	2	long	long	ADV
cjfa-35471	397	3	as	as	SCONJ
cjfa-35471	397	4	the	the	DET
cjfa-35471	397	5	condition	condition	NOUN
cjfa-35471	397	6	specified	specify	VERB
cjfa-35471	397	7	by	by	ADP
cjfa-35471	397	8	this	this	DET
cjfa-35471	397	9	inequality	inequality	NOUN
cjfa-35471	397	10	is	be	AUX
cjfa-35471	397	11	satisfied	satisfied	ADJ
cjfa-35471	397	12	it	it	PRON
cjfa-35471	397	13	will	will	AUX
cjfa-35471	397	14	be	be	AUX
cjfa-35471	397	15	optimal	optimal	ADJ
cjfa-35471	397	16	to	to	PART
cjfa-35471	397	17	keep	keep	VERB
cjfa-35471	397	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	397	19	𝑢	𝑢	ADP
cjfa-35471	397	20	𝐼	𝐼	ADP
cjfa-35471	397	21	implying	imply	VERB
cjfa-35471	397	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	397	23	𝑢	𝑢	PRON
cjfa-35471	397	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	397	25	this	this	PRON
cjfa-35471	397	26	means	mean	VERB
cjfa-35471	397	27	that	that	SCONJ
cjfa-35471	397	28	during	during	ADP
cjfa-35471	397	29	the	the	DET
cjfa-35471	397	30	intervals	interval	NOUN
cjfa-35471	397	31	where	where	SCONJ
cjfa-35471	397	32	this	this	DET
cjfa-35471	397	33	inequality	inequality	NOUN
cjfa-35471	397	34	is	be	AUX
cjfa-35471	397	35	satisfied	satisfied	ADJ
cjfa-35471	397	36	the	the	DET
cjfa-35471	397	37	firm	firm	NOUN
cjfa-35471	397	38	will	will	AUX
cjfa-35471	397	39	produce	produce	VERB
cjfa-35471	397	40	just	just	ADV
cjfa-35471	397	41	enough	enough	ADJ
cjfa-35471	397	42	to	to	PART
cjfa-35471	397	43	satisfy	satisfy	VERB
cjfa-35471	397	44	the	the	DET
cjfa-35471	397	45	demand	demand	NOUN
cjfa-35471	397	46	.	.	PUNCT
cjfa-35471	398	1	so	so	ADV
cjfa-35471	398	2	,	,	PUNCT
cjfa-35471	398	3	the	the	DET
cjfa-35471	398	4	condition	condition	NOUN
cjfa-35471	398	5	above	above	ADV
cjfa-35471	398	6	will	will	AUX
cjfa-35471	398	7	synthesize	synthesize	VERB
cjfa-35471	398	8	the	the	DET
cjfa-35471	398	9	periods	period	NOUN
cjfa-35471	398	10	where	where	SCONJ
cjfa-35471	398	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	398	12	𝑢	𝑢	PRON
cjfa-35471	398	13	𝐼	𝐼	PROPN
cjfa-35471	398	14	or	or	CCONJ
cjfa-35471	398	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	398	16	𝑢	𝑢	PROPN
cjfa-35471	398	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	398	18	and	and	CCONJ
cjfa-35471	398	19	the	the	DET
cjfa-35471	398	20	periods	period	NOUN
cjfa-35471	398	21	where	where	SCONJ
cjfa-35471	398	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	398	23	𝐼	𝐼	ADP
cjfa-35471	398	24	𝐼.	𝐼.	PROPN
cjfa-35471	398	25	notice	notice	VERB
cjfa-35471	398	26	that	that	SCONJ
cjfa-35471	398	27	for	for	ADP
cjfa-35471	398	28	the	the	DET
cjfa-35471	398	29	condition	condition	NOUN
cjfa-35471	398	30	above	above	ADV
cjfa-35471	398	31	(	(	PUNCT
cjfa-35471	398	32	equation	equation	NOUN
cjfa-35471	398	33	4	4	NUM
cjfa-35471	398	34	)	)	PUNCT
cjfa-35471	398	35	to	to	PART
cjfa-35471	398	36	be	be	AUX
cjfa-35471	398	37	kept	keep	VERB
cjfa-35471	398	38	satisfied	satisfied	ADJ
cjfa-35471	398	39	depends	depend	VERB
cjfa-35471	398	40	on	on	ADP
cjfa-35471	398	41	ℎ	ℎ	PROPN
cjfa-35471	398	42	(	(	PUNCT
cjfa-35471	398	43	inventory	inventory	NOUN
cjfa-35471	398	44	holding	hold	VERB
cjfa-35471	398	45	cost	cost	NOUN
cjfa-35471	398	46	)	)	PUNCT
cjfa-35471	398	47	,	,	PUNCT
cjfa-35471	398	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	398	49	the	the	DET
cjfa-35471	398	50	interest	interest	NOUN
cjfa-35471	398	51	rates	rate	NOUN
cjfa-35471	398	52	,	,	PUNCT
cjfa-35471	398	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	398	54	,	,	PUNCT
cjfa-35471	398	55	the	the	DET
cjfa-35471	398	56	marginal	marginal	ADJ
cjfa-35471	398	57	cost	cost	NOUN
cjfa-35471	398	58	of	of	ADP
cjfa-35471	398	59	production	production	NOUN
cjfa-35471	398	60	,	,	PUNCT
cjfa-35471	398	61	and	and	CCONJ
cjfa-35471	398	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	398	63	change	change	NOUN
cjfa-35471	398	64	in	in	ADP
cjfa-35471	398	65	the	the	DET
cjfa-35471	398	66	marginal	marginal	ADJ
cjfa-35471	398	67	cost	cost	NOUN
cjfa-35471	398	68	.	.	PUNCT
cjfa-35471	399	1	following	follow	VERB
cjfa-35471	399	2	conclusions	conclusion	NOUN
cjfa-35471	399	3	can	can	AUX
cjfa-35471	399	4	be	be	AUX
cjfa-35471	399	5	made	make	VERB
cjfa-35471	399	6	even	even	ADV
cjfa-35471	399	7	without	without	ADP
cjfa-35471	399	8	specific	specific	ADJ
cjfa-35471	399	9	forms	form	NOUN
cjfa-35471	399	10	of	of	ADP
cjfa-35471	399	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	399	12	,	,	PUNCT
cjfa-35471	399	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	399	14	,	,	PUNCT
cjfa-35471	399	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	399	16	and	and	CCONJ
cjfa-35471	399	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	399	18	on	on	ADP
cjfa-35471	399	19	the	the	DET
cjfa-35471	399	20	basis	basis	NOUN
cjfa-35471	399	21	of	of	ADP
cjfa-35471	399	22	equation	equation	NOUN
cjfa-35471	399	23	(	(	PUNCT
cjfa-35471	399	24	4	4	NUM
cjfa-35471	399	25	):	):	PUNCT
cjfa-35471	399	26	1	1	NUM
cjfa-35471	399	27	.	.	PUNCT
cjfa-35471	400	1	the	the	DET
cjfa-35471	400	2	firm	firm	NOUN
cjfa-35471	400	3	will	will	AUX
cjfa-35471	400	4	keep	keep	VERB
cjfa-35471	400	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	400	6	𝑢	𝑢	ADP
cjfa-35471	400	7	𝐼	𝐼	PROPN
cjfa-35471	400	8	as	as	ADV
cjfa-35471	400	9	long	long	ADV
cjfa-35471	400	10	as	as	SCONJ
cjfa-35471	400	11	demand	demand	NOUN
cjfa-35471	400	12	is	be	AUX
cjfa-35471	400	13	falling	fall	VERB
cjfa-35471	400	14	or	or	CCONJ
cjfa-35471	400	15	constant	constant	ADJ
cjfa-35471	400	16	i.e.	i.e.	X
cjfa-35471	400	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	400	18	0	0	NOUN
cjfa-35471	400	19	implying	imply	VERB
cjfa-35471	400	20	that	that	SCONJ
cjfa-35471	400	21	the	the	DET
cjfa-35471	400	22	firm	firm	NOUN
cjfa-35471	400	23	will	will	AUX
cjfa-35471	400	24	choose	choose	VERB
cjfa-35471	400	25	to	to	PART
cjfa-35471	400	26	produce	produce	VERB
cjfa-35471	400	27	just	just	ADV
cjfa-35471	400	28	enough	enough	ADJ
cjfa-35471	400	29	to	to	PART
cjfa-35471	400	30	meet	meet	VERB
cjfa-35471	400	31	the	the	DET
cjfa-35471	400	32	demand	demand	NOUN
cjfa-35471	400	33	if	if	SCONJ
cjfa-35471	400	34	demand	demand	NOUN
cjfa-35471	400	35	is	be	AUX
cjfa-35471	400	36	falling	fall	VERB
cjfa-35471	400	37	since	since	SCONJ
cjfa-35471	400	38	both	both	PRON
cjfa-35471	400	39	ℎ	ℎ	NOUN
cjfa-35471	400	40	and	and	CCONJ
cjfa-35471	400	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	400	42	are	be	AUX
cjfa-35471	400	43	positive	positive	ADJ
cjfa-35471	400	44	.	.	PUNCT
cjfa-35471	401	1	2	2	X
cjfa-35471	401	2	.	.	X
cjfa-35471	401	3	the	the	DET
cjfa-35471	401	4	firm	firm	NOUN
cjfa-35471	401	5	will	will	AUX
cjfa-35471	401	6	keep	keep	VERB
cjfa-35471	401	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	401	8	𝑢	𝑢	ADP
cjfa-35471	401	9	𝐼	𝐼	NOUN
cjfa-35471	401	10	even	even	ADV
cjfa-35471	401	11	if	if	SCONJ
cjfa-35471	401	12	demand	demand	NOUN
cjfa-35471	401	13	is	be	AUX
cjfa-35471	401	14	increasing	increase	VERB
cjfa-35471	401	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	401	16	𝑟	𝑟	X
cjfa-35471	401	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	401	18	but	but	CCONJ
cjfa-35471	401	19	the	the	DET
cjfa-35471	401	20	term	term	NOUN
cjfa-35471	401	21	ℎ	ℎ	PROPN
cjfa-35471	401	22	+	+	CCONJ
cjfa-35471	401	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	401	24	�	�	PROPN
cjfa-35471	401	25	�	�	PROPN
cjfa-35471	401	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	401	27	�	�	PROPN
cjfa-35471	401	28	is	be	AUX
cjfa-35471	401	29	large	large	ADJ
cjfa-35471	401	30	enough	enough	ADV
cjfa-35471	401	31	to	to	PART
cjfa-35471	401	32	keep	keep	VERB
cjfa-35471	401	33	inequality	inequality	NOUN
cjfa-35471	401	34	(	(	PUNCT
cjfa-35471	401	35	4	4	NUM
cjfa-35471	401	36	)	)	PUNCT
cjfa-35471	401	37	satisfied	satisfied	ADJ
cjfa-35471	401	38	.	.	PUNCT
cjfa-35471	402	1	decreasing	decrease	VERB
cjfa-35471	402	2	interest	interest	NOUN
cjfa-35471	402	3	rates	rate	NOUN
cjfa-35471	402	4	will	will	AUX
cjfa-35471	402	5	not	not	PART
cjfa-35471	402	6	be	be	AUX
cjfa-35471	402	7	a	a	DET
cjfa-35471	402	8	remedy	remedy	NOUN
cjfa-35471	402	9	in	in	ADP
cjfa-35471	402	10	this	this	DET
cjfa-35471	402	11	case	case	NOUN
cjfa-35471	402	12	if	if	SCONJ
cjfa-35471	402	13	they	they	PRON
cjfa-35471	402	14	are	be	AUX
cjfa-35471	402	15	already	already	ADV
cjfa-35471	402	16	low	low	ADJ
cjfa-35471	402	17	.	.	PUNCT
cjfa-35471	403	1	firms	firm	NOUN
cjfa-35471	403	2	where	where	SCONJ
cjfa-35471	403	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	403	4	�	�	PROPN
cjfa-35471	403	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	403	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	403	7	�	�	PROPN
cjfa-35471	403	8	is	be	AUX
cjfa-35471	403	9	low	low	ADJ
cjfa-35471	403	10	(	(	PUNCT
cjfa-35471	403	11	large	large	ADJ
cjfa-35471	403	12	and	and	CCONJ
cjfa-35471	403	13	already	already	ADV
cjfa-35471	403	14	very	very	ADV
cjfa-35471	403	15	efficient	efficient	ADJ
cjfa-35471	403	16	firms	firm	NOUN
cjfa-35471	403	17	)	)	PUNCT
cjfa-35471	403	18	will	will	AUX
cjfa-35471	403	19	have	have	VERB
cjfa-35471	403	20	more	more	ADJ
cjfa-35471	403	21	difficulty	difficulty	NOUN
cjfa-35471	403	22	to	to	PART
cjfa-35471	403	23	produce	produce	VERB
cjfa-35471	403	24	to	to	PART
cjfa-35471	403	25	build	build	VERB
cjfa-35471	403	26	up	up	ADP
cjfa-35471	403	27	inventories	inventory	NOUN
cjfa-35471	403	28	.	.	PUNCT
cjfa-35471	404	1	currently	currently	ADV
cjfa-35471	404	2	,	,	PUNCT
cjfa-35471	404	3	this	this	PRON
cjfa-35471	404	4	seems	seem	VERB
cjfa-35471	404	5	to	to	PART
cjfa-35471	404	6	be	be	AUX
cjfa-35471	404	7	the	the	DET
cjfa-35471	404	8	case	case	NOUN
cjfa-35471	404	9	in	in	ADP
cjfa-35471	404	10	major	major	ADJ
cjfa-35471	404	11	economies	economy	NOUN
cjfa-35471	404	12	.	.	PUNCT
cjfa-35471	405	1	3	3	X
cjfa-35471	405	2	.	.	X
cjfa-35471	405	3	higher	high	ADJ
cjfa-35471	405	4	interest	interest	NOUN
cjfa-35471	405	5	rates	rate	NOUN
cjfa-35471	405	6	and	and	CCONJ
cjfa-35471	405	7	the	the	DET
cjfa-35471	405	8	use	use	NOUN
cjfa-35471	405	9	of	of	ADP
cjfa-35471	405	10	inefficient	inefficient	ADJ
cjfa-35471	405	11	technologies	technology	NOUN
cjfa-35471	405	12	(	(	PUNCT
cjfa-35471	405	13	large	large	ADJ
cjfa-35471	405	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	405	15	)	)	PUNCT
cjfa-35471	405	16	implies	imply	VERB
cjfa-35471	405	17	high	high	ADJ
cjfa-35471	405	18	marginal	marginal	ADJ
cjfa-35471	405	19	cost	cost	NOUN
cjfa-35471	405	20	)	)	PUNCT
cjfa-35471	405	21	will	will	AUX
cjfa-35471	405	22	induce	induce	VERB
cjfa-35471	405	23	firms	firm	NOUN
cjfa-35471	405	24	to	to	PART
cjfa-35471	405	25	wait	wait	VERB
cjfa-35471	405	26	longer	long	ADV
cjfa-35471	405	27	for	for	ADP
cjfa-35471	405	28	inventory	inventory	NOUN
cjfa-35471	405	29	build	build	NOUN
cjfa-35471	405	30	-	-	PUNCT
cjfa-35471	405	31	up	up	NOUN
cjfa-35471	405	32	even	even	ADV
cjfa-35471	405	33	if	if	SCONJ
cjfa-35471	405	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	405	35	is	be	AUX
cjfa-35471	405	36	positive	positive	ADJ
cjfa-35471	405	37	.	.	PUNCT
cjfa-35471	406	1	4	4	X
cjfa-35471	406	2	.	.	X
cjfa-35471	406	3	the	the	DET
cjfa-35471	406	4	level	level	NOUN
cjfa-35471	406	5	of	of	ADP
cjfa-35471	406	6	technology	technology	NOUN
cjfa-35471	406	7	used	use	VERB
cjfa-35471	406	8	will	will	AUX
cjfa-35471	406	9	not	not	PART
cjfa-35471	406	10	affect	affect	VERB
cjfa-35471	406	11	the	the	DET
cjfa-35471	406	12	behavior	behavior	NOUN
cjfa-35471	406	13	of	of	ADP
cjfa-35471	406	14	the	the	DET
cjfa-35471	406	15	firms	firm	NOUN
cjfa-35471	406	16	if	if	SCONJ
cjfa-35471	406	17	the	the	DET
cjfa-35471	406	18	interest	interest	NOUN
cjfa-35471	406	19	rates	rate	NOUN
cjfa-35471	406	20	are	be	AUX
cjfa-35471	406	21	very	very	ADV
cjfa-35471	406	22	low	low	ADJ
cjfa-35471	406	23	as	as	SCONJ
cjfa-35471	406	24	they	they	PRON
cjfa-35471	406	25	are	be	AUX
cjfa-35471	406	26	now	now	ADV
cjfa-35471	406	27	in	in	ADP
cjfa-35471	406	28	many	many	ADJ
cjfa-35471	406	29	developed	develop	VERB
cjfa-35471	406	30	nations	nation	NOUN
cjfa-35471	406	31	since	since	SCONJ
cjfa-35471	406	32	the	the	DET
cjfa-35471	406	33	term	term	NOUN
cjfa-35471	406	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	406	35	in	in	ADP
cjfa-35471	406	36	or	or	CCONJ
cjfa-35471	406	37	then	then	ADV
cjfa-35471	406	38	using	use	VERB
cjfa-35471	406	39	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	406	40	𝑢	𝑢	PROPN
cjfa-35471	406	41	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	406	42	,	,	PUNCT
cjfa-35471	406	43	equation	equation	NOUN
cjfa-35471	406	44	(	(	PUNCT
cjfa-35471	406	45	1	1	NUM
cjfa-35471	406	46	)	)	PUNCT
cjfa-35471	406	47	,	,	PUNCT
cjfa-35471	406	48	and	and	CCONJ
cjfa-35471	406	49	the	the	DET
cjfa-35471	406	50	conditions	condition	NOUN
cjfa-35471	406	51	(	(	PUNCT
cjfa-35471	406	52	the	the	DET
cjfa-35471	406	53	necessary	necessary	ADJ
cjfa-35471	406	54	condition	condition	NOUN
cjfa-35471	406	55	to	to	PART
cjfa-35471	406	56	keep	keep	VERB
cjfa-35471	406	57	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	406	58	𝑢	𝑢	ADP
cjfa-35471	406	59	𝐼	𝐼	PROPN
cjfa-35471	406	60	optimal	optimal	ADJ
cjfa-35471	406	61	)	)	PUNCT
cjfa-35471	406	62	developed	develop	VERB
cjfa-35471	406	63	by	by	ADP
cjfa-35471	406	64	pontryagin	pontryagin	NOUN
cjfa-35471	406	65	,	,	PUNCT
cjfa-35471	406	66	boltyanskii	boltyanskii	ADJ
cjfa-35471	406	67	,	,	PUNCT
cjfa-35471	406	68	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	406	69	and	and	CCONJ
cjfa-35471	406	70	mishechenko	mishechenko	NOUN
cjfa-35471	406	71	(	(	PUNCT
cjfa-35471	406	72	1962	1962	NUM
cjfa-35471	406	73	)	)	PUNCT
cjfa-35471	406	74	,	,	PUNCT
cjfa-35471	406	75	hestenes	hestene	NOUN
cjfa-35471	406	76	(	(	PUNCT
cjfa-35471	406	77	1966	1966	NUM
cjfa-35471	406	78	)	)	PUNCT
cjfa-35471	406	79	,	,	PUNCT
cjfa-35471	406	80	kamien	kamien	NOUN
cjfa-35471	406	81	and	and	CCONJ
cjfa-35471	406	82	schwartz	schwartz	PROPN
cjfa-35471	406	83	(	(	PUNCT
cjfa-35471	406	84	2012	2012	NUM
cjfa-35471	406	85	)	)	PUNCT
cjfa-35471	406	86	among	among	ADP
cjfa-35471	406	87	many	many	ADJ
cjfa-35471	406	88	others	other	NOUN
cjfa-35471	406	89	,	,	PUNCT
cjfa-35471	406	90	we	we	PRON
cjfa-35471	406	91	have	have	AUX
cjfa-35471	406	92	;	;	PUNCT
cjfa-35471	406	93	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	406	94	�	�	NOUN
cjfa-35471	406	95	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	406	96	≤	≤	PUNCT
cjfa-35471	406	97	𝐼	𝐼	PROPN
cjfa-35471	406	98	for	for	ADP
cjfa-35471	406	99	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	406	100	�	�	PROPN
cjfa-35471	406	101	≤	≤	NUM
cjfa-35471	407	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	407	2	≤	≤	NUM
cjfa-35471	407	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	407	4	�	�	PROPN
cjfa-35471	407	5	implies	imply	VERB
cjfa-35471	407	6	:	:	PUNCT
cjfa-35471	407	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	407	8	�	�	PROPN
cjfa-35471	407	9	�	�	PROPN
cjfa-35471	407	10	�	�	PROPN
cjfa-35471	407	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	407	12	�	�	PROPN
cjfa-35471	407	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	407	14	�	�	PROPN
cjfa-35471	407	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	407	16	≤	≤	PUNCT
cjfa-35471	407	17	ℎ	ℎ	PROPN
cjfa-35471	407	18	+	+	PROPN
cjfa-35471	407	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	407	20	�	�	PROPN
cjfa-35471	407	21	�	�	PROPN
cjfa-35471	407	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	407	23	�	�	PROPN
cjfa-35471	407	24	(	(	PUNCT
cjfa-35471	407	25	4	4	NUM
cjfa-35471	407	26	)	)	PUNCT
cjfa-35471	407	27	where	where	SCONJ
cjfa-35471	407	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	407	29	𝑢	𝑢	PROPN
cjfa-35471	407	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	407	31	�	�	NOUN
cjfa-35471	407	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	407	33	denotes	denote	VERB
cjfa-35471	407	34	the	the	DET
cjfa-35471	407	35	interest	interest	NOUN
cjfa-35471	407	36	rate	rate	NOUN
cjfa-35471	407	37	.	.	PUNCT
cjfa-35471	408	1	as	as	ADV
cjfa-35471	408	2	long	long	ADV
cjfa-35471	408	3	as	as	SCONJ
cjfa-35471	408	4	the	the	DET
cjfa-35471	408	5	condition	condition	NOUN
cjfa-35471	408	6	specified	specify	VERB
cjfa-35471	408	7	by	by	ADP
cjfa-35471	408	8	this	this	DET
cjfa-35471	408	9	inequality	inequality	NOUN
cjfa-35471	408	10	is	be	AUX
cjfa-35471	408	11	satisfied	satisfied	ADJ
cjfa-35471	408	12	it	it	PRON
cjfa-35471	408	13	will	will	AUX
cjfa-35471	408	14	be	be	AUX
cjfa-35471	408	15	optimal	optimal	ADJ
cjfa-35471	408	16	to	to	PART
cjfa-35471	408	17	keep	keep	VERB
cjfa-35471	408	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	408	19	𝑢	𝑢	ADP
cjfa-35471	408	20	𝐼	𝐼	ADP
cjfa-35471	408	21	implying	imply	VERB
cjfa-35471	408	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	408	23	𝑢	𝑢	PRON
cjfa-35471	408	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	408	25	this	this	PRON
cjfa-35471	408	26	means	mean	VERB
cjfa-35471	408	27	that	that	SCONJ
cjfa-35471	408	28	during	during	ADP
cjfa-35471	408	29	the	the	DET
cjfa-35471	408	30	intervals	interval	NOUN
cjfa-35471	408	31	where	where	SCONJ
cjfa-35471	408	32	this	this	DET
cjfa-35471	408	33	inequality	inequality	NOUN
cjfa-35471	408	34	is	be	AUX
cjfa-35471	408	35	satisfied	satisfied	ADJ
cjfa-35471	408	36	the	the	DET
cjfa-35471	408	37	firm	firm	NOUN
cjfa-35471	408	38	will	will	AUX
cjfa-35471	408	39	produce	produce	VERB
cjfa-35471	408	40	just	just	ADV
cjfa-35471	408	41	enough	enough	ADJ
cjfa-35471	408	42	to	to	PART
cjfa-35471	408	43	satisfy	satisfy	VERB
cjfa-35471	408	44	the	the	DET
cjfa-35471	408	45	demand	demand	NOUN
cjfa-35471	408	46	.	.	PUNCT
cjfa-35471	409	1	so	so	ADV
cjfa-35471	409	2	,	,	PUNCT
cjfa-35471	409	3	the	the	DET
cjfa-35471	409	4	condition	condition	NOUN
cjfa-35471	409	5	above	above	ADV
cjfa-35471	409	6	will	will	AUX
cjfa-35471	409	7	synthesize	synthesize	VERB
cjfa-35471	409	8	the	the	DET
cjfa-35471	409	9	periods	period	NOUN
cjfa-35471	409	10	where	where	SCONJ
cjfa-35471	409	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	409	12	𝑢	𝑢	PRON
cjfa-35471	409	13	𝐼	𝐼	PROPN
cjfa-35471	409	14	or	or	CCONJ
cjfa-35471	409	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	409	16	𝑢	𝑢	PROPN
cjfa-35471	409	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	409	18	and	and	CCONJ
cjfa-35471	409	19	the	the	DET
cjfa-35471	409	20	periods	period	NOUN
cjfa-35471	409	21	where	where	SCONJ
cjfa-35471	409	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	409	23	𝐼	𝐼	ADP
cjfa-35471	409	24	𝐼.	𝐼.	PROPN
cjfa-35471	409	25	notice	notice	VERB
cjfa-35471	409	26	that	that	SCONJ
cjfa-35471	409	27	for	for	ADP
cjfa-35471	409	28	the	the	DET
cjfa-35471	409	29	condition	condition	NOUN
cjfa-35471	409	30	above	above	ADV
cjfa-35471	409	31	(	(	PUNCT
cjfa-35471	409	32	equation	equation	NOUN
cjfa-35471	409	33	4	4	NUM
cjfa-35471	409	34	)	)	PUNCT
cjfa-35471	409	35	to	to	PART
cjfa-35471	409	36	be	be	AUX
cjfa-35471	409	37	kept	keep	VERB
cjfa-35471	409	38	satisfied	satisfied	ADJ
cjfa-35471	409	39	depends	depend	VERB
cjfa-35471	409	40	on	on	ADP
cjfa-35471	409	41	ℎ	ℎ	PROPN
cjfa-35471	409	42	(	(	PUNCT
cjfa-35471	409	43	inventory	inventory	NOUN
cjfa-35471	409	44	holding	hold	VERB
cjfa-35471	409	45	cost	cost	NOUN
cjfa-35471	409	46	)	)	PUNCT
cjfa-35471	409	47	,	,	PUNCT
cjfa-35471	409	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	409	49	the	the	DET
cjfa-35471	409	50	interest	interest	NOUN
cjfa-35471	409	51	rates	rate	NOUN
cjfa-35471	409	52	,	,	PUNCT
cjfa-35471	409	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	409	54	,	,	PUNCT
cjfa-35471	409	55	the	the	DET
cjfa-35471	409	56	marginal	marginal	ADJ
cjfa-35471	409	57	cost	cost	NOUN
cjfa-35471	409	58	of	of	ADP
cjfa-35471	409	59	production	production	NOUN
cjfa-35471	409	60	,	,	PUNCT
cjfa-35471	409	61	and	and	CCONJ
cjfa-35471	409	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	409	63	change	change	NOUN
cjfa-35471	409	64	in	in	ADP
cjfa-35471	409	65	the	the	DET
cjfa-35471	409	66	marginal	marginal	ADJ
cjfa-35471	409	67	cost	cost	NOUN
cjfa-35471	409	68	.	.	PUNCT
cjfa-35471	410	1	following	follow	VERB
cjfa-35471	410	2	conclusions	conclusion	NOUN
cjfa-35471	410	3	can	can	AUX
cjfa-35471	410	4	be	be	AUX
cjfa-35471	410	5	made	make	VERB
cjfa-35471	410	6	even	even	ADV
cjfa-35471	410	7	without	without	ADP
cjfa-35471	410	8	specific	specific	ADJ
cjfa-35471	410	9	forms	form	NOUN
cjfa-35471	410	10	of	of	ADP
cjfa-35471	410	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	410	12	,	,	PUNCT
cjfa-35471	410	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	410	14	,	,	PUNCT
cjfa-35471	410	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	410	16	and	and	CCONJ
cjfa-35471	410	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	410	18	on	on	ADP
cjfa-35471	410	19	the	the	DET
cjfa-35471	410	20	basis	basis	NOUN
cjfa-35471	410	21	of	of	ADP
cjfa-35471	410	22	equation	equation	NOUN
cjfa-35471	410	23	(	(	PUNCT
cjfa-35471	410	24	4	4	NUM
cjfa-35471	410	25	):	):	PUNCT
cjfa-35471	410	26	1	1	NUM
cjfa-35471	410	27	.	.	PUNCT
cjfa-35471	411	1	the	the	DET
cjfa-35471	411	2	firm	firm	NOUN
cjfa-35471	411	3	will	will	AUX
cjfa-35471	411	4	keep	keep	VERB
cjfa-35471	411	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	411	6	𝑢	𝑢	ADP
cjfa-35471	411	7	𝐼	𝐼	PROPN
cjfa-35471	411	8	as	as	ADV
cjfa-35471	411	9	long	long	ADV
cjfa-35471	411	10	as	as	SCONJ
cjfa-35471	411	11	demand	demand	NOUN
cjfa-35471	411	12	is	be	AUX
cjfa-35471	411	13	falling	fall	VERB
cjfa-35471	411	14	or	or	CCONJ
cjfa-35471	411	15	constant	constant	ADJ
cjfa-35471	411	16	i.e.	i.e.	X
cjfa-35471	411	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	411	18	0	0	NOUN
cjfa-35471	411	19	implying	imply	VERB
cjfa-35471	411	20	that	that	SCONJ
cjfa-35471	411	21	the	the	DET
cjfa-35471	411	22	firm	firm	NOUN
cjfa-35471	411	23	will	will	AUX
cjfa-35471	411	24	choose	choose	VERB
cjfa-35471	411	25	to	to	PART
cjfa-35471	411	26	produce	produce	VERB
cjfa-35471	411	27	just	just	ADV
cjfa-35471	411	28	enough	enough	ADJ
cjfa-35471	411	29	to	to	PART
cjfa-35471	411	30	meet	meet	VERB
cjfa-35471	411	31	the	the	DET
cjfa-35471	411	32	demand	demand	NOUN
cjfa-35471	411	33	if	if	SCONJ
cjfa-35471	411	34	demand	demand	NOUN
cjfa-35471	411	35	is	be	AUX
cjfa-35471	411	36	falling	fall	VERB
cjfa-35471	411	37	since	since	SCONJ
cjfa-35471	411	38	both	both	PRON
cjfa-35471	411	39	ℎ	ℎ	NOUN
cjfa-35471	411	40	and	and	CCONJ
cjfa-35471	411	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	411	42	are	be	AUX
cjfa-35471	411	43	positive	positive	ADJ
cjfa-35471	411	44	.	.	PUNCT
cjfa-35471	412	1	2	2	X
cjfa-35471	412	2	.	.	X
cjfa-35471	412	3	the	the	DET
cjfa-35471	412	4	firm	firm	NOUN
cjfa-35471	412	5	will	will	AUX
cjfa-35471	412	6	keep	keep	VERB
cjfa-35471	412	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	412	8	𝑢	𝑢	ADP
cjfa-35471	412	9	𝐼	𝐼	NOUN
cjfa-35471	412	10	even	even	ADV
cjfa-35471	412	11	if	if	SCONJ
cjfa-35471	412	12	demand	demand	NOUN
cjfa-35471	412	13	is	be	AUX
cjfa-35471	412	14	increasing	increase	VERB
cjfa-35471	412	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	412	16	𝑟	𝑟	X
cjfa-35471	412	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	412	18	but	but	CCONJ
cjfa-35471	412	19	the	the	DET
cjfa-35471	412	20	term	term	NOUN
cjfa-35471	412	21	ℎ	ℎ	PROPN
cjfa-35471	412	22	+	+	CCONJ
cjfa-35471	412	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	412	24	�	�	PROPN
cjfa-35471	412	25	�	�	PROPN
cjfa-35471	412	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	412	27	�	�	PROPN
cjfa-35471	412	28	is	be	AUX
cjfa-35471	412	29	large	large	ADJ
cjfa-35471	412	30	enough	enough	ADV
cjfa-35471	412	31	to	to	PART
cjfa-35471	412	32	keep	keep	VERB
cjfa-35471	412	33	inequality	inequality	NOUN
cjfa-35471	412	34	(	(	PUNCT
cjfa-35471	412	35	4	4	NUM
cjfa-35471	412	36	)	)	PUNCT
cjfa-35471	412	37	satisfied	satisfied	ADJ
cjfa-35471	412	38	.	.	PUNCT
cjfa-35471	413	1	decreasing	decrease	VERB
cjfa-35471	413	2	interest	interest	NOUN
cjfa-35471	413	3	rates	rate	NOUN
cjfa-35471	413	4	will	will	AUX
cjfa-35471	413	5	not	not	PART
cjfa-35471	413	6	be	be	AUX
cjfa-35471	413	7	a	a	DET
cjfa-35471	413	8	remedy	remedy	NOUN
cjfa-35471	413	9	in	in	ADP
cjfa-35471	413	10	this	this	DET
cjfa-35471	413	11	case	case	NOUN
cjfa-35471	413	12	if	if	SCONJ
cjfa-35471	413	13	they	they	PRON
cjfa-35471	413	14	are	be	AUX
cjfa-35471	413	15	already	already	ADV
cjfa-35471	413	16	low	low	ADJ
cjfa-35471	413	17	.	.	PUNCT
cjfa-35471	414	1	firms	firm	NOUN
cjfa-35471	414	2	where	where	SCONJ
cjfa-35471	414	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	414	4	�	�	PROPN
cjfa-35471	414	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	414	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	414	7	�	�	PROPN
cjfa-35471	414	8	is	be	AUX
cjfa-35471	414	9	low	low	ADJ
cjfa-35471	414	10	(	(	PUNCT
cjfa-35471	414	11	large	large	ADJ
cjfa-35471	414	12	and	and	CCONJ
cjfa-35471	414	13	already	already	ADV
cjfa-35471	414	14	very	very	ADV
cjfa-35471	414	15	efficient	efficient	ADJ
cjfa-35471	414	16	firms	firm	NOUN
cjfa-35471	414	17	)	)	PUNCT
cjfa-35471	414	18	will	will	AUX
cjfa-35471	414	19	have	have	VERB
cjfa-35471	414	20	more	more	ADJ
cjfa-35471	414	21	difficulty	difficulty	NOUN
cjfa-35471	414	22	to	to	PART
cjfa-35471	414	23	produce	produce	VERB
cjfa-35471	414	24	to	to	PART
cjfa-35471	414	25	build	build	VERB
cjfa-35471	414	26	up	up	ADP
cjfa-35471	414	27	inventories	inventory	NOUN
cjfa-35471	414	28	.	.	PUNCT
cjfa-35471	415	1	currently	currently	ADV
cjfa-35471	415	2	,	,	PUNCT
cjfa-35471	415	3	this	this	PRON
cjfa-35471	415	4	seems	seem	VERB
cjfa-35471	415	5	to	to	PART
cjfa-35471	415	6	be	be	AUX
cjfa-35471	415	7	the	the	DET
cjfa-35471	415	8	case	case	NOUN
cjfa-35471	415	9	in	in	ADP
cjfa-35471	415	10	major	major	ADJ
cjfa-35471	415	11	economies	economy	NOUN
cjfa-35471	415	12	.	.	PUNCT
cjfa-35471	416	1	3	3	X
cjfa-35471	416	2	.	.	X
cjfa-35471	416	3	higher	high	ADJ
cjfa-35471	416	4	interest	interest	NOUN
cjfa-35471	416	5	rates	rate	NOUN
cjfa-35471	416	6	and	and	CCONJ
cjfa-35471	416	7	the	the	DET
cjfa-35471	416	8	use	use	NOUN
cjfa-35471	416	9	of	of	ADP
cjfa-35471	416	10	inefficient	inefficient	ADJ
cjfa-35471	416	11	technologies	technology	NOUN
cjfa-35471	416	12	(	(	PUNCT
cjfa-35471	416	13	large	large	ADJ
cjfa-35471	416	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	416	15	)	)	PUNCT
cjfa-35471	416	16	implies	imply	VERB
cjfa-35471	416	17	high	high	ADJ
cjfa-35471	416	18	marginal	marginal	ADJ
cjfa-35471	416	19	cost	cost	NOUN
cjfa-35471	416	20	)	)	PUNCT
cjfa-35471	416	21	will	will	AUX
cjfa-35471	416	22	induce	induce	VERB
cjfa-35471	416	23	firms	firm	NOUN
cjfa-35471	416	24	to	to	PART
cjfa-35471	416	25	wait	wait	VERB
cjfa-35471	416	26	longer	long	ADV
cjfa-35471	416	27	for	for	ADP
cjfa-35471	416	28	inventory	inventory	NOUN
cjfa-35471	416	29	build	build	NOUN
cjfa-35471	416	30	-	-	PUNCT
cjfa-35471	416	31	up	up	NOUN
cjfa-35471	416	32	even	even	ADV
cjfa-35471	416	33	if	if	SCONJ
cjfa-35471	416	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	416	35	is	be	AUX
cjfa-35471	416	36	positive	positive	ADJ
cjfa-35471	416	37	.	.	PUNCT
cjfa-35471	417	1	4	4	X
cjfa-35471	417	2	.	.	X
cjfa-35471	417	3	the	the	DET
cjfa-35471	417	4	level	level	NOUN
cjfa-35471	417	5	of	of	ADP
cjfa-35471	417	6	technology	technology	NOUN
cjfa-35471	417	7	used	use	VERB
cjfa-35471	417	8	will	will	AUX
cjfa-35471	417	9	not	not	PART
cjfa-35471	417	10	affect	affect	VERB
cjfa-35471	417	11	the	the	DET
cjfa-35471	417	12	behavior	behavior	NOUN
cjfa-35471	417	13	of	of	ADP
cjfa-35471	417	14	the	the	DET
cjfa-35471	417	15	firms	firm	NOUN
cjfa-35471	417	16	if	if	SCONJ
cjfa-35471	417	17	the	the	DET
cjfa-35471	417	18	interest	interest	NOUN
cjfa-35471	417	19	rates	rate	NOUN
cjfa-35471	417	20	are	be	AUX
cjfa-35471	417	21	very	very	ADV
cjfa-35471	417	22	low	low	ADJ
cjfa-35471	417	23	as	as	SCONJ
cjfa-35471	417	24	they	they	PRON
cjfa-35471	417	25	are	be	AUX
cjfa-35471	417	26	now	now	ADV
cjfa-35471	417	27	in	in	ADP
cjfa-35471	417	28	many	many	ADJ
cjfa-35471	417	29	developed	develop	VERB
cjfa-35471	417	30	nations	nation	NOUN
cjfa-35471	417	31	since	since	SCONJ
cjfa-35471	417	32	the	the	DET
cjfa-35471	417	33	term	term	NOUN
cjfa-35471	417	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	417	35	in	in	ADP
cjfa-35471	417	36	and	and	CCONJ
cjfa-35471	417	37	the	the	DET
cjfa-35471	417	38	periods	period	NOUN
cjfa-35471	417	39	where	where	SCONJ
cjfa-35471	417	40	then	then	ADV
cjfa-35471	417	41	using	use	VERB
cjfa-35471	417	42	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	417	43	𝑢	𝑢	PROPN
cjfa-35471	417	44	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	417	45	,	,	PUNCT
cjfa-35471	417	46	equation	equation	NOUN
cjfa-35471	417	47	(	(	PUNCT
cjfa-35471	417	48	1	1	NUM
cjfa-35471	417	49	)	)	PUNCT
cjfa-35471	417	50	,	,	PUNCT
cjfa-35471	417	51	and	and	CCONJ
cjfa-35471	417	52	the	the	DET
cjfa-35471	417	53	conditions	condition	NOUN
cjfa-35471	417	54	(	(	PUNCT
cjfa-35471	417	55	the	the	DET
cjfa-35471	417	56	necessary	necessary	ADJ
cjfa-35471	417	57	condition	condition	NOUN
cjfa-35471	417	58	to	to	PART
cjfa-35471	417	59	keep	keep	VERB
cjfa-35471	417	60	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	417	61	𝑢	𝑢	ADP
cjfa-35471	417	62	𝐼	𝐼	PROPN
cjfa-35471	417	63	optimal	optimal	ADJ
cjfa-35471	417	64	)	)	PUNCT
cjfa-35471	417	65	developed	develop	VERB
cjfa-35471	417	66	by	by	ADP
cjfa-35471	417	67	pontryagin	pontryagin	NOUN
cjfa-35471	417	68	,	,	PUNCT
cjfa-35471	417	69	boltyanskii	boltyanskii	ADJ
cjfa-35471	417	70	,	,	PUNCT
cjfa-35471	417	71	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	417	72	and	and	CCONJ
cjfa-35471	417	73	mishechenko	mishechenko	NOUN
cjfa-35471	417	74	(	(	PUNCT
cjfa-35471	417	75	1962	1962	NUM
cjfa-35471	417	76	)	)	PUNCT
cjfa-35471	417	77	,	,	PUNCT
cjfa-35471	417	78	hestenes	hestene	NOUN
cjfa-35471	417	79	(	(	PUNCT
cjfa-35471	417	80	1966	1966	NUM
cjfa-35471	417	81	)	)	PUNCT
cjfa-35471	417	82	,	,	PUNCT
cjfa-35471	417	83	kamien	kamien	NOUN
cjfa-35471	417	84	and	and	CCONJ
cjfa-35471	417	85	schwartz	schwartz	PROPN
cjfa-35471	417	86	(	(	PUNCT
cjfa-35471	417	87	2012	2012	NUM
cjfa-35471	417	88	)	)	PUNCT
cjfa-35471	417	89	among	among	ADP
cjfa-35471	417	90	many	many	ADJ
cjfa-35471	417	91	others	other	NOUN
cjfa-35471	417	92	,	,	PUNCT
cjfa-35471	417	93	we	we	PRON
cjfa-35471	417	94	have	have	AUX
cjfa-35471	417	95	;	;	PUNCT
cjfa-35471	417	96	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	417	97	�	�	NOUN
cjfa-35471	417	98	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	417	99	≤	≤	PUNCT
cjfa-35471	417	100	𝐼	𝐼	PROPN
cjfa-35471	417	101	for	for	ADP
cjfa-35471	417	102	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	417	103	�	�	PROPN
cjfa-35471	417	104	≤	≤	NUM
cjfa-35471	418	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	418	2	≤	≤	NUM
cjfa-35471	418	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	418	4	�	�	PROPN
cjfa-35471	418	5	implies	imply	VERB
cjfa-35471	418	6	:	:	PUNCT
cjfa-35471	418	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	418	8	�	�	PROPN
cjfa-35471	418	9	�	�	PROPN
cjfa-35471	418	10	�	�	PROPN
cjfa-35471	418	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	418	12	�	�	PROPN
cjfa-35471	418	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	418	14	�	�	PROPN
cjfa-35471	418	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	418	16	≤	≤	PUNCT
cjfa-35471	418	17	ℎ	ℎ	PROPN
cjfa-35471	418	18	+	+	PROPN
cjfa-35471	418	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	418	20	�	�	PROPN
cjfa-35471	418	21	�	�	PROPN
cjfa-35471	418	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	418	23	�	�	PROPN
cjfa-35471	418	24	(	(	PUNCT
cjfa-35471	418	25	4	4	NUM
cjfa-35471	418	26	)	)	PUNCT
cjfa-35471	418	27	where	where	SCONJ
cjfa-35471	418	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	418	29	𝑢	𝑢	PROPN
cjfa-35471	418	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	418	31	�	�	NOUN
cjfa-35471	418	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	418	33	denotes	denote	VERB
cjfa-35471	418	34	the	the	DET
cjfa-35471	418	35	interest	interest	NOUN
cjfa-35471	418	36	rate	rate	NOUN
cjfa-35471	418	37	.	.	PUNCT
cjfa-35471	419	1	as	as	ADV
cjfa-35471	419	2	long	long	ADV
cjfa-35471	419	3	as	as	SCONJ
cjfa-35471	419	4	the	the	DET
cjfa-35471	419	5	condition	condition	NOUN
cjfa-35471	419	6	specified	specify	VERB
cjfa-35471	419	7	by	by	ADP
cjfa-35471	419	8	this	this	DET
cjfa-35471	419	9	inequality	inequality	NOUN
cjfa-35471	419	10	is	be	AUX
cjfa-35471	419	11	satisfied	satisfied	ADJ
cjfa-35471	419	12	it	it	PRON
cjfa-35471	419	13	will	will	AUX
cjfa-35471	419	14	be	be	AUX
cjfa-35471	419	15	optimal	optimal	ADJ
cjfa-35471	419	16	to	to	PART
cjfa-35471	419	17	keep	keep	VERB
cjfa-35471	419	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	419	19	𝑢	𝑢	ADP
cjfa-35471	419	20	𝐼	𝐼	ADP
cjfa-35471	419	21	implying	imply	VERB
cjfa-35471	419	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	419	23	𝑢	𝑢	PRON
cjfa-35471	419	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	419	25	this	this	PRON
cjfa-35471	419	26	means	mean	VERB
cjfa-35471	419	27	that	that	SCONJ
cjfa-35471	419	28	during	during	ADP
cjfa-35471	419	29	the	the	DET
cjfa-35471	419	30	intervals	interval	NOUN
cjfa-35471	419	31	where	where	SCONJ
cjfa-35471	419	32	this	this	DET
cjfa-35471	419	33	inequality	inequality	NOUN
cjfa-35471	419	34	is	be	AUX
cjfa-35471	419	35	satisfied	satisfied	ADJ
cjfa-35471	419	36	the	the	DET
cjfa-35471	419	37	firm	firm	NOUN
cjfa-35471	419	38	will	will	AUX
cjfa-35471	419	39	produce	produce	VERB
cjfa-35471	419	40	just	just	ADV
cjfa-35471	419	41	enough	enough	ADJ
cjfa-35471	419	42	to	to	PART
cjfa-35471	419	43	satisfy	satisfy	VERB
cjfa-35471	419	44	the	the	DET
cjfa-35471	419	45	demand	demand	NOUN
cjfa-35471	419	46	.	.	PUNCT
cjfa-35471	420	1	so	so	ADV
cjfa-35471	420	2	,	,	PUNCT
cjfa-35471	420	3	the	the	DET
cjfa-35471	420	4	condition	condition	NOUN
cjfa-35471	420	5	above	above	ADV
cjfa-35471	420	6	will	will	AUX
cjfa-35471	420	7	synthesize	synthesize	VERB
cjfa-35471	420	8	the	the	DET
cjfa-35471	420	9	periods	period	NOUN
cjfa-35471	420	10	where	where	SCONJ
cjfa-35471	420	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	420	12	𝑢	𝑢	PRON
cjfa-35471	420	13	𝐼	𝐼	PROPN
cjfa-35471	420	14	or	or	CCONJ
cjfa-35471	420	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	420	16	𝑢	𝑢	PROPN
cjfa-35471	420	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	420	18	and	and	CCONJ
cjfa-35471	420	19	the	the	DET
cjfa-35471	420	20	periods	period	NOUN
cjfa-35471	420	21	where	where	SCONJ
cjfa-35471	420	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	420	23	𝐼	𝐼	ADP
cjfa-35471	420	24	𝐼.	𝐼.	PROPN
cjfa-35471	420	25	notice	notice	VERB
cjfa-35471	420	26	that	that	SCONJ
cjfa-35471	420	27	for	for	ADP
cjfa-35471	420	28	the	the	DET
cjfa-35471	420	29	condition	condition	NOUN
cjfa-35471	420	30	above	above	ADV
cjfa-35471	420	31	(	(	PUNCT
cjfa-35471	420	32	equation	equation	NOUN
cjfa-35471	420	33	4	4	NUM
cjfa-35471	420	34	)	)	PUNCT
cjfa-35471	420	35	to	to	PART
cjfa-35471	420	36	be	be	AUX
cjfa-35471	420	37	kept	keep	VERB
cjfa-35471	420	38	satisfied	satisfied	ADJ
cjfa-35471	420	39	depends	depend	VERB
cjfa-35471	420	40	on	on	ADP
cjfa-35471	420	41	ℎ	ℎ	PROPN
cjfa-35471	420	42	(	(	PUNCT
cjfa-35471	420	43	inventory	inventory	NOUN
cjfa-35471	420	44	holding	hold	VERB
cjfa-35471	420	45	cost	cost	NOUN
cjfa-35471	420	46	)	)	PUNCT
cjfa-35471	420	47	,	,	PUNCT
cjfa-35471	420	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	420	49	the	the	DET
cjfa-35471	420	50	interest	interest	NOUN
cjfa-35471	420	51	rates	rate	NOUN
cjfa-35471	420	52	,	,	PUNCT
cjfa-35471	420	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	420	54	,	,	PUNCT
cjfa-35471	420	55	the	the	DET
cjfa-35471	420	56	marginal	marginal	ADJ
cjfa-35471	420	57	cost	cost	NOUN
cjfa-35471	420	58	of	of	ADP
cjfa-35471	420	59	production	production	NOUN
cjfa-35471	420	60	,	,	PUNCT
cjfa-35471	420	61	and	and	CCONJ
cjfa-35471	420	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	420	63	change	change	NOUN
cjfa-35471	420	64	in	in	ADP
cjfa-35471	420	65	the	the	DET
cjfa-35471	420	66	marginal	marginal	ADJ
cjfa-35471	420	67	cost	cost	NOUN
cjfa-35471	420	68	.	.	PUNCT
cjfa-35471	421	1	following	follow	VERB
cjfa-35471	421	2	conclusions	conclusion	NOUN
cjfa-35471	421	3	can	can	AUX
cjfa-35471	421	4	be	be	AUX
cjfa-35471	421	5	made	make	VERB
cjfa-35471	421	6	even	even	ADV
cjfa-35471	421	7	without	without	ADP
cjfa-35471	421	8	specific	specific	ADJ
cjfa-35471	421	9	forms	form	NOUN
cjfa-35471	421	10	of	of	ADP
cjfa-35471	421	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	421	12	,	,	PUNCT
cjfa-35471	421	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	421	14	,	,	PUNCT
cjfa-35471	421	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	421	16	and	and	CCONJ
cjfa-35471	421	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	421	18	on	on	ADP
cjfa-35471	421	19	the	the	DET
cjfa-35471	421	20	basis	basis	NOUN
cjfa-35471	421	21	of	of	ADP
cjfa-35471	421	22	equation	equation	NOUN
cjfa-35471	421	23	(	(	PUNCT
cjfa-35471	421	24	4	4	NUM
cjfa-35471	421	25	):	):	PUNCT
cjfa-35471	421	26	1	1	NUM
cjfa-35471	421	27	.	.	PUNCT
cjfa-35471	422	1	the	the	DET
cjfa-35471	422	2	firm	firm	NOUN
cjfa-35471	422	3	will	will	AUX
cjfa-35471	422	4	keep	keep	VERB
cjfa-35471	422	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	422	6	𝑢	𝑢	ADP
cjfa-35471	422	7	𝐼	𝐼	PROPN
cjfa-35471	422	8	as	as	ADV
cjfa-35471	422	9	long	long	ADV
cjfa-35471	422	10	as	as	SCONJ
cjfa-35471	422	11	demand	demand	NOUN
cjfa-35471	422	12	is	be	AUX
cjfa-35471	422	13	falling	fall	VERB
cjfa-35471	422	14	or	or	CCONJ
cjfa-35471	422	15	constant	constant	ADJ
cjfa-35471	422	16	i.e.	i.e.	X
cjfa-35471	422	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	422	18	0	0	NOUN
cjfa-35471	422	19	implying	imply	VERB
cjfa-35471	422	20	that	that	SCONJ
cjfa-35471	422	21	the	the	DET
cjfa-35471	422	22	firm	firm	NOUN
cjfa-35471	422	23	will	will	AUX
cjfa-35471	422	24	choose	choose	VERB
cjfa-35471	422	25	to	to	PART
cjfa-35471	422	26	produce	produce	VERB
cjfa-35471	422	27	just	just	ADV
cjfa-35471	422	28	enough	enough	ADJ
cjfa-35471	422	29	to	to	PART
cjfa-35471	422	30	meet	meet	VERB
cjfa-35471	422	31	the	the	DET
cjfa-35471	422	32	demand	demand	NOUN
cjfa-35471	422	33	if	if	SCONJ
cjfa-35471	422	34	demand	demand	NOUN
cjfa-35471	422	35	is	be	AUX
cjfa-35471	422	36	falling	fall	VERB
cjfa-35471	422	37	since	since	SCONJ
cjfa-35471	422	38	both	both	PRON
cjfa-35471	422	39	ℎ	ℎ	NOUN
cjfa-35471	422	40	and	and	CCONJ
cjfa-35471	422	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	422	42	are	be	AUX
cjfa-35471	422	43	positive	positive	ADJ
cjfa-35471	422	44	.	.	PUNCT
cjfa-35471	423	1	2	2	X
cjfa-35471	423	2	.	.	X
cjfa-35471	423	3	the	the	DET
cjfa-35471	423	4	firm	firm	NOUN
cjfa-35471	423	5	will	will	AUX
cjfa-35471	423	6	keep	keep	VERB
cjfa-35471	423	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	423	8	𝑢	𝑢	ADP
cjfa-35471	423	9	𝐼	𝐼	NOUN
cjfa-35471	423	10	even	even	ADV
cjfa-35471	423	11	if	if	SCONJ
cjfa-35471	423	12	demand	demand	NOUN
cjfa-35471	423	13	is	be	AUX
cjfa-35471	423	14	increasing	increase	VERB
cjfa-35471	423	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	423	16	𝑟	𝑟	X
cjfa-35471	423	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	423	18	but	but	CCONJ
cjfa-35471	423	19	the	the	DET
cjfa-35471	423	20	term	term	NOUN
cjfa-35471	423	21	ℎ	ℎ	PROPN
cjfa-35471	423	22	+	+	CCONJ
cjfa-35471	423	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	423	24	�	�	PROPN
cjfa-35471	423	25	�	�	PROPN
cjfa-35471	423	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	423	27	�	�	PROPN
cjfa-35471	423	28	is	be	AUX
cjfa-35471	423	29	large	large	ADJ
cjfa-35471	423	30	enough	enough	ADV
cjfa-35471	423	31	to	to	PART
cjfa-35471	423	32	keep	keep	VERB
cjfa-35471	423	33	inequality	inequality	NOUN
cjfa-35471	423	34	(	(	PUNCT
cjfa-35471	423	35	4	4	NUM
cjfa-35471	423	36	)	)	PUNCT
cjfa-35471	423	37	satisfied	satisfied	ADJ
cjfa-35471	423	38	.	.	PUNCT
cjfa-35471	424	1	decreasing	decrease	VERB
cjfa-35471	424	2	interest	interest	NOUN
cjfa-35471	424	3	rates	rate	NOUN
cjfa-35471	424	4	will	will	AUX
cjfa-35471	424	5	not	not	PART
cjfa-35471	424	6	be	be	AUX
cjfa-35471	424	7	a	a	DET
cjfa-35471	424	8	remedy	remedy	NOUN
cjfa-35471	424	9	in	in	ADP
cjfa-35471	424	10	this	this	DET
cjfa-35471	424	11	case	case	NOUN
cjfa-35471	424	12	if	if	SCONJ
cjfa-35471	424	13	they	they	PRON
cjfa-35471	424	14	are	be	AUX
cjfa-35471	424	15	already	already	ADV
cjfa-35471	424	16	low	low	ADJ
cjfa-35471	424	17	.	.	PUNCT
cjfa-35471	425	1	firms	firm	NOUN
cjfa-35471	425	2	where	where	SCONJ
cjfa-35471	425	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	425	4	�	�	PROPN
cjfa-35471	425	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	425	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	425	7	�	�	PROPN
cjfa-35471	425	8	is	be	AUX
cjfa-35471	425	9	low	low	ADJ
cjfa-35471	425	10	(	(	PUNCT
cjfa-35471	425	11	large	large	ADJ
cjfa-35471	425	12	and	and	CCONJ
cjfa-35471	425	13	already	already	ADV
cjfa-35471	425	14	very	very	ADV
cjfa-35471	425	15	efficient	efficient	ADJ
cjfa-35471	425	16	firms	firm	NOUN
cjfa-35471	425	17	)	)	PUNCT
cjfa-35471	425	18	will	will	AUX
cjfa-35471	425	19	have	have	VERB
cjfa-35471	425	20	more	more	ADJ
cjfa-35471	425	21	difficulty	difficulty	NOUN
cjfa-35471	425	22	to	to	PART
cjfa-35471	425	23	produce	produce	VERB
cjfa-35471	425	24	to	to	PART
cjfa-35471	425	25	build	build	VERB
cjfa-35471	425	26	up	up	ADP
cjfa-35471	425	27	inventories	inventory	NOUN
cjfa-35471	425	28	.	.	PUNCT
cjfa-35471	426	1	currently	currently	ADV
cjfa-35471	426	2	,	,	PUNCT
cjfa-35471	426	3	this	this	PRON
cjfa-35471	426	4	seems	seem	VERB
cjfa-35471	426	5	to	to	PART
cjfa-35471	426	6	be	be	AUX
cjfa-35471	426	7	the	the	DET
cjfa-35471	426	8	case	case	NOUN
cjfa-35471	426	9	in	in	ADP
cjfa-35471	426	10	major	major	ADJ
cjfa-35471	426	11	economies	economy	NOUN
cjfa-35471	426	12	.	.	PUNCT
cjfa-35471	427	1	3	3	X
cjfa-35471	427	2	.	.	X
cjfa-35471	427	3	higher	high	ADJ
cjfa-35471	427	4	interest	interest	NOUN
cjfa-35471	427	5	rates	rate	NOUN
cjfa-35471	427	6	and	and	CCONJ
cjfa-35471	427	7	the	the	DET
cjfa-35471	427	8	use	use	NOUN
cjfa-35471	427	9	of	of	ADP
cjfa-35471	427	10	inefficient	inefficient	ADJ
cjfa-35471	427	11	technologies	technology	NOUN
cjfa-35471	427	12	(	(	PUNCT
cjfa-35471	427	13	large	large	ADJ
cjfa-35471	427	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	427	15	)	)	PUNCT
cjfa-35471	427	16	implies	imply	VERB
cjfa-35471	427	17	high	high	ADJ
cjfa-35471	427	18	marginal	marginal	ADJ
cjfa-35471	427	19	cost	cost	NOUN
cjfa-35471	427	20	)	)	PUNCT
cjfa-35471	427	21	will	will	AUX
cjfa-35471	427	22	induce	induce	VERB
cjfa-35471	427	23	firms	firm	NOUN
cjfa-35471	427	24	to	to	PART
cjfa-35471	427	25	wait	wait	VERB
cjfa-35471	427	26	longer	long	ADV
cjfa-35471	427	27	for	for	ADP
cjfa-35471	427	28	inventory	inventory	NOUN
cjfa-35471	427	29	build	build	NOUN
cjfa-35471	427	30	-	-	PUNCT
cjfa-35471	427	31	up	up	NOUN
cjfa-35471	427	32	even	even	ADV
cjfa-35471	427	33	if	if	SCONJ
cjfa-35471	427	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	427	35	is	be	AUX
cjfa-35471	427	36	positive	positive	ADJ
cjfa-35471	427	37	.	.	PUNCT
cjfa-35471	428	1	4	4	X
cjfa-35471	428	2	.	.	X
cjfa-35471	428	3	the	the	DET
cjfa-35471	428	4	level	level	NOUN
cjfa-35471	428	5	of	of	ADP
cjfa-35471	428	6	technology	technology	NOUN
cjfa-35471	428	7	used	use	VERB
cjfa-35471	428	8	will	will	AUX
cjfa-35471	428	9	not	not	PART
cjfa-35471	428	10	affect	affect	VERB
cjfa-35471	428	11	the	the	DET
cjfa-35471	428	12	behavior	behavior	NOUN
cjfa-35471	428	13	of	of	ADP
cjfa-35471	428	14	the	the	DET
cjfa-35471	428	15	firms	firm	NOUN
cjfa-35471	428	16	if	if	SCONJ
cjfa-35471	428	17	the	the	DET
cjfa-35471	428	18	interest	interest	NOUN
cjfa-35471	428	19	rates	rate	NOUN
cjfa-35471	428	20	are	be	AUX
cjfa-35471	428	21	very	very	ADV
cjfa-35471	428	22	low	low	ADJ
cjfa-35471	428	23	as	as	SCONJ
cjfa-35471	428	24	they	they	PRON
cjfa-35471	428	25	are	be	AUX
cjfa-35471	428	26	now	now	ADV
cjfa-35471	428	27	in	in	ADP
cjfa-35471	428	28	many	many	ADJ
cjfa-35471	428	29	developed	develop	VERB
cjfa-35471	428	30	nations	nation	NOUN
cjfa-35471	428	31	since	since	SCONJ
cjfa-35471	428	32	the	the	DET
cjfa-35471	428	33	term	term	NOUN
cjfa-35471	428	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	428	35	in	in	ADP
cjfa-35471	428	36	notice	notice	NOUN
cjfa-35471	428	37	that	that	SCONJ
cjfa-35471	428	38	for	for	ADP
cjfa-35471	428	39	the	the	DET
cjfa-35471	428	40	condition	condition	NOUN
cjfa-35471	428	41	above	above	ADV
cjfa-35471	428	42	(	(	PUNCT
cjfa-35471	428	43	equation	equation	NOUN
cjfa-35471	428	44	4	4	NUM
cjfa-35471	428	45	)	)	PUNCT
cjfa-35471	428	46	to	to	PART
cjfa-35471	428	47	be	be	AUX
cjfa-35471	428	48	kept	keep	VERB
cjfa-35471	428	49	satisfied	satisfied	ADJ
cjfa-35471	428	50	depends	depend	VERB
cjfa-35471	428	51	on	on	ADP
cjfa-35471	428	52	h	h	NOUN
cjfa-35471	428	53	(	(	PUNCT
cjfa-35471	428	54	inventory	inventory	NOUN
cjfa-35471	428	55	holding	hold	VERB
cjfa-35471	428	56	cost	cost	NOUN
cjfa-35471	428	57	)	)	PUNCT
cjfa-35471	428	58	,	,	PUNCT
cjfa-35471	428	59	f(t	f(t	PROPN
cjfa-35471	428	60	)	)	PUNCT
cjfa-35471	428	61	the	the	DET
cjfa-35471	428	62	interest	interest	NOUN
cjfa-35471	428	63	rates	rate	NOUN
cjfa-35471	428	64	,	,	PUNCT
cjfa-35471	428	65	then	then	ADV
cjfa-35471	428	66	using	use	VERB
cjfa-35471	428	67	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	428	68	𝑢	𝑢	PROPN
cjfa-35471	428	69	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	428	70	,	,	PUNCT
cjfa-35471	428	71	equation	equation	NOUN
cjfa-35471	428	72	(	(	PUNCT
cjfa-35471	428	73	1	1	NUM
cjfa-35471	428	74	)	)	PUNCT
cjfa-35471	428	75	,	,	PUNCT
cjfa-35471	428	76	and	and	CCONJ
cjfa-35471	428	77	the	the	DET
cjfa-35471	428	78	conditions	condition	NOUN
cjfa-35471	428	79	(	(	PUNCT
cjfa-35471	428	80	the	the	DET
cjfa-35471	428	81	necessary	necessary	ADJ
cjfa-35471	428	82	condition	condition	NOUN
cjfa-35471	428	83	to	to	PART
cjfa-35471	428	84	keep	keep	VERB
cjfa-35471	428	85	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	428	86	𝑢	𝑢	ADP
cjfa-35471	428	87	𝐼	𝐼	PROPN
cjfa-35471	428	88	optimal	optimal	ADJ
cjfa-35471	428	89	)	)	PUNCT
cjfa-35471	428	90	developed	develop	VERB
cjfa-35471	428	91	by	by	ADP
cjfa-35471	428	92	pontryagin	pontryagin	NOUN
cjfa-35471	428	93	,	,	PUNCT
cjfa-35471	428	94	boltyanskii	boltyanskii	ADJ
cjfa-35471	428	95	,	,	PUNCT
cjfa-35471	428	96	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	428	97	and	and	CCONJ
cjfa-35471	428	98	mishechenko	mishechenko	NOUN
cjfa-35471	428	99	(	(	PUNCT
cjfa-35471	428	100	1962	1962	NUM
cjfa-35471	428	101	)	)	PUNCT
cjfa-35471	428	102	,	,	PUNCT
cjfa-35471	428	103	hestenes	hestene	NOUN
cjfa-35471	428	104	(	(	PUNCT
cjfa-35471	428	105	1966	1966	NUM
cjfa-35471	428	106	)	)	PUNCT
cjfa-35471	428	107	,	,	PUNCT
cjfa-35471	428	108	kamien	kamien	NOUN
cjfa-35471	428	109	and	and	CCONJ
cjfa-35471	428	110	schwartz	schwartz	PROPN
cjfa-35471	428	111	(	(	PUNCT
cjfa-35471	428	112	2012	2012	NUM
cjfa-35471	428	113	)	)	PUNCT
cjfa-35471	428	114	among	among	ADP
cjfa-35471	428	115	many	many	ADJ
cjfa-35471	428	116	others	other	NOUN
cjfa-35471	428	117	,	,	PUNCT
cjfa-35471	428	118	we	we	PRON
cjfa-35471	428	119	have	have	AUX
cjfa-35471	428	120	;	;	PUNCT
cjfa-35471	428	121	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	428	122	�	�	NOUN
cjfa-35471	428	123	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	428	124	≤	≤	PUNCT
cjfa-35471	428	125	𝐼	𝐼	PROPN
cjfa-35471	428	126	for	for	ADP
cjfa-35471	428	127	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	428	128	�	�	PROPN
cjfa-35471	428	129	≤	≤	NUM
cjfa-35471	429	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	429	2	≤	≤	NUM
cjfa-35471	429	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	429	4	�	�	PROPN
cjfa-35471	429	5	implies	imply	VERB
cjfa-35471	429	6	:	:	PUNCT
cjfa-35471	429	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	429	8	�	�	PROPN
cjfa-35471	429	9	�	�	PROPN
cjfa-35471	429	10	�	�	PROPN
cjfa-35471	429	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	429	12	�	�	PROPN
cjfa-35471	429	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	429	14	�	�	PROPN
cjfa-35471	429	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	429	16	≤	≤	PUNCT
cjfa-35471	429	17	ℎ	ℎ	PROPN
cjfa-35471	429	18	+	+	PROPN
cjfa-35471	429	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	429	20	�	�	PROPN
cjfa-35471	429	21	�	�	PROPN
cjfa-35471	429	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	429	23	�	�	PROPN
cjfa-35471	429	24	(	(	PUNCT
cjfa-35471	429	25	4	4	NUM
cjfa-35471	429	26	)	)	PUNCT
cjfa-35471	429	27	where	where	SCONJ
cjfa-35471	429	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	429	29	𝑢	𝑢	PROPN
cjfa-35471	429	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	429	31	�	�	NOUN
cjfa-35471	429	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	429	33	denotes	denote	VERB
cjfa-35471	429	34	the	the	DET
cjfa-35471	429	35	interest	interest	NOUN
cjfa-35471	429	36	rate	rate	NOUN
cjfa-35471	429	37	.	.	PUNCT
cjfa-35471	430	1	as	as	ADV
cjfa-35471	430	2	long	long	ADV
cjfa-35471	430	3	as	as	SCONJ
cjfa-35471	430	4	the	the	DET
cjfa-35471	430	5	condition	condition	NOUN
cjfa-35471	430	6	specified	specify	VERB
cjfa-35471	430	7	by	by	ADP
cjfa-35471	430	8	this	this	DET
cjfa-35471	430	9	inequality	inequality	NOUN
cjfa-35471	430	10	is	be	AUX
cjfa-35471	430	11	satisfied	satisfied	ADJ
cjfa-35471	430	12	it	it	PRON
cjfa-35471	430	13	will	will	AUX
cjfa-35471	430	14	be	be	AUX
cjfa-35471	430	15	optimal	optimal	ADJ
cjfa-35471	430	16	to	to	PART
cjfa-35471	430	17	keep	keep	VERB
cjfa-35471	430	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	430	19	𝑢	𝑢	ADP
cjfa-35471	430	20	𝐼	𝐼	ADP
cjfa-35471	430	21	implying	imply	VERB
cjfa-35471	430	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	430	23	𝑢	𝑢	PRON
cjfa-35471	430	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	430	25	this	this	PRON
cjfa-35471	430	26	means	mean	VERB
cjfa-35471	430	27	that	that	SCONJ
cjfa-35471	430	28	during	during	ADP
cjfa-35471	430	29	the	the	DET
cjfa-35471	430	30	intervals	interval	NOUN
cjfa-35471	430	31	where	where	SCONJ
cjfa-35471	430	32	this	this	DET
cjfa-35471	430	33	inequality	inequality	NOUN
cjfa-35471	430	34	is	be	AUX
cjfa-35471	430	35	satisfied	satisfied	ADJ
cjfa-35471	430	36	the	the	DET
cjfa-35471	430	37	firm	firm	NOUN
cjfa-35471	430	38	will	will	AUX
cjfa-35471	430	39	produce	produce	VERB
cjfa-35471	430	40	just	just	ADV
cjfa-35471	430	41	enough	enough	ADJ
cjfa-35471	430	42	to	to	PART
cjfa-35471	430	43	satisfy	satisfy	VERB
cjfa-35471	430	44	the	the	DET
cjfa-35471	430	45	demand	demand	NOUN
cjfa-35471	430	46	.	.	PUNCT
cjfa-35471	431	1	so	so	ADV
cjfa-35471	431	2	,	,	PUNCT
cjfa-35471	431	3	the	the	DET
cjfa-35471	431	4	condition	condition	NOUN
cjfa-35471	431	5	above	above	ADV
cjfa-35471	431	6	will	will	AUX
cjfa-35471	431	7	synthesize	synthesize	VERB
cjfa-35471	431	8	the	the	DET
cjfa-35471	431	9	periods	period	NOUN
cjfa-35471	431	10	where	where	SCONJ
cjfa-35471	431	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	431	12	𝑢	𝑢	PRON
cjfa-35471	431	13	𝐼	𝐼	PROPN
cjfa-35471	431	14	or	or	CCONJ
cjfa-35471	431	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	431	16	𝑢	𝑢	PROPN
cjfa-35471	431	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	431	18	and	and	CCONJ
cjfa-35471	431	19	the	the	DET
cjfa-35471	431	20	periods	period	NOUN
cjfa-35471	431	21	where	where	SCONJ
cjfa-35471	431	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	431	23	𝐼	𝐼	ADP
cjfa-35471	431	24	𝐼.	𝐼.	PROPN
cjfa-35471	431	25	notice	notice	VERB
cjfa-35471	431	26	that	that	SCONJ
cjfa-35471	431	27	for	for	ADP
cjfa-35471	431	28	the	the	DET
cjfa-35471	431	29	condition	condition	NOUN
cjfa-35471	431	30	above	above	ADV
cjfa-35471	431	31	(	(	PUNCT
cjfa-35471	431	32	equation	equation	NOUN
cjfa-35471	431	33	4	4	NUM
cjfa-35471	431	34	)	)	PUNCT
cjfa-35471	431	35	to	to	PART
cjfa-35471	431	36	be	be	AUX
cjfa-35471	431	37	kept	keep	VERB
cjfa-35471	431	38	satisfied	satisfied	ADJ
cjfa-35471	431	39	depends	depend	VERB
cjfa-35471	431	40	on	on	ADP
cjfa-35471	431	41	ℎ	ℎ	PROPN
cjfa-35471	431	42	(	(	PUNCT
cjfa-35471	431	43	inventory	inventory	NOUN
cjfa-35471	431	44	holding	hold	VERB
cjfa-35471	431	45	cost	cost	NOUN
cjfa-35471	431	46	)	)	PUNCT
cjfa-35471	431	47	,	,	PUNCT
cjfa-35471	431	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	431	49	the	the	DET
cjfa-35471	431	50	interest	interest	NOUN
cjfa-35471	431	51	rates	rate	NOUN
cjfa-35471	431	52	,	,	PUNCT
cjfa-35471	431	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	431	54	,	,	PUNCT
cjfa-35471	431	55	the	the	DET
cjfa-35471	431	56	marginal	marginal	ADJ
cjfa-35471	431	57	cost	cost	NOUN
cjfa-35471	431	58	of	of	ADP
cjfa-35471	431	59	production	production	NOUN
cjfa-35471	431	60	,	,	PUNCT
cjfa-35471	431	61	and	and	CCONJ
cjfa-35471	431	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	431	63	change	change	NOUN
cjfa-35471	431	64	in	in	ADP
cjfa-35471	431	65	the	the	DET
cjfa-35471	431	66	marginal	marginal	ADJ
cjfa-35471	431	67	cost	cost	NOUN
cjfa-35471	431	68	.	.	PUNCT
cjfa-35471	432	1	following	follow	VERB
cjfa-35471	432	2	conclusions	conclusion	NOUN
cjfa-35471	432	3	can	can	AUX
cjfa-35471	432	4	be	be	AUX
cjfa-35471	432	5	made	make	VERB
cjfa-35471	432	6	even	even	ADV
cjfa-35471	432	7	without	without	ADP
cjfa-35471	432	8	specific	specific	ADJ
cjfa-35471	432	9	forms	form	NOUN
cjfa-35471	432	10	of	of	ADP
cjfa-35471	432	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	432	12	,	,	PUNCT
cjfa-35471	432	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	432	14	,	,	PUNCT
cjfa-35471	432	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	432	16	and	and	CCONJ
cjfa-35471	432	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	432	18	on	on	ADP
cjfa-35471	432	19	the	the	DET
cjfa-35471	432	20	basis	basis	NOUN
cjfa-35471	432	21	of	of	ADP
cjfa-35471	432	22	equation	equation	NOUN
cjfa-35471	432	23	(	(	PUNCT
cjfa-35471	432	24	4	4	NUM
cjfa-35471	432	25	):	):	PUNCT
cjfa-35471	432	26	1	1	NUM
cjfa-35471	432	27	.	.	PUNCT
cjfa-35471	433	1	the	the	DET
cjfa-35471	433	2	firm	firm	NOUN
cjfa-35471	433	3	will	will	AUX
cjfa-35471	433	4	keep	keep	VERB
cjfa-35471	433	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	433	6	𝑢	𝑢	ADP
cjfa-35471	433	7	𝐼	𝐼	PROPN
cjfa-35471	433	8	as	as	ADV
cjfa-35471	433	9	long	long	ADV
cjfa-35471	433	10	as	as	SCONJ
cjfa-35471	433	11	demand	demand	NOUN
cjfa-35471	433	12	is	be	AUX
cjfa-35471	433	13	falling	fall	VERB
cjfa-35471	433	14	or	or	CCONJ
cjfa-35471	433	15	constant	constant	ADJ
cjfa-35471	433	16	i.e.	i.e.	X
cjfa-35471	433	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	433	18	0	0	NOUN
cjfa-35471	433	19	implying	imply	VERB
cjfa-35471	433	20	that	that	SCONJ
cjfa-35471	433	21	the	the	DET
cjfa-35471	433	22	firm	firm	NOUN
cjfa-35471	433	23	will	will	AUX
cjfa-35471	433	24	choose	choose	VERB
cjfa-35471	433	25	to	to	PART
cjfa-35471	433	26	produce	produce	VERB
cjfa-35471	433	27	just	just	ADV
cjfa-35471	433	28	enough	enough	ADJ
cjfa-35471	433	29	to	to	PART
cjfa-35471	433	30	meet	meet	VERB
cjfa-35471	433	31	the	the	DET
cjfa-35471	433	32	demand	demand	NOUN
cjfa-35471	433	33	if	if	SCONJ
cjfa-35471	433	34	demand	demand	NOUN
cjfa-35471	433	35	is	be	AUX
cjfa-35471	433	36	falling	fall	VERB
cjfa-35471	433	37	since	since	SCONJ
cjfa-35471	433	38	both	both	PRON
cjfa-35471	433	39	ℎ	ℎ	NOUN
cjfa-35471	433	40	and	and	CCONJ
cjfa-35471	433	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	433	42	are	be	AUX
cjfa-35471	433	43	positive	positive	ADJ
cjfa-35471	433	44	.	.	PUNCT
cjfa-35471	434	1	2	2	X
cjfa-35471	434	2	.	.	X
cjfa-35471	434	3	the	the	DET
cjfa-35471	434	4	firm	firm	NOUN
cjfa-35471	434	5	will	will	AUX
cjfa-35471	434	6	keep	keep	VERB
cjfa-35471	434	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	434	8	𝑢	𝑢	ADP
cjfa-35471	434	9	𝐼	𝐼	NOUN
cjfa-35471	434	10	even	even	ADV
cjfa-35471	434	11	if	if	SCONJ
cjfa-35471	434	12	demand	demand	NOUN
cjfa-35471	434	13	is	be	AUX
cjfa-35471	434	14	increasing	increase	VERB
cjfa-35471	434	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	434	16	𝑟	𝑟	X
cjfa-35471	434	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	434	18	but	but	CCONJ
cjfa-35471	434	19	the	the	DET
cjfa-35471	434	20	term	term	NOUN
cjfa-35471	434	21	ℎ	ℎ	PROPN
cjfa-35471	434	22	+	+	CCONJ
cjfa-35471	434	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	434	24	�	�	PROPN
cjfa-35471	434	25	�	�	PROPN
cjfa-35471	434	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	434	27	�	�	PROPN
cjfa-35471	434	28	is	be	AUX
cjfa-35471	434	29	large	large	ADJ
cjfa-35471	434	30	enough	enough	ADV
cjfa-35471	434	31	to	to	PART
cjfa-35471	434	32	keep	keep	VERB
cjfa-35471	434	33	inequality	inequality	NOUN
cjfa-35471	434	34	(	(	PUNCT
cjfa-35471	434	35	4	4	NUM
cjfa-35471	434	36	)	)	PUNCT
cjfa-35471	434	37	satisfied	satisfied	ADJ
cjfa-35471	434	38	.	.	PUNCT
cjfa-35471	435	1	decreasing	decrease	VERB
cjfa-35471	435	2	interest	interest	NOUN
cjfa-35471	435	3	rates	rate	NOUN
cjfa-35471	435	4	will	will	AUX
cjfa-35471	435	5	not	not	PART
cjfa-35471	435	6	be	be	AUX
cjfa-35471	435	7	a	a	DET
cjfa-35471	435	8	remedy	remedy	NOUN
cjfa-35471	435	9	in	in	ADP
cjfa-35471	435	10	this	this	DET
cjfa-35471	435	11	case	case	NOUN
cjfa-35471	435	12	if	if	SCONJ
cjfa-35471	435	13	they	they	PRON
cjfa-35471	435	14	are	be	AUX
cjfa-35471	435	15	already	already	ADV
cjfa-35471	435	16	low	low	ADJ
cjfa-35471	435	17	.	.	PUNCT
cjfa-35471	436	1	firms	firm	NOUN
cjfa-35471	436	2	where	where	SCONJ
cjfa-35471	436	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	436	4	�	�	PROPN
cjfa-35471	436	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	436	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	436	7	�	�	PROPN
cjfa-35471	436	8	is	be	AUX
cjfa-35471	436	9	low	low	ADJ
cjfa-35471	436	10	(	(	PUNCT
cjfa-35471	436	11	large	large	ADJ
cjfa-35471	436	12	and	and	CCONJ
cjfa-35471	436	13	already	already	ADV
cjfa-35471	436	14	very	very	ADV
cjfa-35471	436	15	efficient	efficient	ADJ
cjfa-35471	436	16	firms	firm	NOUN
cjfa-35471	436	17	)	)	PUNCT
cjfa-35471	436	18	will	will	AUX
cjfa-35471	436	19	have	have	VERB
cjfa-35471	436	20	more	more	ADJ
cjfa-35471	436	21	difficulty	difficulty	NOUN
cjfa-35471	436	22	to	to	PART
cjfa-35471	436	23	produce	produce	VERB
cjfa-35471	436	24	to	to	PART
cjfa-35471	436	25	build	build	VERB
cjfa-35471	436	26	up	up	ADP
cjfa-35471	436	27	inventories	inventory	NOUN
cjfa-35471	436	28	.	.	PUNCT
cjfa-35471	437	1	currently	currently	ADV
cjfa-35471	437	2	,	,	PUNCT
cjfa-35471	437	3	this	this	PRON
cjfa-35471	437	4	seems	seem	VERB
cjfa-35471	437	5	to	to	PART
cjfa-35471	437	6	be	be	AUX
cjfa-35471	437	7	the	the	DET
cjfa-35471	437	8	case	case	NOUN
cjfa-35471	437	9	in	in	ADP
cjfa-35471	437	10	major	major	ADJ
cjfa-35471	437	11	economies	economy	NOUN
cjfa-35471	437	12	.	.	PUNCT
cjfa-35471	438	1	3	3	X
cjfa-35471	438	2	.	.	X
cjfa-35471	438	3	higher	high	ADJ
cjfa-35471	438	4	interest	interest	NOUN
cjfa-35471	438	5	rates	rate	NOUN
cjfa-35471	438	6	and	and	CCONJ
cjfa-35471	438	7	the	the	DET
cjfa-35471	438	8	use	use	NOUN
cjfa-35471	438	9	of	of	ADP
cjfa-35471	438	10	inefficient	inefficient	ADJ
cjfa-35471	438	11	technologies	technology	NOUN
cjfa-35471	438	12	(	(	PUNCT
cjfa-35471	438	13	large	large	ADJ
cjfa-35471	438	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	438	15	)	)	PUNCT
cjfa-35471	438	16	implies	imply	VERB
cjfa-35471	438	17	high	high	ADJ
cjfa-35471	438	18	marginal	marginal	ADJ
cjfa-35471	438	19	cost	cost	NOUN
cjfa-35471	438	20	)	)	PUNCT
cjfa-35471	438	21	will	will	AUX
cjfa-35471	438	22	induce	induce	VERB
cjfa-35471	438	23	firms	firm	NOUN
cjfa-35471	438	24	to	to	PART
cjfa-35471	438	25	wait	wait	VERB
cjfa-35471	438	26	longer	long	ADV
cjfa-35471	438	27	for	for	ADP
cjfa-35471	438	28	inventory	inventory	NOUN
cjfa-35471	438	29	build	build	NOUN
cjfa-35471	438	30	-	-	PUNCT
cjfa-35471	438	31	up	up	NOUN
cjfa-35471	438	32	even	even	ADV
cjfa-35471	438	33	if	if	SCONJ
cjfa-35471	438	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	438	35	is	be	AUX
cjfa-35471	438	36	positive	positive	ADJ
cjfa-35471	438	37	.	.	PUNCT
cjfa-35471	439	1	4	4	X
cjfa-35471	439	2	.	.	X
cjfa-35471	439	3	the	the	DET
cjfa-35471	439	4	level	level	NOUN
cjfa-35471	439	5	of	of	ADP
cjfa-35471	439	6	technology	technology	NOUN
cjfa-35471	439	7	used	use	VERB
cjfa-35471	439	8	will	will	AUX
cjfa-35471	439	9	not	not	PART
cjfa-35471	439	10	affect	affect	VERB
cjfa-35471	439	11	the	the	DET
cjfa-35471	439	12	behavior	behavior	NOUN
cjfa-35471	439	13	of	of	ADP
cjfa-35471	439	14	the	the	DET
cjfa-35471	439	15	firms	firm	NOUN
cjfa-35471	439	16	if	if	SCONJ
cjfa-35471	439	17	the	the	DET
cjfa-35471	439	18	interest	interest	NOUN
cjfa-35471	439	19	rates	rate	NOUN
cjfa-35471	439	20	are	be	AUX
cjfa-35471	439	21	very	very	ADV
cjfa-35471	439	22	low	low	ADJ
cjfa-35471	439	23	as	as	SCONJ
cjfa-35471	439	24	they	they	PRON
cjfa-35471	439	25	are	be	AUX
cjfa-35471	439	26	now	now	ADV
cjfa-35471	439	27	in	in	ADP
cjfa-35471	439	28	many	many	ADJ
cjfa-35471	439	29	developed	develop	VERB
cjfa-35471	439	30	nations	nation	NOUN
cjfa-35471	439	31	since	since	SCONJ
cjfa-35471	439	32	the	the	DET
cjfa-35471	439	33	term	term	NOUN
cjfa-35471	439	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	439	35	in	in	ADP
cjfa-35471	439	36	,	,	PUNCT
cjfa-35471	439	37	the	the	DET
cjfa-35471	439	38	marginal	marginal	ADJ
cjfa-35471	439	39	cost	cost	NOUN
cjfa-35471	439	40	of	of	ADP
cjfa-35471	439	41	production	production	NOUN
cjfa-35471	439	42	,	,	PUNCT
cjfa-35471	439	43	and	and	CCONJ
cjfa-35471	439	44	then	then	ADV
cjfa-35471	439	45	using	use	VERB
cjfa-35471	439	46	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	439	47	𝑢	𝑢	PROPN
cjfa-35471	439	48	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	439	49	,	,	PUNCT
cjfa-35471	439	50	equation	equation	NOUN
cjfa-35471	439	51	(	(	PUNCT
cjfa-35471	439	52	1	1	NUM
cjfa-35471	439	53	)	)	PUNCT
cjfa-35471	439	54	,	,	PUNCT
cjfa-35471	439	55	and	and	CCONJ
cjfa-35471	439	56	the	the	DET
cjfa-35471	439	57	conditions	condition	NOUN
cjfa-35471	439	58	(	(	PUNCT
cjfa-35471	439	59	the	the	DET
cjfa-35471	439	60	necessary	necessary	ADJ
cjfa-35471	439	61	condition	condition	NOUN
cjfa-35471	439	62	to	to	PART
cjfa-35471	439	63	keep	keep	VERB
cjfa-35471	439	64	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	439	65	𝑢	𝑢	ADP
cjfa-35471	439	66	𝐼	𝐼	PROPN
cjfa-35471	439	67	optimal	optimal	ADJ
cjfa-35471	439	68	)	)	PUNCT
cjfa-35471	439	69	developed	develop	VERB
cjfa-35471	439	70	by	by	ADP
cjfa-35471	439	71	pontryagin	pontryagin	NOUN
cjfa-35471	439	72	,	,	PUNCT
cjfa-35471	439	73	boltyanskii	boltyanskii	ADJ
cjfa-35471	439	74	,	,	PUNCT
cjfa-35471	439	75	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	439	76	and	and	CCONJ
cjfa-35471	439	77	mishechenko	mishechenko	NOUN
cjfa-35471	439	78	(	(	PUNCT
cjfa-35471	439	79	1962	1962	NUM
cjfa-35471	439	80	)	)	PUNCT
cjfa-35471	439	81	,	,	PUNCT
cjfa-35471	439	82	hestenes	hestene	NOUN
cjfa-35471	439	83	(	(	PUNCT
cjfa-35471	439	84	1966	1966	NUM
cjfa-35471	439	85	)	)	PUNCT
cjfa-35471	439	86	,	,	PUNCT
cjfa-35471	439	87	kamien	kamien	NOUN
cjfa-35471	439	88	and	and	CCONJ
cjfa-35471	439	89	schwartz	schwartz	PROPN
cjfa-35471	439	90	(	(	PUNCT
cjfa-35471	439	91	2012	2012	NUM
cjfa-35471	439	92	)	)	PUNCT
cjfa-35471	439	93	among	among	ADP
cjfa-35471	439	94	many	many	ADJ
cjfa-35471	439	95	others	other	NOUN
cjfa-35471	439	96	,	,	PUNCT
cjfa-35471	439	97	we	we	PRON
cjfa-35471	439	98	have	have	VERB
cjfa-35471	439	99	;	;	PUNCT
cjfa-35471	439	100	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	439	101	�	�	NOUN
cjfa-35471	439	102	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	439	103	≤	≤	PUNCT
cjfa-35471	439	104	𝐼	𝐼	PROPN
cjfa-35471	439	105	for	for	ADP
cjfa-35471	439	106	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	439	107	�	�	PROPN
cjfa-35471	439	108	≤	≤	NUM
cjfa-35471	440	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	440	2	≤	≤	NUM
cjfa-35471	440	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	440	4	�	�	PROPN
cjfa-35471	440	5	implies	imply	VERB
cjfa-35471	440	6	:	:	PUNCT
cjfa-35471	440	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	440	8	�	�	PROPN
cjfa-35471	440	9	�	�	PROPN
cjfa-35471	440	10	�	�	PROPN
cjfa-35471	440	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	440	12	�	�	PROPN
cjfa-35471	440	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	440	14	�	�	PROPN
cjfa-35471	440	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	440	16	≤	≤	PUNCT
cjfa-35471	440	17	ℎ	ℎ	PROPN
cjfa-35471	440	18	+	+	PROPN
cjfa-35471	440	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	440	20	�	�	PROPN
cjfa-35471	440	21	�	�	PROPN
cjfa-35471	440	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	440	23	�	�	PROPN
cjfa-35471	440	24	(	(	PUNCT
cjfa-35471	440	25	4	4	NUM
cjfa-35471	440	26	)	)	PUNCT
cjfa-35471	440	27	where	where	SCONJ
cjfa-35471	440	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	440	29	𝑢	𝑢	PROPN
cjfa-35471	440	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	440	31	�	�	NOUN
cjfa-35471	440	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	440	33	denotes	denote	VERB
cjfa-35471	440	34	the	the	DET
cjfa-35471	440	35	interest	interest	NOUN
cjfa-35471	440	36	rate	rate	NOUN
cjfa-35471	440	37	.	.	PUNCT
cjfa-35471	441	1	as	as	ADV
cjfa-35471	441	2	long	long	ADV
cjfa-35471	441	3	as	as	SCONJ
cjfa-35471	441	4	the	the	DET
cjfa-35471	441	5	condition	condition	NOUN
cjfa-35471	441	6	specified	specify	VERB
cjfa-35471	441	7	by	by	ADP
cjfa-35471	441	8	this	this	DET
cjfa-35471	441	9	inequality	inequality	NOUN
cjfa-35471	441	10	is	be	AUX
cjfa-35471	441	11	satisfied	satisfied	ADJ
cjfa-35471	441	12	it	it	PRON
cjfa-35471	441	13	will	will	AUX
cjfa-35471	441	14	be	be	AUX
cjfa-35471	441	15	optimal	optimal	ADJ
cjfa-35471	441	16	to	to	PART
cjfa-35471	441	17	keep	keep	VERB
cjfa-35471	441	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	441	19	𝑢	𝑢	ADP
cjfa-35471	441	20	𝐼	𝐼	ADP
cjfa-35471	441	21	implying	imply	VERB
cjfa-35471	441	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	441	23	𝑢	𝑢	PRON
cjfa-35471	441	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	441	25	this	this	PRON
cjfa-35471	441	26	means	mean	VERB
cjfa-35471	441	27	that	that	SCONJ
cjfa-35471	441	28	during	during	ADP
cjfa-35471	441	29	the	the	DET
cjfa-35471	441	30	intervals	interval	NOUN
cjfa-35471	441	31	where	where	SCONJ
cjfa-35471	441	32	this	this	DET
cjfa-35471	441	33	inequality	inequality	NOUN
cjfa-35471	441	34	is	be	AUX
cjfa-35471	441	35	satisfied	satisfied	ADJ
cjfa-35471	441	36	the	the	DET
cjfa-35471	441	37	firm	firm	NOUN
cjfa-35471	441	38	will	will	AUX
cjfa-35471	441	39	produce	produce	VERB
cjfa-35471	441	40	just	just	ADV
cjfa-35471	441	41	enough	enough	ADJ
cjfa-35471	441	42	to	to	PART
cjfa-35471	441	43	satisfy	satisfy	VERB
cjfa-35471	441	44	the	the	DET
cjfa-35471	441	45	demand	demand	NOUN
cjfa-35471	441	46	.	.	PUNCT
cjfa-35471	442	1	so	so	ADV
cjfa-35471	442	2	,	,	PUNCT
cjfa-35471	442	3	the	the	DET
cjfa-35471	442	4	condition	condition	NOUN
cjfa-35471	442	5	above	above	ADV
cjfa-35471	442	6	will	will	AUX
cjfa-35471	442	7	synthesize	synthesize	VERB
cjfa-35471	442	8	the	the	DET
cjfa-35471	442	9	periods	period	NOUN
cjfa-35471	442	10	where	where	SCONJ
cjfa-35471	442	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	442	12	𝑢	𝑢	PRON
cjfa-35471	442	13	𝐼	𝐼	PROPN
cjfa-35471	442	14	or	or	CCONJ
cjfa-35471	442	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	442	16	𝑢	𝑢	PROPN
cjfa-35471	442	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	442	18	and	and	CCONJ
cjfa-35471	442	19	the	the	DET
cjfa-35471	442	20	periods	period	NOUN
cjfa-35471	442	21	where	where	SCONJ
cjfa-35471	442	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	442	23	𝐼	𝐼	ADP
cjfa-35471	442	24	𝐼.	𝐼.	PROPN
cjfa-35471	442	25	notice	notice	VERB
cjfa-35471	442	26	that	that	SCONJ
cjfa-35471	442	27	for	for	ADP
cjfa-35471	442	28	the	the	DET
cjfa-35471	442	29	condition	condition	NOUN
cjfa-35471	442	30	above	above	ADV
cjfa-35471	442	31	(	(	PUNCT
cjfa-35471	442	32	equation	equation	NOUN
cjfa-35471	442	33	4	4	NUM
cjfa-35471	442	34	)	)	PUNCT
cjfa-35471	442	35	to	to	PART
cjfa-35471	442	36	be	be	AUX
cjfa-35471	442	37	kept	keep	VERB
cjfa-35471	442	38	satisfied	satisfied	ADJ
cjfa-35471	442	39	depends	depend	VERB
cjfa-35471	442	40	on	on	ADP
cjfa-35471	442	41	ℎ	ℎ	PROPN
cjfa-35471	442	42	(	(	PUNCT
cjfa-35471	442	43	inventory	inventory	NOUN
cjfa-35471	442	44	holding	hold	VERB
cjfa-35471	442	45	cost	cost	NOUN
cjfa-35471	442	46	)	)	PUNCT
cjfa-35471	442	47	,	,	PUNCT
cjfa-35471	442	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	442	49	the	the	DET
cjfa-35471	442	50	interest	interest	NOUN
cjfa-35471	442	51	rates	rate	NOUN
cjfa-35471	442	52	,	,	PUNCT
cjfa-35471	442	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	442	54	,	,	PUNCT
cjfa-35471	442	55	the	the	DET
cjfa-35471	442	56	marginal	marginal	ADJ
cjfa-35471	442	57	cost	cost	NOUN
cjfa-35471	442	58	of	of	ADP
cjfa-35471	442	59	production	production	NOUN
cjfa-35471	442	60	,	,	PUNCT
cjfa-35471	442	61	and	and	CCONJ
cjfa-35471	442	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	442	63	change	change	NOUN
cjfa-35471	442	64	in	in	ADP
cjfa-35471	442	65	the	the	DET
cjfa-35471	442	66	marginal	marginal	ADJ
cjfa-35471	442	67	cost	cost	NOUN
cjfa-35471	442	68	.	.	PUNCT
cjfa-35471	443	1	following	follow	VERB
cjfa-35471	443	2	conclusions	conclusion	NOUN
cjfa-35471	443	3	can	can	AUX
cjfa-35471	443	4	be	be	AUX
cjfa-35471	443	5	made	make	VERB
cjfa-35471	443	6	even	even	ADV
cjfa-35471	443	7	without	without	ADP
cjfa-35471	443	8	specific	specific	ADJ
cjfa-35471	443	9	forms	form	NOUN
cjfa-35471	443	10	of	of	ADP
cjfa-35471	443	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	443	12	,	,	PUNCT
cjfa-35471	443	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	443	14	,	,	PUNCT
cjfa-35471	443	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	443	16	and	and	CCONJ
cjfa-35471	443	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	443	18	on	on	ADP
cjfa-35471	443	19	the	the	DET
cjfa-35471	443	20	basis	basis	NOUN
cjfa-35471	443	21	of	of	ADP
cjfa-35471	443	22	equation	equation	NOUN
cjfa-35471	443	23	(	(	PUNCT
cjfa-35471	443	24	4	4	NUM
cjfa-35471	443	25	):	):	PUNCT
cjfa-35471	443	26	1	1	NUM
cjfa-35471	443	27	.	.	PUNCT
cjfa-35471	444	1	the	the	DET
cjfa-35471	444	2	firm	firm	NOUN
cjfa-35471	444	3	will	will	AUX
cjfa-35471	444	4	keep	keep	VERB
cjfa-35471	444	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	444	6	𝑢	𝑢	ADP
cjfa-35471	444	7	𝐼	𝐼	PROPN
cjfa-35471	444	8	as	as	ADV
cjfa-35471	444	9	long	long	ADV
cjfa-35471	444	10	as	as	SCONJ
cjfa-35471	444	11	demand	demand	NOUN
cjfa-35471	444	12	is	be	AUX
cjfa-35471	444	13	falling	fall	VERB
cjfa-35471	444	14	or	or	CCONJ
cjfa-35471	444	15	constant	constant	ADJ
cjfa-35471	444	16	i.e.	i.e.	X
cjfa-35471	444	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	444	18	0	0	NOUN
cjfa-35471	444	19	implying	imply	VERB
cjfa-35471	444	20	that	that	SCONJ
cjfa-35471	444	21	the	the	DET
cjfa-35471	444	22	firm	firm	NOUN
cjfa-35471	444	23	will	will	AUX
cjfa-35471	444	24	choose	choose	VERB
cjfa-35471	444	25	to	to	PART
cjfa-35471	444	26	produce	produce	VERB
cjfa-35471	444	27	just	just	ADV
cjfa-35471	444	28	enough	enough	ADJ
cjfa-35471	444	29	to	to	PART
cjfa-35471	444	30	meet	meet	VERB
cjfa-35471	444	31	the	the	DET
cjfa-35471	444	32	demand	demand	NOUN
cjfa-35471	444	33	if	if	SCONJ
cjfa-35471	444	34	demand	demand	NOUN
cjfa-35471	444	35	is	be	AUX
cjfa-35471	444	36	falling	fall	VERB
cjfa-35471	444	37	since	since	SCONJ
cjfa-35471	444	38	both	both	PRON
cjfa-35471	444	39	ℎ	ℎ	NOUN
cjfa-35471	444	40	and	and	CCONJ
cjfa-35471	444	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	444	42	are	be	AUX
cjfa-35471	444	43	positive	positive	ADJ
cjfa-35471	444	44	.	.	PUNCT
cjfa-35471	445	1	2	2	X
cjfa-35471	445	2	.	.	X
cjfa-35471	445	3	the	the	DET
cjfa-35471	445	4	firm	firm	NOUN
cjfa-35471	445	5	will	will	AUX
cjfa-35471	445	6	keep	keep	VERB
cjfa-35471	445	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	445	8	𝑢	𝑢	ADP
cjfa-35471	445	9	𝐼	𝐼	NOUN
cjfa-35471	445	10	even	even	ADV
cjfa-35471	445	11	if	if	SCONJ
cjfa-35471	445	12	demand	demand	NOUN
cjfa-35471	445	13	is	be	AUX
cjfa-35471	445	14	increasing	increase	VERB
cjfa-35471	445	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	445	16	𝑟	𝑟	X
cjfa-35471	445	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	445	18	but	but	CCONJ
cjfa-35471	445	19	the	the	DET
cjfa-35471	445	20	term	term	NOUN
cjfa-35471	445	21	ℎ	ℎ	PROPN
cjfa-35471	445	22	+	+	CCONJ
cjfa-35471	445	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	445	24	�	�	PROPN
cjfa-35471	445	25	�	�	PROPN
cjfa-35471	445	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	445	27	�	�	PROPN
cjfa-35471	445	28	is	be	AUX
cjfa-35471	445	29	large	large	ADJ
cjfa-35471	445	30	enough	enough	ADV
cjfa-35471	445	31	to	to	PART
cjfa-35471	445	32	keep	keep	VERB
cjfa-35471	445	33	inequality	inequality	NOUN
cjfa-35471	445	34	(	(	PUNCT
cjfa-35471	445	35	4	4	NUM
cjfa-35471	445	36	)	)	PUNCT
cjfa-35471	445	37	satisfied	satisfied	ADJ
cjfa-35471	445	38	.	.	PUNCT
cjfa-35471	446	1	decreasing	decrease	VERB
cjfa-35471	446	2	interest	interest	NOUN
cjfa-35471	446	3	rates	rate	NOUN
cjfa-35471	446	4	will	will	AUX
cjfa-35471	446	5	not	not	PART
cjfa-35471	446	6	be	be	AUX
cjfa-35471	446	7	a	a	DET
cjfa-35471	446	8	remedy	remedy	NOUN
cjfa-35471	446	9	in	in	ADP
cjfa-35471	446	10	this	this	DET
cjfa-35471	446	11	case	case	NOUN
cjfa-35471	446	12	if	if	SCONJ
cjfa-35471	446	13	they	they	PRON
cjfa-35471	446	14	are	be	AUX
cjfa-35471	446	15	already	already	ADV
cjfa-35471	446	16	low	low	ADJ
cjfa-35471	446	17	.	.	PUNCT
cjfa-35471	447	1	firms	firm	NOUN
cjfa-35471	447	2	where	where	SCONJ
cjfa-35471	447	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	447	4	�	�	PROPN
cjfa-35471	447	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	447	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	447	7	�	�	PROPN
cjfa-35471	447	8	is	be	AUX
cjfa-35471	447	9	low	low	ADJ
cjfa-35471	447	10	(	(	PUNCT
cjfa-35471	447	11	large	large	ADJ
cjfa-35471	447	12	and	and	CCONJ
cjfa-35471	447	13	already	already	ADV
cjfa-35471	447	14	very	very	ADV
cjfa-35471	447	15	efficient	efficient	ADJ
cjfa-35471	447	16	firms	firm	NOUN
cjfa-35471	447	17	)	)	PUNCT
cjfa-35471	447	18	will	will	AUX
cjfa-35471	447	19	have	have	VERB
cjfa-35471	447	20	more	more	ADJ
cjfa-35471	447	21	difficulty	difficulty	NOUN
cjfa-35471	447	22	to	to	PART
cjfa-35471	447	23	produce	produce	VERB
cjfa-35471	447	24	to	to	PART
cjfa-35471	447	25	build	build	VERB
cjfa-35471	447	26	up	up	ADP
cjfa-35471	447	27	inventories	inventory	NOUN
cjfa-35471	447	28	.	.	PUNCT
cjfa-35471	448	1	currently	currently	ADV
cjfa-35471	448	2	,	,	PUNCT
cjfa-35471	448	3	this	this	PRON
cjfa-35471	448	4	seems	seem	VERB
cjfa-35471	448	5	to	to	PART
cjfa-35471	448	6	be	be	AUX
cjfa-35471	448	7	the	the	DET
cjfa-35471	448	8	case	case	NOUN
cjfa-35471	448	9	in	in	ADP
cjfa-35471	448	10	major	major	ADJ
cjfa-35471	448	11	economies	economy	NOUN
cjfa-35471	448	12	.	.	PUNCT
cjfa-35471	449	1	3	3	X
cjfa-35471	449	2	.	.	X
cjfa-35471	449	3	higher	high	ADJ
cjfa-35471	449	4	interest	interest	NOUN
cjfa-35471	449	5	rates	rate	NOUN
cjfa-35471	449	6	and	and	CCONJ
cjfa-35471	449	7	the	the	DET
cjfa-35471	449	8	use	use	NOUN
cjfa-35471	449	9	of	of	ADP
cjfa-35471	449	10	inefficient	inefficient	ADJ
cjfa-35471	449	11	technologies	technology	NOUN
cjfa-35471	449	12	(	(	PUNCT
cjfa-35471	449	13	large	large	ADJ
cjfa-35471	449	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	449	15	)	)	PUNCT
cjfa-35471	449	16	implies	imply	VERB
cjfa-35471	449	17	high	high	ADJ
cjfa-35471	449	18	marginal	marginal	ADJ
cjfa-35471	449	19	cost	cost	NOUN
cjfa-35471	449	20	)	)	PUNCT
cjfa-35471	449	21	will	will	AUX
cjfa-35471	449	22	induce	induce	VERB
cjfa-35471	449	23	firms	firm	NOUN
cjfa-35471	449	24	to	to	PART
cjfa-35471	449	25	wait	wait	VERB
cjfa-35471	449	26	longer	long	ADV
cjfa-35471	449	27	for	for	ADP
cjfa-35471	449	28	inventory	inventory	NOUN
cjfa-35471	449	29	build	build	NOUN
cjfa-35471	449	30	-	-	PUNCT
cjfa-35471	449	31	up	up	NOUN
cjfa-35471	449	32	even	even	ADV
cjfa-35471	449	33	if	if	SCONJ
cjfa-35471	449	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	449	35	is	be	AUX
cjfa-35471	449	36	positive	positive	ADJ
cjfa-35471	449	37	.	.	PUNCT
cjfa-35471	450	1	4	4	X
cjfa-35471	450	2	.	.	X
cjfa-35471	450	3	the	the	DET
cjfa-35471	450	4	level	level	NOUN
cjfa-35471	450	5	of	of	ADP
cjfa-35471	450	6	technology	technology	NOUN
cjfa-35471	450	7	used	use	VERB
cjfa-35471	450	8	will	will	AUX
cjfa-35471	450	9	not	not	PART
cjfa-35471	450	10	affect	affect	VERB
cjfa-35471	450	11	the	the	DET
cjfa-35471	450	12	behavior	behavior	NOUN
cjfa-35471	450	13	of	of	ADP
cjfa-35471	450	14	the	the	DET
cjfa-35471	450	15	firms	firm	NOUN
cjfa-35471	450	16	if	if	SCONJ
cjfa-35471	450	17	the	the	DET
cjfa-35471	450	18	interest	interest	NOUN
cjfa-35471	450	19	rates	rate	NOUN
cjfa-35471	450	20	are	be	AUX
cjfa-35471	450	21	very	very	ADV
cjfa-35471	450	22	low	low	ADJ
cjfa-35471	450	23	as	as	SCONJ
cjfa-35471	450	24	they	they	PRON
cjfa-35471	450	25	are	be	AUX
cjfa-35471	450	26	now	now	ADV
cjfa-35471	450	27	in	in	ADP
cjfa-35471	450	28	many	many	ADJ
cjfa-35471	450	29	developed	develop	VERB
cjfa-35471	450	30	nations	nation	NOUN
cjfa-35471	450	31	since	since	SCONJ
cjfa-35471	450	32	the	the	DET
cjfa-35471	450	33	term	term	NOUN
cjfa-35471	450	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	450	35	in	in	ADP
cjfa-35471	450	36	change	change	NOUN
cjfa-35471	450	37	in	in	ADP
cjfa-35471	450	38	the	the	DET
cjfa-35471	450	39	marginal	marginal	ADJ
cjfa-35471	450	40	cost	cost	NOUN
cjfa-35471	450	41	.	.	PUNCT
cjfa-35471	451	1	following	follow	VERB
cjfa-35471	451	2	conclusions	conclusion	NOUN
cjfa-35471	451	3	can	can	AUX
cjfa-35471	451	4	be	be	AUX
cjfa-35471	451	5	made	make	VERB
cjfa-35471	451	6	even	even	ADV
cjfa-35471	451	7	without	without	ADP
cjfa-35471	451	8	specific	specific	ADJ
cjfa-35471	451	9	forms	form	NOUN
cjfa-35471	451	10	of	of	ADP
cjfa-35471	451	11	c(t	c(t	PROPN
cjfa-35471	451	12	)	)	PUNCT
cjfa-35471	451	13	,	,	PUNCT
cjfa-35471	451	14	f(t	f(t	PROPN
cjfa-35471	451	15	)	)	PUNCT
cjfa-35471	451	16	,	,	PUNCT
cjfa-35471	451	17	r(t	r(t	NOUN
cjfa-35471	451	18	)	)	PUNCT
cjfa-35471	451	19	and	and	CCONJ
cjfa-35471	451	20	i(t	i(t	NOUN
cjfa-35471	451	21	)	)	PUNCT
cjfa-35471	451	22	on	on	ADP
cjfa-35471	451	23	the	the	DET
cjfa-35471	451	24	basis	basis	NOUN
cjfa-35471	451	25	of	of	ADP
cjfa-35471	451	26	equation	equation	NOUN
cjfa-35471	451	27	(	(	PUNCT
cjfa-35471	451	28	4	4	NUM
cjfa-35471	451	29	):	):	PUNCT
cjfa-35471	451	30	mustafa	mustafa	PROPN
cjfa-35471	451	31	akan	akan	PROPN
cjfa-35471	451	32	,	,	PUNCT
cjfa-35471	451	33	natalia	natalia	PROPN
cjfa-35471	451	34	konovalova16	konovalova16	PROPN
cjfa-35471	452	1	1	1	NUM
cjfa-35471	452	2	.	.	PUNCT
cjfa-35471	453	1	the	the	DET
cjfa-35471	453	2	firm	firm	NOUN
cjfa-35471	453	3	will	will	AUX
cjfa-35471	453	4	keep	keep	VERB
cjfa-35471	453	5	l(t	l(t	NOUN
cjfa-35471	453	6	)	)	PUNCT
cjfa-35471	454	1	=	=	SYM
cjfa-35471	454	2	0	0	PUNCT
cjfa-35471	454	3	as	as	ADV
cjfa-35471	454	4	long	long	ADV
cjfa-35471	454	5	as	as	SCONJ
cjfa-35471	454	6	demand	demand	NOUN
cjfa-35471	454	7	is	be	AUX
cjfa-35471	454	8	falling	fall	VERB
cjfa-35471	454	9	or	or	CCONJ
cjfa-35471	454	10	constant	constant	ADJ
cjfa-35471	454	11	i.e.	i.e.	ADV
cjfa-35471	454	12	then	then	ADV
cjfa-35471	454	13	using	use	VERB
cjfa-35471	454	14	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	454	15	𝑢	𝑢	PROPN
cjfa-35471	454	16	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	454	17	,	,	PUNCT
cjfa-35471	454	18	equation	equation	NOUN
cjfa-35471	454	19	(	(	PUNCT
cjfa-35471	454	20	1	1	NUM
cjfa-35471	454	21	)	)	PUNCT
cjfa-35471	454	22	,	,	PUNCT
cjfa-35471	454	23	and	and	CCONJ
cjfa-35471	454	24	the	the	DET
cjfa-35471	454	25	conditions	condition	NOUN
cjfa-35471	454	26	(	(	PUNCT
cjfa-35471	454	27	the	the	DET
cjfa-35471	454	28	necessary	necessary	ADJ
cjfa-35471	454	29	condition	condition	NOUN
cjfa-35471	454	30	to	to	PART
cjfa-35471	454	31	keep	keep	VERB
cjfa-35471	454	32	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	454	33	𝑢	𝑢	ADP
cjfa-35471	454	34	𝐼	𝐼	PROPN
cjfa-35471	454	35	optimal	optimal	ADJ
cjfa-35471	454	36	)	)	PUNCT
cjfa-35471	454	37	developed	develop	VERB
cjfa-35471	454	38	by	by	ADP
cjfa-35471	454	39	pontryagin	pontryagin	NOUN
cjfa-35471	454	40	,	,	PUNCT
cjfa-35471	454	41	boltyanskii	boltyanskii	ADJ
cjfa-35471	454	42	,	,	PUNCT
cjfa-35471	454	43	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	454	44	and	and	CCONJ
cjfa-35471	454	45	mishechenko	mishechenko	NOUN
cjfa-35471	454	46	(	(	PUNCT
cjfa-35471	454	47	1962	1962	NUM
cjfa-35471	454	48	)	)	PUNCT
cjfa-35471	454	49	,	,	PUNCT
cjfa-35471	454	50	hestenes	hestene	NOUN
cjfa-35471	454	51	(	(	PUNCT
cjfa-35471	454	52	1966	1966	NUM
cjfa-35471	454	53	)	)	PUNCT
cjfa-35471	454	54	,	,	PUNCT
cjfa-35471	454	55	kamien	kamien	NOUN
cjfa-35471	454	56	and	and	CCONJ
cjfa-35471	454	57	schwartz	schwartz	PROPN
cjfa-35471	454	58	(	(	PUNCT
cjfa-35471	454	59	2012	2012	NUM
cjfa-35471	454	60	)	)	PUNCT
cjfa-35471	454	61	among	among	ADP
cjfa-35471	454	62	many	many	ADJ
cjfa-35471	454	63	others	other	NOUN
cjfa-35471	454	64	,	,	PUNCT
cjfa-35471	454	65	we	we	PRON
cjfa-35471	454	66	have	have	VERB
cjfa-35471	454	67	;	;	PUNCT
cjfa-35471	454	68	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	454	69	�	�	NOUN
cjfa-35471	454	70	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	454	71	≤	≤	PUNCT
cjfa-35471	454	72	𝐼	𝐼	PROPN
cjfa-35471	454	73	for	for	ADP
cjfa-35471	454	74	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	454	75	�	�	PROPN
cjfa-35471	454	76	≤	≤	NUM
cjfa-35471	455	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	455	2	≤	≤	NUM
cjfa-35471	455	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	455	4	�	�	PROPN
cjfa-35471	455	5	implies	imply	VERB
cjfa-35471	455	6	:	:	PUNCT
cjfa-35471	455	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	455	8	�	�	PROPN
cjfa-35471	455	9	�	�	PROPN
cjfa-35471	455	10	�	�	PROPN
cjfa-35471	455	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	455	12	�	�	PROPN
cjfa-35471	455	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	455	14	�	�	PROPN
cjfa-35471	455	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	455	16	≤	≤	PUNCT
cjfa-35471	455	17	ℎ	ℎ	PROPN
cjfa-35471	455	18	+	+	PROPN
cjfa-35471	455	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	455	20	�	�	PROPN
cjfa-35471	455	21	�	�	PROPN
cjfa-35471	455	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	455	23	�	�	PROPN
cjfa-35471	455	24	(	(	PUNCT
cjfa-35471	455	25	4	4	NUM
cjfa-35471	455	26	)	)	PUNCT
cjfa-35471	455	27	where	where	SCONJ
cjfa-35471	455	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	455	29	𝑢	𝑢	PROPN
cjfa-35471	455	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	455	31	�	�	NOUN
cjfa-35471	455	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	455	33	denotes	denote	VERB
cjfa-35471	455	34	the	the	DET
cjfa-35471	455	35	interest	interest	NOUN
cjfa-35471	455	36	rate	rate	NOUN
cjfa-35471	455	37	.	.	PUNCT
cjfa-35471	456	1	as	as	ADV
cjfa-35471	456	2	long	long	ADV
cjfa-35471	456	3	as	as	SCONJ
cjfa-35471	456	4	the	the	DET
cjfa-35471	456	5	condition	condition	NOUN
cjfa-35471	456	6	specified	specify	VERB
cjfa-35471	456	7	by	by	ADP
cjfa-35471	456	8	this	this	DET
cjfa-35471	456	9	inequality	inequality	NOUN
cjfa-35471	456	10	is	be	AUX
cjfa-35471	456	11	satisfied	satisfied	ADJ
cjfa-35471	456	12	it	it	PRON
cjfa-35471	456	13	will	will	AUX
cjfa-35471	456	14	be	be	AUX
cjfa-35471	456	15	optimal	optimal	ADJ
cjfa-35471	456	16	to	to	PART
cjfa-35471	456	17	keep	keep	VERB
cjfa-35471	456	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	456	19	𝑢	𝑢	ADP
cjfa-35471	456	20	𝐼	𝐼	ADP
cjfa-35471	456	21	implying	imply	VERB
cjfa-35471	456	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	456	23	𝑢	𝑢	PRON
cjfa-35471	456	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	456	25	this	this	PRON
cjfa-35471	456	26	means	mean	VERB
cjfa-35471	456	27	that	that	SCONJ
cjfa-35471	456	28	during	during	ADP
cjfa-35471	456	29	the	the	DET
cjfa-35471	456	30	intervals	interval	NOUN
cjfa-35471	456	31	where	where	SCONJ
cjfa-35471	456	32	this	this	DET
cjfa-35471	456	33	inequality	inequality	NOUN
cjfa-35471	456	34	is	be	AUX
cjfa-35471	456	35	satisfied	satisfied	ADJ
cjfa-35471	456	36	the	the	DET
cjfa-35471	456	37	firm	firm	NOUN
cjfa-35471	456	38	will	will	AUX
cjfa-35471	456	39	produce	produce	VERB
cjfa-35471	456	40	just	just	ADV
cjfa-35471	456	41	enough	enough	ADJ
cjfa-35471	456	42	to	to	PART
cjfa-35471	456	43	satisfy	satisfy	VERB
cjfa-35471	456	44	the	the	DET
cjfa-35471	456	45	demand	demand	NOUN
cjfa-35471	456	46	.	.	PUNCT
cjfa-35471	457	1	so	so	ADV
cjfa-35471	457	2	,	,	PUNCT
cjfa-35471	457	3	the	the	DET
cjfa-35471	457	4	condition	condition	NOUN
cjfa-35471	457	5	above	above	ADV
cjfa-35471	457	6	will	will	AUX
cjfa-35471	457	7	synthesize	synthesize	VERB
cjfa-35471	457	8	the	the	DET
cjfa-35471	457	9	periods	period	NOUN
cjfa-35471	457	10	where	where	SCONJ
cjfa-35471	457	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	457	12	𝑢	𝑢	PRON
cjfa-35471	457	13	𝐼	𝐼	PROPN
cjfa-35471	457	14	or	or	CCONJ
cjfa-35471	457	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	457	16	𝑢	𝑢	PROPN
cjfa-35471	457	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	457	18	and	and	CCONJ
cjfa-35471	457	19	the	the	DET
cjfa-35471	457	20	periods	period	NOUN
cjfa-35471	457	21	where	where	SCONJ
cjfa-35471	457	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	457	23	𝐼	𝐼	ADP
cjfa-35471	457	24	𝐼.	𝐼.	PROPN
cjfa-35471	457	25	notice	notice	VERB
cjfa-35471	457	26	that	that	SCONJ
cjfa-35471	457	27	for	for	ADP
cjfa-35471	457	28	the	the	DET
cjfa-35471	457	29	condition	condition	NOUN
cjfa-35471	457	30	above	above	ADV
cjfa-35471	457	31	(	(	PUNCT
cjfa-35471	457	32	equation	equation	NOUN
cjfa-35471	457	33	4	4	NUM
cjfa-35471	457	34	)	)	PUNCT
cjfa-35471	457	35	to	to	PART
cjfa-35471	457	36	be	be	AUX
cjfa-35471	457	37	kept	keep	VERB
cjfa-35471	457	38	satisfied	satisfied	ADJ
cjfa-35471	457	39	depends	depend	VERB
cjfa-35471	457	40	on	on	ADP
cjfa-35471	457	41	ℎ	ℎ	PROPN
cjfa-35471	457	42	(	(	PUNCT
cjfa-35471	457	43	inventory	inventory	NOUN
cjfa-35471	457	44	holding	hold	VERB
cjfa-35471	457	45	cost	cost	NOUN
cjfa-35471	457	46	)	)	PUNCT
cjfa-35471	457	47	,	,	PUNCT
cjfa-35471	457	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	457	49	the	the	DET
cjfa-35471	457	50	interest	interest	NOUN
cjfa-35471	457	51	rates	rate	NOUN
cjfa-35471	457	52	,	,	PUNCT
cjfa-35471	457	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	457	54	,	,	PUNCT
cjfa-35471	457	55	the	the	DET
cjfa-35471	457	56	marginal	marginal	ADJ
cjfa-35471	457	57	cost	cost	NOUN
cjfa-35471	457	58	of	of	ADP
cjfa-35471	457	59	production	production	NOUN
cjfa-35471	457	60	,	,	PUNCT
cjfa-35471	457	61	and	and	CCONJ
cjfa-35471	457	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	457	63	change	change	NOUN
cjfa-35471	457	64	in	in	ADP
cjfa-35471	457	65	the	the	DET
cjfa-35471	457	66	marginal	marginal	ADJ
cjfa-35471	457	67	cost	cost	NOUN
cjfa-35471	457	68	.	.	PUNCT
cjfa-35471	458	1	following	follow	VERB
cjfa-35471	458	2	conclusions	conclusion	NOUN
cjfa-35471	458	3	can	can	AUX
cjfa-35471	458	4	be	be	AUX
cjfa-35471	458	5	made	make	VERB
cjfa-35471	458	6	even	even	ADV
cjfa-35471	458	7	without	without	ADP
cjfa-35471	458	8	specific	specific	ADJ
cjfa-35471	458	9	forms	form	NOUN
cjfa-35471	458	10	of	of	ADP
cjfa-35471	458	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	458	12	,	,	PUNCT
cjfa-35471	458	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	458	14	,	,	PUNCT
cjfa-35471	458	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	458	16	and	and	CCONJ
cjfa-35471	458	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	458	18	on	on	ADP
cjfa-35471	458	19	the	the	DET
cjfa-35471	458	20	basis	basis	NOUN
cjfa-35471	458	21	of	of	ADP
cjfa-35471	458	22	equation	equation	NOUN
cjfa-35471	458	23	(	(	PUNCT
cjfa-35471	458	24	4	4	NUM
cjfa-35471	458	25	):	):	PUNCT
cjfa-35471	458	26	1	1	NUM
cjfa-35471	458	27	.	.	PUNCT
cjfa-35471	459	1	the	the	DET
cjfa-35471	459	2	firm	firm	NOUN
cjfa-35471	459	3	will	will	AUX
cjfa-35471	459	4	keep	keep	VERB
cjfa-35471	459	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	459	6	𝑢	𝑢	ADP
cjfa-35471	459	7	𝐼	𝐼	PROPN
cjfa-35471	459	8	as	as	ADV
cjfa-35471	459	9	long	long	ADV
cjfa-35471	459	10	as	as	SCONJ
cjfa-35471	459	11	demand	demand	NOUN
cjfa-35471	459	12	is	be	AUX
cjfa-35471	459	13	falling	fall	VERB
cjfa-35471	459	14	or	or	CCONJ
cjfa-35471	459	15	constant	constant	ADJ
cjfa-35471	459	16	i.e.	i.e.	X
cjfa-35471	459	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	459	18	0	0	NOUN
cjfa-35471	459	19	implying	imply	VERB
cjfa-35471	459	20	that	that	SCONJ
cjfa-35471	459	21	the	the	DET
cjfa-35471	459	22	firm	firm	NOUN
cjfa-35471	459	23	will	will	AUX
cjfa-35471	459	24	choose	choose	VERB
cjfa-35471	459	25	to	to	PART
cjfa-35471	459	26	produce	produce	VERB
cjfa-35471	459	27	just	just	ADV
cjfa-35471	459	28	enough	enough	ADJ
cjfa-35471	459	29	to	to	PART
cjfa-35471	459	30	meet	meet	VERB
cjfa-35471	459	31	the	the	DET
cjfa-35471	459	32	demand	demand	NOUN
cjfa-35471	459	33	if	if	SCONJ
cjfa-35471	459	34	demand	demand	NOUN
cjfa-35471	459	35	is	be	AUX
cjfa-35471	459	36	falling	fall	VERB
cjfa-35471	459	37	since	since	SCONJ
cjfa-35471	459	38	both	both	PRON
cjfa-35471	459	39	ℎ	ℎ	NOUN
cjfa-35471	459	40	and	and	CCONJ
cjfa-35471	459	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	459	42	are	be	AUX
cjfa-35471	459	43	positive	positive	ADJ
cjfa-35471	459	44	.	.	PUNCT
cjfa-35471	460	1	2	2	X
cjfa-35471	460	2	.	.	X
cjfa-35471	460	3	the	the	DET
cjfa-35471	460	4	firm	firm	NOUN
cjfa-35471	460	5	will	will	AUX
cjfa-35471	460	6	keep	keep	VERB
cjfa-35471	460	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	460	8	𝑢	𝑢	ADP
cjfa-35471	460	9	𝐼	𝐼	NOUN
cjfa-35471	460	10	even	even	ADV
cjfa-35471	460	11	if	if	SCONJ
cjfa-35471	460	12	demand	demand	NOUN
cjfa-35471	460	13	is	be	AUX
cjfa-35471	460	14	increasing	increase	VERB
cjfa-35471	460	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	460	16	𝑟	𝑟	X
cjfa-35471	460	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	460	18	but	but	CCONJ
cjfa-35471	460	19	the	the	DET
cjfa-35471	460	20	term	term	NOUN
cjfa-35471	460	21	ℎ	ℎ	PROPN
cjfa-35471	460	22	+	+	CCONJ
cjfa-35471	460	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	460	24	�	�	PROPN
cjfa-35471	460	25	�	�	PROPN
cjfa-35471	460	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	460	27	�	�	PROPN
cjfa-35471	460	28	is	be	AUX
cjfa-35471	460	29	large	large	ADJ
cjfa-35471	460	30	enough	enough	ADV
cjfa-35471	460	31	to	to	PART
cjfa-35471	460	32	keep	keep	VERB
cjfa-35471	460	33	inequality	inequality	NOUN
cjfa-35471	460	34	(	(	PUNCT
cjfa-35471	460	35	4	4	NUM
cjfa-35471	460	36	)	)	PUNCT
cjfa-35471	460	37	satisfied	satisfied	ADJ
cjfa-35471	460	38	.	.	PUNCT
cjfa-35471	461	1	decreasing	decrease	VERB
cjfa-35471	461	2	interest	interest	NOUN
cjfa-35471	461	3	rates	rate	NOUN
cjfa-35471	461	4	will	will	AUX
cjfa-35471	461	5	not	not	PART
cjfa-35471	461	6	be	be	AUX
cjfa-35471	461	7	a	a	DET
cjfa-35471	461	8	remedy	remedy	NOUN
cjfa-35471	461	9	in	in	ADP
cjfa-35471	461	10	this	this	DET
cjfa-35471	461	11	case	case	NOUN
cjfa-35471	461	12	if	if	SCONJ
cjfa-35471	461	13	they	they	PRON
cjfa-35471	461	14	are	be	AUX
cjfa-35471	461	15	already	already	ADV
cjfa-35471	461	16	low	low	ADJ
cjfa-35471	461	17	.	.	PUNCT
cjfa-35471	462	1	firms	firm	NOUN
cjfa-35471	462	2	where	where	SCONJ
cjfa-35471	462	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	462	4	�	�	PROPN
cjfa-35471	462	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	462	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	462	7	�	�	PROPN
cjfa-35471	462	8	is	be	AUX
cjfa-35471	462	9	low	low	ADJ
cjfa-35471	462	10	(	(	PUNCT
cjfa-35471	462	11	large	large	ADJ
cjfa-35471	462	12	and	and	CCONJ
cjfa-35471	462	13	already	already	ADV
cjfa-35471	462	14	very	very	ADV
cjfa-35471	462	15	efficient	efficient	ADJ
cjfa-35471	462	16	firms	firm	NOUN
cjfa-35471	462	17	)	)	PUNCT
cjfa-35471	462	18	will	will	AUX
cjfa-35471	462	19	have	have	VERB
cjfa-35471	462	20	more	more	ADJ
cjfa-35471	462	21	difficulty	difficulty	NOUN
cjfa-35471	462	22	to	to	PART
cjfa-35471	462	23	produce	produce	VERB
cjfa-35471	462	24	to	to	PART
cjfa-35471	462	25	build	build	VERB
cjfa-35471	462	26	up	up	ADP
cjfa-35471	462	27	inventories	inventory	NOUN
cjfa-35471	462	28	.	.	PUNCT
cjfa-35471	463	1	currently	currently	ADV
cjfa-35471	463	2	,	,	PUNCT
cjfa-35471	463	3	this	this	PRON
cjfa-35471	463	4	seems	seem	VERB
cjfa-35471	463	5	to	to	PART
cjfa-35471	463	6	be	be	AUX
cjfa-35471	463	7	the	the	DET
cjfa-35471	463	8	case	case	NOUN
cjfa-35471	463	9	in	in	ADP
cjfa-35471	463	10	major	major	ADJ
cjfa-35471	463	11	economies	economy	NOUN
cjfa-35471	463	12	.	.	PUNCT
cjfa-35471	464	1	3	3	X
cjfa-35471	464	2	.	.	X
cjfa-35471	464	3	higher	high	ADJ
cjfa-35471	464	4	interest	interest	NOUN
cjfa-35471	464	5	rates	rate	NOUN
cjfa-35471	464	6	and	and	CCONJ
cjfa-35471	464	7	the	the	DET
cjfa-35471	464	8	use	use	NOUN
cjfa-35471	464	9	of	of	ADP
cjfa-35471	464	10	inefficient	inefficient	ADJ
cjfa-35471	464	11	technologies	technology	NOUN
cjfa-35471	464	12	(	(	PUNCT
cjfa-35471	464	13	large	large	ADJ
cjfa-35471	464	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	464	15	)	)	PUNCT
cjfa-35471	464	16	implies	imply	VERB
cjfa-35471	464	17	high	high	ADJ
cjfa-35471	464	18	marginal	marginal	ADJ
cjfa-35471	464	19	cost	cost	NOUN
cjfa-35471	464	20	)	)	PUNCT
cjfa-35471	464	21	will	will	AUX
cjfa-35471	464	22	induce	induce	VERB
cjfa-35471	464	23	firms	firm	NOUN
cjfa-35471	464	24	to	to	PART
cjfa-35471	464	25	wait	wait	VERB
cjfa-35471	464	26	longer	long	ADV
cjfa-35471	464	27	for	for	ADP
cjfa-35471	464	28	inventory	inventory	NOUN
cjfa-35471	464	29	build	build	NOUN
cjfa-35471	464	30	-	-	PUNCT
cjfa-35471	464	31	up	up	NOUN
cjfa-35471	464	32	even	even	ADV
cjfa-35471	464	33	if	if	SCONJ
cjfa-35471	464	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	464	35	is	be	AUX
cjfa-35471	464	36	positive	positive	ADJ
cjfa-35471	464	37	.	.	PUNCT
cjfa-35471	465	1	4	4	X
cjfa-35471	465	2	.	.	X
cjfa-35471	465	3	the	the	DET
cjfa-35471	465	4	level	level	NOUN
cjfa-35471	465	5	of	of	ADP
cjfa-35471	465	6	technology	technology	NOUN
cjfa-35471	465	7	used	use	VERB
cjfa-35471	465	8	will	will	AUX
cjfa-35471	465	9	not	not	PART
cjfa-35471	465	10	affect	affect	VERB
cjfa-35471	465	11	the	the	DET
cjfa-35471	465	12	behavior	behavior	NOUN
cjfa-35471	465	13	of	of	ADP
cjfa-35471	465	14	the	the	DET
cjfa-35471	465	15	firms	firm	NOUN
cjfa-35471	465	16	if	if	SCONJ
cjfa-35471	465	17	the	the	DET
cjfa-35471	465	18	interest	interest	NOUN
cjfa-35471	465	19	rates	rate	NOUN
cjfa-35471	465	20	are	be	AUX
cjfa-35471	465	21	very	very	ADV
cjfa-35471	465	22	low	low	ADJ
cjfa-35471	465	23	as	as	SCONJ
cjfa-35471	465	24	they	they	PRON
cjfa-35471	465	25	are	be	AUX
cjfa-35471	465	26	now	now	ADV
cjfa-35471	465	27	in	in	ADP
cjfa-35471	465	28	many	many	ADJ
cjfa-35471	465	29	developed	develop	VERB
cjfa-35471	465	30	nations	nation	NOUN
cjfa-35471	465	31	since	since	SCONJ
cjfa-35471	465	32	the	the	DET
cjfa-35471	465	33	term	term	NOUN
cjfa-35471	465	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	465	35	in	in	ADP
cjfa-35471	465	36	implying	imply	VERB
cjfa-35471	465	37	that	that	SCONJ
cjfa-35471	465	38	the	the	DET
cjfa-35471	465	39	firm	firm	NOUN
cjfa-35471	465	40	will	will	AUX
cjfa-35471	465	41	choose	choose	VERB
cjfa-35471	465	42	to	to	PART
cjfa-35471	465	43	produce	produce	VERB
cjfa-35471	465	44	just	just	ADV
cjfa-35471	465	45	enough	enough	ADJ
cjfa-35471	465	46	to	to	PART
cjfa-35471	465	47	meet	meet	VERB
cjfa-35471	465	48	the	the	DET
cjfa-35471	465	49	demand	demand	NOUN
cjfa-35471	465	50	if	if	SCONJ
cjfa-35471	465	51	demand	demand	NOUN
cjfa-35471	465	52	is	be	AUX
cjfa-35471	465	53	falling	fall	VERB
cjfa-35471	465	54	since	since	SCONJ
cjfa-35471	465	55	both	both	PRON
cjfa-35471	465	56	then	then	ADV
cjfa-35471	465	57	using	use	VERB
cjfa-35471	465	58	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	465	59	𝑢	𝑢	PROPN
cjfa-35471	465	60	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	465	61	,	,	PUNCT
cjfa-35471	465	62	equation	equation	NOUN
cjfa-35471	465	63	(	(	PUNCT
cjfa-35471	465	64	1	1	NUM
cjfa-35471	465	65	)	)	PUNCT
cjfa-35471	465	66	,	,	PUNCT
cjfa-35471	465	67	and	and	CCONJ
cjfa-35471	465	68	the	the	DET
cjfa-35471	465	69	conditions	condition	NOUN
cjfa-35471	465	70	(	(	PUNCT
cjfa-35471	465	71	the	the	DET
cjfa-35471	465	72	necessary	necessary	ADJ
cjfa-35471	465	73	condition	condition	NOUN
cjfa-35471	465	74	to	to	PART
cjfa-35471	465	75	keep	keep	VERB
cjfa-35471	465	76	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	465	77	𝑢	𝑢	ADP
cjfa-35471	465	78	𝐼	𝐼	PROPN
cjfa-35471	465	79	optimal	optimal	ADJ
cjfa-35471	465	80	)	)	PUNCT
cjfa-35471	465	81	developed	develop	VERB
cjfa-35471	465	82	by	by	ADP
cjfa-35471	465	83	pontryagin	pontryagin	NOUN
cjfa-35471	465	84	,	,	PUNCT
cjfa-35471	465	85	boltyanskii	boltyanskii	ADJ
cjfa-35471	465	86	,	,	PUNCT
cjfa-35471	465	87	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	465	88	and	and	CCONJ
cjfa-35471	465	89	mishechenko	mishechenko	NOUN
cjfa-35471	465	90	(	(	PUNCT
cjfa-35471	465	91	1962	1962	NUM
cjfa-35471	465	92	)	)	PUNCT
cjfa-35471	465	93	,	,	PUNCT
cjfa-35471	465	94	hestenes	hestene	NOUN
cjfa-35471	465	95	(	(	PUNCT
cjfa-35471	465	96	1966	1966	NUM
cjfa-35471	465	97	)	)	PUNCT
cjfa-35471	465	98	,	,	PUNCT
cjfa-35471	465	99	kamien	kamien	NOUN
cjfa-35471	465	100	and	and	CCONJ
cjfa-35471	465	101	schwartz	schwartz	PROPN
cjfa-35471	465	102	(	(	PUNCT
cjfa-35471	465	103	2012	2012	NUM
cjfa-35471	465	104	)	)	PUNCT
cjfa-35471	465	105	among	among	ADP
cjfa-35471	465	106	many	many	ADJ
cjfa-35471	465	107	others	other	NOUN
cjfa-35471	465	108	,	,	PUNCT
cjfa-35471	465	109	we	we	PRON
cjfa-35471	465	110	have	have	VERB
cjfa-35471	465	111	;	;	PUNCT
cjfa-35471	465	112	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	465	113	�	�	NOUN
cjfa-35471	465	114	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	465	115	≤	≤	PUNCT
cjfa-35471	465	116	𝐼	𝐼	PROPN
cjfa-35471	465	117	for	for	ADP
cjfa-35471	465	118	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	465	119	�	�	PROPN
cjfa-35471	465	120	≤	≤	NUM
cjfa-35471	466	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	466	2	≤	≤	NUM
cjfa-35471	466	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	466	4	�	�	PROPN
cjfa-35471	466	5	implies	imply	VERB
cjfa-35471	466	6	:	:	PUNCT
cjfa-35471	466	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	466	8	�	�	PROPN
cjfa-35471	466	9	�	�	PROPN
cjfa-35471	466	10	�	�	PROPN
cjfa-35471	466	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	466	12	�	�	PROPN
cjfa-35471	466	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	466	14	�	�	PROPN
cjfa-35471	466	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	466	16	≤	≤	PUNCT
cjfa-35471	466	17	ℎ	ℎ	PROPN
cjfa-35471	466	18	+	+	PROPN
cjfa-35471	466	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	466	20	�	�	PROPN
cjfa-35471	466	21	�	�	PROPN
cjfa-35471	466	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	466	23	�	�	PROPN
cjfa-35471	466	24	(	(	PUNCT
cjfa-35471	466	25	4	4	NUM
cjfa-35471	466	26	)	)	PUNCT
cjfa-35471	466	27	where	where	SCONJ
cjfa-35471	466	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	466	29	𝑢	𝑢	PROPN
cjfa-35471	466	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	466	31	�	�	NOUN
cjfa-35471	466	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	466	33	denotes	denote	VERB
cjfa-35471	466	34	the	the	DET
cjfa-35471	466	35	interest	interest	NOUN
cjfa-35471	466	36	rate	rate	NOUN
cjfa-35471	466	37	.	.	PUNCT
cjfa-35471	467	1	as	as	ADV
cjfa-35471	467	2	long	long	ADV
cjfa-35471	467	3	as	as	SCONJ
cjfa-35471	467	4	the	the	DET
cjfa-35471	467	5	condition	condition	NOUN
cjfa-35471	467	6	specified	specify	VERB
cjfa-35471	467	7	by	by	ADP
cjfa-35471	467	8	this	this	DET
cjfa-35471	467	9	inequality	inequality	NOUN
cjfa-35471	467	10	is	be	AUX
cjfa-35471	467	11	satisfied	satisfied	ADJ
cjfa-35471	467	12	it	it	PRON
cjfa-35471	467	13	will	will	AUX
cjfa-35471	467	14	be	be	AUX
cjfa-35471	467	15	optimal	optimal	ADJ
cjfa-35471	467	16	to	to	PART
cjfa-35471	467	17	keep	keep	VERB
cjfa-35471	467	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	467	19	𝑢	𝑢	ADP
cjfa-35471	467	20	𝐼	𝐼	ADP
cjfa-35471	467	21	implying	imply	VERB
cjfa-35471	467	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	467	23	𝑢	𝑢	PRON
cjfa-35471	467	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	467	25	this	this	PRON
cjfa-35471	467	26	means	mean	VERB
cjfa-35471	467	27	that	that	SCONJ
cjfa-35471	467	28	during	during	ADP
cjfa-35471	467	29	the	the	DET
cjfa-35471	467	30	intervals	interval	NOUN
cjfa-35471	467	31	where	where	SCONJ
cjfa-35471	467	32	this	this	DET
cjfa-35471	467	33	inequality	inequality	NOUN
cjfa-35471	467	34	is	be	AUX
cjfa-35471	467	35	satisfied	satisfied	ADJ
cjfa-35471	467	36	the	the	DET
cjfa-35471	467	37	firm	firm	NOUN
cjfa-35471	467	38	will	will	AUX
cjfa-35471	467	39	produce	produce	VERB
cjfa-35471	467	40	just	just	ADV
cjfa-35471	467	41	enough	enough	ADJ
cjfa-35471	467	42	to	to	PART
cjfa-35471	467	43	satisfy	satisfy	VERB
cjfa-35471	467	44	the	the	DET
cjfa-35471	467	45	demand	demand	NOUN
cjfa-35471	467	46	.	.	PUNCT
cjfa-35471	468	1	so	so	ADV
cjfa-35471	468	2	,	,	PUNCT
cjfa-35471	468	3	the	the	DET
cjfa-35471	468	4	condition	condition	NOUN
cjfa-35471	468	5	above	above	ADV
cjfa-35471	468	6	will	will	AUX
cjfa-35471	468	7	synthesize	synthesize	VERB
cjfa-35471	468	8	the	the	DET
cjfa-35471	468	9	periods	period	NOUN
cjfa-35471	468	10	where	where	SCONJ
cjfa-35471	468	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	468	12	𝑢	𝑢	PRON
cjfa-35471	468	13	𝐼	𝐼	PROPN
cjfa-35471	468	14	or	or	CCONJ
cjfa-35471	468	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	468	16	𝑢	𝑢	PROPN
cjfa-35471	468	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	468	18	and	and	CCONJ
cjfa-35471	468	19	the	the	DET
cjfa-35471	468	20	periods	period	NOUN
cjfa-35471	468	21	where	where	SCONJ
cjfa-35471	468	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	468	23	𝐼	𝐼	ADP
cjfa-35471	468	24	𝐼.	𝐼.	PROPN
cjfa-35471	468	25	notice	notice	VERB
cjfa-35471	468	26	that	that	SCONJ
cjfa-35471	468	27	for	for	ADP
cjfa-35471	468	28	the	the	DET
cjfa-35471	468	29	condition	condition	NOUN
cjfa-35471	468	30	above	above	ADV
cjfa-35471	468	31	(	(	PUNCT
cjfa-35471	468	32	equation	equation	NOUN
cjfa-35471	468	33	4	4	NUM
cjfa-35471	468	34	)	)	PUNCT
cjfa-35471	468	35	to	to	PART
cjfa-35471	468	36	be	be	AUX
cjfa-35471	468	37	kept	keep	VERB
cjfa-35471	468	38	satisfied	satisfied	ADJ
cjfa-35471	468	39	depends	depend	VERB
cjfa-35471	468	40	on	on	ADP
cjfa-35471	468	41	ℎ	ℎ	PROPN
cjfa-35471	468	42	(	(	PUNCT
cjfa-35471	468	43	inventory	inventory	NOUN
cjfa-35471	468	44	holding	hold	VERB
cjfa-35471	468	45	cost	cost	NOUN
cjfa-35471	468	46	)	)	PUNCT
cjfa-35471	468	47	,	,	PUNCT
cjfa-35471	468	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	468	49	the	the	DET
cjfa-35471	468	50	interest	interest	NOUN
cjfa-35471	468	51	rates	rate	NOUN
cjfa-35471	468	52	,	,	PUNCT
cjfa-35471	468	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	468	54	,	,	PUNCT
cjfa-35471	468	55	the	the	DET
cjfa-35471	468	56	marginal	marginal	ADJ
cjfa-35471	468	57	cost	cost	NOUN
cjfa-35471	468	58	of	of	ADP
cjfa-35471	468	59	production	production	NOUN
cjfa-35471	468	60	,	,	PUNCT
cjfa-35471	468	61	and	and	CCONJ
cjfa-35471	468	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	468	63	change	change	NOUN
cjfa-35471	468	64	in	in	ADP
cjfa-35471	468	65	the	the	DET
cjfa-35471	468	66	marginal	marginal	ADJ
cjfa-35471	468	67	cost	cost	NOUN
cjfa-35471	468	68	.	.	PUNCT
cjfa-35471	469	1	following	follow	VERB
cjfa-35471	469	2	conclusions	conclusion	NOUN
cjfa-35471	469	3	can	can	AUX
cjfa-35471	469	4	be	be	AUX
cjfa-35471	469	5	made	make	VERB
cjfa-35471	469	6	even	even	ADV
cjfa-35471	469	7	without	without	ADP
cjfa-35471	469	8	specific	specific	ADJ
cjfa-35471	469	9	forms	form	NOUN
cjfa-35471	469	10	of	of	ADP
cjfa-35471	469	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	469	12	,	,	PUNCT
cjfa-35471	469	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	469	14	,	,	PUNCT
cjfa-35471	469	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	469	16	and	and	CCONJ
cjfa-35471	469	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	469	18	on	on	ADP
cjfa-35471	469	19	the	the	DET
cjfa-35471	469	20	basis	basis	NOUN
cjfa-35471	469	21	of	of	ADP
cjfa-35471	469	22	equation	equation	NOUN
cjfa-35471	469	23	(	(	PUNCT
cjfa-35471	469	24	4	4	NUM
cjfa-35471	469	25	):	):	PUNCT
cjfa-35471	469	26	1	1	NUM
cjfa-35471	469	27	.	.	PUNCT
cjfa-35471	470	1	the	the	DET
cjfa-35471	470	2	firm	firm	NOUN
cjfa-35471	470	3	will	will	AUX
cjfa-35471	470	4	keep	keep	VERB
cjfa-35471	470	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	470	6	𝑢	𝑢	ADP
cjfa-35471	470	7	𝐼	𝐼	PROPN
cjfa-35471	470	8	as	as	ADV
cjfa-35471	470	9	long	long	ADV
cjfa-35471	470	10	as	as	SCONJ
cjfa-35471	470	11	demand	demand	NOUN
cjfa-35471	470	12	is	be	AUX
cjfa-35471	470	13	falling	fall	VERB
cjfa-35471	470	14	or	or	CCONJ
cjfa-35471	470	15	constant	constant	ADJ
cjfa-35471	470	16	i.e.	i.e.	X
cjfa-35471	470	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	470	18	0	0	NOUN
cjfa-35471	470	19	implying	imply	VERB
cjfa-35471	470	20	that	that	SCONJ
cjfa-35471	470	21	the	the	DET
cjfa-35471	470	22	firm	firm	NOUN
cjfa-35471	470	23	will	will	AUX
cjfa-35471	470	24	choose	choose	VERB
cjfa-35471	470	25	to	to	PART
cjfa-35471	470	26	produce	produce	VERB
cjfa-35471	470	27	just	just	ADV
cjfa-35471	470	28	enough	enough	ADJ
cjfa-35471	470	29	to	to	PART
cjfa-35471	470	30	meet	meet	VERB
cjfa-35471	470	31	the	the	DET
cjfa-35471	470	32	demand	demand	NOUN
cjfa-35471	470	33	if	if	SCONJ
cjfa-35471	470	34	demand	demand	NOUN
cjfa-35471	470	35	is	be	AUX
cjfa-35471	470	36	falling	fall	VERB
cjfa-35471	470	37	since	since	SCONJ
cjfa-35471	470	38	both	both	PRON
cjfa-35471	470	39	ℎ	ℎ	NOUN
cjfa-35471	470	40	and	and	CCONJ
cjfa-35471	470	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	470	42	are	be	AUX
cjfa-35471	470	43	positive	positive	ADJ
cjfa-35471	470	44	.	.	PUNCT
cjfa-35471	471	1	2	2	X
cjfa-35471	471	2	.	.	X
cjfa-35471	471	3	the	the	DET
cjfa-35471	471	4	firm	firm	NOUN
cjfa-35471	471	5	will	will	AUX
cjfa-35471	471	6	keep	keep	VERB
cjfa-35471	471	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	471	8	𝑢	𝑢	ADP
cjfa-35471	471	9	𝐼	𝐼	NOUN
cjfa-35471	471	10	even	even	ADV
cjfa-35471	471	11	if	if	SCONJ
cjfa-35471	471	12	demand	demand	NOUN
cjfa-35471	471	13	is	be	AUX
cjfa-35471	471	14	increasing	increase	VERB
cjfa-35471	471	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	471	16	𝑟	𝑟	X
cjfa-35471	471	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	471	18	but	but	CCONJ
cjfa-35471	471	19	the	the	DET
cjfa-35471	471	20	term	term	NOUN
cjfa-35471	471	21	ℎ	ℎ	PROPN
cjfa-35471	471	22	+	+	CCONJ
cjfa-35471	471	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	471	24	�	�	PROPN
cjfa-35471	471	25	�	�	PROPN
cjfa-35471	471	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	471	27	�	�	PROPN
cjfa-35471	471	28	is	be	AUX
cjfa-35471	471	29	large	large	ADJ
cjfa-35471	471	30	enough	enough	ADV
cjfa-35471	471	31	to	to	PART
cjfa-35471	471	32	keep	keep	VERB
cjfa-35471	471	33	inequality	inequality	NOUN
cjfa-35471	471	34	(	(	PUNCT
cjfa-35471	471	35	4	4	NUM
cjfa-35471	471	36	)	)	PUNCT
cjfa-35471	471	37	satisfied	satisfied	ADJ
cjfa-35471	471	38	.	.	PUNCT
cjfa-35471	472	1	decreasing	decrease	VERB
cjfa-35471	472	2	interest	interest	NOUN
cjfa-35471	472	3	rates	rate	NOUN
cjfa-35471	472	4	will	will	AUX
cjfa-35471	472	5	not	not	PART
cjfa-35471	472	6	be	be	AUX
cjfa-35471	472	7	a	a	DET
cjfa-35471	472	8	remedy	remedy	NOUN
cjfa-35471	472	9	in	in	ADP
cjfa-35471	472	10	this	this	DET
cjfa-35471	472	11	case	case	NOUN
cjfa-35471	472	12	if	if	SCONJ
cjfa-35471	472	13	they	they	PRON
cjfa-35471	472	14	are	be	AUX
cjfa-35471	472	15	already	already	ADV
cjfa-35471	472	16	low	low	ADJ
cjfa-35471	472	17	.	.	PUNCT
cjfa-35471	473	1	firms	firm	NOUN
cjfa-35471	473	2	where	where	SCONJ
cjfa-35471	473	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	473	4	�	�	PROPN
cjfa-35471	473	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	473	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	473	7	�	�	PROPN
cjfa-35471	473	8	is	be	AUX
cjfa-35471	473	9	low	low	ADJ
cjfa-35471	473	10	(	(	PUNCT
cjfa-35471	473	11	large	large	ADJ
cjfa-35471	473	12	and	and	CCONJ
cjfa-35471	473	13	already	already	ADV
cjfa-35471	473	14	very	very	ADV
cjfa-35471	473	15	efficient	efficient	ADJ
cjfa-35471	473	16	firms	firm	NOUN
cjfa-35471	473	17	)	)	PUNCT
cjfa-35471	473	18	will	will	AUX
cjfa-35471	473	19	have	have	VERB
cjfa-35471	473	20	more	more	ADJ
cjfa-35471	473	21	difficulty	difficulty	NOUN
cjfa-35471	473	22	to	to	PART
cjfa-35471	473	23	produce	produce	VERB
cjfa-35471	473	24	to	to	PART
cjfa-35471	473	25	build	build	VERB
cjfa-35471	473	26	up	up	ADP
cjfa-35471	473	27	inventories	inventory	NOUN
cjfa-35471	473	28	.	.	PUNCT
cjfa-35471	474	1	currently	currently	ADV
cjfa-35471	474	2	,	,	PUNCT
cjfa-35471	474	3	this	this	PRON
cjfa-35471	474	4	seems	seem	VERB
cjfa-35471	474	5	to	to	PART
cjfa-35471	474	6	be	be	AUX
cjfa-35471	474	7	the	the	DET
cjfa-35471	474	8	case	case	NOUN
cjfa-35471	474	9	in	in	ADP
cjfa-35471	474	10	major	major	ADJ
cjfa-35471	474	11	economies	economy	NOUN
cjfa-35471	474	12	.	.	PUNCT
cjfa-35471	475	1	3	3	X
cjfa-35471	475	2	.	.	X
cjfa-35471	475	3	higher	high	ADJ
cjfa-35471	475	4	interest	interest	NOUN
cjfa-35471	475	5	rates	rate	NOUN
cjfa-35471	475	6	and	and	CCONJ
cjfa-35471	475	7	the	the	DET
cjfa-35471	475	8	use	use	NOUN
cjfa-35471	475	9	of	of	ADP
cjfa-35471	475	10	inefficient	inefficient	ADJ
cjfa-35471	475	11	technologies	technology	NOUN
cjfa-35471	475	12	(	(	PUNCT
cjfa-35471	475	13	large	large	ADJ
cjfa-35471	475	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	475	15	)	)	PUNCT
cjfa-35471	475	16	implies	imply	VERB
cjfa-35471	475	17	high	high	ADJ
cjfa-35471	475	18	marginal	marginal	ADJ
cjfa-35471	475	19	cost	cost	NOUN
cjfa-35471	475	20	)	)	PUNCT
cjfa-35471	475	21	will	will	AUX
cjfa-35471	475	22	induce	induce	VERB
cjfa-35471	475	23	firms	firm	NOUN
cjfa-35471	475	24	to	to	PART
cjfa-35471	475	25	wait	wait	VERB
cjfa-35471	475	26	longer	long	ADV
cjfa-35471	475	27	for	for	ADP
cjfa-35471	475	28	inventory	inventory	NOUN
cjfa-35471	475	29	build	build	NOUN
cjfa-35471	475	30	-	-	PUNCT
cjfa-35471	475	31	up	up	NOUN
cjfa-35471	475	32	even	even	ADV
cjfa-35471	475	33	if	if	SCONJ
cjfa-35471	475	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	475	35	is	be	AUX
cjfa-35471	475	36	positive	positive	ADJ
cjfa-35471	475	37	.	.	PUNCT
cjfa-35471	476	1	4	4	X
cjfa-35471	476	2	.	.	X
cjfa-35471	476	3	the	the	DET
cjfa-35471	476	4	level	level	NOUN
cjfa-35471	476	5	of	of	ADP
cjfa-35471	476	6	technology	technology	NOUN
cjfa-35471	476	7	used	use	VERB
cjfa-35471	476	8	will	will	AUX
cjfa-35471	476	9	not	not	PART
cjfa-35471	476	10	affect	affect	VERB
cjfa-35471	476	11	the	the	DET
cjfa-35471	476	12	behavior	behavior	NOUN
cjfa-35471	476	13	of	of	ADP
cjfa-35471	476	14	the	the	DET
cjfa-35471	476	15	firms	firm	NOUN
cjfa-35471	476	16	if	if	SCONJ
cjfa-35471	476	17	the	the	DET
cjfa-35471	476	18	interest	interest	NOUN
cjfa-35471	476	19	rates	rate	NOUN
cjfa-35471	476	20	are	be	AUX
cjfa-35471	476	21	very	very	ADV
cjfa-35471	476	22	low	low	ADJ
cjfa-35471	476	23	as	as	SCONJ
cjfa-35471	476	24	they	they	PRON
cjfa-35471	476	25	are	be	AUX
cjfa-35471	476	26	now	now	ADV
cjfa-35471	476	27	in	in	ADP
cjfa-35471	476	28	many	many	ADJ
cjfa-35471	476	29	developed	develop	VERB
cjfa-35471	476	30	nations	nation	NOUN
cjfa-35471	476	31	since	since	SCONJ
cjfa-35471	476	32	the	the	DET
cjfa-35471	476	33	term	term	NOUN
cjfa-35471	476	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	476	35	in	in	ADP
cjfa-35471	476	36	and	and	CCONJ
cjfa-35471	476	37	then	then	ADV
cjfa-35471	476	38	using	use	VERB
cjfa-35471	476	39	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	476	40	𝑢	𝑢	PROPN
cjfa-35471	476	41	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	476	42	,	,	PUNCT
cjfa-35471	476	43	equation	equation	NOUN
cjfa-35471	476	44	(	(	PUNCT
cjfa-35471	476	45	1	1	NUM
cjfa-35471	476	46	)	)	PUNCT
cjfa-35471	476	47	,	,	PUNCT
cjfa-35471	476	48	and	and	CCONJ
cjfa-35471	476	49	the	the	DET
cjfa-35471	476	50	conditions	condition	NOUN
cjfa-35471	476	51	(	(	PUNCT
cjfa-35471	476	52	the	the	DET
cjfa-35471	476	53	necessary	necessary	ADJ
cjfa-35471	476	54	condition	condition	NOUN
cjfa-35471	476	55	to	to	PART
cjfa-35471	476	56	keep	keep	VERB
cjfa-35471	476	57	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	476	58	𝑢	𝑢	ADP
cjfa-35471	476	59	𝐼	𝐼	PROPN
cjfa-35471	476	60	optimal	optimal	ADJ
cjfa-35471	476	61	)	)	PUNCT
cjfa-35471	476	62	developed	develop	VERB
cjfa-35471	476	63	by	by	ADP
cjfa-35471	476	64	pontryagin	pontryagin	NOUN
cjfa-35471	476	65	,	,	PUNCT
cjfa-35471	476	66	boltyanskii	boltyanskii	ADJ
cjfa-35471	476	67	,	,	PUNCT
cjfa-35471	476	68	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	476	69	and	and	CCONJ
cjfa-35471	476	70	mishechenko	mishechenko	NOUN
cjfa-35471	476	71	(	(	PUNCT
cjfa-35471	476	72	1962	1962	NUM
cjfa-35471	476	73	)	)	PUNCT
cjfa-35471	476	74	,	,	PUNCT
cjfa-35471	476	75	hestenes	hestene	NOUN
cjfa-35471	476	76	(	(	PUNCT
cjfa-35471	476	77	1966	1966	NUM
cjfa-35471	476	78	)	)	PUNCT
cjfa-35471	476	79	,	,	PUNCT
cjfa-35471	476	80	kamien	kamien	NOUN
cjfa-35471	476	81	and	and	CCONJ
cjfa-35471	476	82	schwartz	schwartz	PROPN
cjfa-35471	476	83	(	(	PUNCT
cjfa-35471	476	84	2012	2012	NUM
cjfa-35471	476	85	)	)	PUNCT
cjfa-35471	476	86	among	among	ADP
cjfa-35471	476	87	many	many	ADJ
cjfa-35471	476	88	others	other	NOUN
cjfa-35471	476	89	,	,	PUNCT
cjfa-35471	476	90	we	we	PRON
cjfa-35471	476	91	have	have	AUX
cjfa-35471	476	92	;	;	PUNCT
cjfa-35471	476	93	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	476	94	�	�	NOUN
cjfa-35471	476	95	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	476	96	≤	≤	PUNCT
cjfa-35471	476	97	𝐼	𝐼	PROPN
cjfa-35471	476	98	for	for	ADP
cjfa-35471	476	99	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	476	100	�	�	PROPN
cjfa-35471	476	101	≤	≤	NUM
cjfa-35471	477	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	477	2	≤	≤	NUM
cjfa-35471	477	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	477	4	�	�	PROPN
cjfa-35471	477	5	implies	imply	VERB
cjfa-35471	477	6	:	:	PUNCT
cjfa-35471	477	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	477	8	�	�	PROPN
cjfa-35471	477	9	�	�	PROPN
cjfa-35471	477	10	�	�	PROPN
cjfa-35471	477	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	477	12	�	�	PROPN
cjfa-35471	477	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	477	14	�	�	PROPN
cjfa-35471	477	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	477	16	≤	≤	PUNCT
cjfa-35471	477	17	ℎ	ℎ	PROPN
cjfa-35471	477	18	+	+	PROPN
cjfa-35471	477	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	477	20	�	�	PROPN
cjfa-35471	477	21	�	�	PROPN
cjfa-35471	477	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	477	23	�	�	PROPN
cjfa-35471	477	24	(	(	PUNCT
cjfa-35471	477	25	4	4	NUM
cjfa-35471	477	26	)	)	PUNCT
cjfa-35471	477	27	where	where	SCONJ
cjfa-35471	477	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	477	29	𝑢	𝑢	PROPN
cjfa-35471	477	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	477	31	�	�	NOUN
cjfa-35471	477	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	477	33	denotes	denote	VERB
cjfa-35471	477	34	the	the	DET
cjfa-35471	477	35	interest	interest	NOUN
cjfa-35471	477	36	rate	rate	NOUN
cjfa-35471	477	37	.	.	PUNCT
cjfa-35471	478	1	as	as	ADV
cjfa-35471	478	2	long	long	ADV
cjfa-35471	478	3	as	as	SCONJ
cjfa-35471	478	4	the	the	DET
cjfa-35471	478	5	condition	condition	NOUN
cjfa-35471	478	6	specified	specify	VERB
cjfa-35471	478	7	by	by	ADP
cjfa-35471	478	8	this	this	DET
cjfa-35471	478	9	inequality	inequality	NOUN
cjfa-35471	478	10	is	be	AUX
cjfa-35471	478	11	satisfied	satisfied	ADJ
cjfa-35471	478	12	it	it	PRON
cjfa-35471	478	13	will	will	AUX
cjfa-35471	478	14	be	be	AUX
cjfa-35471	478	15	optimal	optimal	ADJ
cjfa-35471	478	16	to	to	PART
cjfa-35471	478	17	keep	keep	VERB
cjfa-35471	478	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	478	19	𝑢	𝑢	ADP
cjfa-35471	478	20	𝐼	𝐼	ADP
cjfa-35471	478	21	implying	imply	VERB
cjfa-35471	478	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	478	23	𝑢	𝑢	PRON
cjfa-35471	478	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	478	25	this	this	PRON
cjfa-35471	478	26	means	mean	VERB
cjfa-35471	478	27	that	that	SCONJ
cjfa-35471	478	28	during	during	ADP
cjfa-35471	478	29	the	the	DET
cjfa-35471	478	30	intervals	interval	NOUN
cjfa-35471	478	31	where	where	SCONJ
cjfa-35471	478	32	this	this	DET
cjfa-35471	478	33	inequality	inequality	NOUN
cjfa-35471	478	34	is	be	AUX
cjfa-35471	478	35	satisfied	satisfied	ADJ
cjfa-35471	478	36	the	the	DET
cjfa-35471	478	37	firm	firm	NOUN
cjfa-35471	478	38	will	will	AUX
cjfa-35471	478	39	produce	produce	VERB
cjfa-35471	478	40	just	just	ADV
cjfa-35471	478	41	enough	enough	ADJ
cjfa-35471	478	42	to	to	PART
cjfa-35471	478	43	satisfy	satisfy	VERB
cjfa-35471	478	44	the	the	DET
cjfa-35471	478	45	demand	demand	NOUN
cjfa-35471	478	46	.	.	PUNCT
cjfa-35471	479	1	so	so	ADV
cjfa-35471	479	2	,	,	PUNCT
cjfa-35471	479	3	the	the	DET
cjfa-35471	479	4	condition	condition	NOUN
cjfa-35471	479	5	above	above	ADV
cjfa-35471	479	6	will	will	AUX
cjfa-35471	479	7	synthesize	synthesize	VERB
cjfa-35471	479	8	the	the	DET
cjfa-35471	479	9	periods	period	NOUN
cjfa-35471	479	10	where	where	SCONJ
cjfa-35471	479	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	479	12	𝑢	𝑢	PRON
cjfa-35471	479	13	𝐼	𝐼	PROPN
cjfa-35471	479	14	or	or	CCONJ
cjfa-35471	479	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	479	16	𝑢	𝑢	PROPN
cjfa-35471	479	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	479	18	and	and	CCONJ
cjfa-35471	479	19	the	the	DET
cjfa-35471	479	20	periods	period	NOUN
cjfa-35471	479	21	where	where	SCONJ
cjfa-35471	479	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	479	23	𝐼	𝐼	ADP
cjfa-35471	479	24	𝐼.	𝐼.	PROPN
cjfa-35471	479	25	notice	notice	VERB
cjfa-35471	479	26	that	that	SCONJ
cjfa-35471	479	27	for	for	ADP
cjfa-35471	479	28	the	the	DET
cjfa-35471	479	29	condition	condition	NOUN
cjfa-35471	479	30	above	above	ADV
cjfa-35471	479	31	(	(	PUNCT
cjfa-35471	479	32	equation	equation	NOUN
cjfa-35471	479	33	4	4	NUM
cjfa-35471	479	34	)	)	PUNCT
cjfa-35471	479	35	to	to	PART
cjfa-35471	479	36	be	be	AUX
cjfa-35471	479	37	kept	keep	VERB
cjfa-35471	479	38	satisfied	satisfied	ADJ
cjfa-35471	479	39	depends	depend	VERB
cjfa-35471	479	40	on	on	ADP
cjfa-35471	479	41	ℎ	ℎ	PROPN
cjfa-35471	479	42	(	(	PUNCT
cjfa-35471	479	43	inventory	inventory	NOUN
cjfa-35471	479	44	holding	hold	VERB
cjfa-35471	479	45	cost	cost	NOUN
cjfa-35471	479	46	)	)	PUNCT
cjfa-35471	479	47	,	,	PUNCT
cjfa-35471	479	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	479	49	the	the	DET
cjfa-35471	479	50	interest	interest	NOUN
cjfa-35471	479	51	rates	rate	NOUN
cjfa-35471	479	52	,	,	PUNCT
cjfa-35471	479	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	479	54	,	,	PUNCT
cjfa-35471	479	55	the	the	DET
cjfa-35471	479	56	marginal	marginal	ADJ
cjfa-35471	479	57	cost	cost	NOUN
cjfa-35471	479	58	of	of	ADP
cjfa-35471	479	59	production	production	NOUN
cjfa-35471	479	60	,	,	PUNCT
cjfa-35471	479	61	and	and	CCONJ
cjfa-35471	479	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	479	63	change	change	NOUN
cjfa-35471	479	64	in	in	ADP
cjfa-35471	479	65	the	the	DET
cjfa-35471	479	66	marginal	marginal	ADJ
cjfa-35471	479	67	cost	cost	NOUN
cjfa-35471	479	68	.	.	PUNCT
cjfa-35471	480	1	following	follow	VERB
cjfa-35471	480	2	conclusions	conclusion	NOUN
cjfa-35471	480	3	can	can	AUX
cjfa-35471	480	4	be	be	AUX
cjfa-35471	480	5	made	make	VERB
cjfa-35471	480	6	even	even	ADV
cjfa-35471	480	7	without	without	ADP
cjfa-35471	480	8	specific	specific	ADJ
cjfa-35471	480	9	forms	form	NOUN
cjfa-35471	480	10	of	of	ADP
cjfa-35471	480	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	480	12	,	,	PUNCT
cjfa-35471	480	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	480	14	,	,	PUNCT
cjfa-35471	480	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	480	16	and	and	CCONJ
cjfa-35471	480	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	480	18	on	on	ADP
cjfa-35471	480	19	the	the	DET
cjfa-35471	480	20	basis	basis	NOUN
cjfa-35471	480	21	of	of	ADP
cjfa-35471	480	22	equation	equation	NOUN
cjfa-35471	480	23	(	(	PUNCT
cjfa-35471	480	24	4	4	NUM
cjfa-35471	480	25	):	):	PUNCT
cjfa-35471	480	26	1	1	NUM
cjfa-35471	480	27	.	.	PUNCT
cjfa-35471	481	1	the	the	DET
cjfa-35471	481	2	firm	firm	NOUN
cjfa-35471	481	3	will	will	AUX
cjfa-35471	481	4	keep	keep	VERB
cjfa-35471	481	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	481	6	𝑢	𝑢	ADP
cjfa-35471	481	7	𝐼	𝐼	PROPN
cjfa-35471	481	8	as	as	ADV
cjfa-35471	481	9	long	long	ADV
cjfa-35471	481	10	as	as	SCONJ
cjfa-35471	481	11	demand	demand	NOUN
cjfa-35471	481	12	is	be	AUX
cjfa-35471	481	13	falling	fall	VERB
cjfa-35471	481	14	or	or	CCONJ
cjfa-35471	481	15	constant	constant	ADJ
cjfa-35471	481	16	i.e.	i.e.	X
cjfa-35471	481	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	481	18	0	0	NOUN
cjfa-35471	481	19	implying	imply	VERB
cjfa-35471	481	20	that	that	SCONJ
cjfa-35471	481	21	the	the	DET
cjfa-35471	481	22	firm	firm	NOUN
cjfa-35471	481	23	will	will	AUX
cjfa-35471	481	24	choose	choose	VERB
cjfa-35471	481	25	to	to	PART
cjfa-35471	481	26	produce	produce	VERB
cjfa-35471	481	27	just	just	ADV
cjfa-35471	481	28	enough	enough	ADJ
cjfa-35471	481	29	to	to	PART
cjfa-35471	481	30	meet	meet	VERB
cjfa-35471	481	31	the	the	DET
cjfa-35471	481	32	demand	demand	NOUN
cjfa-35471	481	33	if	if	SCONJ
cjfa-35471	481	34	demand	demand	NOUN
cjfa-35471	481	35	is	be	AUX
cjfa-35471	481	36	falling	fall	VERB
cjfa-35471	481	37	since	since	SCONJ
cjfa-35471	481	38	both	both	PRON
cjfa-35471	481	39	ℎ	ℎ	NOUN
cjfa-35471	481	40	and	and	CCONJ
cjfa-35471	481	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	481	42	are	be	AUX
cjfa-35471	481	43	positive	positive	ADJ
cjfa-35471	481	44	.	.	PUNCT
cjfa-35471	482	1	2	2	X
cjfa-35471	482	2	.	.	X
cjfa-35471	482	3	the	the	DET
cjfa-35471	482	4	firm	firm	NOUN
cjfa-35471	482	5	will	will	AUX
cjfa-35471	482	6	keep	keep	VERB
cjfa-35471	482	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	482	8	𝑢	𝑢	ADP
cjfa-35471	482	9	𝐼	𝐼	NOUN
cjfa-35471	482	10	even	even	ADV
cjfa-35471	482	11	if	if	SCONJ
cjfa-35471	482	12	demand	demand	NOUN
cjfa-35471	482	13	is	be	AUX
cjfa-35471	482	14	increasing	increase	VERB
cjfa-35471	482	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	482	16	𝑟	𝑟	X
cjfa-35471	482	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	482	18	but	but	CCONJ
cjfa-35471	482	19	the	the	DET
cjfa-35471	482	20	term	term	NOUN
cjfa-35471	482	21	ℎ	ℎ	PROPN
cjfa-35471	482	22	+	+	CCONJ
cjfa-35471	482	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	482	24	�	�	PROPN
cjfa-35471	482	25	�	�	PROPN
cjfa-35471	482	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	482	27	�	�	PROPN
cjfa-35471	482	28	is	be	AUX
cjfa-35471	482	29	large	large	ADJ
cjfa-35471	482	30	enough	enough	ADV
cjfa-35471	482	31	to	to	PART
cjfa-35471	482	32	keep	keep	VERB
cjfa-35471	482	33	inequality	inequality	NOUN
cjfa-35471	482	34	(	(	PUNCT
cjfa-35471	482	35	4	4	NUM
cjfa-35471	482	36	)	)	PUNCT
cjfa-35471	482	37	satisfied	satisfied	ADJ
cjfa-35471	482	38	.	.	PUNCT
cjfa-35471	483	1	decreasing	decrease	VERB
cjfa-35471	483	2	interest	interest	NOUN
cjfa-35471	483	3	rates	rate	NOUN
cjfa-35471	483	4	will	will	AUX
cjfa-35471	483	5	not	not	PART
cjfa-35471	483	6	be	be	AUX
cjfa-35471	483	7	a	a	DET
cjfa-35471	483	8	remedy	remedy	NOUN
cjfa-35471	483	9	in	in	ADP
cjfa-35471	483	10	this	this	DET
cjfa-35471	483	11	case	case	NOUN
cjfa-35471	483	12	if	if	SCONJ
cjfa-35471	483	13	they	they	PRON
cjfa-35471	483	14	are	be	AUX
cjfa-35471	483	15	already	already	ADV
cjfa-35471	483	16	low	low	ADJ
cjfa-35471	483	17	.	.	PUNCT
cjfa-35471	484	1	firms	firm	NOUN
cjfa-35471	484	2	where	where	SCONJ
cjfa-35471	484	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	484	4	�	�	PROPN
cjfa-35471	484	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	484	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	484	7	�	�	PROPN
cjfa-35471	484	8	is	be	AUX
cjfa-35471	484	9	low	low	ADJ
cjfa-35471	484	10	(	(	PUNCT
cjfa-35471	484	11	large	large	ADJ
cjfa-35471	484	12	and	and	CCONJ
cjfa-35471	484	13	already	already	ADV
cjfa-35471	484	14	very	very	ADV
cjfa-35471	484	15	efficient	efficient	ADJ
cjfa-35471	484	16	firms	firm	NOUN
cjfa-35471	484	17	)	)	PUNCT
cjfa-35471	484	18	will	will	AUX
cjfa-35471	484	19	have	have	VERB
cjfa-35471	484	20	more	more	ADJ
cjfa-35471	484	21	difficulty	difficulty	NOUN
cjfa-35471	484	22	to	to	PART
cjfa-35471	484	23	produce	produce	VERB
cjfa-35471	484	24	to	to	PART
cjfa-35471	484	25	build	build	VERB
cjfa-35471	484	26	up	up	ADP
cjfa-35471	484	27	inventories	inventory	NOUN
cjfa-35471	484	28	.	.	PUNCT
cjfa-35471	485	1	currently	currently	ADV
cjfa-35471	485	2	,	,	PUNCT
cjfa-35471	485	3	this	this	PRON
cjfa-35471	485	4	seems	seem	VERB
cjfa-35471	485	5	to	to	PART
cjfa-35471	485	6	be	be	AUX
cjfa-35471	485	7	the	the	DET
cjfa-35471	485	8	case	case	NOUN
cjfa-35471	485	9	in	in	ADP
cjfa-35471	485	10	major	major	ADJ
cjfa-35471	485	11	economies	economy	NOUN
cjfa-35471	485	12	.	.	PUNCT
cjfa-35471	486	1	3	3	X
cjfa-35471	486	2	.	.	X
cjfa-35471	486	3	higher	high	ADJ
cjfa-35471	486	4	interest	interest	NOUN
cjfa-35471	486	5	rates	rate	NOUN
cjfa-35471	486	6	and	and	CCONJ
cjfa-35471	486	7	the	the	DET
cjfa-35471	486	8	use	use	NOUN
cjfa-35471	486	9	of	of	ADP
cjfa-35471	486	10	inefficient	inefficient	ADJ
cjfa-35471	486	11	technologies	technology	NOUN
cjfa-35471	486	12	(	(	PUNCT
cjfa-35471	486	13	large	large	ADJ
cjfa-35471	486	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	486	15	)	)	PUNCT
cjfa-35471	486	16	implies	imply	VERB
cjfa-35471	486	17	high	high	ADJ
cjfa-35471	486	18	marginal	marginal	ADJ
cjfa-35471	486	19	cost	cost	NOUN
cjfa-35471	486	20	)	)	PUNCT
cjfa-35471	486	21	will	will	AUX
cjfa-35471	486	22	induce	induce	VERB
cjfa-35471	486	23	firms	firm	NOUN
cjfa-35471	486	24	to	to	PART
cjfa-35471	486	25	wait	wait	VERB
cjfa-35471	486	26	longer	long	ADV
cjfa-35471	486	27	for	for	ADP
cjfa-35471	486	28	inventory	inventory	NOUN
cjfa-35471	486	29	build	build	NOUN
cjfa-35471	486	30	-	-	PUNCT
cjfa-35471	486	31	up	up	NOUN
cjfa-35471	486	32	even	even	ADV
cjfa-35471	486	33	if	if	SCONJ
cjfa-35471	486	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	486	35	is	be	AUX
cjfa-35471	486	36	positive	positive	ADJ
cjfa-35471	486	37	.	.	PUNCT
cjfa-35471	487	1	4	4	X
cjfa-35471	487	2	.	.	X
cjfa-35471	487	3	the	the	DET
cjfa-35471	487	4	level	level	NOUN
cjfa-35471	487	5	of	of	ADP
cjfa-35471	487	6	technology	technology	NOUN
cjfa-35471	487	7	used	use	VERB
cjfa-35471	487	8	will	will	AUX
cjfa-35471	487	9	not	not	PART
cjfa-35471	487	10	affect	affect	VERB
cjfa-35471	487	11	the	the	DET
cjfa-35471	487	12	behavior	behavior	NOUN
cjfa-35471	487	13	of	of	ADP
cjfa-35471	487	14	the	the	DET
cjfa-35471	487	15	firms	firm	NOUN
cjfa-35471	487	16	if	if	SCONJ
cjfa-35471	487	17	the	the	DET
cjfa-35471	487	18	interest	interest	NOUN
cjfa-35471	487	19	rates	rate	NOUN
cjfa-35471	487	20	are	be	AUX
cjfa-35471	487	21	very	very	ADV
cjfa-35471	487	22	low	low	ADJ
cjfa-35471	487	23	as	as	SCONJ
cjfa-35471	487	24	they	they	PRON
cjfa-35471	487	25	are	be	AUX
cjfa-35471	487	26	now	now	ADV
cjfa-35471	487	27	in	in	ADP
cjfa-35471	487	28	many	many	ADJ
cjfa-35471	487	29	developed	develop	VERB
cjfa-35471	487	30	nations	nation	NOUN
cjfa-35471	487	31	since	since	SCONJ
cjfa-35471	487	32	the	the	DET
cjfa-35471	487	33	term	term	NOUN
cjfa-35471	487	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	487	35	in	in	ADP
cjfa-35471	487	36	are	be	AUX
cjfa-35471	487	37	positive	positive	ADJ
cjfa-35471	487	38	.	.	PUNCT
cjfa-35471	488	1	2	2	X
cjfa-35471	488	2	.	.	X
cjfa-35471	488	3	the	the	DET
cjfa-35471	488	4	firm	firm	NOUN
cjfa-35471	488	5	will	will	AUX
cjfa-35471	488	6	keep	keep	VERB
cjfa-35471	488	7	l(t	l(t	NOUN
cjfa-35471	488	8	)	)	PUNCT
cjfa-35471	489	1	=	=	SYM
cjfa-35471	489	2	0	0	PUNCT
cjfa-35471	490	1	even	even	ADV
cjfa-35471	490	2	if	if	SCONJ
cjfa-35471	490	3	demand	demand	NOUN
cjfa-35471	490	4	is	be	AUX
cjfa-35471	490	5	increasing	increase	VERB
cjfa-35471	490	6	then	then	ADV
cjfa-35471	490	7	using	use	VERB
cjfa-35471	490	8	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	490	9	𝑢	𝑢	PROPN
cjfa-35471	490	10	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	490	11	,	,	PUNCT
cjfa-35471	490	12	equation	equation	NOUN
cjfa-35471	490	13	(	(	PUNCT
cjfa-35471	490	14	1	1	NUM
cjfa-35471	490	15	)	)	PUNCT
cjfa-35471	490	16	,	,	PUNCT
cjfa-35471	490	17	and	and	CCONJ
cjfa-35471	490	18	the	the	DET
cjfa-35471	490	19	conditions	condition	NOUN
cjfa-35471	490	20	(	(	PUNCT
cjfa-35471	490	21	the	the	DET
cjfa-35471	490	22	necessary	necessary	ADJ
cjfa-35471	490	23	condition	condition	NOUN
cjfa-35471	490	24	to	to	PART
cjfa-35471	490	25	keep	keep	VERB
cjfa-35471	490	26	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	490	27	𝑢	𝑢	ADP
cjfa-35471	490	28	𝐼	𝐼	PROPN
cjfa-35471	490	29	optimal	optimal	ADJ
cjfa-35471	490	30	)	)	PUNCT
cjfa-35471	490	31	developed	develop	VERB
cjfa-35471	490	32	by	by	ADP
cjfa-35471	490	33	pontryagin	pontryagin	NOUN
cjfa-35471	490	34	,	,	PUNCT
cjfa-35471	490	35	boltyanskii	boltyanskii	ADJ
cjfa-35471	490	36	,	,	PUNCT
cjfa-35471	490	37	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	490	38	and	and	CCONJ
cjfa-35471	490	39	mishechenko	mishechenko	NOUN
cjfa-35471	490	40	(	(	PUNCT
cjfa-35471	490	41	1962	1962	NUM
cjfa-35471	490	42	)	)	PUNCT
cjfa-35471	490	43	,	,	PUNCT
cjfa-35471	490	44	hestenes	hestene	NOUN
cjfa-35471	490	45	(	(	PUNCT
cjfa-35471	490	46	1966	1966	NUM
cjfa-35471	490	47	)	)	PUNCT
cjfa-35471	490	48	,	,	PUNCT
cjfa-35471	490	49	kamien	kamien	NOUN
cjfa-35471	490	50	and	and	CCONJ
cjfa-35471	490	51	schwartz	schwartz	PROPN
cjfa-35471	490	52	(	(	PUNCT
cjfa-35471	490	53	2012	2012	NUM
cjfa-35471	490	54	)	)	PUNCT
cjfa-35471	490	55	among	among	ADP
cjfa-35471	490	56	many	many	ADJ
cjfa-35471	490	57	others	other	NOUN
cjfa-35471	490	58	,	,	PUNCT
cjfa-35471	490	59	we	we	PRON
cjfa-35471	490	60	have	have	VERB
cjfa-35471	490	61	;	;	PUNCT
cjfa-35471	490	62	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	490	63	�	�	NOUN
cjfa-35471	490	64	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	490	65	≤	≤	PUNCT
cjfa-35471	490	66	𝐼	𝐼	PROPN
cjfa-35471	490	67	for	for	ADP
cjfa-35471	490	68	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	490	69	�	�	PROPN
cjfa-35471	490	70	≤	≤	NUM
cjfa-35471	491	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	491	2	≤	≤	NUM
cjfa-35471	491	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	491	4	�	�	PROPN
cjfa-35471	491	5	implies	imply	VERB
cjfa-35471	491	6	:	:	PUNCT
cjfa-35471	491	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	491	8	�	�	PROPN
cjfa-35471	491	9	�	�	PROPN
cjfa-35471	491	10	�	�	PROPN
cjfa-35471	491	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	491	12	�	�	PROPN
cjfa-35471	491	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	491	14	�	�	PROPN
cjfa-35471	491	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	491	16	≤	≤	PUNCT
cjfa-35471	491	17	ℎ	ℎ	PROPN
cjfa-35471	491	18	+	+	PROPN
cjfa-35471	491	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	491	20	�	�	PROPN
cjfa-35471	491	21	�	�	PROPN
cjfa-35471	491	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	491	23	�	�	PROPN
cjfa-35471	491	24	(	(	PUNCT
cjfa-35471	491	25	4	4	NUM
cjfa-35471	491	26	)	)	PUNCT
cjfa-35471	491	27	where	where	SCONJ
cjfa-35471	491	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	491	29	𝑢	𝑢	PROPN
cjfa-35471	491	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	491	31	�	�	NOUN
cjfa-35471	491	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	491	33	denotes	denote	VERB
cjfa-35471	491	34	the	the	DET
cjfa-35471	491	35	interest	interest	NOUN
cjfa-35471	491	36	rate	rate	NOUN
cjfa-35471	491	37	.	.	PUNCT
cjfa-35471	492	1	as	as	ADV
cjfa-35471	492	2	long	long	ADV
cjfa-35471	492	3	as	as	SCONJ
cjfa-35471	492	4	the	the	DET
cjfa-35471	492	5	condition	condition	NOUN
cjfa-35471	492	6	specified	specify	VERB
cjfa-35471	492	7	by	by	ADP
cjfa-35471	492	8	this	this	DET
cjfa-35471	492	9	inequality	inequality	NOUN
cjfa-35471	492	10	is	be	AUX
cjfa-35471	492	11	satisfied	satisfied	ADJ
cjfa-35471	492	12	it	it	PRON
cjfa-35471	492	13	will	will	AUX
cjfa-35471	492	14	be	be	AUX
cjfa-35471	492	15	optimal	optimal	ADJ
cjfa-35471	492	16	to	to	PART
cjfa-35471	492	17	keep	keep	VERB
cjfa-35471	492	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	492	19	𝑢	𝑢	ADP
cjfa-35471	492	20	𝐼	𝐼	ADP
cjfa-35471	492	21	implying	imply	VERB
cjfa-35471	492	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	492	23	𝑢	𝑢	PRON
cjfa-35471	492	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	492	25	this	this	PRON
cjfa-35471	492	26	means	mean	VERB
cjfa-35471	492	27	that	that	SCONJ
cjfa-35471	492	28	during	during	ADP
cjfa-35471	492	29	the	the	DET
cjfa-35471	492	30	intervals	interval	NOUN
cjfa-35471	492	31	where	where	SCONJ
cjfa-35471	492	32	this	this	DET
cjfa-35471	492	33	inequality	inequality	NOUN
cjfa-35471	492	34	is	be	AUX
cjfa-35471	492	35	satisfied	satisfied	ADJ
cjfa-35471	492	36	the	the	DET
cjfa-35471	492	37	firm	firm	NOUN
cjfa-35471	492	38	will	will	AUX
cjfa-35471	492	39	produce	produce	VERB
cjfa-35471	492	40	just	just	ADV
cjfa-35471	492	41	enough	enough	ADJ
cjfa-35471	492	42	to	to	PART
cjfa-35471	492	43	satisfy	satisfy	VERB
cjfa-35471	492	44	the	the	DET
cjfa-35471	492	45	demand	demand	NOUN
cjfa-35471	492	46	.	.	PUNCT
cjfa-35471	493	1	so	so	ADV
cjfa-35471	493	2	,	,	PUNCT
cjfa-35471	493	3	the	the	DET
cjfa-35471	493	4	condition	condition	NOUN
cjfa-35471	493	5	above	above	ADV
cjfa-35471	493	6	will	will	AUX
cjfa-35471	493	7	synthesize	synthesize	VERB
cjfa-35471	493	8	the	the	DET
cjfa-35471	493	9	periods	period	NOUN
cjfa-35471	493	10	where	where	SCONJ
cjfa-35471	493	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	493	12	𝑢	𝑢	PRON
cjfa-35471	493	13	𝐼	𝐼	PROPN
cjfa-35471	493	14	or	or	CCONJ
cjfa-35471	493	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	493	16	𝑢	𝑢	PROPN
cjfa-35471	493	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	493	18	and	and	CCONJ
cjfa-35471	493	19	the	the	DET
cjfa-35471	493	20	periods	period	NOUN
cjfa-35471	493	21	where	where	SCONJ
cjfa-35471	493	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	493	23	𝐼	𝐼	ADP
cjfa-35471	493	24	𝐼.	𝐼.	PROPN
cjfa-35471	493	25	notice	notice	VERB
cjfa-35471	493	26	that	that	SCONJ
cjfa-35471	493	27	for	for	ADP
cjfa-35471	493	28	the	the	DET
cjfa-35471	493	29	condition	condition	NOUN
cjfa-35471	493	30	above	above	ADV
cjfa-35471	493	31	(	(	PUNCT
cjfa-35471	493	32	equation	equation	NOUN
cjfa-35471	493	33	4	4	NUM
cjfa-35471	493	34	)	)	PUNCT
cjfa-35471	493	35	to	to	PART
cjfa-35471	493	36	be	be	AUX
cjfa-35471	493	37	kept	keep	VERB
cjfa-35471	493	38	satisfied	satisfied	ADJ
cjfa-35471	493	39	depends	depend	VERB
cjfa-35471	493	40	on	on	ADP
cjfa-35471	493	41	ℎ	ℎ	PROPN
cjfa-35471	493	42	(	(	PUNCT
cjfa-35471	493	43	inventory	inventory	NOUN
cjfa-35471	493	44	holding	hold	VERB
cjfa-35471	493	45	cost	cost	NOUN
cjfa-35471	493	46	)	)	PUNCT
cjfa-35471	493	47	,	,	PUNCT
cjfa-35471	493	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	493	49	the	the	DET
cjfa-35471	493	50	interest	interest	NOUN
cjfa-35471	493	51	rates	rate	NOUN
cjfa-35471	493	52	,	,	PUNCT
cjfa-35471	493	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	493	54	,	,	PUNCT
cjfa-35471	493	55	the	the	DET
cjfa-35471	493	56	marginal	marginal	ADJ
cjfa-35471	493	57	cost	cost	NOUN
cjfa-35471	493	58	of	of	ADP
cjfa-35471	493	59	production	production	NOUN
cjfa-35471	493	60	,	,	PUNCT
cjfa-35471	493	61	and	and	CCONJ
cjfa-35471	493	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	493	63	change	change	NOUN
cjfa-35471	493	64	in	in	ADP
cjfa-35471	493	65	the	the	DET
cjfa-35471	493	66	marginal	marginal	ADJ
cjfa-35471	493	67	cost	cost	NOUN
cjfa-35471	493	68	.	.	PUNCT
cjfa-35471	494	1	following	follow	VERB
cjfa-35471	494	2	conclusions	conclusion	NOUN
cjfa-35471	494	3	can	can	AUX
cjfa-35471	494	4	be	be	AUX
cjfa-35471	494	5	made	make	VERB
cjfa-35471	494	6	even	even	ADV
cjfa-35471	494	7	without	without	ADP
cjfa-35471	494	8	specific	specific	ADJ
cjfa-35471	494	9	forms	form	NOUN
cjfa-35471	494	10	of	of	ADP
cjfa-35471	494	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	494	12	,	,	PUNCT
cjfa-35471	494	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	494	14	,	,	PUNCT
cjfa-35471	494	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	494	16	and	and	CCONJ
cjfa-35471	494	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	494	18	on	on	ADP
cjfa-35471	494	19	the	the	DET
cjfa-35471	494	20	basis	basis	NOUN
cjfa-35471	494	21	of	of	ADP
cjfa-35471	494	22	equation	equation	NOUN
cjfa-35471	494	23	(	(	PUNCT
cjfa-35471	494	24	4	4	NUM
cjfa-35471	494	25	):	):	PUNCT
cjfa-35471	494	26	1	1	NUM
cjfa-35471	494	27	.	.	PUNCT
cjfa-35471	495	1	the	the	DET
cjfa-35471	495	2	firm	firm	NOUN
cjfa-35471	495	3	will	will	AUX
cjfa-35471	495	4	keep	keep	VERB
cjfa-35471	495	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	495	6	𝑢	𝑢	ADP
cjfa-35471	495	7	𝐼	𝐼	PROPN
cjfa-35471	495	8	as	as	ADV
cjfa-35471	495	9	long	long	ADV
cjfa-35471	495	10	as	as	SCONJ
cjfa-35471	495	11	demand	demand	NOUN
cjfa-35471	495	12	is	be	AUX
cjfa-35471	495	13	falling	fall	VERB
cjfa-35471	495	14	or	or	CCONJ
cjfa-35471	495	15	constant	constant	ADJ
cjfa-35471	495	16	i.e.	i.e.	X
cjfa-35471	495	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	495	18	0	0	NOUN
cjfa-35471	495	19	implying	imply	VERB
cjfa-35471	495	20	that	that	SCONJ
cjfa-35471	495	21	the	the	DET
cjfa-35471	495	22	firm	firm	NOUN
cjfa-35471	495	23	will	will	AUX
cjfa-35471	495	24	choose	choose	VERB
cjfa-35471	495	25	to	to	PART
cjfa-35471	495	26	produce	produce	VERB
cjfa-35471	495	27	just	just	ADV
cjfa-35471	495	28	enough	enough	ADJ
cjfa-35471	495	29	to	to	PART
cjfa-35471	495	30	meet	meet	VERB
cjfa-35471	495	31	the	the	DET
cjfa-35471	495	32	demand	demand	NOUN
cjfa-35471	495	33	if	if	SCONJ
cjfa-35471	495	34	demand	demand	NOUN
cjfa-35471	495	35	is	be	AUX
cjfa-35471	495	36	falling	fall	VERB
cjfa-35471	495	37	since	since	SCONJ
cjfa-35471	495	38	both	both	PRON
cjfa-35471	495	39	ℎ	ℎ	NOUN
cjfa-35471	495	40	and	and	CCONJ
cjfa-35471	495	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	495	42	are	be	AUX
cjfa-35471	495	43	positive	positive	ADJ
cjfa-35471	495	44	.	.	PUNCT
cjfa-35471	496	1	2	2	X
cjfa-35471	496	2	.	.	X
cjfa-35471	496	3	the	the	DET
cjfa-35471	496	4	firm	firm	NOUN
cjfa-35471	496	5	will	will	AUX
cjfa-35471	496	6	keep	keep	VERB
cjfa-35471	496	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	496	8	𝑢	𝑢	ADP
cjfa-35471	496	9	𝐼	𝐼	NOUN
cjfa-35471	496	10	even	even	ADV
cjfa-35471	496	11	if	if	SCONJ
cjfa-35471	496	12	demand	demand	NOUN
cjfa-35471	496	13	is	be	AUX
cjfa-35471	496	14	increasing	increase	VERB
cjfa-35471	496	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	496	16	𝑟	𝑟	X
cjfa-35471	496	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	496	18	but	but	CCONJ
cjfa-35471	496	19	the	the	DET
cjfa-35471	496	20	term	term	NOUN
cjfa-35471	496	21	ℎ	ℎ	PROPN
cjfa-35471	496	22	+	+	CCONJ
cjfa-35471	496	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	496	24	�	�	PROPN
cjfa-35471	496	25	�	�	PROPN
cjfa-35471	496	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	496	27	�	�	PROPN
cjfa-35471	496	28	is	be	AUX
cjfa-35471	496	29	large	large	ADJ
cjfa-35471	496	30	enough	enough	ADV
cjfa-35471	496	31	to	to	PART
cjfa-35471	496	32	keep	keep	VERB
cjfa-35471	496	33	inequality	inequality	NOUN
cjfa-35471	496	34	(	(	PUNCT
cjfa-35471	496	35	4	4	NUM
cjfa-35471	496	36	)	)	PUNCT
cjfa-35471	496	37	satisfied	satisfied	ADJ
cjfa-35471	496	38	.	.	PUNCT
cjfa-35471	497	1	decreasing	decrease	VERB
cjfa-35471	497	2	interest	interest	NOUN
cjfa-35471	497	3	rates	rate	NOUN
cjfa-35471	497	4	will	will	AUX
cjfa-35471	497	5	not	not	PART
cjfa-35471	497	6	be	be	AUX
cjfa-35471	497	7	a	a	DET
cjfa-35471	497	8	remedy	remedy	NOUN
cjfa-35471	497	9	in	in	ADP
cjfa-35471	497	10	this	this	DET
cjfa-35471	497	11	case	case	NOUN
cjfa-35471	497	12	if	if	SCONJ
cjfa-35471	497	13	they	they	PRON
cjfa-35471	497	14	are	be	AUX
cjfa-35471	497	15	already	already	ADV
cjfa-35471	497	16	low	low	ADJ
cjfa-35471	497	17	.	.	PUNCT
cjfa-35471	498	1	firms	firm	NOUN
cjfa-35471	498	2	where	where	SCONJ
cjfa-35471	498	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	498	4	�	�	PROPN
cjfa-35471	498	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	498	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	498	7	�	�	PROPN
cjfa-35471	498	8	is	be	AUX
cjfa-35471	498	9	low	low	ADJ
cjfa-35471	498	10	(	(	PUNCT
cjfa-35471	498	11	large	large	ADJ
cjfa-35471	498	12	and	and	CCONJ
cjfa-35471	498	13	already	already	ADV
cjfa-35471	498	14	very	very	ADV
cjfa-35471	498	15	efficient	efficient	ADJ
cjfa-35471	498	16	firms	firm	NOUN
cjfa-35471	498	17	)	)	PUNCT
cjfa-35471	498	18	will	will	AUX
cjfa-35471	498	19	have	have	VERB
cjfa-35471	498	20	more	more	ADJ
cjfa-35471	498	21	difficulty	difficulty	NOUN
cjfa-35471	498	22	to	to	PART
cjfa-35471	498	23	produce	produce	VERB
cjfa-35471	498	24	to	to	PART
cjfa-35471	498	25	build	build	VERB
cjfa-35471	498	26	up	up	ADP
cjfa-35471	498	27	inventories	inventory	NOUN
cjfa-35471	498	28	.	.	PUNCT
cjfa-35471	499	1	currently	currently	ADV
cjfa-35471	499	2	,	,	PUNCT
cjfa-35471	499	3	this	this	PRON
cjfa-35471	499	4	seems	seem	VERB
cjfa-35471	499	5	to	to	PART
cjfa-35471	499	6	be	be	AUX
cjfa-35471	499	7	the	the	DET
cjfa-35471	499	8	case	case	NOUN
cjfa-35471	499	9	in	in	ADP
cjfa-35471	499	10	major	major	ADJ
cjfa-35471	499	11	economies	economy	NOUN
cjfa-35471	499	12	.	.	PUNCT
cjfa-35471	500	1	3	3	X
cjfa-35471	500	2	.	.	X
cjfa-35471	500	3	higher	high	ADJ
cjfa-35471	500	4	interest	interest	NOUN
cjfa-35471	500	5	rates	rate	NOUN
cjfa-35471	500	6	and	and	CCONJ
cjfa-35471	500	7	the	the	DET
cjfa-35471	500	8	use	use	NOUN
cjfa-35471	500	9	of	of	ADP
cjfa-35471	500	10	inefficient	inefficient	ADJ
cjfa-35471	500	11	technologies	technology	NOUN
cjfa-35471	500	12	(	(	PUNCT
cjfa-35471	500	13	large	large	ADJ
cjfa-35471	500	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	500	15	)	)	PUNCT
cjfa-35471	500	16	implies	imply	VERB
cjfa-35471	500	17	high	high	ADJ
cjfa-35471	500	18	marginal	marginal	ADJ
cjfa-35471	500	19	cost	cost	NOUN
cjfa-35471	500	20	)	)	PUNCT
cjfa-35471	500	21	will	will	AUX
cjfa-35471	500	22	induce	induce	VERB
cjfa-35471	500	23	firms	firm	NOUN
cjfa-35471	500	24	to	to	PART
cjfa-35471	500	25	wait	wait	VERB
cjfa-35471	500	26	longer	long	ADV
cjfa-35471	500	27	for	for	ADP
cjfa-35471	500	28	inventory	inventory	NOUN
cjfa-35471	500	29	build	build	NOUN
cjfa-35471	500	30	-	-	PUNCT
cjfa-35471	500	31	up	up	NOUN
cjfa-35471	500	32	even	even	ADV
cjfa-35471	500	33	if	if	SCONJ
cjfa-35471	500	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	500	35	is	be	AUX
cjfa-35471	500	36	positive	positive	ADJ
cjfa-35471	500	37	.	.	PUNCT
cjfa-35471	501	1	4	4	X
cjfa-35471	501	2	.	.	X
cjfa-35471	501	3	the	the	DET
cjfa-35471	501	4	level	level	NOUN
cjfa-35471	501	5	of	of	ADP
cjfa-35471	501	6	technology	technology	NOUN
cjfa-35471	501	7	used	use	VERB
cjfa-35471	501	8	will	will	AUX
cjfa-35471	501	9	not	not	PART
cjfa-35471	501	10	affect	affect	VERB
cjfa-35471	501	11	the	the	DET
cjfa-35471	501	12	behavior	behavior	NOUN
cjfa-35471	501	13	of	of	ADP
cjfa-35471	501	14	the	the	DET
cjfa-35471	501	15	firms	firm	NOUN
cjfa-35471	501	16	if	if	SCONJ
cjfa-35471	501	17	the	the	DET
cjfa-35471	501	18	interest	interest	NOUN
cjfa-35471	501	19	rates	rate	NOUN
cjfa-35471	501	20	are	be	AUX
cjfa-35471	501	21	very	very	ADV
cjfa-35471	501	22	low	low	ADJ
cjfa-35471	501	23	as	as	SCONJ
cjfa-35471	501	24	they	they	PRON
cjfa-35471	501	25	are	be	AUX
cjfa-35471	501	26	now	now	ADV
cjfa-35471	501	27	in	in	ADP
cjfa-35471	501	28	many	many	ADJ
cjfa-35471	501	29	developed	develop	VERB
cjfa-35471	501	30	nations	nation	NOUN
cjfa-35471	501	31	since	since	SCONJ
cjfa-35471	501	32	the	the	DET
cjfa-35471	501	33	term	term	NOUN
cjfa-35471	501	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	501	35	in	in	ADP
cjfa-35471	501	36	but	but	CCONJ
cjfa-35471	501	37	the	the	DET
cjfa-35471	501	38	term	term	NOUN
cjfa-35471	501	39	then	then	ADV
cjfa-35471	501	40	using	use	VERB
cjfa-35471	501	41	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	501	42	𝑢	𝑢	PROPN
cjfa-35471	501	43	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	501	44	,	,	PUNCT
cjfa-35471	501	45	equation	equation	NOUN
cjfa-35471	501	46	(	(	PUNCT
cjfa-35471	501	47	1	1	NUM
cjfa-35471	501	48	)	)	PUNCT
cjfa-35471	501	49	,	,	PUNCT
cjfa-35471	501	50	and	and	CCONJ
cjfa-35471	501	51	the	the	DET
cjfa-35471	501	52	conditions	condition	NOUN
cjfa-35471	501	53	(	(	PUNCT
cjfa-35471	501	54	the	the	DET
cjfa-35471	501	55	necessary	necessary	ADJ
cjfa-35471	501	56	condition	condition	NOUN
cjfa-35471	501	57	to	to	PART
cjfa-35471	501	58	keep	keep	VERB
cjfa-35471	501	59	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	501	60	𝑢	𝑢	ADP
cjfa-35471	501	61	𝐼	𝐼	PROPN
cjfa-35471	501	62	optimal	optimal	ADJ
cjfa-35471	501	63	)	)	PUNCT
cjfa-35471	501	64	developed	develop	VERB
cjfa-35471	501	65	by	by	ADP
cjfa-35471	501	66	pontryagin	pontryagin	NOUN
cjfa-35471	501	67	,	,	PUNCT
cjfa-35471	501	68	boltyanskii	boltyanskii	ADJ
cjfa-35471	501	69	,	,	PUNCT
cjfa-35471	501	70	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	501	71	and	and	CCONJ
cjfa-35471	501	72	mishechenko	mishechenko	NOUN
cjfa-35471	501	73	(	(	PUNCT
cjfa-35471	501	74	1962	1962	NUM
cjfa-35471	501	75	)	)	PUNCT
cjfa-35471	501	76	,	,	PUNCT
cjfa-35471	501	77	hestenes	hestene	NOUN
cjfa-35471	501	78	(	(	PUNCT
cjfa-35471	501	79	1966	1966	NUM
cjfa-35471	501	80	)	)	PUNCT
cjfa-35471	501	81	,	,	PUNCT
cjfa-35471	501	82	kamien	kamien	NOUN
cjfa-35471	501	83	and	and	CCONJ
cjfa-35471	501	84	schwartz	schwartz	PROPN
cjfa-35471	501	85	(	(	PUNCT
cjfa-35471	501	86	2012	2012	NUM
cjfa-35471	501	87	)	)	PUNCT
cjfa-35471	501	88	among	among	ADP
cjfa-35471	501	89	many	many	ADJ
cjfa-35471	501	90	others	other	NOUN
cjfa-35471	501	91	,	,	PUNCT
cjfa-35471	501	92	we	we	PRON
cjfa-35471	501	93	have	have	VERB
cjfa-35471	501	94	;	;	PUNCT
cjfa-35471	501	95	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	501	96	�	�	NOUN
cjfa-35471	501	97	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	501	98	≤	≤	PUNCT
cjfa-35471	501	99	𝐼	𝐼	PROPN
cjfa-35471	501	100	for	for	ADP
cjfa-35471	501	101	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	501	102	�	�	PROPN
cjfa-35471	501	103	≤	≤	NUM
cjfa-35471	502	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	502	2	≤	≤	NUM
cjfa-35471	502	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	502	4	�	�	PROPN
cjfa-35471	502	5	implies	imply	VERB
cjfa-35471	502	6	:	:	PUNCT
cjfa-35471	502	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	502	8	�	�	PROPN
cjfa-35471	502	9	�	�	PROPN
cjfa-35471	502	10	�	�	PROPN
cjfa-35471	502	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	502	12	�	�	PROPN
cjfa-35471	502	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	502	14	�	�	PROPN
cjfa-35471	502	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	502	16	≤	≤	PUNCT
cjfa-35471	502	17	ℎ	ℎ	PROPN
cjfa-35471	502	18	+	+	PROPN
cjfa-35471	502	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	502	20	�	�	PROPN
cjfa-35471	502	21	�	�	PROPN
cjfa-35471	502	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	502	23	�	�	PROPN
cjfa-35471	502	24	(	(	PUNCT
cjfa-35471	502	25	4	4	NUM
cjfa-35471	502	26	)	)	PUNCT
cjfa-35471	502	27	where	where	SCONJ
cjfa-35471	502	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	502	29	𝑢	𝑢	PROPN
cjfa-35471	502	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	502	31	�	�	NOUN
cjfa-35471	502	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	502	33	denotes	denote	VERB
cjfa-35471	502	34	the	the	DET
cjfa-35471	502	35	interest	interest	NOUN
cjfa-35471	502	36	rate	rate	NOUN
cjfa-35471	502	37	.	.	PUNCT
cjfa-35471	503	1	as	as	ADV
cjfa-35471	503	2	long	long	ADV
cjfa-35471	503	3	as	as	SCONJ
cjfa-35471	503	4	the	the	DET
cjfa-35471	503	5	condition	condition	NOUN
cjfa-35471	503	6	specified	specify	VERB
cjfa-35471	503	7	by	by	ADP
cjfa-35471	503	8	this	this	DET
cjfa-35471	503	9	inequality	inequality	NOUN
cjfa-35471	503	10	is	be	AUX
cjfa-35471	503	11	satisfied	satisfied	ADJ
cjfa-35471	503	12	it	it	PRON
cjfa-35471	503	13	will	will	AUX
cjfa-35471	503	14	be	be	AUX
cjfa-35471	503	15	optimal	optimal	ADJ
cjfa-35471	503	16	to	to	PART
cjfa-35471	503	17	keep	keep	VERB
cjfa-35471	503	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	503	19	𝑢	𝑢	ADP
cjfa-35471	503	20	𝐼	𝐼	ADP
cjfa-35471	503	21	implying	imply	VERB
cjfa-35471	503	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	503	23	𝑢	𝑢	PRON
cjfa-35471	503	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	503	25	this	this	PRON
cjfa-35471	503	26	means	mean	VERB
cjfa-35471	503	27	that	that	SCONJ
cjfa-35471	503	28	during	during	ADP
cjfa-35471	503	29	the	the	DET
cjfa-35471	503	30	intervals	interval	NOUN
cjfa-35471	503	31	where	where	SCONJ
cjfa-35471	503	32	this	this	DET
cjfa-35471	503	33	inequality	inequality	NOUN
cjfa-35471	503	34	is	be	AUX
cjfa-35471	503	35	satisfied	satisfied	ADJ
cjfa-35471	503	36	the	the	DET
cjfa-35471	503	37	firm	firm	NOUN
cjfa-35471	503	38	will	will	AUX
cjfa-35471	503	39	produce	produce	VERB
cjfa-35471	503	40	just	just	ADV
cjfa-35471	503	41	enough	enough	ADJ
cjfa-35471	503	42	to	to	PART
cjfa-35471	503	43	satisfy	satisfy	VERB
cjfa-35471	503	44	the	the	DET
cjfa-35471	503	45	demand	demand	NOUN
cjfa-35471	503	46	.	.	PUNCT
cjfa-35471	504	1	so	so	ADV
cjfa-35471	504	2	,	,	PUNCT
cjfa-35471	504	3	the	the	DET
cjfa-35471	504	4	condition	condition	NOUN
cjfa-35471	504	5	above	above	ADV
cjfa-35471	504	6	will	will	AUX
cjfa-35471	504	7	synthesize	synthesize	VERB
cjfa-35471	504	8	the	the	DET
cjfa-35471	504	9	periods	period	NOUN
cjfa-35471	504	10	where	where	SCONJ
cjfa-35471	504	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	504	12	𝑢	𝑢	PRON
cjfa-35471	504	13	𝐼	𝐼	PROPN
cjfa-35471	504	14	or	or	CCONJ
cjfa-35471	504	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	504	16	𝑢	𝑢	PROPN
cjfa-35471	504	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	504	18	and	and	CCONJ
cjfa-35471	504	19	the	the	DET
cjfa-35471	504	20	periods	period	NOUN
cjfa-35471	504	21	where	where	SCONJ
cjfa-35471	504	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	504	23	𝐼	𝐼	ADP
cjfa-35471	504	24	𝐼.	𝐼.	PROPN
cjfa-35471	504	25	notice	notice	VERB
cjfa-35471	504	26	that	that	SCONJ
cjfa-35471	504	27	for	for	ADP
cjfa-35471	504	28	the	the	DET
cjfa-35471	504	29	condition	condition	NOUN
cjfa-35471	504	30	above	above	ADV
cjfa-35471	504	31	(	(	PUNCT
cjfa-35471	504	32	equation	equation	NOUN
cjfa-35471	504	33	4	4	NUM
cjfa-35471	504	34	)	)	PUNCT
cjfa-35471	504	35	to	to	PART
cjfa-35471	504	36	be	be	AUX
cjfa-35471	504	37	kept	keep	VERB
cjfa-35471	504	38	satisfied	satisfied	ADJ
cjfa-35471	504	39	depends	depend	VERB
cjfa-35471	504	40	on	on	ADP
cjfa-35471	504	41	ℎ	ℎ	PROPN
cjfa-35471	504	42	(	(	PUNCT
cjfa-35471	504	43	inventory	inventory	NOUN
cjfa-35471	504	44	holding	hold	VERB
cjfa-35471	504	45	cost	cost	NOUN
cjfa-35471	504	46	)	)	PUNCT
cjfa-35471	504	47	,	,	PUNCT
cjfa-35471	504	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	504	49	the	the	DET
cjfa-35471	504	50	interest	interest	NOUN
cjfa-35471	504	51	rates	rate	NOUN
cjfa-35471	504	52	,	,	PUNCT
cjfa-35471	504	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	504	54	,	,	PUNCT
cjfa-35471	504	55	the	the	DET
cjfa-35471	504	56	marginal	marginal	ADJ
cjfa-35471	504	57	cost	cost	NOUN
cjfa-35471	504	58	of	of	ADP
cjfa-35471	504	59	production	production	NOUN
cjfa-35471	504	60	,	,	PUNCT
cjfa-35471	504	61	and	and	CCONJ
cjfa-35471	504	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	504	63	change	change	NOUN
cjfa-35471	504	64	in	in	ADP
cjfa-35471	504	65	the	the	DET
cjfa-35471	504	66	marginal	marginal	ADJ
cjfa-35471	504	67	cost	cost	NOUN
cjfa-35471	504	68	.	.	PUNCT
cjfa-35471	505	1	following	follow	VERB
cjfa-35471	505	2	conclusions	conclusion	NOUN
cjfa-35471	505	3	can	can	AUX
cjfa-35471	505	4	be	be	AUX
cjfa-35471	505	5	made	make	VERB
cjfa-35471	505	6	even	even	ADV
cjfa-35471	505	7	without	without	ADP
cjfa-35471	505	8	specific	specific	ADJ
cjfa-35471	505	9	forms	form	NOUN
cjfa-35471	505	10	of	of	ADP
cjfa-35471	505	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	505	12	,	,	PUNCT
cjfa-35471	505	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	505	14	,	,	PUNCT
cjfa-35471	505	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	505	16	and	and	CCONJ
cjfa-35471	505	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	505	18	on	on	ADP
cjfa-35471	505	19	the	the	DET
cjfa-35471	505	20	basis	basis	NOUN
cjfa-35471	505	21	of	of	ADP
cjfa-35471	505	22	equation	equation	NOUN
cjfa-35471	505	23	(	(	PUNCT
cjfa-35471	505	24	4	4	NUM
cjfa-35471	505	25	):	):	PUNCT
cjfa-35471	505	26	1	1	NUM
cjfa-35471	505	27	.	.	PUNCT
cjfa-35471	506	1	the	the	DET
cjfa-35471	506	2	firm	firm	NOUN
cjfa-35471	506	3	will	will	AUX
cjfa-35471	506	4	keep	keep	VERB
cjfa-35471	506	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	506	6	𝑢	𝑢	ADP
cjfa-35471	506	7	𝐼	𝐼	PROPN
cjfa-35471	506	8	as	as	ADV
cjfa-35471	506	9	long	long	ADV
cjfa-35471	506	10	as	as	SCONJ
cjfa-35471	506	11	demand	demand	NOUN
cjfa-35471	506	12	is	be	AUX
cjfa-35471	506	13	falling	fall	VERB
cjfa-35471	506	14	or	or	CCONJ
cjfa-35471	506	15	constant	constant	ADJ
cjfa-35471	506	16	i.e.	i.e.	X
cjfa-35471	506	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	506	18	0	0	NOUN
cjfa-35471	506	19	implying	imply	VERB
cjfa-35471	506	20	that	that	SCONJ
cjfa-35471	506	21	the	the	DET
cjfa-35471	506	22	firm	firm	NOUN
cjfa-35471	506	23	will	will	AUX
cjfa-35471	506	24	choose	choose	VERB
cjfa-35471	506	25	to	to	PART
cjfa-35471	506	26	produce	produce	VERB
cjfa-35471	506	27	just	just	ADV
cjfa-35471	506	28	enough	enough	ADJ
cjfa-35471	506	29	to	to	PART
cjfa-35471	506	30	meet	meet	VERB
cjfa-35471	506	31	the	the	DET
cjfa-35471	506	32	demand	demand	NOUN
cjfa-35471	506	33	if	if	SCONJ
cjfa-35471	506	34	demand	demand	NOUN
cjfa-35471	506	35	is	be	AUX
cjfa-35471	506	36	falling	fall	VERB
cjfa-35471	506	37	since	since	SCONJ
cjfa-35471	506	38	both	both	PRON
cjfa-35471	506	39	ℎ	ℎ	NOUN
cjfa-35471	506	40	and	and	CCONJ
cjfa-35471	506	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	506	42	are	be	AUX
cjfa-35471	506	43	positive	positive	ADJ
cjfa-35471	506	44	.	.	PUNCT
cjfa-35471	507	1	2	2	X
cjfa-35471	507	2	.	.	X
cjfa-35471	507	3	the	the	DET
cjfa-35471	507	4	firm	firm	NOUN
cjfa-35471	507	5	will	will	AUX
cjfa-35471	507	6	keep	keep	VERB
cjfa-35471	507	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	507	8	𝑢	𝑢	ADP
cjfa-35471	507	9	𝐼	𝐼	NOUN
cjfa-35471	507	10	even	even	ADV
cjfa-35471	507	11	if	if	SCONJ
cjfa-35471	507	12	demand	demand	NOUN
cjfa-35471	507	13	is	be	AUX
cjfa-35471	507	14	increasing	increase	VERB
cjfa-35471	507	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	507	16	𝑟	𝑟	X
cjfa-35471	507	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	507	18	but	but	CCONJ
cjfa-35471	507	19	the	the	DET
cjfa-35471	507	20	term	term	NOUN
cjfa-35471	507	21	ℎ	ℎ	PROPN
cjfa-35471	507	22	+	+	CCONJ
cjfa-35471	507	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	507	24	�	�	PROPN
cjfa-35471	507	25	�	�	PROPN
cjfa-35471	507	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	507	27	�	�	PROPN
cjfa-35471	507	28	is	be	AUX
cjfa-35471	507	29	large	large	ADJ
cjfa-35471	507	30	enough	enough	ADV
cjfa-35471	507	31	to	to	PART
cjfa-35471	507	32	keep	keep	VERB
cjfa-35471	507	33	inequality	inequality	NOUN
cjfa-35471	507	34	(	(	PUNCT
cjfa-35471	507	35	4	4	NUM
cjfa-35471	507	36	)	)	PUNCT
cjfa-35471	507	37	satisfied	satisfied	ADJ
cjfa-35471	507	38	.	.	PUNCT
cjfa-35471	508	1	decreasing	decrease	VERB
cjfa-35471	508	2	interest	interest	NOUN
cjfa-35471	508	3	rates	rate	NOUN
cjfa-35471	508	4	will	will	AUX
cjfa-35471	508	5	not	not	PART
cjfa-35471	508	6	be	be	AUX
cjfa-35471	508	7	a	a	DET
cjfa-35471	508	8	remedy	remedy	NOUN
cjfa-35471	508	9	in	in	ADP
cjfa-35471	508	10	this	this	DET
cjfa-35471	508	11	case	case	NOUN
cjfa-35471	508	12	if	if	SCONJ
cjfa-35471	508	13	they	they	PRON
cjfa-35471	508	14	are	be	AUX
cjfa-35471	508	15	already	already	ADV
cjfa-35471	508	16	low	low	ADJ
cjfa-35471	508	17	.	.	PUNCT
cjfa-35471	509	1	firms	firm	NOUN
cjfa-35471	509	2	where	where	SCONJ
cjfa-35471	509	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	509	4	�	�	PROPN
cjfa-35471	509	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	509	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	509	7	�	�	PROPN
cjfa-35471	509	8	is	be	AUX
cjfa-35471	509	9	low	low	ADJ
cjfa-35471	509	10	(	(	PUNCT
cjfa-35471	509	11	large	large	ADJ
cjfa-35471	509	12	and	and	CCONJ
cjfa-35471	509	13	already	already	ADV
cjfa-35471	509	14	very	very	ADV
cjfa-35471	509	15	efficient	efficient	ADJ
cjfa-35471	509	16	firms	firm	NOUN
cjfa-35471	509	17	)	)	PUNCT
cjfa-35471	509	18	will	will	AUX
cjfa-35471	509	19	have	have	VERB
cjfa-35471	509	20	more	more	ADJ
cjfa-35471	509	21	difficulty	difficulty	NOUN
cjfa-35471	509	22	to	to	PART
cjfa-35471	509	23	produce	produce	VERB
cjfa-35471	509	24	to	to	PART
cjfa-35471	509	25	build	build	VERB
cjfa-35471	509	26	up	up	ADP
cjfa-35471	509	27	inventories	inventory	NOUN
cjfa-35471	509	28	.	.	PUNCT
cjfa-35471	510	1	currently	currently	ADV
cjfa-35471	510	2	,	,	PUNCT
cjfa-35471	510	3	this	this	PRON
cjfa-35471	510	4	seems	seem	VERB
cjfa-35471	510	5	to	to	PART
cjfa-35471	510	6	be	be	AUX
cjfa-35471	510	7	the	the	DET
cjfa-35471	510	8	case	case	NOUN
cjfa-35471	510	9	in	in	ADP
cjfa-35471	510	10	major	major	ADJ
cjfa-35471	510	11	economies	economy	NOUN
cjfa-35471	510	12	.	.	PUNCT
cjfa-35471	511	1	3	3	X
cjfa-35471	511	2	.	.	X
cjfa-35471	511	3	higher	high	ADJ
cjfa-35471	511	4	interest	interest	NOUN
cjfa-35471	511	5	rates	rate	NOUN
cjfa-35471	511	6	and	and	CCONJ
cjfa-35471	511	7	the	the	DET
cjfa-35471	511	8	use	use	NOUN
cjfa-35471	511	9	of	of	ADP
cjfa-35471	511	10	inefficient	inefficient	ADJ
cjfa-35471	511	11	technologies	technology	NOUN
cjfa-35471	511	12	(	(	PUNCT
cjfa-35471	511	13	large	large	ADJ
cjfa-35471	511	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	511	15	)	)	PUNCT
cjfa-35471	511	16	implies	imply	VERB
cjfa-35471	511	17	high	high	ADJ
cjfa-35471	511	18	marginal	marginal	ADJ
cjfa-35471	511	19	cost	cost	NOUN
cjfa-35471	511	20	)	)	PUNCT
cjfa-35471	511	21	will	will	AUX
cjfa-35471	511	22	induce	induce	VERB
cjfa-35471	511	23	firms	firm	NOUN
cjfa-35471	511	24	to	to	PART
cjfa-35471	511	25	wait	wait	VERB
cjfa-35471	511	26	longer	long	ADV
cjfa-35471	511	27	for	for	ADP
cjfa-35471	511	28	inventory	inventory	NOUN
cjfa-35471	511	29	build	build	NOUN
cjfa-35471	511	30	-	-	PUNCT
cjfa-35471	511	31	up	up	NOUN
cjfa-35471	511	32	even	even	ADV
cjfa-35471	511	33	if	if	SCONJ
cjfa-35471	511	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	511	35	is	be	AUX
cjfa-35471	511	36	positive	positive	ADJ
cjfa-35471	511	37	.	.	PUNCT
cjfa-35471	512	1	4	4	X
cjfa-35471	512	2	.	.	X
cjfa-35471	512	3	the	the	DET
cjfa-35471	512	4	level	level	NOUN
cjfa-35471	512	5	of	of	ADP
cjfa-35471	512	6	technology	technology	NOUN
cjfa-35471	512	7	used	use	VERB
cjfa-35471	512	8	will	will	AUX
cjfa-35471	512	9	not	not	PART
cjfa-35471	512	10	affect	affect	VERB
cjfa-35471	512	11	the	the	DET
cjfa-35471	512	12	behavior	behavior	NOUN
cjfa-35471	512	13	of	of	ADP
cjfa-35471	512	14	the	the	DET
cjfa-35471	512	15	firms	firm	NOUN
cjfa-35471	512	16	if	if	SCONJ
cjfa-35471	512	17	the	the	DET
cjfa-35471	512	18	interest	interest	NOUN
cjfa-35471	512	19	rates	rate	NOUN
cjfa-35471	512	20	are	be	AUX
cjfa-35471	512	21	very	very	ADV
cjfa-35471	512	22	low	low	ADJ
cjfa-35471	512	23	as	as	SCONJ
cjfa-35471	512	24	they	they	PRON
cjfa-35471	512	25	are	be	AUX
cjfa-35471	512	26	now	now	ADV
cjfa-35471	512	27	in	in	ADP
cjfa-35471	512	28	many	many	ADJ
cjfa-35471	512	29	developed	develop	VERB
cjfa-35471	512	30	nations	nation	NOUN
cjfa-35471	512	31	since	since	SCONJ
cjfa-35471	512	32	the	the	DET
cjfa-35471	512	33	term	term	NOUN
cjfa-35471	512	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	512	35	in	in	ADP
cjfa-35471	512	36	is	be	AUX
cjfa-35471	512	37	large	large	ADJ
cjfa-35471	512	38	enough	enough	ADV
cjfa-35471	512	39	to	to	PART
cjfa-35471	512	40	keep	keep	VERB
cjfa-35471	512	41	inequality	inequality	NOUN
cjfa-35471	512	42	(	(	PUNCT
cjfa-35471	512	43	4	4	NUM
cjfa-35471	512	44	)	)	PUNCT
cjfa-35471	512	45	satisfied	satisfied	ADJ
cjfa-35471	512	46	.	.	PUNCT
cjfa-35471	513	1	decreasing	decrease	VERB
cjfa-35471	513	2	interest	interest	NOUN
cjfa-35471	513	3	rates	rate	NOUN
cjfa-35471	513	4	will	will	AUX
cjfa-35471	513	5	not	not	PART
cjfa-35471	513	6	be	be	AUX
cjfa-35471	513	7	a	a	DET
cjfa-35471	513	8	remedy	remedy	NOUN
cjfa-35471	513	9	in	in	ADP
cjfa-35471	513	10	this	this	DET
cjfa-35471	513	11	case	case	NOUN
cjfa-35471	513	12	if	if	SCONJ
cjfa-35471	513	13	they	they	PRON
cjfa-35471	513	14	are	be	AUX
cjfa-35471	513	15	already	already	ADV
cjfa-35471	513	16	low	low	ADJ
cjfa-35471	513	17	.	.	PUNCT
cjfa-35471	514	1	firms	firm	NOUN
cjfa-35471	514	2	where	where	SCONJ
cjfa-35471	514	3	then	then	ADV
cjfa-35471	514	4	using	use	VERB
cjfa-35471	514	5	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	514	6	𝑢	𝑢	PROPN
cjfa-35471	514	7	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	514	8	,	,	PUNCT
cjfa-35471	514	9	equation	equation	NOUN
cjfa-35471	514	10	(	(	PUNCT
cjfa-35471	514	11	1	1	NUM
cjfa-35471	514	12	)	)	PUNCT
cjfa-35471	514	13	,	,	PUNCT
cjfa-35471	514	14	and	and	CCONJ
cjfa-35471	514	15	the	the	DET
cjfa-35471	514	16	conditions	condition	NOUN
cjfa-35471	514	17	(	(	PUNCT
cjfa-35471	514	18	the	the	DET
cjfa-35471	514	19	necessary	necessary	ADJ
cjfa-35471	514	20	condition	condition	NOUN
cjfa-35471	514	21	to	to	PART
cjfa-35471	514	22	keep	keep	VERB
cjfa-35471	514	23	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	514	24	𝑢	𝑢	ADP
cjfa-35471	514	25	𝐼	𝐼	PROPN
cjfa-35471	514	26	optimal	optimal	ADJ
cjfa-35471	514	27	)	)	PUNCT
cjfa-35471	514	28	developed	develop	VERB
cjfa-35471	514	29	by	by	ADP
cjfa-35471	514	30	pontryagin	pontryagin	NOUN
cjfa-35471	514	31	,	,	PUNCT
cjfa-35471	514	32	boltyanskii	boltyanskii	ADJ
cjfa-35471	514	33	,	,	PUNCT
cjfa-35471	514	34	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	514	35	and	and	CCONJ
cjfa-35471	514	36	mishechenko	mishechenko	NOUN
cjfa-35471	514	37	(	(	PUNCT
cjfa-35471	514	38	1962	1962	NUM
cjfa-35471	514	39	)	)	PUNCT
cjfa-35471	514	40	,	,	PUNCT
cjfa-35471	514	41	hestenes	hestene	NOUN
cjfa-35471	514	42	(	(	PUNCT
cjfa-35471	514	43	1966	1966	NUM
cjfa-35471	514	44	)	)	PUNCT
cjfa-35471	514	45	,	,	PUNCT
cjfa-35471	514	46	kamien	kamien	NOUN
cjfa-35471	514	47	and	and	CCONJ
cjfa-35471	514	48	schwartz	schwartz	PROPN
cjfa-35471	514	49	(	(	PUNCT
cjfa-35471	514	50	2012	2012	NUM
cjfa-35471	514	51	)	)	PUNCT
cjfa-35471	514	52	among	among	ADP
cjfa-35471	514	53	many	many	ADJ
cjfa-35471	514	54	others	other	NOUN
cjfa-35471	514	55	,	,	PUNCT
cjfa-35471	514	56	we	we	PRON
cjfa-35471	514	57	have	have	AUX
cjfa-35471	514	58	;	;	PUNCT
cjfa-35471	514	59	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	514	60	�	�	NOUN
cjfa-35471	514	61	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	514	62	≤	≤	PUNCT
cjfa-35471	514	63	𝐼	𝐼	PROPN
cjfa-35471	514	64	for	for	ADP
cjfa-35471	514	65	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	514	66	�	�	PROPN
cjfa-35471	514	67	≤	≤	NUM
cjfa-35471	515	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	515	2	≤	≤	NUM
cjfa-35471	515	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	515	4	�	�	PROPN
cjfa-35471	515	5	implies	imply	VERB
cjfa-35471	515	6	:	:	PUNCT
cjfa-35471	515	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	515	8	�	�	PROPN
cjfa-35471	515	9	�	�	PROPN
cjfa-35471	515	10	�	�	PROPN
cjfa-35471	515	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	515	12	�	�	PROPN
cjfa-35471	515	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	515	14	�	�	PROPN
cjfa-35471	515	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	515	16	≤	≤	PUNCT
cjfa-35471	515	17	ℎ	ℎ	PROPN
cjfa-35471	515	18	+	+	PROPN
cjfa-35471	515	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	515	20	�	�	PROPN
cjfa-35471	515	21	�	�	PROPN
cjfa-35471	515	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	515	23	�	�	PROPN
cjfa-35471	515	24	(	(	PUNCT
cjfa-35471	515	25	4	4	NUM
cjfa-35471	515	26	)	)	PUNCT
cjfa-35471	515	27	where	where	SCONJ
cjfa-35471	515	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	515	29	𝑢	𝑢	PROPN
cjfa-35471	515	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	515	31	�	�	NOUN
cjfa-35471	515	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	515	33	denotes	denote	VERB
cjfa-35471	515	34	the	the	DET
cjfa-35471	515	35	interest	interest	NOUN
cjfa-35471	515	36	rate	rate	NOUN
cjfa-35471	515	37	.	.	PUNCT
cjfa-35471	516	1	as	as	ADV
cjfa-35471	516	2	long	long	ADV
cjfa-35471	516	3	as	as	SCONJ
cjfa-35471	516	4	the	the	DET
cjfa-35471	516	5	condition	condition	NOUN
cjfa-35471	516	6	specified	specify	VERB
cjfa-35471	516	7	by	by	ADP
cjfa-35471	516	8	this	this	DET
cjfa-35471	516	9	inequality	inequality	NOUN
cjfa-35471	516	10	is	be	AUX
cjfa-35471	516	11	satisfied	satisfied	ADJ
cjfa-35471	516	12	it	it	PRON
cjfa-35471	516	13	will	will	AUX
cjfa-35471	516	14	be	be	AUX
cjfa-35471	516	15	optimal	optimal	ADJ
cjfa-35471	516	16	to	to	PART
cjfa-35471	516	17	keep	keep	VERB
cjfa-35471	516	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	516	19	𝑢	𝑢	ADP
cjfa-35471	516	20	𝐼	𝐼	ADP
cjfa-35471	516	21	implying	imply	VERB
cjfa-35471	516	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	516	23	𝑢	𝑢	PRON
cjfa-35471	516	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	516	25	this	this	PRON
cjfa-35471	516	26	means	mean	VERB
cjfa-35471	516	27	that	that	SCONJ
cjfa-35471	516	28	during	during	ADP
cjfa-35471	516	29	the	the	DET
cjfa-35471	516	30	intervals	interval	NOUN
cjfa-35471	516	31	where	where	SCONJ
cjfa-35471	516	32	this	this	DET
cjfa-35471	516	33	inequality	inequality	NOUN
cjfa-35471	516	34	is	be	AUX
cjfa-35471	516	35	satisfied	satisfied	ADJ
cjfa-35471	516	36	the	the	DET
cjfa-35471	516	37	firm	firm	NOUN
cjfa-35471	516	38	will	will	AUX
cjfa-35471	516	39	produce	produce	VERB
cjfa-35471	516	40	just	just	ADV
cjfa-35471	516	41	enough	enough	ADJ
cjfa-35471	516	42	to	to	PART
cjfa-35471	516	43	satisfy	satisfy	VERB
cjfa-35471	516	44	the	the	DET
cjfa-35471	516	45	demand	demand	NOUN
cjfa-35471	516	46	.	.	PUNCT
cjfa-35471	517	1	so	so	ADV
cjfa-35471	517	2	,	,	PUNCT
cjfa-35471	517	3	the	the	DET
cjfa-35471	517	4	condition	condition	NOUN
cjfa-35471	517	5	above	above	ADV
cjfa-35471	517	6	will	will	AUX
cjfa-35471	517	7	synthesize	synthesize	VERB
cjfa-35471	517	8	the	the	DET
cjfa-35471	517	9	periods	period	NOUN
cjfa-35471	517	10	where	where	SCONJ
cjfa-35471	517	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	517	12	𝑢	𝑢	PRON
cjfa-35471	517	13	𝐼	𝐼	PROPN
cjfa-35471	517	14	or	or	CCONJ
cjfa-35471	517	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	517	16	𝑢	𝑢	PROPN
cjfa-35471	517	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	517	18	and	and	CCONJ
cjfa-35471	517	19	the	the	DET
cjfa-35471	517	20	periods	period	NOUN
cjfa-35471	517	21	where	where	SCONJ
cjfa-35471	517	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	517	23	𝐼	𝐼	ADP
cjfa-35471	517	24	𝐼.	𝐼.	PROPN
cjfa-35471	517	25	notice	notice	VERB
cjfa-35471	517	26	that	that	SCONJ
cjfa-35471	517	27	for	for	ADP
cjfa-35471	517	28	the	the	DET
cjfa-35471	517	29	condition	condition	NOUN
cjfa-35471	517	30	above	above	ADV
cjfa-35471	517	31	(	(	PUNCT
cjfa-35471	517	32	equation	equation	NOUN
cjfa-35471	517	33	4	4	NUM
cjfa-35471	517	34	)	)	PUNCT
cjfa-35471	517	35	to	to	PART
cjfa-35471	517	36	be	be	AUX
cjfa-35471	517	37	kept	keep	VERB
cjfa-35471	517	38	satisfied	satisfied	ADJ
cjfa-35471	517	39	depends	depend	VERB
cjfa-35471	517	40	on	on	ADP
cjfa-35471	517	41	ℎ	ℎ	PROPN
cjfa-35471	517	42	(	(	PUNCT
cjfa-35471	517	43	inventory	inventory	NOUN
cjfa-35471	517	44	holding	hold	VERB
cjfa-35471	517	45	cost	cost	NOUN
cjfa-35471	517	46	)	)	PUNCT
cjfa-35471	517	47	,	,	PUNCT
cjfa-35471	517	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	517	49	the	the	DET
cjfa-35471	517	50	interest	interest	NOUN
cjfa-35471	517	51	rates	rate	NOUN
cjfa-35471	517	52	,	,	PUNCT
cjfa-35471	517	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	517	54	,	,	PUNCT
cjfa-35471	517	55	the	the	DET
cjfa-35471	517	56	marginal	marginal	ADJ
cjfa-35471	517	57	cost	cost	NOUN
cjfa-35471	517	58	of	of	ADP
cjfa-35471	517	59	production	production	NOUN
cjfa-35471	517	60	,	,	PUNCT
cjfa-35471	517	61	and	and	CCONJ
cjfa-35471	517	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	517	63	change	change	NOUN
cjfa-35471	517	64	in	in	ADP
cjfa-35471	517	65	the	the	DET
cjfa-35471	517	66	marginal	marginal	ADJ
cjfa-35471	517	67	cost	cost	NOUN
cjfa-35471	517	68	.	.	PUNCT
cjfa-35471	518	1	following	follow	VERB
cjfa-35471	518	2	conclusions	conclusion	NOUN
cjfa-35471	518	3	can	can	AUX
cjfa-35471	518	4	be	be	AUX
cjfa-35471	518	5	made	make	VERB
cjfa-35471	518	6	even	even	ADV
cjfa-35471	518	7	without	without	ADP
cjfa-35471	518	8	specific	specific	ADJ
cjfa-35471	518	9	forms	form	NOUN
cjfa-35471	518	10	of	of	ADP
cjfa-35471	518	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	518	12	,	,	PUNCT
cjfa-35471	518	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	518	14	,	,	PUNCT
cjfa-35471	518	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	518	16	and	and	CCONJ
cjfa-35471	518	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	518	18	on	on	ADP
cjfa-35471	518	19	the	the	DET
cjfa-35471	518	20	basis	basis	NOUN
cjfa-35471	518	21	of	of	ADP
cjfa-35471	518	22	equation	equation	NOUN
cjfa-35471	518	23	(	(	PUNCT
cjfa-35471	518	24	4	4	NUM
cjfa-35471	518	25	):	):	PUNCT
cjfa-35471	518	26	1	1	NUM
cjfa-35471	518	27	.	.	PUNCT
cjfa-35471	519	1	the	the	DET
cjfa-35471	519	2	firm	firm	NOUN
cjfa-35471	519	3	will	will	AUX
cjfa-35471	519	4	keep	keep	VERB
cjfa-35471	519	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	519	6	𝑢	𝑢	ADP
cjfa-35471	519	7	𝐼	𝐼	PROPN
cjfa-35471	519	8	as	as	ADV
cjfa-35471	519	9	long	long	ADV
cjfa-35471	519	10	as	as	SCONJ
cjfa-35471	519	11	demand	demand	NOUN
cjfa-35471	519	12	is	be	AUX
cjfa-35471	519	13	falling	fall	VERB
cjfa-35471	519	14	or	or	CCONJ
cjfa-35471	519	15	constant	constant	ADJ
cjfa-35471	519	16	i.e.	i.e.	X
cjfa-35471	519	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	519	18	0	0	NOUN
cjfa-35471	519	19	implying	imply	VERB
cjfa-35471	519	20	that	that	SCONJ
cjfa-35471	519	21	the	the	DET
cjfa-35471	519	22	firm	firm	NOUN
cjfa-35471	519	23	will	will	AUX
cjfa-35471	519	24	choose	choose	VERB
cjfa-35471	519	25	to	to	PART
cjfa-35471	519	26	produce	produce	VERB
cjfa-35471	519	27	just	just	ADV
cjfa-35471	519	28	enough	enough	ADJ
cjfa-35471	519	29	to	to	PART
cjfa-35471	519	30	meet	meet	VERB
cjfa-35471	519	31	the	the	DET
cjfa-35471	519	32	demand	demand	NOUN
cjfa-35471	519	33	if	if	SCONJ
cjfa-35471	519	34	demand	demand	NOUN
cjfa-35471	519	35	is	be	AUX
cjfa-35471	519	36	falling	fall	VERB
cjfa-35471	519	37	since	since	SCONJ
cjfa-35471	519	38	both	both	PRON
cjfa-35471	519	39	ℎ	ℎ	NOUN
cjfa-35471	519	40	and	and	CCONJ
cjfa-35471	519	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	519	42	are	be	AUX
cjfa-35471	519	43	positive	positive	ADJ
cjfa-35471	519	44	.	.	PUNCT
cjfa-35471	520	1	2	2	X
cjfa-35471	520	2	.	.	X
cjfa-35471	520	3	the	the	DET
cjfa-35471	520	4	firm	firm	NOUN
cjfa-35471	520	5	will	will	AUX
cjfa-35471	520	6	keep	keep	VERB
cjfa-35471	520	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	520	8	𝑢	𝑢	ADP
cjfa-35471	520	9	𝐼	𝐼	NOUN
cjfa-35471	520	10	even	even	ADV
cjfa-35471	520	11	if	if	SCONJ
cjfa-35471	520	12	demand	demand	NOUN
cjfa-35471	520	13	is	be	AUX
cjfa-35471	520	14	increasing	increase	VERB
cjfa-35471	520	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	520	16	𝑟	𝑟	X
cjfa-35471	520	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	520	18	but	but	CCONJ
cjfa-35471	520	19	the	the	DET
cjfa-35471	520	20	term	term	NOUN
cjfa-35471	520	21	ℎ	ℎ	PROPN
cjfa-35471	520	22	+	+	CCONJ
cjfa-35471	520	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	520	24	�	�	PROPN
cjfa-35471	520	25	�	�	PROPN
cjfa-35471	520	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	520	27	�	�	PROPN
cjfa-35471	520	28	is	be	AUX
cjfa-35471	520	29	large	large	ADJ
cjfa-35471	520	30	enough	enough	ADV
cjfa-35471	520	31	to	to	PART
cjfa-35471	520	32	keep	keep	VERB
cjfa-35471	520	33	inequality	inequality	NOUN
cjfa-35471	520	34	(	(	PUNCT
cjfa-35471	520	35	4	4	NUM
cjfa-35471	520	36	)	)	PUNCT
cjfa-35471	520	37	satisfied	satisfied	ADJ
cjfa-35471	520	38	.	.	PUNCT
cjfa-35471	521	1	decreasing	decrease	VERB
cjfa-35471	521	2	interest	interest	NOUN
cjfa-35471	521	3	rates	rate	NOUN
cjfa-35471	521	4	will	will	AUX
cjfa-35471	521	5	not	not	PART
cjfa-35471	521	6	be	be	AUX
cjfa-35471	521	7	a	a	DET
cjfa-35471	521	8	remedy	remedy	NOUN
cjfa-35471	521	9	in	in	ADP
cjfa-35471	521	10	this	this	DET
cjfa-35471	521	11	case	case	NOUN
cjfa-35471	521	12	if	if	SCONJ
cjfa-35471	521	13	they	they	PRON
cjfa-35471	521	14	are	be	AUX
cjfa-35471	521	15	already	already	ADV
cjfa-35471	521	16	low	low	ADJ
cjfa-35471	521	17	.	.	PUNCT
cjfa-35471	522	1	firms	firm	NOUN
cjfa-35471	522	2	where	where	SCONJ
cjfa-35471	522	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	522	4	�	�	PROPN
cjfa-35471	522	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	522	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	522	7	�	�	PROPN
cjfa-35471	522	8	is	be	AUX
cjfa-35471	522	9	low	low	ADJ
cjfa-35471	522	10	(	(	PUNCT
cjfa-35471	522	11	large	large	ADJ
cjfa-35471	522	12	and	and	CCONJ
cjfa-35471	522	13	already	already	ADV
cjfa-35471	522	14	very	very	ADV
cjfa-35471	522	15	efficient	efficient	ADJ
cjfa-35471	522	16	firms	firm	NOUN
cjfa-35471	522	17	)	)	PUNCT
cjfa-35471	522	18	will	will	AUX
cjfa-35471	522	19	have	have	VERB
cjfa-35471	522	20	more	more	ADJ
cjfa-35471	522	21	difficulty	difficulty	NOUN
cjfa-35471	522	22	to	to	PART
cjfa-35471	522	23	produce	produce	VERB
cjfa-35471	522	24	to	to	PART
cjfa-35471	522	25	build	build	VERB
cjfa-35471	522	26	up	up	ADP
cjfa-35471	522	27	inventories	inventory	NOUN
cjfa-35471	522	28	.	.	PUNCT
cjfa-35471	523	1	currently	currently	ADV
cjfa-35471	523	2	,	,	PUNCT
cjfa-35471	523	3	this	this	PRON
cjfa-35471	523	4	seems	seem	VERB
cjfa-35471	523	5	to	to	PART
cjfa-35471	523	6	be	be	AUX
cjfa-35471	523	7	the	the	DET
cjfa-35471	523	8	case	case	NOUN
cjfa-35471	523	9	in	in	ADP
cjfa-35471	523	10	major	major	ADJ
cjfa-35471	523	11	economies	economy	NOUN
cjfa-35471	523	12	.	.	PUNCT
cjfa-35471	524	1	3	3	X
cjfa-35471	524	2	.	.	X
cjfa-35471	524	3	higher	high	ADJ
cjfa-35471	524	4	interest	interest	NOUN
cjfa-35471	524	5	rates	rate	NOUN
cjfa-35471	524	6	and	and	CCONJ
cjfa-35471	524	7	the	the	DET
cjfa-35471	524	8	use	use	NOUN
cjfa-35471	524	9	of	of	ADP
cjfa-35471	524	10	inefficient	inefficient	ADJ
cjfa-35471	524	11	technologies	technology	NOUN
cjfa-35471	524	12	(	(	PUNCT
cjfa-35471	524	13	large	large	ADJ
cjfa-35471	524	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	524	15	)	)	PUNCT
cjfa-35471	524	16	implies	imply	VERB
cjfa-35471	524	17	high	high	ADJ
cjfa-35471	524	18	marginal	marginal	ADJ
cjfa-35471	524	19	cost	cost	NOUN
cjfa-35471	524	20	)	)	PUNCT
cjfa-35471	524	21	will	will	AUX
cjfa-35471	524	22	induce	induce	VERB
cjfa-35471	524	23	firms	firm	NOUN
cjfa-35471	524	24	to	to	PART
cjfa-35471	524	25	wait	wait	VERB
cjfa-35471	524	26	longer	long	ADV
cjfa-35471	524	27	for	for	ADP
cjfa-35471	524	28	inventory	inventory	NOUN
cjfa-35471	524	29	build	build	NOUN
cjfa-35471	524	30	-	-	PUNCT
cjfa-35471	524	31	up	up	NOUN
cjfa-35471	524	32	even	even	ADV
cjfa-35471	524	33	if	if	SCONJ
cjfa-35471	524	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	524	35	is	be	AUX
cjfa-35471	524	36	positive	positive	ADJ
cjfa-35471	524	37	.	.	PUNCT
cjfa-35471	525	1	4	4	X
cjfa-35471	525	2	.	.	X
cjfa-35471	525	3	the	the	DET
cjfa-35471	525	4	level	level	NOUN
cjfa-35471	525	5	of	of	ADP
cjfa-35471	525	6	technology	technology	NOUN
cjfa-35471	525	7	used	use	VERB
cjfa-35471	525	8	will	will	AUX
cjfa-35471	525	9	not	not	PART
cjfa-35471	525	10	affect	affect	VERB
cjfa-35471	525	11	the	the	DET
cjfa-35471	525	12	behavior	behavior	NOUN
cjfa-35471	525	13	of	of	ADP
cjfa-35471	525	14	the	the	DET
cjfa-35471	525	15	firms	firm	NOUN
cjfa-35471	525	16	if	if	SCONJ
cjfa-35471	525	17	the	the	DET
cjfa-35471	525	18	interest	interest	NOUN
cjfa-35471	525	19	rates	rate	NOUN
cjfa-35471	525	20	are	be	AUX
cjfa-35471	525	21	very	very	ADV
cjfa-35471	525	22	low	low	ADJ
cjfa-35471	525	23	as	as	SCONJ
cjfa-35471	525	24	they	they	PRON
cjfa-35471	525	25	are	be	AUX
cjfa-35471	525	26	now	now	ADV
cjfa-35471	525	27	in	in	ADP
cjfa-35471	525	28	many	many	ADJ
cjfa-35471	525	29	developed	develop	VERB
cjfa-35471	525	30	nations	nation	NOUN
cjfa-35471	525	31	since	since	SCONJ
cjfa-35471	525	32	the	the	DET
cjfa-35471	525	33	term	term	NOUN
cjfa-35471	525	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	525	35	in	in	ADP
cjfa-35471	525	36	is	be	AUX
cjfa-35471	525	37	low	low	ADJ
cjfa-35471	525	38	(	(	PUNCT
cjfa-35471	525	39	large	large	ADJ
cjfa-35471	525	40	and	and	CCONJ
cjfa-35471	525	41	already	already	ADV
cjfa-35471	525	42	very	very	ADV
cjfa-35471	525	43	efficient	efficient	ADJ
cjfa-35471	525	44	firms	firm	NOUN
cjfa-35471	525	45	)	)	PUNCT
cjfa-35471	525	46	will	will	AUX
cjfa-35471	525	47	have	have	VERB
cjfa-35471	525	48	more	more	ADJ
cjfa-35471	525	49	difficulty	difficulty	NOUN
cjfa-35471	525	50	to	to	PART
cjfa-35471	525	51	produce	produce	VERB
cjfa-35471	525	52	to	to	PART
cjfa-35471	525	53	build	build	VERB
cjfa-35471	525	54	up	up	ADP
cjfa-35471	525	55	inventories	inventory	NOUN
cjfa-35471	525	56	.	.	PUNCT
cjfa-35471	526	1	currently	currently	ADV
cjfa-35471	526	2	,	,	PUNCT
cjfa-35471	526	3	this	this	PRON
cjfa-35471	526	4	seems	seem	VERB
cjfa-35471	526	5	to	to	PART
cjfa-35471	526	6	be	be	AUX
cjfa-35471	526	7	the	the	DET
cjfa-35471	526	8	case	case	NOUN
cjfa-35471	526	9	in	in	ADP
cjfa-35471	526	10	major	major	ADJ
cjfa-35471	526	11	economies	economy	NOUN
cjfa-35471	526	12	.	.	PUNCT
cjfa-35471	527	1	3	3	X
cjfa-35471	527	2	.	.	X
cjfa-35471	527	3	higher	high	ADJ
cjfa-35471	527	4	interest	interest	NOUN
cjfa-35471	527	5	rates	rate	NOUN
cjfa-35471	527	6	and	and	CCONJ
cjfa-35471	527	7	the	the	DET
cjfa-35471	527	8	use	use	NOUN
cjfa-35471	527	9	of	of	ADP
cjfa-35471	527	10	inefficient	inefficient	ADJ
cjfa-35471	527	11	technologies	technology	NOUN
cjfa-35471	527	12	(	(	PUNCT
cjfa-35471	527	13	large	large	ADJ
cjfa-35471	527	14	then	then	ADV
cjfa-35471	527	15	using	use	VERB
cjfa-35471	527	16	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	527	17	𝑢	𝑢	PROPN
cjfa-35471	527	18	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	527	19	,	,	PUNCT
cjfa-35471	527	20	equation	equation	NOUN
cjfa-35471	527	21	(	(	PUNCT
cjfa-35471	527	22	1	1	NUM
cjfa-35471	527	23	)	)	PUNCT
cjfa-35471	527	24	,	,	PUNCT
cjfa-35471	527	25	and	and	CCONJ
cjfa-35471	527	26	the	the	DET
cjfa-35471	527	27	conditions	condition	NOUN
cjfa-35471	527	28	(	(	PUNCT
cjfa-35471	527	29	the	the	DET
cjfa-35471	527	30	necessary	necessary	ADJ
cjfa-35471	527	31	condition	condition	NOUN
cjfa-35471	527	32	to	to	PART
cjfa-35471	527	33	keep	keep	VERB
cjfa-35471	527	34	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	527	35	𝑢	𝑢	ADP
cjfa-35471	527	36	𝐼	𝐼	PROPN
cjfa-35471	527	37	optimal	optimal	ADJ
cjfa-35471	527	38	)	)	PUNCT
cjfa-35471	527	39	developed	develop	VERB
cjfa-35471	527	40	by	by	ADP
cjfa-35471	527	41	pontryagin	pontryagin	NOUN
cjfa-35471	527	42	,	,	PUNCT
cjfa-35471	527	43	boltyanskii	boltyanskii	ADJ
cjfa-35471	527	44	,	,	PUNCT
cjfa-35471	527	45	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	527	46	and	and	CCONJ
cjfa-35471	527	47	mishechenko	mishechenko	NOUN
cjfa-35471	527	48	(	(	PUNCT
cjfa-35471	527	49	1962	1962	NUM
cjfa-35471	527	50	)	)	PUNCT
cjfa-35471	527	51	,	,	PUNCT
cjfa-35471	527	52	hestenes	hestene	NOUN
cjfa-35471	527	53	(	(	PUNCT
cjfa-35471	527	54	1966	1966	NUM
cjfa-35471	527	55	)	)	PUNCT
cjfa-35471	527	56	,	,	PUNCT
cjfa-35471	527	57	kamien	kamien	NOUN
cjfa-35471	527	58	and	and	CCONJ
cjfa-35471	527	59	schwartz	schwartz	PROPN
cjfa-35471	527	60	(	(	PUNCT
cjfa-35471	527	61	2012	2012	NUM
cjfa-35471	527	62	)	)	PUNCT
cjfa-35471	527	63	among	among	ADP
cjfa-35471	527	64	many	many	ADJ
cjfa-35471	527	65	others	other	NOUN
cjfa-35471	527	66	,	,	PUNCT
cjfa-35471	527	67	we	we	PRON
cjfa-35471	527	68	have	have	AUX
cjfa-35471	527	69	;	;	PUNCT
cjfa-35471	528	1	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	528	2	�	�	NOUN
cjfa-35471	528	3	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	528	4	≤	≤	PUNCT
cjfa-35471	528	5	𝐼	𝐼	PROPN
cjfa-35471	528	6	for	for	ADP
cjfa-35471	528	7	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	528	8	�	�	PROPN
cjfa-35471	528	9	≤	≤	NUM
cjfa-35471	528	10	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	528	11	≤	≤	NUM
cjfa-35471	528	12	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	528	13	�	�	PROPN
cjfa-35471	528	14	implies	imply	VERB
cjfa-35471	528	15	:	:	PUNCT
cjfa-35471	528	16	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	528	17	�	�	PROPN
cjfa-35471	528	18	�	�	PROPN
cjfa-35471	528	19	�	�	PROPN
cjfa-35471	528	20	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	528	21	�	�	PROPN
cjfa-35471	528	22	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	528	23	�	�	PROPN
cjfa-35471	528	24	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	528	25	≤	≤	PUNCT
cjfa-35471	528	26	ℎ	ℎ	PROPN
cjfa-35471	528	27	+	+	PROPN
cjfa-35471	528	28	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	528	29	�	�	PROPN
cjfa-35471	528	30	�	�	PROPN
cjfa-35471	528	31	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	528	32	�	�	PROPN
cjfa-35471	528	33	(	(	PUNCT
cjfa-35471	528	34	4	4	NUM
cjfa-35471	528	35	)	)	PUNCT
cjfa-35471	528	36	where	where	SCONJ
cjfa-35471	528	37	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	528	38	𝑢	𝑢	PROPN
cjfa-35471	528	39	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	528	40	�	�	NOUN
cjfa-35471	528	41	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	528	42	denotes	denote	VERB
cjfa-35471	528	43	the	the	DET
cjfa-35471	528	44	interest	interest	NOUN
cjfa-35471	528	45	rate	rate	NOUN
cjfa-35471	528	46	.	.	PUNCT
cjfa-35471	529	1	as	as	ADV
cjfa-35471	529	2	long	long	ADV
cjfa-35471	529	3	as	as	SCONJ
cjfa-35471	529	4	the	the	DET
cjfa-35471	529	5	condition	condition	NOUN
cjfa-35471	529	6	specified	specify	VERB
cjfa-35471	529	7	by	by	ADP
cjfa-35471	529	8	this	this	DET
cjfa-35471	529	9	inequality	inequality	NOUN
cjfa-35471	529	10	is	be	AUX
cjfa-35471	529	11	satisfied	satisfied	ADJ
cjfa-35471	529	12	it	it	PRON
cjfa-35471	529	13	will	will	AUX
cjfa-35471	529	14	be	be	AUX
cjfa-35471	529	15	optimal	optimal	ADJ
cjfa-35471	529	16	to	to	PART
cjfa-35471	529	17	keep	keep	VERB
cjfa-35471	529	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	529	19	𝑢	𝑢	ADP
cjfa-35471	529	20	𝐼	𝐼	ADP
cjfa-35471	529	21	implying	imply	VERB
cjfa-35471	529	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	529	23	𝑢	𝑢	PRON
cjfa-35471	529	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	529	25	this	this	PRON
cjfa-35471	529	26	means	mean	VERB
cjfa-35471	529	27	that	that	SCONJ
cjfa-35471	529	28	during	during	ADP
cjfa-35471	529	29	the	the	DET
cjfa-35471	529	30	intervals	interval	NOUN
cjfa-35471	529	31	where	where	SCONJ
cjfa-35471	529	32	this	this	DET
cjfa-35471	529	33	inequality	inequality	NOUN
cjfa-35471	529	34	is	be	AUX
cjfa-35471	529	35	satisfied	satisfied	ADJ
cjfa-35471	529	36	the	the	DET
cjfa-35471	529	37	firm	firm	NOUN
cjfa-35471	529	38	will	will	AUX
cjfa-35471	529	39	produce	produce	VERB
cjfa-35471	529	40	just	just	ADV
cjfa-35471	529	41	enough	enough	ADJ
cjfa-35471	529	42	to	to	PART
cjfa-35471	529	43	satisfy	satisfy	VERB
cjfa-35471	529	44	the	the	DET
cjfa-35471	529	45	demand	demand	NOUN
cjfa-35471	529	46	.	.	PUNCT
cjfa-35471	530	1	so	so	ADV
cjfa-35471	530	2	,	,	PUNCT
cjfa-35471	530	3	the	the	DET
cjfa-35471	530	4	condition	condition	NOUN
cjfa-35471	530	5	above	above	ADV
cjfa-35471	530	6	will	will	AUX
cjfa-35471	530	7	synthesize	synthesize	VERB
cjfa-35471	530	8	the	the	DET
cjfa-35471	530	9	periods	period	NOUN
cjfa-35471	530	10	where	where	SCONJ
cjfa-35471	530	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	530	12	𝑢	𝑢	PRON
cjfa-35471	530	13	𝐼	𝐼	PROPN
cjfa-35471	530	14	or	or	CCONJ
cjfa-35471	530	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	530	16	𝑢	𝑢	PROPN
cjfa-35471	530	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	530	18	and	and	CCONJ
cjfa-35471	530	19	the	the	DET
cjfa-35471	530	20	periods	period	NOUN
cjfa-35471	530	21	where	where	SCONJ
cjfa-35471	530	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	530	23	𝐼	𝐼	ADP
cjfa-35471	530	24	𝐼.	𝐼.	PROPN
cjfa-35471	530	25	notice	notice	VERB
cjfa-35471	530	26	that	that	SCONJ
cjfa-35471	530	27	for	for	ADP
cjfa-35471	530	28	the	the	DET
cjfa-35471	530	29	condition	condition	NOUN
cjfa-35471	530	30	above	above	ADV
cjfa-35471	530	31	(	(	PUNCT
cjfa-35471	530	32	equation	equation	NOUN
cjfa-35471	530	33	4	4	NUM
cjfa-35471	530	34	)	)	PUNCT
cjfa-35471	530	35	to	to	PART
cjfa-35471	530	36	be	be	AUX
cjfa-35471	530	37	kept	keep	VERB
cjfa-35471	530	38	satisfied	satisfied	ADJ
cjfa-35471	530	39	depends	depend	VERB
cjfa-35471	530	40	on	on	ADP
cjfa-35471	530	41	ℎ	ℎ	PROPN
cjfa-35471	530	42	(	(	PUNCT
cjfa-35471	530	43	inventory	inventory	NOUN
cjfa-35471	530	44	holding	hold	VERB
cjfa-35471	530	45	cost	cost	NOUN
cjfa-35471	530	46	)	)	PUNCT
cjfa-35471	530	47	,	,	PUNCT
cjfa-35471	530	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	530	49	the	the	DET
cjfa-35471	530	50	interest	interest	NOUN
cjfa-35471	530	51	rates	rate	NOUN
cjfa-35471	530	52	,	,	PUNCT
cjfa-35471	530	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	530	54	,	,	PUNCT
cjfa-35471	530	55	the	the	DET
cjfa-35471	530	56	marginal	marginal	ADJ
cjfa-35471	530	57	cost	cost	NOUN
cjfa-35471	530	58	of	of	ADP
cjfa-35471	530	59	production	production	NOUN
cjfa-35471	530	60	,	,	PUNCT
cjfa-35471	530	61	and	and	CCONJ
cjfa-35471	530	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	530	63	change	change	NOUN
cjfa-35471	530	64	in	in	ADP
cjfa-35471	530	65	the	the	DET
cjfa-35471	530	66	marginal	marginal	ADJ
cjfa-35471	530	67	cost	cost	NOUN
cjfa-35471	530	68	.	.	PUNCT
cjfa-35471	531	1	following	follow	VERB
cjfa-35471	531	2	conclusions	conclusion	NOUN
cjfa-35471	531	3	can	can	AUX
cjfa-35471	531	4	be	be	AUX
cjfa-35471	531	5	made	make	VERB
cjfa-35471	531	6	even	even	ADV
cjfa-35471	531	7	without	without	ADP
cjfa-35471	531	8	specific	specific	ADJ
cjfa-35471	531	9	forms	form	NOUN
cjfa-35471	531	10	of	of	ADP
cjfa-35471	531	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	531	12	,	,	PUNCT
cjfa-35471	531	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	531	14	,	,	PUNCT
cjfa-35471	531	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	531	16	and	and	CCONJ
cjfa-35471	531	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	531	18	on	on	ADP
cjfa-35471	531	19	the	the	DET
cjfa-35471	531	20	basis	basis	NOUN
cjfa-35471	531	21	of	of	ADP
cjfa-35471	531	22	equation	equation	NOUN
cjfa-35471	531	23	(	(	PUNCT
cjfa-35471	531	24	4	4	NUM
cjfa-35471	531	25	):	):	PUNCT
cjfa-35471	531	26	1	1	NUM
cjfa-35471	531	27	.	.	PUNCT
cjfa-35471	532	1	the	the	DET
cjfa-35471	532	2	firm	firm	NOUN
cjfa-35471	532	3	will	will	AUX
cjfa-35471	532	4	keep	keep	VERB
cjfa-35471	532	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	532	6	𝑢	𝑢	ADP
cjfa-35471	532	7	𝐼	𝐼	PROPN
cjfa-35471	532	8	as	as	ADV
cjfa-35471	532	9	long	long	ADV
cjfa-35471	532	10	as	as	SCONJ
cjfa-35471	532	11	demand	demand	NOUN
cjfa-35471	532	12	is	be	AUX
cjfa-35471	532	13	falling	fall	VERB
cjfa-35471	532	14	or	or	CCONJ
cjfa-35471	532	15	constant	constant	ADJ
cjfa-35471	532	16	i.e.	i.e.	X
cjfa-35471	532	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	532	18	0	0	NOUN
cjfa-35471	532	19	implying	imply	VERB
cjfa-35471	532	20	that	that	SCONJ
cjfa-35471	532	21	the	the	DET
cjfa-35471	532	22	firm	firm	NOUN
cjfa-35471	532	23	will	will	AUX
cjfa-35471	532	24	choose	choose	VERB
cjfa-35471	532	25	to	to	PART
cjfa-35471	532	26	produce	produce	VERB
cjfa-35471	532	27	just	just	ADV
cjfa-35471	532	28	enough	enough	ADJ
cjfa-35471	532	29	to	to	PART
cjfa-35471	532	30	meet	meet	VERB
cjfa-35471	532	31	the	the	DET
cjfa-35471	532	32	demand	demand	NOUN
cjfa-35471	532	33	if	if	SCONJ
cjfa-35471	532	34	demand	demand	NOUN
cjfa-35471	532	35	is	be	AUX
cjfa-35471	532	36	falling	fall	VERB
cjfa-35471	532	37	since	since	SCONJ
cjfa-35471	532	38	both	both	PRON
cjfa-35471	532	39	ℎ	ℎ	NOUN
cjfa-35471	532	40	and	and	CCONJ
cjfa-35471	532	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	532	42	are	be	AUX
cjfa-35471	532	43	positive	positive	ADJ
cjfa-35471	532	44	.	.	PUNCT
cjfa-35471	533	1	2	2	X
cjfa-35471	533	2	.	.	X
cjfa-35471	533	3	the	the	DET
cjfa-35471	533	4	firm	firm	NOUN
cjfa-35471	533	5	will	will	AUX
cjfa-35471	533	6	keep	keep	VERB
cjfa-35471	533	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	533	8	𝑢	𝑢	ADP
cjfa-35471	533	9	𝐼	𝐼	NOUN
cjfa-35471	533	10	even	even	ADV
cjfa-35471	533	11	if	if	SCONJ
cjfa-35471	533	12	demand	demand	NOUN
cjfa-35471	533	13	is	be	AUX
cjfa-35471	533	14	increasing	increase	VERB
cjfa-35471	533	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	533	16	𝑟	𝑟	X
cjfa-35471	533	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	533	18	but	but	CCONJ
cjfa-35471	533	19	the	the	DET
cjfa-35471	533	20	term	term	NOUN
cjfa-35471	533	21	ℎ	ℎ	PROPN
cjfa-35471	533	22	+	+	CCONJ
cjfa-35471	533	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	533	24	�	�	PROPN
cjfa-35471	533	25	�	�	PROPN
cjfa-35471	533	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	533	27	�	�	PROPN
cjfa-35471	533	28	is	be	AUX
cjfa-35471	533	29	large	large	ADJ
cjfa-35471	533	30	enough	enough	ADV
cjfa-35471	533	31	to	to	PART
cjfa-35471	533	32	keep	keep	VERB
cjfa-35471	533	33	inequality	inequality	NOUN
cjfa-35471	533	34	(	(	PUNCT
cjfa-35471	533	35	4	4	NUM
cjfa-35471	533	36	)	)	PUNCT
cjfa-35471	533	37	satisfied	satisfied	ADJ
cjfa-35471	533	38	.	.	PUNCT
cjfa-35471	534	1	decreasing	decrease	VERB
cjfa-35471	534	2	interest	interest	NOUN
cjfa-35471	534	3	rates	rate	NOUN
cjfa-35471	534	4	will	will	AUX
cjfa-35471	534	5	not	not	PART
cjfa-35471	534	6	be	be	AUX
cjfa-35471	534	7	a	a	DET
cjfa-35471	534	8	remedy	remedy	NOUN
cjfa-35471	534	9	in	in	ADP
cjfa-35471	534	10	this	this	DET
cjfa-35471	534	11	case	case	NOUN
cjfa-35471	534	12	if	if	SCONJ
cjfa-35471	534	13	they	they	PRON
cjfa-35471	534	14	are	be	AUX
cjfa-35471	534	15	already	already	ADV
cjfa-35471	534	16	low	low	ADJ
cjfa-35471	534	17	.	.	PUNCT
cjfa-35471	535	1	firms	firm	NOUN
cjfa-35471	535	2	where	where	SCONJ
cjfa-35471	535	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	535	4	�	�	PROPN
cjfa-35471	535	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	535	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	535	7	�	�	PROPN
cjfa-35471	535	8	is	be	AUX
cjfa-35471	535	9	low	low	ADJ
cjfa-35471	535	10	(	(	PUNCT
cjfa-35471	535	11	large	large	ADJ
cjfa-35471	535	12	and	and	CCONJ
cjfa-35471	535	13	already	already	ADV
cjfa-35471	535	14	very	very	ADV
cjfa-35471	535	15	efficient	efficient	ADJ
cjfa-35471	535	16	firms	firm	NOUN
cjfa-35471	535	17	)	)	PUNCT
cjfa-35471	535	18	will	will	AUX
cjfa-35471	535	19	have	have	VERB
cjfa-35471	535	20	more	more	ADJ
cjfa-35471	535	21	difficulty	difficulty	NOUN
cjfa-35471	535	22	to	to	PART
cjfa-35471	535	23	produce	produce	VERB
cjfa-35471	535	24	to	to	PART
cjfa-35471	535	25	build	build	VERB
cjfa-35471	535	26	up	up	ADP
cjfa-35471	535	27	inventories	inventory	NOUN
cjfa-35471	535	28	.	.	PUNCT
cjfa-35471	536	1	currently	currently	ADV
cjfa-35471	536	2	,	,	PUNCT
cjfa-35471	536	3	this	this	PRON
cjfa-35471	536	4	seems	seem	VERB
cjfa-35471	536	5	to	to	PART
cjfa-35471	536	6	be	be	AUX
cjfa-35471	536	7	the	the	DET
cjfa-35471	536	8	case	case	NOUN
cjfa-35471	536	9	in	in	ADP
cjfa-35471	536	10	major	major	ADJ
cjfa-35471	536	11	economies	economy	NOUN
cjfa-35471	536	12	.	.	PUNCT
cjfa-35471	537	1	3	3	X
cjfa-35471	537	2	.	.	X
cjfa-35471	537	3	higher	high	ADJ
cjfa-35471	537	4	interest	interest	NOUN
cjfa-35471	537	5	rates	rate	NOUN
cjfa-35471	537	6	and	and	CCONJ
cjfa-35471	537	7	the	the	DET
cjfa-35471	537	8	use	use	NOUN
cjfa-35471	537	9	of	of	ADP
cjfa-35471	537	10	inefficient	inefficient	ADJ
cjfa-35471	537	11	technologies	technology	NOUN
cjfa-35471	537	12	(	(	PUNCT
cjfa-35471	537	13	large	large	ADJ
cjfa-35471	537	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	537	15	)	)	PUNCT
cjfa-35471	537	16	implies	imply	VERB
cjfa-35471	537	17	high	high	ADJ
cjfa-35471	537	18	marginal	marginal	ADJ
cjfa-35471	537	19	cost	cost	NOUN
cjfa-35471	537	20	)	)	PUNCT
cjfa-35471	537	21	will	will	AUX
cjfa-35471	537	22	induce	induce	VERB
cjfa-35471	537	23	firms	firm	NOUN
cjfa-35471	537	24	to	to	PART
cjfa-35471	537	25	wait	wait	VERB
cjfa-35471	537	26	longer	long	ADV
cjfa-35471	537	27	for	for	ADP
cjfa-35471	537	28	inventory	inventory	NOUN
cjfa-35471	537	29	build	build	NOUN
cjfa-35471	537	30	-	-	PUNCT
cjfa-35471	537	31	up	up	NOUN
cjfa-35471	537	32	even	even	ADV
cjfa-35471	537	33	if	if	SCONJ
cjfa-35471	537	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	537	35	is	be	AUX
cjfa-35471	537	36	positive	positive	ADJ
cjfa-35471	537	37	.	.	PUNCT
cjfa-35471	538	1	4	4	X
cjfa-35471	538	2	.	.	X
cjfa-35471	538	3	the	the	DET
cjfa-35471	538	4	level	level	NOUN
cjfa-35471	538	5	of	of	ADP
cjfa-35471	538	6	technology	technology	NOUN
cjfa-35471	538	7	used	use	VERB
cjfa-35471	538	8	will	will	AUX
cjfa-35471	538	9	not	not	PART
cjfa-35471	538	10	affect	affect	VERB
cjfa-35471	538	11	the	the	DET
cjfa-35471	538	12	behavior	behavior	NOUN
cjfa-35471	538	13	of	of	ADP
cjfa-35471	538	14	the	the	DET
cjfa-35471	538	15	firms	firm	NOUN
cjfa-35471	538	16	if	if	SCONJ
cjfa-35471	538	17	the	the	DET
cjfa-35471	538	18	interest	interest	NOUN
cjfa-35471	538	19	rates	rate	NOUN
cjfa-35471	538	20	are	be	AUX
cjfa-35471	538	21	very	very	ADV
cjfa-35471	538	22	low	low	ADJ
cjfa-35471	538	23	as	as	SCONJ
cjfa-35471	538	24	they	they	PRON
cjfa-35471	538	25	are	be	AUX
cjfa-35471	538	26	now	now	ADV
cjfa-35471	538	27	in	in	ADP
cjfa-35471	538	28	many	many	ADJ
cjfa-35471	538	29	developed	develop	VERB
cjfa-35471	538	30	nations	nation	NOUN
cjfa-35471	538	31	since	since	SCONJ
cjfa-35471	538	32	the	the	DET
cjfa-35471	538	33	term	term	NOUN
cjfa-35471	538	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	538	35	in	in	ADP
cjfa-35471	538	36	)	)	PUNCT
cjfa-35471	538	37	implies	imply	VERB
cjfa-35471	538	38	high	high	ADJ
cjfa-35471	538	39	marginal	marginal	ADJ
cjfa-35471	538	40	cost	cost	NOUN
cjfa-35471	538	41	)	)	PUNCT
cjfa-35471	538	42	will	will	AUX
cjfa-35471	538	43	induce	induce	VERB
cjfa-35471	538	44	firms	firm	NOUN
cjfa-35471	538	45	to	to	PART
cjfa-35471	538	46	wait	wait	VERB
cjfa-35471	538	47	longer	long	ADV
cjfa-35471	538	48	for	for	ADP
cjfa-35471	538	49	inventory	inventory	NOUN
cjfa-35471	538	50	build	build	NOUN
cjfa-35471	538	51	-	-	PUNCT
cjfa-35471	538	52	up	up	NOUN
cjfa-35471	538	53	even	even	ADV
cjfa-35471	538	54	if	if	SCONJ
cjfa-35471	538	55	then	then	ADV
cjfa-35471	538	56	using	use	VERB
cjfa-35471	538	57	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	538	58	𝑢	𝑢	PROPN
cjfa-35471	538	59	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	538	60	,	,	PUNCT
cjfa-35471	538	61	equation	equation	NOUN
cjfa-35471	538	62	(	(	PUNCT
cjfa-35471	538	63	1	1	NUM
cjfa-35471	538	64	)	)	PUNCT
cjfa-35471	538	65	,	,	PUNCT
cjfa-35471	538	66	and	and	CCONJ
cjfa-35471	538	67	the	the	DET
cjfa-35471	538	68	conditions	condition	NOUN
cjfa-35471	538	69	(	(	PUNCT
cjfa-35471	538	70	the	the	DET
cjfa-35471	538	71	necessary	necessary	ADJ
cjfa-35471	538	72	condition	condition	NOUN
cjfa-35471	538	73	to	to	PART
cjfa-35471	538	74	keep	keep	VERB
cjfa-35471	538	75	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	538	76	𝑢	𝑢	ADP
cjfa-35471	538	77	𝐼	𝐼	PROPN
cjfa-35471	538	78	optimal	optimal	ADJ
cjfa-35471	538	79	)	)	PUNCT
cjfa-35471	538	80	developed	develop	VERB
cjfa-35471	538	81	by	by	ADP
cjfa-35471	538	82	pontryagin	pontryagin	NOUN
cjfa-35471	538	83	,	,	PUNCT
cjfa-35471	538	84	boltyanskii	boltyanskii	ADJ
cjfa-35471	538	85	,	,	PUNCT
cjfa-35471	538	86	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	538	87	and	and	CCONJ
cjfa-35471	538	88	mishechenko	mishechenko	NOUN
cjfa-35471	538	89	(	(	PUNCT
cjfa-35471	538	90	1962	1962	NUM
cjfa-35471	538	91	)	)	PUNCT
cjfa-35471	538	92	,	,	PUNCT
cjfa-35471	538	93	hestenes	hestene	NOUN
cjfa-35471	538	94	(	(	PUNCT
cjfa-35471	538	95	1966	1966	NUM
cjfa-35471	538	96	)	)	PUNCT
cjfa-35471	538	97	,	,	PUNCT
cjfa-35471	538	98	kamien	kamien	NOUN
cjfa-35471	538	99	and	and	CCONJ
cjfa-35471	538	100	schwartz	schwartz	PROPN
cjfa-35471	538	101	(	(	PUNCT
cjfa-35471	538	102	2012	2012	NUM
cjfa-35471	538	103	)	)	PUNCT
cjfa-35471	538	104	among	among	ADP
cjfa-35471	538	105	many	many	ADJ
cjfa-35471	538	106	others	other	NOUN
cjfa-35471	538	107	,	,	PUNCT
cjfa-35471	538	108	we	we	PRON
cjfa-35471	538	109	have	have	VERB
cjfa-35471	538	110	;	;	PUNCT
cjfa-35471	539	1	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	539	2	�	�	NOUN
cjfa-35471	539	3	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	539	4	≤	≤	PUNCT
cjfa-35471	539	5	𝐼	𝐼	PROPN
cjfa-35471	539	6	for	for	ADP
cjfa-35471	539	7	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	539	8	�	�	PROPN
cjfa-35471	539	9	≤	≤	NUM
cjfa-35471	539	10	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	539	11	≤	≤	NUM
cjfa-35471	539	12	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	539	13	�	�	PROPN
cjfa-35471	539	14	implies	imply	VERB
cjfa-35471	539	15	:	:	PUNCT
cjfa-35471	539	16	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	539	17	�	�	PROPN
cjfa-35471	539	18	�	�	PROPN
cjfa-35471	539	19	�	�	PROPN
cjfa-35471	539	20	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	539	21	�	�	PROPN
cjfa-35471	539	22	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	539	23	�	�	PROPN
cjfa-35471	539	24	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	539	25	≤	≤	PUNCT
cjfa-35471	539	26	ℎ	ℎ	PROPN
cjfa-35471	539	27	+	+	PROPN
cjfa-35471	539	28	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	539	29	�	�	PROPN
cjfa-35471	539	30	�	�	PROPN
cjfa-35471	539	31	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	539	32	�	�	PROPN
cjfa-35471	539	33	(	(	PUNCT
cjfa-35471	539	34	4	4	NUM
cjfa-35471	539	35	)	)	PUNCT
cjfa-35471	539	36	where	where	SCONJ
cjfa-35471	539	37	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	539	38	𝑢	𝑢	PROPN
cjfa-35471	539	39	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	539	40	�	�	NOUN
cjfa-35471	539	41	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	539	42	denotes	denote	VERB
cjfa-35471	539	43	the	the	DET
cjfa-35471	539	44	interest	interest	NOUN
cjfa-35471	539	45	rate	rate	NOUN
cjfa-35471	539	46	.	.	PUNCT
cjfa-35471	540	1	as	as	ADV
cjfa-35471	540	2	long	long	ADV
cjfa-35471	540	3	as	as	SCONJ
cjfa-35471	540	4	the	the	DET
cjfa-35471	540	5	condition	condition	NOUN
cjfa-35471	540	6	specified	specify	VERB
cjfa-35471	540	7	by	by	ADP
cjfa-35471	540	8	this	this	DET
cjfa-35471	540	9	inequality	inequality	NOUN
cjfa-35471	540	10	is	be	AUX
cjfa-35471	540	11	satisfied	satisfied	ADJ
cjfa-35471	540	12	it	it	PRON
cjfa-35471	540	13	will	will	AUX
cjfa-35471	540	14	be	be	AUX
cjfa-35471	540	15	optimal	optimal	ADJ
cjfa-35471	540	16	to	to	PART
cjfa-35471	540	17	keep	keep	VERB
cjfa-35471	540	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	540	19	𝑢	𝑢	ADP
cjfa-35471	540	20	𝐼	𝐼	ADP
cjfa-35471	540	21	implying	imply	VERB
cjfa-35471	540	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	540	23	𝑢	𝑢	PRON
cjfa-35471	540	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	540	25	this	this	PRON
cjfa-35471	540	26	means	mean	VERB
cjfa-35471	540	27	that	that	SCONJ
cjfa-35471	540	28	during	during	ADP
cjfa-35471	540	29	the	the	DET
cjfa-35471	540	30	intervals	interval	NOUN
cjfa-35471	540	31	where	where	SCONJ
cjfa-35471	540	32	this	this	DET
cjfa-35471	540	33	inequality	inequality	NOUN
cjfa-35471	540	34	is	be	AUX
cjfa-35471	540	35	satisfied	satisfied	ADJ
cjfa-35471	540	36	the	the	DET
cjfa-35471	540	37	firm	firm	NOUN
cjfa-35471	540	38	will	will	AUX
cjfa-35471	540	39	produce	produce	VERB
cjfa-35471	540	40	just	just	ADV
cjfa-35471	540	41	enough	enough	ADJ
cjfa-35471	540	42	to	to	PART
cjfa-35471	540	43	satisfy	satisfy	VERB
cjfa-35471	540	44	the	the	DET
cjfa-35471	540	45	demand	demand	NOUN
cjfa-35471	540	46	.	.	PUNCT
cjfa-35471	541	1	so	so	ADV
cjfa-35471	541	2	,	,	PUNCT
cjfa-35471	541	3	the	the	DET
cjfa-35471	541	4	condition	condition	NOUN
cjfa-35471	541	5	above	above	ADV
cjfa-35471	541	6	will	will	AUX
cjfa-35471	541	7	synthesize	synthesize	VERB
cjfa-35471	541	8	the	the	DET
cjfa-35471	541	9	periods	period	NOUN
cjfa-35471	541	10	where	where	SCONJ
cjfa-35471	541	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	541	12	𝑢	𝑢	PRON
cjfa-35471	541	13	𝐼	𝐼	PROPN
cjfa-35471	541	14	or	or	CCONJ
cjfa-35471	541	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	541	16	𝑢	𝑢	PROPN
cjfa-35471	541	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	541	18	and	and	CCONJ
cjfa-35471	541	19	the	the	DET
cjfa-35471	541	20	periods	period	NOUN
cjfa-35471	541	21	where	where	SCONJ
cjfa-35471	541	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	541	23	𝐼	𝐼	ADP
cjfa-35471	541	24	𝐼.	𝐼.	PROPN
cjfa-35471	541	25	notice	notice	VERB
cjfa-35471	541	26	that	that	SCONJ
cjfa-35471	541	27	for	for	ADP
cjfa-35471	541	28	the	the	DET
cjfa-35471	541	29	condition	condition	NOUN
cjfa-35471	541	30	above	above	ADV
cjfa-35471	541	31	(	(	PUNCT
cjfa-35471	541	32	equation	equation	NOUN
cjfa-35471	541	33	4	4	NUM
cjfa-35471	541	34	)	)	PUNCT
cjfa-35471	541	35	to	to	PART
cjfa-35471	541	36	be	be	AUX
cjfa-35471	541	37	kept	keep	VERB
cjfa-35471	541	38	satisfied	satisfied	ADJ
cjfa-35471	541	39	depends	depend	VERB
cjfa-35471	541	40	on	on	ADP
cjfa-35471	541	41	ℎ	ℎ	PROPN
cjfa-35471	541	42	(	(	PUNCT
cjfa-35471	541	43	inventory	inventory	NOUN
cjfa-35471	541	44	holding	hold	VERB
cjfa-35471	541	45	cost	cost	NOUN
cjfa-35471	541	46	)	)	PUNCT
cjfa-35471	541	47	,	,	PUNCT
cjfa-35471	541	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	541	49	the	the	DET
cjfa-35471	541	50	interest	interest	NOUN
cjfa-35471	541	51	rates	rate	NOUN
cjfa-35471	541	52	,	,	PUNCT
cjfa-35471	541	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	541	54	,	,	PUNCT
cjfa-35471	541	55	the	the	DET
cjfa-35471	541	56	marginal	marginal	ADJ
cjfa-35471	541	57	cost	cost	NOUN
cjfa-35471	541	58	of	of	ADP
cjfa-35471	541	59	production	production	NOUN
cjfa-35471	541	60	,	,	PUNCT
cjfa-35471	541	61	and	and	CCONJ
cjfa-35471	541	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	541	63	change	change	NOUN
cjfa-35471	541	64	in	in	ADP
cjfa-35471	541	65	the	the	DET
cjfa-35471	541	66	marginal	marginal	ADJ
cjfa-35471	541	67	cost	cost	NOUN
cjfa-35471	541	68	.	.	PUNCT
cjfa-35471	542	1	following	follow	VERB
cjfa-35471	542	2	conclusions	conclusion	NOUN
cjfa-35471	542	3	can	can	AUX
cjfa-35471	542	4	be	be	AUX
cjfa-35471	542	5	made	make	VERB
cjfa-35471	542	6	even	even	ADV
cjfa-35471	542	7	without	without	ADP
cjfa-35471	542	8	specific	specific	ADJ
cjfa-35471	542	9	forms	form	NOUN
cjfa-35471	542	10	of	of	ADP
cjfa-35471	542	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	542	12	,	,	PUNCT
cjfa-35471	542	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	542	14	,	,	PUNCT
cjfa-35471	542	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	542	16	and	and	CCONJ
cjfa-35471	542	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	542	18	on	on	ADP
cjfa-35471	542	19	the	the	DET
cjfa-35471	542	20	basis	basis	NOUN
cjfa-35471	542	21	of	of	ADP
cjfa-35471	542	22	equation	equation	NOUN
cjfa-35471	542	23	(	(	PUNCT
cjfa-35471	542	24	4	4	NUM
cjfa-35471	542	25	):	):	PUNCT
cjfa-35471	542	26	1	1	NUM
cjfa-35471	542	27	.	.	PUNCT
cjfa-35471	543	1	the	the	DET
cjfa-35471	543	2	firm	firm	NOUN
cjfa-35471	543	3	will	will	AUX
cjfa-35471	543	4	keep	keep	VERB
cjfa-35471	543	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	543	6	𝑢	𝑢	ADP
cjfa-35471	543	7	𝐼	𝐼	PROPN
cjfa-35471	543	8	as	as	ADV
cjfa-35471	543	9	long	long	ADV
cjfa-35471	543	10	as	as	SCONJ
cjfa-35471	543	11	demand	demand	NOUN
cjfa-35471	543	12	is	be	AUX
cjfa-35471	543	13	falling	fall	VERB
cjfa-35471	543	14	or	or	CCONJ
cjfa-35471	543	15	constant	constant	ADJ
cjfa-35471	543	16	i.e.	i.e.	X
cjfa-35471	543	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	543	18	0	0	NOUN
cjfa-35471	543	19	implying	imply	VERB
cjfa-35471	543	20	that	that	SCONJ
cjfa-35471	543	21	the	the	DET
cjfa-35471	543	22	firm	firm	NOUN
cjfa-35471	543	23	will	will	AUX
cjfa-35471	543	24	choose	choose	VERB
cjfa-35471	543	25	to	to	PART
cjfa-35471	543	26	produce	produce	VERB
cjfa-35471	543	27	just	just	ADV
cjfa-35471	543	28	enough	enough	ADJ
cjfa-35471	543	29	to	to	PART
cjfa-35471	543	30	meet	meet	VERB
cjfa-35471	543	31	the	the	DET
cjfa-35471	543	32	demand	demand	NOUN
cjfa-35471	543	33	if	if	SCONJ
cjfa-35471	543	34	demand	demand	NOUN
cjfa-35471	543	35	is	be	AUX
cjfa-35471	543	36	falling	fall	VERB
cjfa-35471	543	37	since	since	SCONJ
cjfa-35471	543	38	both	both	PRON
cjfa-35471	543	39	ℎ	ℎ	NOUN
cjfa-35471	543	40	and	and	CCONJ
cjfa-35471	543	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	543	42	are	be	AUX
cjfa-35471	543	43	positive	positive	ADJ
cjfa-35471	543	44	.	.	PUNCT
cjfa-35471	544	1	2	2	X
cjfa-35471	544	2	.	.	X
cjfa-35471	544	3	the	the	DET
cjfa-35471	544	4	firm	firm	NOUN
cjfa-35471	544	5	will	will	AUX
cjfa-35471	544	6	keep	keep	VERB
cjfa-35471	544	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	544	8	𝑢	𝑢	ADP
cjfa-35471	544	9	𝐼	𝐼	NOUN
cjfa-35471	544	10	even	even	ADV
cjfa-35471	544	11	if	if	SCONJ
cjfa-35471	544	12	demand	demand	NOUN
cjfa-35471	544	13	is	be	AUX
cjfa-35471	544	14	increasing	increase	VERB
cjfa-35471	544	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	544	16	𝑟	𝑟	X
cjfa-35471	544	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	544	18	but	but	CCONJ
cjfa-35471	544	19	the	the	DET
cjfa-35471	544	20	term	term	NOUN
cjfa-35471	544	21	ℎ	ℎ	PROPN
cjfa-35471	544	22	+	+	CCONJ
cjfa-35471	544	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	544	24	�	�	PROPN
cjfa-35471	544	25	�	�	PROPN
cjfa-35471	544	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	544	27	�	�	PROPN
cjfa-35471	544	28	is	be	AUX
cjfa-35471	544	29	large	large	ADJ
cjfa-35471	544	30	enough	enough	ADV
cjfa-35471	544	31	to	to	PART
cjfa-35471	544	32	keep	keep	VERB
cjfa-35471	544	33	inequality	inequality	NOUN
cjfa-35471	544	34	(	(	PUNCT
cjfa-35471	544	35	4	4	NUM
cjfa-35471	544	36	)	)	PUNCT
cjfa-35471	544	37	satisfied	satisfied	ADJ
cjfa-35471	544	38	.	.	PUNCT
cjfa-35471	545	1	decreasing	decrease	VERB
cjfa-35471	545	2	interest	interest	NOUN
cjfa-35471	545	3	rates	rate	NOUN
cjfa-35471	545	4	will	will	AUX
cjfa-35471	545	5	not	not	PART
cjfa-35471	545	6	be	be	AUX
cjfa-35471	545	7	a	a	DET
cjfa-35471	545	8	remedy	remedy	NOUN
cjfa-35471	545	9	in	in	ADP
cjfa-35471	545	10	this	this	DET
cjfa-35471	545	11	case	case	NOUN
cjfa-35471	545	12	if	if	SCONJ
cjfa-35471	545	13	they	they	PRON
cjfa-35471	545	14	are	be	AUX
cjfa-35471	545	15	already	already	ADV
cjfa-35471	545	16	low	low	ADJ
cjfa-35471	545	17	.	.	PUNCT
cjfa-35471	546	1	firms	firm	NOUN
cjfa-35471	546	2	where	where	SCONJ
cjfa-35471	546	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	546	4	�	�	PROPN
cjfa-35471	546	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	546	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	546	7	�	�	PROPN
cjfa-35471	546	8	is	be	AUX
cjfa-35471	546	9	low	low	ADJ
cjfa-35471	546	10	(	(	PUNCT
cjfa-35471	546	11	large	large	ADJ
cjfa-35471	546	12	and	and	CCONJ
cjfa-35471	546	13	already	already	ADV
cjfa-35471	546	14	very	very	ADV
cjfa-35471	546	15	efficient	efficient	ADJ
cjfa-35471	546	16	firms	firm	NOUN
cjfa-35471	546	17	)	)	PUNCT
cjfa-35471	546	18	will	will	AUX
cjfa-35471	546	19	have	have	VERB
cjfa-35471	546	20	more	more	ADJ
cjfa-35471	546	21	difficulty	difficulty	NOUN
cjfa-35471	546	22	to	to	PART
cjfa-35471	546	23	produce	produce	VERB
cjfa-35471	546	24	to	to	PART
cjfa-35471	546	25	build	build	VERB
cjfa-35471	546	26	up	up	ADP
cjfa-35471	546	27	inventories	inventory	NOUN
cjfa-35471	546	28	.	.	PUNCT
cjfa-35471	547	1	currently	currently	ADV
cjfa-35471	547	2	,	,	PUNCT
cjfa-35471	547	3	this	this	PRON
cjfa-35471	547	4	seems	seem	VERB
cjfa-35471	547	5	to	to	PART
cjfa-35471	547	6	be	be	AUX
cjfa-35471	547	7	the	the	DET
cjfa-35471	547	8	case	case	NOUN
cjfa-35471	547	9	in	in	ADP
cjfa-35471	547	10	major	major	ADJ
cjfa-35471	547	11	economies	economy	NOUN
cjfa-35471	547	12	.	.	PUNCT
cjfa-35471	548	1	3	3	X
cjfa-35471	548	2	.	.	X
cjfa-35471	548	3	higher	high	ADJ
cjfa-35471	548	4	interest	interest	NOUN
cjfa-35471	548	5	rates	rate	NOUN
cjfa-35471	548	6	and	and	CCONJ
cjfa-35471	548	7	the	the	DET
cjfa-35471	548	8	use	use	NOUN
cjfa-35471	548	9	of	of	ADP
cjfa-35471	548	10	inefficient	inefficient	ADJ
cjfa-35471	548	11	technologies	technology	NOUN
cjfa-35471	548	12	(	(	PUNCT
cjfa-35471	548	13	large	large	ADJ
cjfa-35471	548	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	548	15	)	)	PUNCT
cjfa-35471	548	16	implies	imply	VERB
cjfa-35471	548	17	high	high	ADJ
cjfa-35471	548	18	marginal	marginal	ADJ
cjfa-35471	548	19	cost	cost	NOUN
cjfa-35471	548	20	)	)	PUNCT
cjfa-35471	548	21	will	will	AUX
cjfa-35471	548	22	induce	induce	VERB
cjfa-35471	548	23	firms	firm	NOUN
cjfa-35471	548	24	to	to	PART
cjfa-35471	548	25	wait	wait	VERB
cjfa-35471	548	26	longer	long	ADV
cjfa-35471	548	27	for	for	ADP
cjfa-35471	548	28	inventory	inventory	NOUN
cjfa-35471	548	29	build	build	NOUN
cjfa-35471	548	30	-	-	PUNCT
cjfa-35471	548	31	up	up	NOUN
cjfa-35471	548	32	even	even	ADV
cjfa-35471	548	33	if	if	SCONJ
cjfa-35471	548	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	548	35	is	be	AUX
cjfa-35471	548	36	positive	positive	ADJ
cjfa-35471	548	37	.	.	PUNCT
cjfa-35471	549	1	4	4	X
cjfa-35471	549	2	.	.	X
cjfa-35471	549	3	the	the	DET
cjfa-35471	549	4	level	level	NOUN
cjfa-35471	549	5	of	of	ADP
cjfa-35471	549	6	technology	technology	NOUN
cjfa-35471	549	7	used	use	VERB
cjfa-35471	549	8	will	will	AUX
cjfa-35471	549	9	not	not	PART
cjfa-35471	549	10	affect	affect	VERB
cjfa-35471	549	11	the	the	DET
cjfa-35471	549	12	behavior	behavior	NOUN
cjfa-35471	549	13	of	of	ADP
cjfa-35471	549	14	the	the	DET
cjfa-35471	549	15	firms	firm	NOUN
cjfa-35471	549	16	if	if	SCONJ
cjfa-35471	549	17	the	the	DET
cjfa-35471	549	18	interest	interest	NOUN
cjfa-35471	549	19	rates	rate	NOUN
cjfa-35471	549	20	are	be	AUX
cjfa-35471	549	21	very	very	ADV
cjfa-35471	549	22	low	low	ADJ
cjfa-35471	549	23	as	as	SCONJ
cjfa-35471	549	24	they	they	PRON
cjfa-35471	549	25	are	be	AUX
cjfa-35471	549	26	now	now	ADV
cjfa-35471	549	27	in	in	ADP
cjfa-35471	549	28	many	many	ADJ
cjfa-35471	549	29	developed	develop	VERB
cjfa-35471	549	30	nations	nation	NOUN
cjfa-35471	549	31	since	since	SCONJ
cjfa-35471	549	32	the	the	DET
cjfa-35471	549	33	term	term	NOUN
cjfa-35471	549	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	549	35	in	in	ADP
cjfa-35471	549	36	is	be	AUX
cjfa-35471	549	37	positive	positive	ADJ
cjfa-35471	549	38	.	.	PUNCT
cjfa-35471	550	1	4	4	X
cjfa-35471	550	2	.	.	X
cjfa-35471	550	3	the	the	DET
cjfa-35471	550	4	level	level	NOUN
cjfa-35471	550	5	of	of	ADP
cjfa-35471	550	6	technology	technology	NOUN
cjfa-35471	550	7	used	use	VERB
cjfa-35471	550	8	will	will	AUX
cjfa-35471	550	9	not	not	PART
cjfa-35471	550	10	affect	affect	VERB
cjfa-35471	550	11	the	the	DET
cjfa-35471	550	12	behavior	behavior	NOUN
cjfa-35471	550	13	of	of	ADP
cjfa-35471	550	14	the	the	DET
cjfa-35471	550	15	firms	firm	NOUN
cjfa-35471	550	16	if	if	SCONJ
cjfa-35471	550	17	the	the	DET
cjfa-35471	550	18	interest	interest	NOUN
cjfa-35471	550	19	rates	rate	NOUN
cjfa-35471	550	20	are	be	AUX
cjfa-35471	550	21	very	very	ADV
cjfa-35471	550	22	low	low	ADJ
cjfa-35471	550	23	as	as	SCONJ
cjfa-35471	550	24	they	they	PRON
cjfa-35471	550	25	are	be	AUX
cjfa-35471	550	26	now	now	ADV
cjfa-35471	550	27	in	in	ADP
cjfa-35471	550	28	many	many	ADJ
cjfa-35471	550	29	developed	develop	VERB
cjfa-35471	550	30	nations	nation	NOUN
cjfa-35471	550	31	since	since	SCONJ
cjfa-35471	550	32	the	the	DET
cjfa-35471	550	33	term	term	NOUN
cjfa-35471	550	34	then	then	ADV
cjfa-35471	550	35	using	use	VERB
cjfa-35471	550	36	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	550	37	𝑢	𝑢	PROPN
cjfa-35471	550	38	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	550	39	,	,	PUNCT
cjfa-35471	550	40	equation	equation	NOUN
cjfa-35471	550	41	(	(	PUNCT
cjfa-35471	550	42	1	1	NUM
cjfa-35471	550	43	)	)	PUNCT
cjfa-35471	550	44	,	,	PUNCT
cjfa-35471	550	45	and	and	CCONJ
cjfa-35471	550	46	the	the	DET
cjfa-35471	550	47	conditions	condition	NOUN
cjfa-35471	550	48	(	(	PUNCT
cjfa-35471	550	49	the	the	DET
cjfa-35471	550	50	necessary	necessary	ADJ
cjfa-35471	550	51	condition	condition	NOUN
cjfa-35471	550	52	to	to	PART
cjfa-35471	550	53	keep	keep	VERB
cjfa-35471	550	54	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	550	55	𝑢	𝑢	ADP
cjfa-35471	550	56	𝐼	𝐼	PROPN
cjfa-35471	550	57	optimal	optimal	ADJ
cjfa-35471	550	58	)	)	PUNCT
cjfa-35471	550	59	developed	develop	VERB
cjfa-35471	550	60	by	by	ADP
cjfa-35471	550	61	pontryagin	pontryagin	NOUN
cjfa-35471	550	62	,	,	PUNCT
cjfa-35471	550	63	boltyanskii	boltyanskii	ADJ
cjfa-35471	550	64	,	,	PUNCT
cjfa-35471	550	65	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	550	66	and	and	CCONJ
cjfa-35471	550	67	mishechenko	mishechenko	NOUN
cjfa-35471	550	68	(	(	PUNCT
cjfa-35471	550	69	1962	1962	NUM
cjfa-35471	550	70	)	)	PUNCT
cjfa-35471	550	71	,	,	PUNCT
cjfa-35471	550	72	hestenes	hestene	NOUN
cjfa-35471	550	73	(	(	PUNCT
cjfa-35471	550	74	1966	1966	NUM
cjfa-35471	550	75	)	)	PUNCT
cjfa-35471	550	76	,	,	PUNCT
cjfa-35471	550	77	kamien	kamien	NOUN
cjfa-35471	550	78	and	and	CCONJ
cjfa-35471	550	79	schwartz	schwartz	PROPN
cjfa-35471	550	80	(	(	PUNCT
cjfa-35471	550	81	2012	2012	NUM
cjfa-35471	550	82	)	)	PUNCT
cjfa-35471	550	83	among	among	ADP
cjfa-35471	550	84	many	many	ADJ
cjfa-35471	550	85	others	other	NOUN
cjfa-35471	550	86	,	,	PUNCT
cjfa-35471	550	87	we	we	PRON
cjfa-35471	550	88	have	have	AUX
cjfa-35471	550	89	;	;	PUNCT
cjfa-35471	550	90	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	550	91	�	�	NOUN
cjfa-35471	550	92	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	550	93	≤	≤	PUNCT
cjfa-35471	550	94	𝐼	𝐼	PROPN
cjfa-35471	550	95	for	for	ADP
cjfa-35471	550	96	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	550	97	�	�	PROPN
cjfa-35471	550	98	≤	≤	NUM
cjfa-35471	551	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	551	2	≤	≤	NUM
cjfa-35471	551	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	551	4	�	�	PROPN
cjfa-35471	551	5	implies	imply	VERB
cjfa-35471	551	6	:	:	PUNCT
cjfa-35471	551	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	551	8	�	�	PROPN
cjfa-35471	551	9	�	�	PROPN
cjfa-35471	551	10	�	�	PROPN
cjfa-35471	551	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	551	12	�	�	PROPN
cjfa-35471	551	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	551	14	�	�	PROPN
cjfa-35471	551	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	551	16	≤	≤	PUNCT
cjfa-35471	551	17	ℎ	ℎ	PROPN
cjfa-35471	551	18	+	+	PROPN
cjfa-35471	551	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	551	20	�	�	PROPN
cjfa-35471	551	21	�	�	PROPN
cjfa-35471	551	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	551	23	�	�	PROPN
cjfa-35471	551	24	(	(	PUNCT
cjfa-35471	551	25	4	4	NUM
cjfa-35471	551	26	)	)	PUNCT
cjfa-35471	551	27	where	where	SCONJ
cjfa-35471	551	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	551	29	𝑢	𝑢	PROPN
cjfa-35471	551	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	551	31	�	�	NOUN
cjfa-35471	551	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	551	33	denotes	denote	VERB
cjfa-35471	551	34	the	the	DET
cjfa-35471	551	35	interest	interest	NOUN
cjfa-35471	551	36	rate	rate	NOUN
cjfa-35471	551	37	.	.	PUNCT
cjfa-35471	552	1	as	as	ADV
cjfa-35471	552	2	long	long	ADV
cjfa-35471	552	3	as	as	SCONJ
cjfa-35471	552	4	the	the	DET
cjfa-35471	552	5	condition	condition	NOUN
cjfa-35471	552	6	specified	specify	VERB
cjfa-35471	552	7	by	by	ADP
cjfa-35471	552	8	this	this	DET
cjfa-35471	552	9	inequality	inequality	NOUN
cjfa-35471	552	10	is	be	AUX
cjfa-35471	552	11	satisfied	satisfied	ADJ
cjfa-35471	552	12	it	it	PRON
cjfa-35471	552	13	will	will	AUX
cjfa-35471	552	14	be	be	AUX
cjfa-35471	552	15	optimal	optimal	ADJ
cjfa-35471	552	16	to	to	PART
cjfa-35471	552	17	keep	keep	VERB
cjfa-35471	552	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	552	19	𝑢	𝑢	ADP
cjfa-35471	552	20	𝐼	𝐼	ADP
cjfa-35471	552	21	implying	imply	VERB
cjfa-35471	552	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	552	23	𝑢	𝑢	PRON
cjfa-35471	552	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	552	25	this	this	PRON
cjfa-35471	552	26	means	mean	VERB
cjfa-35471	552	27	that	that	SCONJ
cjfa-35471	552	28	during	during	ADP
cjfa-35471	552	29	the	the	DET
cjfa-35471	552	30	intervals	interval	NOUN
cjfa-35471	552	31	where	where	SCONJ
cjfa-35471	552	32	this	this	DET
cjfa-35471	552	33	inequality	inequality	NOUN
cjfa-35471	552	34	is	be	AUX
cjfa-35471	552	35	satisfied	satisfied	ADJ
cjfa-35471	552	36	the	the	DET
cjfa-35471	552	37	firm	firm	NOUN
cjfa-35471	552	38	will	will	AUX
cjfa-35471	552	39	produce	produce	VERB
cjfa-35471	552	40	just	just	ADV
cjfa-35471	552	41	enough	enough	ADJ
cjfa-35471	552	42	to	to	PART
cjfa-35471	552	43	satisfy	satisfy	VERB
cjfa-35471	552	44	the	the	DET
cjfa-35471	552	45	demand	demand	NOUN
cjfa-35471	552	46	.	.	PUNCT
cjfa-35471	553	1	so	so	ADV
cjfa-35471	553	2	,	,	PUNCT
cjfa-35471	553	3	the	the	DET
cjfa-35471	553	4	condition	condition	NOUN
cjfa-35471	553	5	above	above	ADV
cjfa-35471	553	6	will	will	AUX
cjfa-35471	553	7	synthesize	synthesize	VERB
cjfa-35471	553	8	the	the	DET
cjfa-35471	553	9	periods	period	NOUN
cjfa-35471	553	10	where	where	SCONJ
cjfa-35471	553	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	553	12	𝑢	𝑢	PRON
cjfa-35471	553	13	𝐼	𝐼	PROPN
cjfa-35471	553	14	or	or	CCONJ
cjfa-35471	553	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	553	16	𝑢	𝑢	PROPN
cjfa-35471	553	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	553	18	and	and	CCONJ
cjfa-35471	553	19	the	the	DET
cjfa-35471	553	20	periods	period	NOUN
cjfa-35471	553	21	where	where	SCONJ
cjfa-35471	553	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	553	23	𝐼	𝐼	ADP
cjfa-35471	553	24	𝐼.	𝐼.	PROPN
cjfa-35471	553	25	notice	notice	VERB
cjfa-35471	553	26	that	that	SCONJ
cjfa-35471	553	27	for	for	ADP
cjfa-35471	553	28	the	the	DET
cjfa-35471	553	29	condition	condition	NOUN
cjfa-35471	553	30	above	above	ADV
cjfa-35471	553	31	(	(	PUNCT
cjfa-35471	553	32	equation	equation	NOUN
cjfa-35471	553	33	4	4	NUM
cjfa-35471	553	34	)	)	PUNCT
cjfa-35471	553	35	to	to	PART
cjfa-35471	553	36	be	be	AUX
cjfa-35471	553	37	kept	keep	VERB
cjfa-35471	553	38	satisfied	satisfied	ADJ
cjfa-35471	553	39	depends	depend	VERB
cjfa-35471	553	40	on	on	ADP
cjfa-35471	553	41	ℎ	ℎ	PROPN
cjfa-35471	553	42	(	(	PUNCT
cjfa-35471	553	43	inventory	inventory	NOUN
cjfa-35471	553	44	holding	hold	VERB
cjfa-35471	553	45	cost	cost	NOUN
cjfa-35471	553	46	)	)	PUNCT
cjfa-35471	553	47	,	,	PUNCT
cjfa-35471	553	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	553	49	the	the	DET
cjfa-35471	553	50	interest	interest	NOUN
cjfa-35471	553	51	rates	rate	NOUN
cjfa-35471	553	52	,	,	PUNCT
cjfa-35471	553	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	553	54	,	,	PUNCT
cjfa-35471	553	55	the	the	DET
cjfa-35471	553	56	marginal	marginal	ADJ
cjfa-35471	553	57	cost	cost	NOUN
cjfa-35471	553	58	of	of	ADP
cjfa-35471	553	59	production	production	NOUN
cjfa-35471	553	60	,	,	PUNCT
cjfa-35471	553	61	and	and	CCONJ
cjfa-35471	553	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	553	63	change	change	NOUN
cjfa-35471	553	64	in	in	ADP
cjfa-35471	553	65	the	the	DET
cjfa-35471	553	66	marginal	marginal	ADJ
cjfa-35471	553	67	cost	cost	NOUN
cjfa-35471	553	68	.	.	PUNCT
cjfa-35471	554	1	following	follow	VERB
cjfa-35471	554	2	conclusions	conclusion	NOUN
cjfa-35471	554	3	can	can	AUX
cjfa-35471	554	4	be	be	AUX
cjfa-35471	554	5	made	make	VERB
cjfa-35471	554	6	even	even	ADV
cjfa-35471	554	7	without	without	ADP
cjfa-35471	554	8	specific	specific	ADJ
cjfa-35471	554	9	forms	form	NOUN
cjfa-35471	554	10	of	of	ADP
cjfa-35471	554	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	554	12	,	,	PUNCT
cjfa-35471	554	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	554	14	,	,	PUNCT
cjfa-35471	554	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	554	16	and	and	CCONJ
cjfa-35471	554	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	554	18	on	on	ADP
cjfa-35471	554	19	the	the	DET
cjfa-35471	554	20	basis	basis	NOUN
cjfa-35471	554	21	of	of	ADP
cjfa-35471	554	22	equation	equation	NOUN
cjfa-35471	554	23	(	(	PUNCT
cjfa-35471	554	24	4	4	NUM
cjfa-35471	554	25	):	):	PUNCT
cjfa-35471	554	26	1	1	NUM
cjfa-35471	554	27	.	.	PUNCT
cjfa-35471	555	1	the	the	DET
cjfa-35471	555	2	firm	firm	NOUN
cjfa-35471	555	3	will	will	AUX
cjfa-35471	555	4	keep	keep	VERB
cjfa-35471	555	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	555	6	𝑢	𝑢	ADP
cjfa-35471	555	7	𝐼	𝐼	PROPN
cjfa-35471	555	8	as	as	ADV
cjfa-35471	555	9	long	long	ADV
cjfa-35471	555	10	as	as	SCONJ
cjfa-35471	555	11	demand	demand	NOUN
cjfa-35471	555	12	is	be	AUX
cjfa-35471	555	13	falling	fall	VERB
cjfa-35471	555	14	or	or	CCONJ
cjfa-35471	555	15	constant	constant	ADJ
cjfa-35471	555	16	i.e.	i.e.	X
cjfa-35471	555	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	555	18	0	0	NOUN
cjfa-35471	555	19	implying	imply	VERB
cjfa-35471	555	20	that	that	SCONJ
cjfa-35471	555	21	the	the	DET
cjfa-35471	555	22	firm	firm	NOUN
cjfa-35471	555	23	will	will	AUX
cjfa-35471	555	24	choose	choose	VERB
cjfa-35471	555	25	to	to	PART
cjfa-35471	555	26	produce	produce	VERB
cjfa-35471	555	27	just	just	ADV
cjfa-35471	555	28	enough	enough	ADJ
cjfa-35471	555	29	to	to	PART
cjfa-35471	555	30	meet	meet	VERB
cjfa-35471	555	31	the	the	DET
cjfa-35471	555	32	demand	demand	NOUN
cjfa-35471	555	33	if	if	SCONJ
cjfa-35471	555	34	demand	demand	NOUN
cjfa-35471	555	35	is	be	AUX
cjfa-35471	555	36	falling	fall	VERB
cjfa-35471	555	37	since	since	SCONJ
cjfa-35471	555	38	both	both	PRON
cjfa-35471	555	39	ℎ	ℎ	NOUN
cjfa-35471	555	40	and	and	CCONJ
cjfa-35471	555	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	555	42	are	be	AUX
cjfa-35471	555	43	positive	positive	ADJ
cjfa-35471	555	44	.	.	PUNCT
cjfa-35471	556	1	2	2	X
cjfa-35471	556	2	.	.	X
cjfa-35471	556	3	the	the	DET
cjfa-35471	556	4	firm	firm	NOUN
cjfa-35471	556	5	will	will	AUX
cjfa-35471	556	6	keep	keep	VERB
cjfa-35471	556	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	556	8	𝑢	𝑢	ADP
cjfa-35471	556	9	𝐼	𝐼	NOUN
cjfa-35471	556	10	even	even	ADV
cjfa-35471	556	11	if	if	SCONJ
cjfa-35471	556	12	demand	demand	NOUN
cjfa-35471	556	13	is	be	AUX
cjfa-35471	556	14	increasing	increase	VERB
cjfa-35471	556	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	556	16	𝑟	𝑟	X
cjfa-35471	556	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	556	18	but	but	CCONJ
cjfa-35471	556	19	the	the	DET
cjfa-35471	556	20	term	term	NOUN
cjfa-35471	556	21	ℎ	ℎ	PROPN
cjfa-35471	556	22	+	+	CCONJ
cjfa-35471	556	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	556	24	�	�	PROPN
cjfa-35471	556	25	�	�	PROPN
cjfa-35471	556	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	556	27	�	�	PROPN
cjfa-35471	556	28	is	be	AUX
cjfa-35471	556	29	large	large	ADJ
cjfa-35471	556	30	enough	enough	ADV
cjfa-35471	556	31	to	to	PART
cjfa-35471	556	32	keep	keep	VERB
cjfa-35471	556	33	inequality	inequality	NOUN
cjfa-35471	556	34	(	(	PUNCT
cjfa-35471	556	35	4	4	NUM
cjfa-35471	556	36	)	)	PUNCT
cjfa-35471	556	37	satisfied	satisfied	ADJ
cjfa-35471	556	38	.	.	PUNCT
cjfa-35471	557	1	decreasing	decrease	VERB
cjfa-35471	557	2	interest	interest	NOUN
cjfa-35471	557	3	rates	rate	NOUN
cjfa-35471	557	4	will	will	AUX
cjfa-35471	557	5	not	not	PART
cjfa-35471	557	6	be	be	AUX
cjfa-35471	557	7	a	a	DET
cjfa-35471	557	8	remedy	remedy	NOUN
cjfa-35471	557	9	in	in	ADP
cjfa-35471	557	10	this	this	DET
cjfa-35471	557	11	case	case	NOUN
cjfa-35471	557	12	if	if	SCONJ
cjfa-35471	557	13	they	they	PRON
cjfa-35471	557	14	are	be	AUX
cjfa-35471	557	15	already	already	ADV
cjfa-35471	557	16	low	low	ADJ
cjfa-35471	557	17	.	.	PUNCT
cjfa-35471	558	1	firms	firm	NOUN
cjfa-35471	558	2	where	where	SCONJ
cjfa-35471	558	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	558	4	�	�	PROPN
cjfa-35471	558	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	558	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	558	7	�	�	PROPN
cjfa-35471	558	8	is	be	AUX
cjfa-35471	558	9	low	low	ADJ
cjfa-35471	558	10	(	(	PUNCT
cjfa-35471	558	11	large	large	ADJ
cjfa-35471	558	12	and	and	CCONJ
cjfa-35471	558	13	already	already	ADV
cjfa-35471	558	14	very	very	ADV
cjfa-35471	558	15	efficient	efficient	ADJ
cjfa-35471	558	16	firms	firm	NOUN
cjfa-35471	558	17	)	)	PUNCT
cjfa-35471	558	18	will	will	AUX
cjfa-35471	558	19	have	have	VERB
cjfa-35471	558	20	more	more	ADJ
cjfa-35471	558	21	difficulty	difficulty	NOUN
cjfa-35471	558	22	to	to	PART
cjfa-35471	558	23	produce	produce	VERB
cjfa-35471	558	24	to	to	PART
cjfa-35471	558	25	build	build	VERB
cjfa-35471	558	26	up	up	ADP
cjfa-35471	558	27	inventories	inventory	NOUN
cjfa-35471	558	28	.	.	PUNCT
cjfa-35471	559	1	currently	currently	ADV
cjfa-35471	559	2	,	,	PUNCT
cjfa-35471	559	3	this	this	PRON
cjfa-35471	559	4	seems	seem	VERB
cjfa-35471	559	5	to	to	PART
cjfa-35471	559	6	be	be	AUX
cjfa-35471	559	7	the	the	DET
cjfa-35471	559	8	case	case	NOUN
cjfa-35471	559	9	in	in	ADP
cjfa-35471	559	10	major	major	ADJ
cjfa-35471	559	11	economies	economy	NOUN
cjfa-35471	559	12	.	.	PUNCT
cjfa-35471	560	1	3	3	X
cjfa-35471	560	2	.	.	X
cjfa-35471	560	3	higher	high	ADJ
cjfa-35471	560	4	interest	interest	NOUN
cjfa-35471	560	5	rates	rate	NOUN
cjfa-35471	560	6	and	and	CCONJ
cjfa-35471	560	7	the	the	DET
cjfa-35471	560	8	use	use	NOUN
cjfa-35471	560	9	of	of	ADP
cjfa-35471	560	10	inefficient	inefficient	ADJ
cjfa-35471	560	11	technologies	technology	NOUN
cjfa-35471	560	12	(	(	PUNCT
cjfa-35471	560	13	large	large	ADJ
cjfa-35471	560	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	560	15	)	)	PUNCT
cjfa-35471	560	16	implies	imply	VERB
cjfa-35471	560	17	high	high	ADJ
cjfa-35471	560	18	marginal	marginal	ADJ
cjfa-35471	560	19	cost	cost	NOUN
cjfa-35471	560	20	)	)	PUNCT
cjfa-35471	560	21	will	will	AUX
cjfa-35471	560	22	induce	induce	VERB
cjfa-35471	560	23	firms	firm	NOUN
cjfa-35471	560	24	to	to	PART
cjfa-35471	560	25	wait	wait	VERB
cjfa-35471	560	26	longer	long	ADV
cjfa-35471	560	27	for	for	ADP
cjfa-35471	560	28	inventory	inventory	NOUN
cjfa-35471	560	29	build	build	NOUN
cjfa-35471	560	30	-	-	PUNCT
cjfa-35471	560	31	up	up	NOUN
cjfa-35471	560	32	even	even	ADV
cjfa-35471	560	33	if	if	SCONJ
cjfa-35471	560	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	560	35	is	be	AUX
cjfa-35471	560	36	positive	positive	ADJ
cjfa-35471	560	37	.	.	PUNCT
cjfa-35471	561	1	4	4	X
cjfa-35471	561	2	.	.	X
cjfa-35471	561	3	the	the	DET
cjfa-35471	561	4	level	level	NOUN
cjfa-35471	561	5	of	of	ADP
cjfa-35471	561	6	technology	technology	NOUN
cjfa-35471	561	7	used	use	VERB
cjfa-35471	561	8	will	will	AUX
cjfa-35471	561	9	not	not	PART
cjfa-35471	561	10	affect	affect	VERB
cjfa-35471	561	11	the	the	DET
cjfa-35471	561	12	behavior	behavior	NOUN
cjfa-35471	561	13	of	of	ADP
cjfa-35471	561	14	the	the	DET
cjfa-35471	561	15	firms	firm	NOUN
cjfa-35471	561	16	if	if	SCONJ
cjfa-35471	561	17	the	the	DET
cjfa-35471	561	18	interest	interest	NOUN
cjfa-35471	561	19	rates	rate	NOUN
cjfa-35471	561	20	are	be	AUX
cjfa-35471	561	21	very	very	ADV
cjfa-35471	561	22	low	low	ADJ
cjfa-35471	561	23	as	as	SCONJ
cjfa-35471	561	24	they	they	PRON
cjfa-35471	561	25	are	be	AUX
cjfa-35471	561	26	now	now	ADV
cjfa-35471	561	27	in	in	ADP
cjfa-35471	561	28	many	many	ADJ
cjfa-35471	561	29	developed	develop	VERB
cjfa-35471	561	30	nations	nation	NOUN
cjfa-35471	561	31	since	since	SCONJ
cjfa-35471	561	32	the	the	DET
cjfa-35471	561	33	term	term	NOUN
cjfa-35471	561	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	561	35	in	in	ADP
cjfa-35471	561	36	in	in	ADP
cjfa-35471	561	37	equation	equation	NOUN
cjfa-35471	561	38	will	will	AUX
cjfa-35471	561	39	be	be	AUX
cjfa-35471	561	40	low	low	ADJ
cjfa-35471	561	41	even	even	ADV
cjfa-35471	561	42	if	if	SCONJ
cjfa-35471	561	43	then	then	ADV
cjfa-35471	561	44	using	use	VERB
cjfa-35471	561	45	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	561	46	𝑢	𝑢	PROPN
cjfa-35471	561	47	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	561	48	,	,	PUNCT
cjfa-35471	561	49	equation	equation	NOUN
cjfa-35471	561	50	(	(	PUNCT
cjfa-35471	561	51	1	1	NUM
cjfa-35471	561	52	)	)	PUNCT
cjfa-35471	561	53	,	,	PUNCT
cjfa-35471	561	54	and	and	CCONJ
cjfa-35471	561	55	the	the	DET
cjfa-35471	561	56	conditions	condition	NOUN
cjfa-35471	561	57	(	(	PUNCT
cjfa-35471	561	58	the	the	DET
cjfa-35471	561	59	necessary	necessary	ADJ
cjfa-35471	561	60	condition	condition	NOUN
cjfa-35471	561	61	to	to	PART
cjfa-35471	561	62	keep	keep	VERB
cjfa-35471	561	63	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	561	64	𝑢	𝑢	ADP
cjfa-35471	561	65	𝐼	𝐼	PROPN
cjfa-35471	561	66	optimal	optimal	ADJ
cjfa-35471	561	67	)	)	PUNCT
cjfa-35471	561	68	developed	develop	VERB
cjfa-35471	561	69	by	by	ADP
cjfa-35471	561	70	pontryagin	pontryagin	NOUN
cjfa-35471	561	71	,	,	PUNCT
cjfa-35471	561	72	boltyanskii	boltyanskii	ADJ
cjfa-35471	561	73	,	,	PUNCT
cjfa-35471	561	74	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	561	75	and	and	CCONJ
cjfa-35471	561	76	mishechenko	mishechenko	NOUN
cjfa-35471	561	77	(	(	PUNCT
cjfa-35471	561	78	1962	1962	NUM
cjfa-35471	561	79	)	)	PUNCT
cjfa-35471	561	80	,	,	PUNCT
cjfa-35471	561	81	hestenes	hestene	NOUN
cjfa-35471	561	82	(	(	PUNCT
cjfa-35471	561	83	1966	1966	NUM
cjfa-35471	561	84	)	)	PUNCT
cjfa-35471	561	85	,	,	PUNCT
cjfa-35471	561	86	kamien	kamien	NOUN
cjfa-35471	561	87	and	and	CCONJ
cjfa-35471	561	88	schwartz	schwartz	PROPN
cjfa-35471	561	89	(	(	PUNCT
cjfa-35471	561	90	2012	2012	NUM
cjfa-35471	561	91	)	)	PUNCT
cjfa-35471	561	92	among	among	ADP
cjfa-35471	561	93	many	many	ADJ
cjfa-35471	561	94	others	other	NOUN
cjfa-35471	561	95	,	,	PUNCT
cjfa-35471	561	96	we	we	PRON
cjfa-35471	561	97	have	have	VERB
cjfa-35471	561	98	;	;	PUNCT
cjfa-35471	561	99	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	561	100	�	�	NOUN
cjfa-35471	561	101	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	561	102	≤	≤	PUNCT
cjfa-35471	561	103	𝐼	𝐼	PROPN
cjfa-35471	561	104	for	for	ADP
cjfa-35471	561	105	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	561	106	�	�	PROPN
cjfa-35471	561	107	≤	≤	NUM
cjfa-35471	562	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	562	2	≤	≤	NUM
cjfa-35471	562	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	562	4	�	�	PROPN
cjfa-35471	562	5	implies	imply	VERB
cjfa-35471	562	6	:	:	PUNCT
cjfa-35471	562	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	562	8	�	�	PROPN
cjfa-35471	562	9	�	�	PROPN
cjfa-35471	562	10	�	�	PROPN
cjfa-35471	562	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	562	12	�	�	PROPN
cjfa-35471	562	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	562	14	�	�	PROPN
cjfa-35471	562	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	562	16	≤	≤	PUNCT
cjfa-35471	562	17	ℎ	ℎ	PROPN
cjfa-35471	562	18	+	+	PROPN
cjfa-35471	562	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	562	20	�	�	PROPN
cjfa-35471	562	21	�	�	PROPN
cjfa-35471	562	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	562	23	�	�	PROPN
cjfa-35471	562	24	(	(	PUNCT
cjfa-35471	562	25	4	4	NUM
cjfa-35471	562	26	)	)	PUNCT
cjfa-35471	562	27	where	where	SCONJ
cjfa-35471	562	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	562	29	𝑢	𝑢	PROPN
cjfa-35471	562	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	562	31	�	�	NOUN
cjfa-35471	562	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	562	33	denotes	denote	VERB
cjfa-35471	562	34	the	the	DET
cjfa-35471	562	35	interest	interest	NOUN
cjfa-35471	562	36	rate	rate	NOUN
cjfa-35471	562	37	.	.	PUNCT
cjfa-35471	563	1	as	as	ADV
cjfa-35471	563	2	long	long	ADV
cjfa-35471	563	3	as	as	SCONJ
cjfa-35471	563	4	the	the	DET
cjfa-35471	563	5	condition	condition	NOUN
cjfa-35471	563	6	specified	specify	VERB
cjfa-35471	563	7	by	by	ADP
cjfa-35471	563	8	this	this	DET
cjfa-35471	563	9	inequality	inequality	NOUN
cjfa-35471	563	10	is	be	AUX
cjfa-35471	563	11	satisfied	satisfied	ADJ
cjfa-35471	563	12	it	it	PRON
cjfa-35471	563	13	will	will	AUX
cjfa-35471	563	14	be	be	AUX
cjfa-35471	563	15	optimal	optimal	ADJ
cjfa-35471	563	16	to	to	PART
cjfa-35471	563	17	keep	keep	VERB
cjfa-35471	563	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	563	19	𝑢	𝑢	ADP
cjfa-35471	563	20	𝐼	𝐼	ADP
cjfa-35471	563	21	implying	imply	VERB
cjfa-35471	563	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	563	23	𝑢	𝑢	PRON
cjfa-35471	563	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	563	25	this	this	PRON
cjfa-35471	563	26	means	mean	VERB
cjfa-35471	563	27	that	that	SCONJ
cjfa-35471	563	28	during	during	ADP
cjfa-35471	563	29	the	the	DET
cjfa-35471	563	30	intervals	interval	NOUN
cjfa-35471	563	31	where	where	SCONJ
cjfa-35471	563	32	this	this	DET
cjfa-35471	563	33	inequality	inequality	NOUN
cjfa-35471	563	34	is	be	AUX
cjfa-35471	563	35	satisfied	satisfied	ADJ
cjfa-35471	563	36	the	the	DET
cjfa-35471	563	37	firm	firm	NOUN
cjfa-35471	563	38	will	will	AUX
cjfa-35471	563	39	produce	produce	VERB
cjfa-35471	563	40	just	just	ADV
cjfa-35471	563	41	enough	enough	ADJ
cjfa-35471	563	42	to	to	PART
cjfa-35471	563	43	satisfy	satisfy	VERB
cjfa-35471	563	44	the	the	DET
cjfa-35471	563	45	demand	demand	NOUN
cjfa-35471	563	46	.	.	PUNCT
cjfa-35471	564	1	so	so	ADV
cjfa-35471	564	2	,	,	PUNCT
cjfa-35471	564	3	the	the	DET
cjfa-35471	564	4	condition	condition	NOUN
cjfa-35471	564	5	above	above	ADV
cjfa-35471	564	6	will	will	AUX
cjfa-35471	564	7	synthesize	synthesize	VERB
cjfa-35471	564	8	the	the	DET
cjfa-35471	564	9	periods	period	NOUN
cjfa-35471	564	10	where	where	SCONJ
cjfa-35471	564	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	564	12	𝑢	𝑢	PRON
cjfa-35471	564	13	𝐼	𝐼	PROPN
cjfa-35471	564	14	or	or	CCONJ
cjfa-35471	564	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	564	16	𝑢	𝑢	PROPN
cjfa-35471	564	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	564	18	and	and	CCONJ
cjfa-35471	564	19	the	the	DET
cjfa-35471	564	20	periods	period	NOUN
cjfa-35471	564	21	where	where	SCONJ
cjfa-35471	564	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	564	23	𝐼	𝐼	ADP
cjfa-35471	564	24	𝐼.	𝐼.	PROPN
cjfa-35471	564	25	notice	notice	VERB
cjfa-35471	564	26	that	that	SCONJ
cjfa-35471	564	27	for	for	ADP
cjfa-35471	564	28	the	the	DET
cjfa-35471	564	29	condition	condition	NOUN
cjfa-35471	564	30	above	above	ADV
cjfa-35471	564	31	(	(	PUNCT
cjfa-35471	564	32	equation	equation	NOUN
cjfa-35471	564	33	4	4	NUM
cjfa-35471	564	34	)	)	PUNCT
cjfa-35471	564	35	to	to	PART
cjfa-35471	564	36	be	be	AUX
cjfa-35471	564	37	kept	keep	VERB
cjfa-35471	564	38	satisfied	satisfied	ADJ
cjfa-35471	564	39	depends	depend	VERB
cjfa-35471	564	40	on	on	ADP
cjfa-35471	564	41	ℎ	ℎ	PROPN
cjfa-35471	564	42	(	(	PUNCT
cjfa-35471	564	43	inventory	inventory	NOUN
cjfa-35471	564	44	holding	hold	VERB
cjfa-35471	564	45	cost	cost	NOUN
cjfa-35471	564	46	)	)	PUNCT
cjfa-35471	564	47	,	,	PUNCT
cjfa-35471	564	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	564	49	the	the	DET
cjfa-35471	564	50	interest	interest	NOUN
cjfa-35471	564	51	rates	rate	NOUN
cjfa-35471	564	52	,	,	PUNCT
cjfa-35471	564	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	564	54	,	,	PUNCT
cjfa-35471	564	55	the	the	DET
cjfa-35471	564	56	marginal	marginal	ADJ
cjfa-35471	564	57	cost	cost	NOUN
cjfa-35471	564	58	of	of	ADP
cjfa-35471	564	59	production	production	NOUN
cjfa-35471	564	60	,	,	PUNCT
cjfa-35471	564	61	and	and	CCONJ
cjfa-35471	564	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	564	63	change	change	NOUN
cjfa-35471	564	64	in	in	ADP
cjfa-35471	564	65	the	the	DET
cjfa-35471	564	66	marginal	marginal	ADJ
cjfa-35471	564	67	cost	cost	NOUN
cjfa-35471	564	68	.	.	PUNCT
cjfa-35471	565	1	following	follow	VERB
cjfa-35471	565	2	conclusions	conclusion	NOUN
cjfa-35471	565	3	can	can	AUX
cjfa-35471	565	4	be	be	AUX
cjfa-35471	565	5	made	make	VERB
cjfa-35471	565	6	even	even	ADV
cjfa-35471	565	7	without	without	ADP
cjfa-35471	565	8	specific	specific	ADJ
cjfa-35471	565	9	forms	form	NOUN
cjfa-35471	565	10	of	of	ADP
cjfa-35471	565	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	565	12	,	,	PUNCT
cjfa-35471	565	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	565	14	,	,	PUNCT
cjfa-35471	565	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	565	16	and	and	CCONJ
cjfa-35471	565	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	565	18	on	on	ADP
cjfa-35471	565	19	the	the	DET
cjfa-35471	565	20	basis	basis	NOUN
cjfa-35471	565	21	of	of	ADP
cjfa-35471	565	22	equation	equation	NOUN
cjfa-35471	565	23	(	(	PUNCT
cjfa-35471	565	24	4	4	NUM
cjfa-35471	565	25	):	):	PUNCT
cjfa-35471	565	26	1	1	NUM
cjfa-35471	565	27	.	.	PUNCT
cjfa-35471	566	1	the	the	DET
cjfa-35471	566	2	firm	firm	NOUN
cjfa-35471	566	3	will	will	AUX
cjfa-35471	566	4	keep	keep	VERB
cjfa-35471	566	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	566	6	𝑢	𝑢	ADP
cjfa-35471	566	7	𝐼	𝐼	PROPN
cjfa-35471	566	8	as	as	ADV
cjfa-35471	566	9	long	long	ADV
cjfa-35471	566	10	as	as	SCONJ
cjfa-35471	566	11	demand	demand	NOUN
cjfa-35471	566	12	is	be	AUX
cjfa-35471	566	13	falling	fall	VERB
cjfa-35471	566	14	or	or	CCONJ
cjfa-35471	566	15	constant	constant	ADJ
cjfa-35471	566	16	i.e.	i.e.	X
cjfa-35471	566	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	566	18	0	0	NOUN
cjfa-35471	566	19	implying	imply	VERB
cjfa-35471	566	20	that	that	SCONJ
cjfa-35471	566	21	the	the	DET
cjfa-35471	566	22	firm	firm	NOUN
cjfa-35471	566	23	will	will	AUX
cjfa-35471	566	24	choose	choose	VERB
cjfa-35471	566	25	to	to	PART
cjfa-35471	566	26	produce	produce	VERB
cjfa-35471	566	27	just	just	ADV
cjfa-35471	566	28	enough	enough	ADJ
cjfa-35471	566	29	to	to	PART
cjfa-35471	566	30	meet	meet	VERB
cjfa-35471	566	31	the	the	DET
cjfa-35471	566	32	demand	demand	NOUN
cjfa-35471	566	33	if	if	SCONJ
cjfa-35471	566	34	demand	demand	NOUN
cjfa-35471	566	35	is	be	AUX
cjfa-35471	566	36	falling	fall	VERB
cjfa-35471	566	37	since	since	SCONJ
cjfa-35471	566	38	both	both	PRON
cjfa-35471	566	39	ℎ	ℎ	NOUN
cjfa-35471	566	40	and	and	CCONJ
cjfa-35471	566	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	566	42	are	be	AUX
cjfa-35471	566	43	positive	positive	ADJ
cjfa-35471	566	44	.	.	PUNCT
cjfa-35471	567	1	2	2	X
cjfa-35471	567	2	.	.	X
cjfa-35471	567	3	the	the	DET
cjfa-35471	567	4	firm	firm	NOUN
cjfa-35471	567	5	will	will	AUX
cjfa-35471	567	6	keep	keep	VERB
cjfa-35471	567	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	567	8	𝑢	𝑢	ADP
cjfa-35471	567	9	𝐼	𝐼	NOUN
cjfa-35471	567	10	even	even	ADV
cjfa-35471	567	11	if	if	SCONJ
cjfa-35471	567	12	demand	demand	NOUN
cjfa-35471	567	13	is	be	AUX
cjfa-35471	567	14	increasing	increase	VERB
cjfa-35471	567	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	567	16	𝑟	𝑟	X
cjfa-35471	567	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	567	18	but	but	CCONJ
cjfa-35471	567	19	the	the	DET
cjfa-35471	567	20	term	term	NOUN
cjfa-35471	567	21	ℎ	ℎ	PROPN
cjfa-35471	567	22	+	+	CCONJ
cjfa-35471	567	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	567	24	�	�	PROPN
cjfa-35471	567	25	�	�	PROPN
cjfa-35471	567	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	567	27	�	�	PROPN
cjfa-35471	567	28	is	be	AUX
cjfa-35471	567	29	large	large	ADJ
cjfa-35471	567	30	enough	enough	ADV
cjfa-35471	567	31	to	to	PART
cjfa-35471	567	32	keep	keep	VERB
cjfa-35471	567	33	inequality	inequality	NOUN
cjfa-35471	567	34	(	(	PUNCT
cjfa-35471	567	35	4	4	NUM
cjfa-35471	567	36	)	)	PUNCT
cjfa-35471	567	37	satisfied	satisfied	ADJ
cjfa-35471	567	38	.	.	PUNCT
cjfa-35471	568	1	decreasing	decrease	VERB
cjfa-35471	568	2	interest	interest	NOUN
cjfa-35471	568	3	rates	rate	NOUN
cjfa-35471	568	4	will	will	AUX
cjfa-35471	568	5	not	not	PART
cjfa-35471	568	6	be	be	AUX
cjfa-35471	568	7	a	a	DET
cjfa-35471	568	8	remedy	remedy	NOUN
cjfa-35471	568	9	in	in	ADP
cjfa-35471	568	10	this	this	DET
cjfa-35471	568	11	case	case	NOUN
cjfa-35471	568	12	if	if	SCONJ
cjfa-35471	568	13	they	they	PRON
cjfa-35471	568	14	are	be	AUX
cjfa-35471	568	15	already	already	ADV
cjfa-35471	568	16	low	low	ADJ
cjfa-35471	568	17	.	.	PUNCT
cjfa-35471	569	1	firms	firm	NOUN
cjfa-35471	569	2	where	where	SCONJ
cjfa-35471	569	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	569	4	�	�	PROPN
cjfa-35471	569	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	569	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	569	7	�	�	PROPN
cjfa-35471	569	8	is	be	AUX
cjfa-35471	569	9	low	low	ADJ
cjfa-35471	569	10	(	(	PUNCT
cjfa-35471	569	11	large	large	ADJ
cjfa-35471	569	12	and	and	CCONJ
cjfa-35471	569	13	already	already	ADV
cjfa-35471	569	14	very	very	ADV
cjfa-35471	569	15	efficient	efficient	ADJ
cjfa-35471	569	16	firms	firm	NOUN
cjfa-35471	569	17	)	)	PUNCT
cjfa-35471	569	18	will	will	AUX
cjfa-35471	569	19	have	have	VERB
cjfa-35471	569	20	more	more	ADJ
cjfa-35471	569	21	difficulty	difficulty	NOUN
cjfa-35471	569	22	to	to	PART
cjfa-35471	569	23	produce	produce	VERB
cjfa-35471	569	24	to	to	PART
cjfa-35471	569	25	build	build	VERB
cjfa-35471	569	26	up	up	ADP
cjfa-35471	569	27	inventories	inventory	NOUN
cjfa-35471	569	28	.	.	PUNCT
cjfa-35471	570	1	currently	currently	ADV
cjfa-35471	570	2	,	,	PUNCT
cjfa-35471	570	3	this	this	PRON
cjfa-35471	570	4	seems	seem	VERB
cjfa-35471	570	5	to	to	PART
cjfa-35471	570	6	be	be	AUX
cjfa-35471	570	7	the	the	DET
cjfa-35471	570	8	case	case	NOUN
cjfa-35471	570	9	in	in	ADP
cjfa-35471	570	10	major	major	ADJ
cjfa-35471	570	11	economies	economy	NOUN
cjfa-35471	570	12	.	.	PUNCT
cjfa-35471	571	1	3	3	X
cjfa-35471	571	2	.	.	X
cjfa-35471	571	3	higher	high	ADJ
cjfa-35471	571	4	interest	interest	NOUN
cjfa-35471	571	5	rates	rate	NOUN
cjfa-35471	571	6	and	and	CCONJ
cjfa-35471	571	7	the	the	DET
cjfa-35471	571	8	use	use	NOUN
cjfa-35471	571	9	of	of	ADP
cjfa-35471	571	10	inefficient	inefficient	ADJ
cjfa-35471	571	11	technologies	technology	NOUN
cjfa-35471	571	12	(	(	PUNCT
cjfa-35471	571	13	large	large	ADJ
cjfa-35471	571	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	571	15	)	)	PUNCT
cjfa-35471	571	16	implies	imply	VERB
cjfa-35471	571	17	high	high	ADJ
cjfa-35471	571	18	marginal	marginal	ADJ
cjfa-35471	571	19	cost	cost	NOUN
cjfa-35471	571	20	)	)	PUNCT
cjfa-35471	571	21	will	will	AUX
cjfa-35471	571	22	induce	induce	VERB
cjfa-35471	571	23	firms	firm	NOUN
cjfa-35471	571	24	to	to	PART
cjfa-35471	571	25	wait	wait	VERB
cjfa-35471	571	26	longer	long	ADV
cjfa-35471	571	27	for	for	ADP
cjfa-35471	571	28	inventory	inventory	NOUN
cjfa-35471	571	29	build	build	NOUN
cjfa-35471	571	30	-	-	PUNCT
cjfa-35471	571	31	up	up	NOUN
cjfa-35471	571	32	even	even	ADV
cjfa-35471	571	33	if	if	SCONJ
cjfa-35471	571	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	571	35	is	be	AUX
cjfa-35471	571	36	positive	positive	ADJ
cjfa-35471	571	37	.	.	PUNCT
cjfa-35471	572	1	4	4	X
cjfa-35471	572	2	.	.	X
cjfa-35471	572	3	the	the	DET
cjfa-35471	572	4	level	level	NOUN
cjfa-35471	572	5	of	of	ADP
cjfa-35471	572	6	technology	technology	NOUN
cjfa-35471	572	7	used	use	VERB
cjfa-35471	572	8	will	will	AUX
cjfa-35471	572	9	not	not	PART
cjfa-35471	572	10	affect	affect	VERB
cjfa-35471	572	11	the	the	DET
cjfa-35471	572	12	behavior	behavior	NOUN
cjfa-35471	572	13	of	of	ADP
cjfa-35471	572	14	the	the	DET
cjfa-35471	572	15	firms	firm	NOUN
cjfa-35471	572	16	if	if	SCONJ
cjfa-35471	572	17	the	the	DET
cjfa-35471	572	18	interest	interest	NOUN
cjfa-35471	572	19	rates	rate	NOUN
cjfa-35471	572	20	are	be	AUX
cjfa-35471	572	21	very	very	ADV
cjfa-35471	572	22	low	low	ADJ
cjfa-35471	572	23	as	as	SCONJ
cjfa-35471	572	24	they	they	PRON
cjfa-35471	572	25	are	be	AUX
cjfa-35471	572	26	now	now	ADV
cjfa-35471	572	27	in	in	ADP
cjfa-35471	572	28	many	many	ADJ
cjfa-35471	572	29	developed	develop	VERB
cjfa-35471	572	30	nations	nation	NOUN
cjfa-35471	572	31	since	since	SCONJ
cjfa-35471	572	32	the	the	DET
cjfa-35471	572	33	term	term	NOUN
cjfa-35471	572	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	572	35	in	in	ADP
cjfa-35471	572	36	is	be	AUX
cjfa-35471	572	37	high	high	ADJ
cjfa-35471	572	38	(	(	PUNCT
cjfa-35471	572	39	a	a	DET
cjfa-35471	572	40	firm	firm	NOUN
cjfa-35471	572	41	technologically	technologically	ADV
cjfa-35471	572	42	inefficient	inefficient	ADJ
cjfa-35471	572	43	.	.	PUNCT
cjfa-35471	572	44	)	)	PUNCT
cjfa-35471	572	45	.	.	PUNCT
cjfa-35471	573	1	in	in	ADP
cjfa-35471	573	2	countries	country	NOUN
cjfa-35471	573	3	with	with	ADP
cjfa-35471	573	4	high	high	ADJ
cjfa-35471	573	5	interest	interest	NOUN
cjfa-35471	573	6	rates	rate	NOUN
cjfa-35471	573	7	,	,	PUNCT
cjfa-35471	573	8	the	the	DET
cjfa-35471	573	9	importance	importance	NOUN
cjfa-35471	573	10	of	of	ADP
cjfa-35471	573	11	efficient	efficient	ADJ
cjfa-35471	573	12	technologies	technology	NOUN
cjfa-35471	573	13	is	be	AUX
cjfa-35471	573	14	evident	evident	ADJ
cjfa-35471	573	15	because	because	SCONJ
cjfa-35471	573	16	both	both	DET
cjfa-35471	573	17	terms	term	NOUN
cjfa-35471	573	18	(	(	PUNCT
cjfa-35471	573	19	 	 	SPACE
cjfa-35471	573	20	f(t	f(t	NOUN
cjfa-35471	573	21	)	)	PUNCT
cjfa-35471	573	22	and	and	CCONJ
cjfa-35471	573	23	then	then	ADV
cjfa-35471	573	24	using	use	VERB
cjfa-35471	573	25	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	573	26	𝑢	𝑢	PROPN
cjfa-35471	573	27	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	573	28	,	,	PUNCT
cjfa-35471	573	29	equation	equation	NOUN
cjfa-35471	573	30	(	(	PUNCT
cjfa-35471	573	31	1	1	NUM
cjfa-35471	573	32	)	)	PUNCT
cjfa-35471	573	33	,	,	PUNCT
cjfa-35471	573	34	and	and	CCONJ
cjfa-35471	573	35	the	the	DET
cjfa-35471	573	36	conditions	condition	NOUN
cjfa-35471	573	37	(	(	PUNCT
cjfa-35471	573	38	the	the	DET
cjfa-35471	573	39	necessary	necessary	ADJ
cjfa-35471	573	40	condition	condition	NOUN
cjfa-35471	573	41	to	to	PART
cjfa-35471	573	42	keep	keep	VERB
cjfa-35471	573	43	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	573	44	𝑢	𝑢	ADP
cjfa-35471	573	45	𝐼	𝐼	PROPN
cjfa-35471	573	46	optimal	optimal	ADJ
cjfa-35471	573	47	)	)	PUNCT
cjfa-35471	573	48	developed	develop	VERB
cjfa-35471	573	49	by	by	ADP
cjfa-35471	573	50	pontryagin	pontryagin	NOUN
cjfa-35471	573	51	,	,	PUNCT
cjfa-35471	573	52	boltyanskii	boltyanskii	ADJ
cjfa-35471	573	53	,	,	PUNCT
cjfa-35471	573	54	gamkrelidze	gamkrelidze	NOUN
cjfa-35471	573	55	and	and	CCONJ
cjfa-35471	573	56	mishechenko	mishechenko	NOUN
cjfa-35471	573	57	(	(	PUNCT
cjfa-35471	573	58	1962	1962	NUM
cjfa-35471	573	59	)	)	PUNCT
cjfa-35471	573	60	,	,	PUNCT
cjfa-35471	573	61	hestenes	hestene	NOUN
cjfa-35471	573	62	(	(	PUNCT
cjfa-35471	573	63	1966	1966	NUM
cjfa-35471	573	64	)	)	PUNCT
cjfa-35471	573	65	,	,	PUNCT
cjfa-35471	573	66	kamien	kamien	NOUN
cjfa-35471	573	67	and	and	CCONJ
cjfa-35471	573	68	schwartz	schwartz	PROPN
cjfa-35471	573	69	(	(	PUNCT
cjfa-35471	573	70	2012	2012	NUM
cjfa-35471	573	71	)	)	PUNCT
cjfa-35471	573	72	among	among	ADP
cjfa-35471	573	73	many	many	ADJ
cjfa-35471	573	74	others	other	NOUN
cjfa-35471	573	75	,	,	PUNCT
cjfa-35471	573	76	we	we	PRON
cjfa-35471	573	77	have	have	VERB
cjfa-35471	573	78	;	;	PUNCT
cjfa-35471	573	79	𝜇𝜇	𝜇𝜇	AUX
cjfa-35471	573	80	�	�	NOUN
cjfa-35471	573	81	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	VERB
cjfa-35471	573	82	≤	≤	PUNCT
cjfa-35471	573	83	𝐼	𝐼	PROPN
cjfa-35471	573	84	for	for	ADP
cjfa-35471	573	85	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	573	86	�	�	PROPN
cjfa-35471	573	87	≤	≤	NUM
cjfa-35471	574	1	𝑢𝑢	𝑢𝑢	INTJ
cjfa-35471	574	2	≤	≤	NUM
cjfa-35471	574	3	𝑢𝑢	𝑢𝑢	PRON
cjfa-35471	574	4	�	�	PROPN
cjfa-35471	574	5	implies	imply	VERB
cjfa-35471	574	6	:	:	PUNCT
cjfa-35471	574	7	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	574	8	�	�	PROPN
cjfa-35471	574	9	�	�	PROPN
cjfa-35471	574	10	�	�	PROPN
cjfa-35471	574	11	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	574	12	�	�	PROPN
cjfa-35471	574	13	𝑢𝑢	𝑢𝑢	SYM
cjfa-35471	574	14	�	�	PROPN
cjfa-35471	574	15	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	574	16	≤	≤	PUNCT
cjfa-35471	574	17	ℎ	ℎ	PROPN
cjfa-35471	574	18	+	+	PROPN
cjfa-35471	574	19	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	574	20	�	�	PROPN
cjfa-35471	574	21	�	�	PROPN
cjfa-35471	574	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	574	23	�	�	PROPN
cjfa-35471	574	24	(	(	PUNCT
cjfa-35471	574	25	4	4	NUM
cjfa-35471	574	26	)	)	PUNCT
cjfa-35471	574	27	where	where	SCONJ
cjfa-35471	574	28	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	574	29	𝑢	𝑢	PROPN
cjfa-35471	574	30	𝑖𝑖	𝑖𝑖	NOUN
cjfa-35471	574	31	�	�	NOUN
cjfa-35471	574	32	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	574	33	denotes	denote	VERB
cjfa-35471	574	34	the	the	DET
cjfa-35471	574	35	interest	interest	NOUN
cjfa-35471	574	36	rate	rate	NOUN
cjfa-35471	574	37	.	.	PUNCT
cjfa-35471	575	1	as	as	ADV
cjfa-35471	575	2	long	long	ADV
cjfa-35471	575	3	as	as	SCONJ
cjfa-35471	575	4	the	the	DET
cjfa-35471	575	5	condition	condition	NOUN
cjfa-35471	575	6	specified	specify	VERB
cjfa-35471	575	7	by	by	ADP
cjfa-35471	575	8	this	this	DET
cjfa-35471	575	9	inequality	inequality	NOUN
cjfa-35471	575	10	is	be	AUX
cjfa-35471	575	11	satisfied	satisfied	ADJ
cjfa-35471	575	12	it	it	PRON
cjfa-35471	575	13	will	will	AUX
cjfa-35471	575	14	be	be	AUX
cjfa-35471	575	15	optimal	optimal	ADJ
cjfa-35471	575	16	to	to	PART
cjfa-35471	575	17	keep	keep	VERB
cjfa-35471	575	18	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	575	19	𝑢	𝑢	ADP
cjfa-35471	575	20	𝐼	𝐼	ADP
cjfa-35471	575	21	implying	imply	VERB
cjfa-35471	575	22	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	575	23	𝑢	𝑢	PRON
cjfa-35471	575	24	𝑢𝑢𝑢𝑢𝑢𝑢.	𝑢𝑢𝑢𝑢𝑢𝑢.	NOUN
cjfa-35471	575	25	this	this	PRON
cjfa-35471	575	26	means	mean	VERB
cjfa-35471	575	27	that	that	SCONJ
cjfa-35471	575	28	during	during	ADP
cjfa-35471	575	29	the	the	DET
cjfa-35471	575	30	intervals	interval	NOUN
cjfa-35471	575	31	where	where	SCONJ
cjfa-35471	575	32	this	this	DET
cjfa-35471	575	33	inequality	inequality	NOUN
cjfa-35471	575	34	is	be	AUX
cjfa-35471	575	35	satisfied	satisfied	ADJ
cjfa-35471	575	36	the	the	DET
cjfa-35471	575	37	firm	firm	NOUN
cjfa-35471	575	38	will	will	AUX
cjfa-35471	575	39	produce	produce	VERB
cjfa-35471	575	40	just	just	ADV
cjfa-35471	575	41	enough	enough	ADJ
cjfa-35471	575	42	to	to	PART
cjfa-35471	575	43	satisfy	satisfy	VERB
cjfa-35471	575	44	the	the	DET
cjfa-35471	575	45	demand	demand	NOUN
cjfa-35471	575	46	.	.	PUNCT
cjfa-35471	576	1	so	so	ADV
cjfa-35471	576	2	,	,	PUNCT
cjfa-35471	576	3	the	the	DET
cjfa-35471	576	4	condition	condition	NOUN
cjfa-35471	576	5	above	above	ADV
cjfa-35471	576	6	will	will	AUX
cjfa-35471	576	7	synthesize	synthesize	VERB
cjfa-35471	576	8	the	the	DET
cjfa-35471	576	9	periods	period	NOUN
cjfa-35471	576	10	where	where	SCONJ
cjfa-35471	576	11	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	576	12	𝑢	𝑢	PRON
cjfa-35471	576	13	𝐼	𝐼	PROPN
cjfa-35471	576	14	or	or	CCONJ
cjfa-35471	576	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	VERB
cjfa-35471	576	16	𝑢	𝑢	PROPN
cjfa-35471	576	17	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	576	18	and	and	CCONJ
cjfa-35471	576	19	the	the	DET
cjfa-35471	576	20	periods	period	NOUN
cjfa-35471	576	21	where	where	SCONJ
cjfa-35471	576	22	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	576	23	𝐼	𝐼	ADP
cjfa-35471	576	24	𝐼.	𝐼.	PROPN
cjfa-35471	576	25	notice	notice	VERB
cjfa-35471	576	26	that	that	SCONJ
cjfa-35471	576	27	for	for	ADP
cjfa-35471	576	28	the	the	DET
cjfa-35471	576	29	condition	condition	NOUN
cjfa-35471	576	30	above	above	ADV
cjfa-35471	576	31	(	(	PUNCT
cjfa-35471	576	32	equation	equation	NOUN
cjfa-35471	576	33	4	4	NUM
cjfa-35471	576	34	)	)	PUNCT
cjfa-35471	576	35	to	to	PART
cjfa-35471	576	36	be	be	AUX
cjfa-35471	576	37	kept	keep	VERB
cjfa-35471	576	38	satisfied	satisfied	ADJ
cjfa-35471	576	39	depends	depend	VERB
cjfa-35471	576	40	on	on	ADP
cjfa-35471	576	41	ℎ	ℎ	PROPN
cjfa-35471	576	42	(	(	PUNCT
cjfa-35471	576	43	inventory	inventory	NOUN
cjfa-35471	576	44	holding	hold	VERB
cjfa-35471	576	45	cost	cost	NOUN
cjfa-35471	576	46	)	)	PUNCT
cjfa-35471	576	47	,	,	PUNCT
cjfa-35471	576	48	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	VERB
cjfa-35471	576	49	the	the	DET
cjfa-35471	576	50	interest	interest	NOUN
cjfa-35471	576	51	rates	rate	NOUN
cjfa-35471	576	52	,	,	PUNCT
cjfa-35471	576	53	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	576	54	,	,	PUNCT
cjfa-35471	576	55	the	the	DET
cjfa-35471	576	56	marginal	marginal	ADJ
cjfa-35471	576	57	cost	cost	NOUN
cjfa-35471	576	58	of	of	ADP
cjfa-35471	576	59	production	production	NOUN
cjfa-35471	576	60	,	,	PUNCT
cjfa-35471	576	61	and	and	CCONJ
cjfa-35471	576	62	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	576	63	change	change	NOUN
cjfa-35471	576	64	in	in	ADP
cjfa-35471	576	65	the	the	DET
cjfa-35471	576	66	marginal	marginal	ADJ
cjfa-35471	576	67	cost	cost	NOUN
cjfa-35471	576	68	.	.	PUNCT
cjfa-35471	577	1	following	follow	VERB
cjfa-35471	577	2	conclusions	conclusion	NOUN
cjfa-35471	577	3	can	can	AUX
cjfa-35471	577	4	be	be	AUX
cjfa-35471	577	5	made	make	VERB
cjfa-35471	577	6	even	even	ADV
cjfa-35471	577	7	without	without	ADP
cjfa-35471	577	8	specific	specific	ADJ
cjfa-35471	577	9	forms	form	NOUN
cjfa-35471	577	10	of	of	ADP
cjfa-35471	577	11	𝑐𝑐𝑢𝑢𝑢𝑢	𝑐𝑐𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	577	12	,	,	PUNCT
cjfa-35471	577	13	𝑓𝑓𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	577	14	,	,	PUNCT
cjfa-35471	577	15	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	577	16	and	and	CCONJ
cjfa-35471	577	17	𝑖𝑖𝑢𝑢𝑢𝑢	𝑖𝑖𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	577	18	on	on	ADP
cjfa-35471	577	19	the	the	DET
cjfa-35471	577	20	basis	basis	NOUN
cjfa-35471	577	21	of	of	ADP
cjfa-35471	577	22	equation	equation	NOUN
cjfa-35471	577	23	(	(	PUNCT
cjfa-35471	577	24	4	4	NUM
cjfa-35471	577	25	):	):	PUNCT
cjfa-35471	577	26	1	1	NUM
cjfa-35471	577	27	.	.	PUNCT
cjfa-35471	578	1	the	the	DET
cjfa-35471	578	2	firm	firm	NOUN
cjfa-35471	578	3	will	will	AUX
cjfa-35471	578	4	keep	keep	VERB
cjfa-35471	578	5	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	578	6	𝑢	𝑢	ADP
cjfa-35471	578	7	𝐼	𝐼	PROPN
cjfa-35471	578	8	as	as	ADV
cjfa-35471	578	9	long	long	ADV
cjfa-35471	578	10	as	as	SCONJ
cjfa-35471	578	11	demand	demand	NOUN
cjfa-35471	578	12	is	be	AUX
cjfa-35471	578	13	falling	fall	VERB
cjfa-35471	578	14	or	or	CCONJ
cjfa-35471	578	15	constant	constant	ADJ
cjfa-35471	578	16	i.e.	i.e.	X
cjfa-35471	578	17	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	X
cjfa-35471	578	18	0	0	NOUN
cjfa-35471	578	19	implying	imply	VERB
cjfa-35471	578	20	that	that	SCONJ
cjfa-35471	578	21	the	the	DET
cjfa-35471	578	22	firm	firm	NOUN
cjfa-35471	578	23	will	will	AUX
cjfa-35471	578	24	choose	choose	VERB
cjfa-35471	578	25	to	to	PART
cjfa-35471	578	26	produce	produce	VERB
cjfa-35471	578	27	just	just	ADV
cjfa-35471	578	28	enough	enough	ADJ
cjfa-35471	578	29	to	to	PART
cjfa-35471	578	30	meet	meet	VERB
cjfa-35471	578	31	the	the	DET
cjfa-35471	578	32	demand	demand	NOUN
cjfa-35471	578	33	if	if	SCONJ
cjfa-35471	578	34	demand	demand	NOUN
cjfa-35471	578	35	is	be	AUX
cjfa-35471	578	36	falling	fall	VERB
cjfa-35471	578	37	since	since	SCONJ
cjfa-35471	578	38	both	both	PRON
cjfa-35471	578	39	ℎ	ℎ	NOUN
cjfa-35471	578	40	and	and	CCONJ
cjfa-35471	578	41	𝑐𝑐𝐼	𝑐𝑐𝐼	PRON
cjfa-35471	578	42	are	be	AUX
cjfa-35471	578	43	positive	positive	ADJ
cjfa-35471	578	44	.	.	PUNCT
cjfa-35471	579	1	2	2	X
cjfa-35471	579	2	.	.	X
cjfa-35471	579	3	the	the	DET
cjfa-35471	579	4	firm	firm	NOUN
cjfa-35471	579	5	will	will	AUX
cjfa-35471	579	6	keep	keep	VERB
cjfa-35471	579	7	𝐼𝐼𝑢𝑢𝑢𝑢	𝐼𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	579	8	𝑢	𝑢	ADP
cjfa-35471	579	9	𝐼	𝐼	NOUN
cjfa-35471	579	10	even	even	ADV
cjfa-35471	579	11	if	if	SCONJ
cjfa-35471	579	12	demand	demand	NOUN
cjfa-35471	579	13	is	be	AUX
cjfa-35471	579	14	increasing	increase	VERB
cjfa-35471	579	15	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	579	16	𝑟	𝑟	X
cjfa-35471	579	17	𝐼𝑢	𝐼𝑢	PROPN
cjfa-35471	579	18	but	but	CCONJ
cjfa-35471	579	19	the	the	DET
cjfa-35471	579	20	term	term	NOUN
cjfa-35471	579	21	ℎ	ℎ	PROPN
cjfa-35471	579	22	+	+	CCONJ
cjfa-35471	579	23	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐	PROPN
cjfa-35471	579	24	�	�	PROPN
cjfa-35471	579	25	�	�	PROPN
cjfa-35471	579	26	𝑢𝑢𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	579	27	�	�	PROPN
cjfa-35471	579	28	is	be	AUX
cjfa-35471	579	29	large	large	ADJ
cjfa-35471	579	30	enough	enough	ADV
cjfa-35471	579	31	to	to	PART
cjfa-35471	579	32	keep	keep	VERB
cjfa-35471	579	33	inequality	inequality	NOUN
cjfa-35471	579	34	(	(	PUNCT
cjfa-35471	579	35	4	4	NUM
cjfa-35471	579	36	)	)	PUNCT
cjfa-35471	579	37	satisfied	satisfied	ADJ
cjfa-35471	579	38	.	.	PUNCT
cjfa-35471	580	1	decreasing	decrease	VERB
cjfa-35471	580	2	interest	interest	NOUN
cjfa-35471	580	3	rates	rate	NOUN
cjfa-35471	580	4	will	will	AUX
cjfa-35471	580	5	not	not	PART
cjfa-35471	580	6	be	be	AUX
cjfa-35471	580	7	a	a	DET
cjfa-35471	580	8	remedy	remedy	NOUN
cjfa-35471	580	9	in	in	ADP
cjfa-35471	580	10	this	this	DET
cjfa-35471	580	11	case	case	NOUN
cjfa-35471	580	12	if	if	SCONJ
cjfa-35471	580	13	they	they	PRON
cjfa-35471	580	14	are	be	AUX
cjfa-35471	580	15	already	already	ADV
cjfa-35471	580	16	low	low	ADJ
cjfa-35471	580	17	.	.	PUNCT
cjfa-35471	581	1	firms	firm	NOUN
cjfa-35471	581	2	where	where	SCONJ
cjfa-35471	581	3	𝑐𝑐𝐼𝐼	𝑐𝑐𝐼𝐼	PROPN
cjfa-35471	581	4	�	�	PROPN
cjfa-35471	581	5	𝑢𝑢	𝑢𝑢	PROPN
cjfa-35471	581	6	𝑢𝑢𝑢𝑢	𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	581	7	�	�	PROPN
cjfa-35471	581	8	is	be	AUX
cjfa-35471	581	9	low	low	ADJ
cjfa-35471	581	10	(	(	PUNCT
cjfa-35471	581	11	large	large	ADJ
cjfa-35471	581	12	and	and	CCONJ
cjfa-35471	581	13	already	already	ADV
cjfa-35471	581	14	very	very	ADV
cjfa-35471	581	15	efficient	efficient	ADJ
cjfa-35471	581	16	firms	firm	NOUN
cjfa-35471	581	17	)	)	PUNCT
cjfa-35471	581	18	will	will	AUX
cjfa-35471	581	19	have	have	VERB
cjfa-35471	581	20	more	more	ADJ
cjfa-35471	581	21	difficulty	difficulty	NOUN
cjfa-35471	581	22	to	to	PART
cjfa-35471	581	23	produce	produce	VERB
cjfa-35471	581	24	to	to	PART
cjfa-35471	581	25	build	build	VERB
cjfa-35471	581	26	up	up	ADP
cjfa-35471	581	27	inventories	inventory	NOUN
cjfa-35471	581	28	.	.	PUNCT
cjfa-35471	582	1	currently	currently	ADV
cjfa-35471	582	2	,	,	PUNCT
cjfa-35471	582	3	this	this	PRON
cjfa-35471	582	4	seems	seem	VERB
cjfa-35471	582	5	to	to	PART
cjfa-35471	582	6	be	be	AUX
cjfa-35471	582	7	the	the	DET
cjfa-35471	582	8	case	case	NOUN
cjfa-35471	582	9	in	in	ADP
cjfa-35471	582	10	major	major	ADJ
cjfa-35471	582	11	economies	economy	NOUN
cjfa-35471	582	12	.	.	PUNCT
cjfa-35471	583	1	3	3	X
cjfa-35471	583	2	.	.	X
cjfa-35471	583	3	higher	high	ADJ
cjfa-35471	583	4	interest	interest	NOUN
cjfa-35471	583	5	rates	rate	NOUN
cjfa-35471	583	6	and	and	CCONJ
cjfa-35471	583	7	the	the	DET
cjfa-35471	583	8	use	use	NOUN
cjfa-35471	583	9	of	of	ADP
cjfa-35471	583	10	inefficient	inefficient	ADJ
cjfa-35471	583	11	technologies	technology	NOUN
cjfa-35471	583	12	(	(	PUNCT
cjfa-35471	583	13	large	large	ADJ
cjfa-35471	583	14	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑐𝑐𝐼𝑢𝑢𝑢𝑢	NOUN
cjfa-35471	583	15	)	)	PUNCT
cjfa-35471	583	16	implies	imply	VERB
cjfa-35471	583	17	high	high	ADJ
cjfa-35471	583	18	marginal	marginal	ADJ
cjfa-35471	583	19	cost	cost	NOUN
cjfa-35471	583	20	)	)	PUNCT
cjfa-35471	583	21	will	will	AUX
cjfa-35471	583	22	induce	induce	VERB
cjfa-35471	583	23	firms	firm	NOUN
cjfa-35471	583	24	to	to	PART
cjfa-35471	583	25	wait	wait	VERB
cjfa-35471	583	26	longer	long	ADV
cjfa-35471	583	27	for	for	ADP
cjfa-35471	583	28	inventory	inventory	NOUN
cjfa-35471	583	29	build	build	NOUN
cjfa-35471	583	30	-	-	PUNCT
cjfa-35471	583	31	up	up	NOUN
cjfa-35471	583	32	even	even	ADV
cjfa-35471	583	33	if	if	SCONJ
cjfa-35471	583	34	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	𝑢𝑢𝐼𝑢𝑢𝑢𝑢	PROPN
cjfa-35471	583	35	is	be	AUX
cjfa-35471	583	36	positive	positive	ADJ
cjfa-35471	583	37	.	.	PUNCT
cjfa-35471	584	1	4	4	X
cjfa-35471	584	2	.	.	X
cjfa-35471	584	3	the	the	DET
cjfa-35471	584	4	level	level	NOUN
cjfa-35471	584	5	of	of	ADP
cjfa-35471	584	6	technology	technology	NOUN
cjfa-35471	584	7	used	use	VERB
cjfa-35471	584	8	will	will	AUX
cjfa-35471	584	9	not	not	PART
cjfa-35471	584	10	affect	affect	VERB
cjfa-35471	584	11	the	the	DET
cjfa-35471	584	12	behavior	behavior	NOUN
cjfa-35471	584	13	of	of	ADP
cjfa-35471	584	14	the	the	DET
cjfa-35471	584	15	firms	firm	NOUN
cjfa-35471	584	16	if	if	SCONJ
cjfa-35471	584	17	the	the	DET
cjfa-35471	584	18	interest	interest	NOUN
cjfa-35471	584	19	rates	rate	NOUN
cjfa-35471	584	20	are	be	AUX
cjfa-35471	584	21	very	very	ADV
cjfa-35471	584	22	low	low	ADJ
cjfa-35471	584	23	as	as	SCONJ
cjfa-35471	584	24	they	they	PRON
cjfa-35471	584	25	are	be	AUX
cjfa-35471	584	26	now	now	ADV
cjfa-35471	584	27	in	in	ADP
cjfa-35471	584	28	many	many	ADJ
cjfa-35471	584	29	developed	develop	VERB
cjfa-35471	584	30	nations	nation	NOUN
cjfa-35471	584	31	since	since	SCONJ
cjfa-35471	584	32	the	the	DET
cjfa-35471	584	33	term	term	NOUN
cjfa-35471	584	34	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	𝑓𝑓𝑢𝑢𝑢𝑢𝑐𝑐𝐼𝑢𝑢𝑢𝑢	VERB
cjfa-35471	584	35	in	in	ADP
cjfa-35471	584	36	are	be	AUX
cjfa-35471	584	37	)	)	PUNCT
cjfa-35471	584	38	large	large	ADJ
cjfa-35471	584	39	.	.	PUNCT
cjfa-35471	585	1	5	5	X
cjfa-35471	585	2	.	.	X
cjfa-35471	585	3	the	the	DET
cjfa-35471	585	4	cyclicality	cyclicality	NOUN
cjfa-35471	585	5	of	of	ADP
cjfa-35471	585	6	demand	demand	NOUN
cjfa-35471	585	7	and	and	CCONJ
cjfa-35471	585	8	the	the	DET
cjfa-35471	585	9	time	time	NOUN
cjfa-35471	585	10	dependency	dependency	NOUN
cjfa-35471	585	11	of	of	ADP
cjfa-35471	585	12	interest	interest	NOUN
cjfa-35471	585	13	rates	rate	NOUN
cjfa-35471	585	14	can	can	AUX
cjfa-35471	585	15	affect	affect	VERB
cjfa-35471	585	16	the	the	DET
cjfa-35471	585	17	producers	producer	NOUN
cjfa-35471	585	18	.	.	PUNCT
cjfa-35471	586	1	producers	producer	NOUN
cjfa-35471	586	2	,	,	PUNCT
cjfa-35471	586	3	facing	face	VERB
cjfa-35471	586	4	cyclical	cyclical	ADJ
cjfa-35471	586	5	demand	demand	NOUN
cjfa-35471	586	6	with	with	ADP
cjfa-35471	586	7	very	very	ADV
cjfa-35471	586	8	high	high	ADJ
cjfa-35471	586	9	periodicity	periodicity	NOUN
cjfa-35471	586	10	will	will	AUX
cjfa-35471	586	11	have	have	VERB
cjfa-35471	586	12	extreme	extreme	ADJ
cjfa-35471	586	13	difficulty	difficulty	NOUN
cjfa-35471	586	14	in	in	ADP
cjfa-35471	586	15	planning	planning	NOUN
cjfa-35471	586	16	and	and	CCONJ
cjfa-35471	586	17	hence	hence	ADV
cjfa-35471	586	18	may	may	AUX
cjfa-35471	586	19	not	not	PART
cjfa-35471	586	20	produce	produce	VERB
cjfa-35471	586	21	for	for	ADP
cjfa-35471	586	22	inventory	inventory	NOUN
cjfa-35471	586	23	buildup	buildup	NOUN
cjfa-35471	586	24	at	at	ADV
cjfa-35471	586	25	all	all	ADV
cjfa-35471	586	26	.	.	PUNCT
cjfa-35471	587	1	cyclicality	cyclicality	NOUN
cjfa-35471	587	2	in	in	ADP
cjfa-35471	587	3	the	the	DET
cjfa-35471	587	4	following	follow	VERB
cjfa-35471	587	5	examples	example	NOUN
cjfa-35471	587	6	is	be	AUX
cjfa-35471	587	7	denoted	denote	VERB
cjfa-35471	587	8	by	by	ADP
cjfa-35471	587	9	the	the	DET
cjfa-35471	587	10	parameter	parameter	NOUN
cjfa-35471	587	11	k.	k.	PROPN
cjfa-35471	588	1	the	the	DET
cjfa-35471	588	2	value	value	NOUN
cjfa-35471	588	3	of	of	ADP
cjfa-35471	588	4	k	k	PROPN
cjfa-35471	588	5	will	will	AUX
cjfa-35471	588	6	be	be	AUX
cjfa-35471	588	7	assumed	assume	VERB
cjfa-35471	588	8	to	to	PART
cjfa-35471	588	9	be	be	AUX
cjfa-35471	588	10	1	1	NUM
cjfa-35471	588	11	in	in	ADP
cjfa-35471	588	12	all	all	DET
cjfa-35471	588	13	cases	case	NOUN
cjfa-35471	588	14	for	for	ADP
cjfa-35471	588	15	simplicity	simplicity	NOUN
cjfa-35471	588	16	.	.	PUNCT
cjfa-35471	589	1	for	for	ADP
cjfa-35471	589	2	higher	high	ADJ
cjfa-35471	589	3	values	value	NOUN
cjfa-35471	589	4	of	of	ADP
cjfa-35471	589	5	k	k	NOUN
cjfa-35471	589	6	,	,	PUNCT
cjfa-35471	589	7	trigonometric	trigonometric	ADJ
cjfa-35471	589	8	functions	function	NOUN
cjfa-35471	589	9	will	will	AUX
cjfa-35471	589	10	complete	complete	VERB
cjfa-35471	589	11	360	360	NUM
cjfa-35471	589	12	-	-	PUNCT
cjfa-35471	589	13	degree	degree	NOUN
cjfa-35471	589	14	cycle	cycle	NOUN
cjfa-35471	589	15	twice	twice	ADV
cjfa-35471	589	16	in	in	ADP
cjfa-35471	589	17	the	the	DET
cjfa-35471	589	18	planning	planning	NOUN
cjfa-35471	589	19	horizon	horizon	NOUN
cjfa-35471	589	20	.	.	PUNCT
cjfa-35471	590	1	the	the	DET
cjfa-35471	590	2	results	result	NOUN
cjfa-35471	590	3	will	will	AUX
cjfa-35471	590	4	not	not	PART
cjfa-35471	590	5	change	change	VERB
cjfa-35471	590	6	except	except	SCONJ
cjfa-35471	590	7	the	the	DET
cjfa-35471	590	8	firms	firm	NOUN
cjfa-35471	590	9	will	will	AUX
cjfa-35471	590	10	stop	stop	VERB
cjfa-35471	590	11	and	and	CCONJ
cjfa-35471	590	12	start	start	VERB
cjfa-35471	590	13	two	two	NUM
cjfa-35471	590	14	times	time	NOUN
cjfa-35471	590	15	in	in	ADP
cjfa-35471	590	16	the	the	DET
cjfa-35471	590	17	planning	planning	NOUN
cjfa-35471	590	18	period	period	NOUN
cjfa-35471	590	19	indicating	indicate	VERB
cjfa-35471	590	20	more	more	ADJ
cjfa-35471	590	21	instability	instability	NOUN
cjfa-35471	590	22	of	of	ADP
cjfa-35471	590	23	demand	demand	NOUN
cjfa-35471	590	24	.	.	PUNCT
cjfa-35471	591	1	6	6	NUM
cjfa-35471	591	2	.	.	NOUN
cjfa-35471	591	3	size	size	NOUN
cjfa-35471	591	4	of	of	ADP
cjfa-35471	591	5	the	the	DET
cjfa-35471	591	6	firms	firm	NOUN
cjfa-35471	591	7	,	,	PUNCT
cjfa-35471	591	8	expressed	express	VERB
cjfa-35471	591	9	as	as	ADP
cjfa-35471	591	10	a	a	DET
cjfa-35471	591	11	constant	constant	ADJ
cjfa-35471	591	12	in	in	ADP
cjfa-35471	591	13	the	the	DET
cjfa-35471	591	14	total	total	ADJ
cjfa-35471	591	15	production	production	NOUN
cjfa-35471	591	16	cost	cost	NOUN
cjfa-35471	591	17	(	(	PUNCT
cjfa-35471	591	18	c(r	c(r	NOUN
cjfa-35471	591	19	)	)	PUNCT
cjfa-35471	591	20	)	)	PUNCT
cjfa-35471	591	21	,	,	PUNCT
cjfa-35471	591	22	is	be	AUX
cjfa-35471	591	23	irrelevant	irrelevant	ADJ
cjfa-35471	591	24	in	in	ADP
cjfa-35471	591	25	production	production	NOUN
cjfa-35471	591	26	decisions	decision	NOUN
cjfa-35471	591	27	since	since	SCONJ
cjfa-35471	591	28	it	it	PRON
cjfa-35471	591	29	will	will	AUX
cjfa-35471	591	30	not	not	PART
cjfa-35471	591	31	appear	appear	VERB
cjfa-35471	591	32	in	in	ADP
cjfa-35471	591	33	equation	equation	NOUN
cjfa-35471	591	34	(	(	PUNCT
cjfa-35471	591	35	4	4	NUM
cjfa-35471	591	36	)	)	PUNCT
cjfa-35471	591	37	.	.	PUNCT
cjfa-35471	592	1	in	in	ADP
cjfa-35471	592	2	the	the	DET
cjfa-35471	592	3	next	next	ADJ
cjfa-35471	592	4	section	section	NOUN
cjfa-35471	592	5	,	,	PUNCT
cjfa-35471	592	6	the	the	DET
cjfa-35471	592	7	impact	impact	NOUN
cjfa-35471	592	8	of	of	ADP
cjfa-35471	592	9	holding	hold	VERB
cjfa-35471	592	10	cost	cost	NOUN
cjfa-35471	592	11	,	,	PUNCT
cjfa-35471	592	12	technology	technology	NOUN
cjfa-35471	592	13	,	,	PUNCT
cjfa-35471	592	14	and	and	CCONJ
cjfa-35471	592	15	interest	interest	NOUN
cjfa-35471	592	16	rates	rate	NOUN
cjfa-35471	592	17	on	on	ADP
cjfa-35471	592	18	the	the	DET
cjfa-35471	592	19	production	production	NOUN
cjfa-35471	592	20	behavior	behavior	NOUN
cjfa-35471	592	21	of	of	ADP
cjfa-35471	592	22	firms	firm	NOUN
cjfa-35471	592	23	is	be	AUX
cjfa-35471	592	24	analyzed	analyze	VERB
cjfa-35471	592	25	with	with	ADP
cjfa-35471	592	26	different	different	ADJ
cjfa-35471	592	27	assumptions	assumption	NOUN
cjfa-35471	592	28	on	on	ADP
cjfa-35471	592	29	interest	interest	NOUN
cjfa-35471	592	30	rates	rate	NOUN
cjfa-35471	592	31	and	and	CCONJ
cjfa-35471	592	32	a	a	DET
cjfa-35471	592	33	specific	specific	ADJ
cjfa-35471	592	34	form	form	NOUN
cjfa-35471	592	35	of	of	ADP
cjfa-35471	592	36	cost	cost	NOUN
cjfa-35471	592	37	function	function	NOUN
cjfa-35471	592	38	(	(	PUNCT
cjfa-35471	592	39	a	a	DET
cjfa-35471	592	40	cubic	cubic	ADJ
cjfa-35471	592	41	function	function	NOUN
cjfa-35471	592	42	of	of	ADP
cjfa-35471	592	43	level	level	NOUN
cjfa-35471	592	44	of	of	ADP
cjfa-35471	592	45	production	production	NOUN
cjfa-35471	592	46	)	)	PUNCT
cjfa-35471	592	47	.	.	PUNCT
cjfa-35471	593	1	graphs	graph	NOUN
cjfa-35471	593	2	are	be	AUX
cjfa-35471	593	3	produced	produce	VERB
cjfa-35471	593	4	to	to	PART
cjfa-35471	593	5	visualize	visualize	VERB
cjfa-35471	593	6	the	the	DET
cjfa-35471	593	7	impact	impact	NOUN
cjfa-35471	593	8	of	of	ADP
cjfa-35471	593	9	assumptions	assumption	NOUN
cjfa-35471	593	10	about	about	ADP
cjfa-35471	593	11	interest	interest	NOUN
cjfa-35471	593	12	rates	rate	NOUN
cjfa-35471	593	13	,	,	PUNCT
cjfa-35471	593	14	parameters	parameter	NOUN
cjfa-35471	593	15	of	of	ADP
cjfa-35471	593	16	demand	demand	NOUN
cjfa-35471	593	17	function	function	NOUN
cjfa-35471	593	18	,	,	PUNCT
cjfa-35471	593	19	and	and	CCONJ
cjfa-35471	593	20	holding	hold	VERB
cjfa-35471	593	21	cost	cost	NOUN
cjfa-35471	593	22	.	.	PUNCT
cjfa-35471	594	1	optimal	optimal	ADJ
cjfa-35471	594	2	incentives	incentive	NOUN
cjfa-35471	594	3	for	for	ADP
cjfa-35471	594	4	economic	economic	ADJ
cjfa-35471	594	5	growth	growth	NOUN
cjfa-35471	594	6	…	…	PUNCT
cjfa-35471	594	7	17	17	NUM
cjfa-35471	594	8	research	research	NOUN
cjfa-35471	594	9	process	process	NOUN
cjfa-35471	594	10	the	the	DET
cjfa-35471	594	11	specific	specific	ADJ
cjfa-35471	594	12	cost	cost	NOUN
cjfa-35471	594	13	function	function	NOUN
cjfa-35471	594	14	,	,	PUNCT
cjfa-35471	594	15	in	in	ADP
cjfa-35471	594	16	this	this	DET
cjfa-35471	594	17	example	example	NOUN
cjfa-35471	594	18	,	,	PUNCT
cjfa-35471	594	19	will	will	AUX
cjfa-35471	594	20	be	be	AUX
cjfa-35471	594	21	assumed	assume	VERB
cjfa-35471	594	22	to	to	PART
cjfa-35471	594	23	have	have	VERB
cjfa-35471	594	24	the	the	DET
cjfa-35471	594	25	more	more	ADV
cjfa-35471	594	26	realistic	realistic	ADJ
cjfa-35471	594	27	form	form	NOUN
cjfa-35471	594	28	of	of	ADP
cjfa-35471	594	29	:	:	PUNCT
cjfa-35471	594	30	equation	equation	NOUN
cjfa-35471	594	31	will	will	AUX
cjfa-35471	594	32	be	be	AUX
cjfa-35471	594	33	low	low	ADJ
cjfa-35471	594	34	even	even	ADV
cjfa-35471	594	35	if	if	SCONJ
cjfa-35471	594	36	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	594	37	is	be	AUX
cjfa-35471	594	38	high	high	ADJ
cjfa-35471	594	39	(	(	PUNCT
cjfa-35471	594	40	a	a	DET
cjfa-35471	594	41	firm	firm	NOUN
cjfa-35471	594	42	technologically	technologically	ADV
cjfa-35471	594	43	inefficient	inefficient	ADJ
cjfa-35471	594	44	.	.	PUNCT
cjfa-35471	594	45	)	)	PUNCT
cjfa-35471	594	46	.	.	PUNCT
cjfa-35471	595	1	in	in	ADP
cjfa-35471	595	2	countries	country	NOUN
cjfa-35471	595	3	with	with	ADP
cjfa-35471	595	4	high	high	ADJ
cjfa-35471	595	5	interest	interest	NOUN
cjfa-35471	595	6	rates	rate	NOUN
cjfa-35471	595	7	,	,	PUNCT
cjfa-35471	595	8	the	the	DET
cjfa-35471	595	9	importance	importance	NOUN
cjfa-35471	595	10	of	of	ADP
cjfa-35471	595	11	efficient	efficient	ADJ
cjfa-35471	595	12	technologies	technology	NOUN
cjfa-35471	595	13	is	be	AUX
cjfa-35471	595	14	evident	evident	ADJ
cjfa-35471	595	15	because	because	SCONJ
cjfa-35471	595	16	both	both	DET
cjfa-35471	595	17	terms	term	NOUN
cjfa-35471	595	18	(	(	PUNCT
cjfa-35471	595	19	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	595	20	and	and	CCONJ
cjfa-35471	595	21	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	595	22	are	be	AUX
cjfa-35471	595	23	)	)	PUNCT
cjfa-35471	595	24	large	large	ADJ
cjfa-35471	595	25	.	.	PUNCT
cjfa-35471	596	1	5	5	X
cjfa-35471	596	2	.	.	X
cjfa-35471	596	3	the	the	DET
cjfa-35471	596	4	cyclicality	cyclicality	NOUN
cjfa-35471	596	5	of	of	ADP
cjfa-35471	596	6	demand	demand	NOUN
cjfa-35471	596	7	and	and	CCONJ
cjfa-35471	596	8	the	the	DET
cjfa-35471	596	9	time	time	NOUN
cjfa-35471	596	10	dependency	dependency	NOUN
cjfa-35471	596	11	of	of	ADP
cjfa-35471	596	12	interest	interest	NOUN
cjfa-35471	596	13	rates	rate	NOUN
cjfa-35471	596	14	can	can	AUX
cjfa-35471	596	15	affect	affect	VERB
cjfa-35471	596	16	the	the	DET
cjfa-35471	596	17	producers	producer	NOUN
cjfa-35471	596	18	.	.	PUNCT
cjfa-35471	597	1	producers	producer	NOUN
cjfa-35471	597	2	,	,	PUNCT
cjfa-35471	597	3	facing	face	VERB
cjfa-35471	597	4	cyclical	cyclical	ADJ
cjfa-35471	597	5	demand	demand	NOUN
cjfa-35471	597	6	with	with	ADP
cjfa-35471	597	7	very	very	ADV
cjfa-35471	597	8	high	high	ADJ
cjfa-35471	597	9	periodicity	periodicity	NOUN
cjfa-35471	597	10	will	will	AUX
cjfa-35471	597	11	have	have	VERB
cjfa-35471	597	12	extreme	extreme	ADJ
cjfa-35471	597	13	difficulty	difficulty	NOUN
cjfa-35471	597	14	in	in	ADP
cjfa-35471	597	15	planning	planning	NOUN
cjfa-35471	597	16	and	and	CCONJ
cjfa-35471	597	17	hence	hence	ADV
cjfa-35471	597	18	may	may	AUX
cjfa-35471	597	19	not	not	PART
cjfa-35471	597	20	produce	produce	VERB
cjfa-35471	597	21	for	for	ADP
cjfa-35471	597	22	inventory	inventory	NOUN
cjfa-35471	597	23	buildup	buildup	NOUN
cjfa-35471	597	24	at	at	ADV
cjfa-35471	597	25	all	all	ADV
cjfa-35471	597	26	.	.	PUNCT
cjfa-35471	598	1	cyclicality	cyclicality	NOUN
cjfa-35471	598	2	in	in	ADP
cjfa-35471	598	3	the	the	DET
cjfa-35471	598	4	following	follow	VERB
cjfa-35471	598	5	examples	example	NOUN
cjfa-35471	598	6	is	be	AUX
cjfa-35471	598	7	denoted	denote	VERB
cjfa-35471	598	8	by	by	ADP
cjfa-35471	598	9	the	the	DET
cjfa-35471	598	10	parameter	parameter	NOUN
cjfa-35471	598	11	k.	k.	PROPN
cjfa-35471	599	1	the	the	DET
cjfa-35471	599	2	value	value	NOUN
cjfa-35471	599	3	of	of	ADP
cjfa-35471	599	4	k	k	PROPN
cjfa-35471	599	5	will	will	AUX
cjfa-35471	599	6	be	be	AUX
cjfa-35471	599	7	assumed	assume	VERB
cjfa-35471	599	8	to	to	PART
cjfa-35471	599	9	be	be	AUX
cjfa-35471	599	10	1	1	NUM
cjfa-35471	599	11	in	in	ADP
cjfa-35471	599	12	all	all	DET
cjfa-35471	599	13	cases	case	NOUN
cjfa-35471	599	14	for	for	ADP
cjfa-35471	599	15	simplicity	simplicity	NOUN
cjfa-35471	599	16	.	.	PUNCT
cjfa-35471	600	1	for	for	ADP
cjfa-35471	600	2	higher	high	ADJ
cjfa-35471	600	3	values	value	NOUN
cjfa-35471	600	4	of	of	ADP
cjfa-35471	600	5	k	k	NOUN
cjfa-35471	600	6	,	,	PUNCT
cjfa-35471	600	7	trigonometric	trigonometric	ADJ
cjfa-35471	600	8	functions	function	NOUN
cjfa-35471	600	9	will	will	AUX
cjfa-35471	600	10	complete	complete	VERB
cjfa-35471	600	11	360	360	NUM
cjfa-35471	600	12	-	-	PUNCT
cjfa-35471	600	13	degree	degree	NOUN
cjfa-35471	600	14	cycle	cycle	NOUN
cjfa-35471	600	15	twice	twice	ADV
cjfa-35471	600	16	in	in	ADP
cjfa-35471	600	17	the	the	DET
cjfa-35471	600	18	planning	planning	NOUN
cjfa-35471	600	19	horizon	horizon	NOUN
cjfa-35471	600	20	.	.	PUNCT
cjfa-35471	601	1	the	the	DET
cjfa-35471	601	2	results	result	NOUN
cjfa-35471	601	3	will	will	AUX
cjfa-35471	601	4	not	not	PART
cjfa-35471	601	5	change	change	VERB
cjfa-35471	601	6	except	except	SCONJ
cjfa-35471	601	7	the	the	DET
cjfa-35471	601	8	firms	firm	NOUN
cjfa-35471	601	9	will	will	AUX
cjfa-35471	601	10	stop	stop	VERB
cjfa-35471	601	11	and	and	CCONJ
cjfa-35471	601	12	start	start	VERB
cjfa-35471	601	13	two	two	NUM
cjfa-35471	601	14	times	time	NOUN
cjfa-35471	601	15	in	in	ADP
cjfa-35471	601	16	the	the	DET
cjfa-35471	601	17	planning	planning	NOUN
cjfa-35471	601	18	period	period	NOUN
cjfa-35471	601	19	indicating	indicate	VERB
cjfa-35471	601	20	more	more	ADJ
cjfa-35471	601	21	instability	instability	NOUN
cjfa-35471	601	22	of	of	ADP
cjfa-35471	601	23	demand	demand	NOUN
cjfa-35471	601	24	.	.	PUNCT
cjfa-35471	602	1	6	6	NUM
cjfa-35471	602	2	.	.	NOUN
cjfa-35471	602	3	size	size	NOUN
cjfa-35471	602	4	of	of	ADP
cjfa-35471	602	5	the	the	DET
cjfa-35471	602	6	firms	firm	NOUN
cjfa-35471	602	7	,	,	PUNCT
cjfa-35471	602	8	expressed	express	VERB
cjfa-35471	602	9	as	as	ADP
cjfa-35471	602	10	a	a	DET
cjfa-35471	602	11	constant	constant	ADJ
cjfa-35471	602	12	in	in	ADP
cjfa-35471	602	13	the	the	DET
cjfa-35471	602	14	total	total	ADJ
cjfa-35471	602	15	production	production	NOUN
cjfa-35471	602	16	cost	cost	NOUN
cjfa-35471	602	17	(	(	PUNCT
cjfa-35471	602	18	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	602	19	)	)	PUNCT
cjfa-35471	602	20	,	,	PUNCT
cjfa-35471	602	21	is	be	AUX
cjfa-35471	602	22	irrelevant	irrelevant	ADJ
cjfa-35471	602	23	in	in	ADP
cjfa-35471	602	24	production	production	NOUN
cjfa-35471	602	25	decisions	decision	NOUN
cjfa-35471	602	26	since	since	SCONJ
cjfa-35471	602	27	it	it	PRON
cjfa-35471	602	28	will	will	AUX
cjfa-35471	602	29	not	not	PART
cjfa-35471	602	30	appear	appear	VERB
cjfa-35471	602	31	in	in	ADP
cjfa-35471	602	32	equation	equation	NOUN
cjfa-35471	602	33	(	(	PUNCT
cjfa-35471	602	34	4	4	NUM
cjfa-35471	602	35	)	)	PUNCT
cjfa-35471	602	36	.	.	PUNCT
cjfa-35471	603	1	in	in	ADP
cjfa-35471	603	2	the	the	DET
cjfa-35471	603	3	next	next	ADJ
cjfa-35471	603	4	section	section	NOUN
cjfa-35471	603	5	,	,	PUNCT
cjfa-35471	603	6	the	the	DET
cjfa-35471	603	7	impact	impact	NOUN
cjfa-35471	603	8	of	of	ADP
cjfa-35471	603	9	holding	hold	VERB
cjfa-35471	603	10	cost	cost	NOUN
cjfa-35471	603	11	,	,	PUNCT
cjfa-35471	603	12	technology	technology	NOUN
cjfa-35471	603	13	,	,	PUNCT
cjfa-35471	603	14	and	and	CCONJ
cjfa-35471	603	15	interest	interest	NOUN
cjfa-35471	603	16	rates	rate	NOUN
cjfa-35471	603	17	on	on	ADP
cjfa-35471	603	18	the	the	DET
cjfa-35471	603	19	production	production	NOUN
cjfa-35471	603	20	behavior	behavior	NOUN
cjfa-35471	603	21	of	of	ADP
cjfa-35471	603	22	firms	firm	NOUN
cjfa-35471	603	23	is	be	AUX
cjfa-35471	603	24	analyzed	analyze	VERB
cjfa-35471	603	25	with	with	ADP
cjfa-35471	603	26	different	different	ADJ
cjfa-35471	603	27	assumptions	assumption	NOUN
cjfa-35471	603	28	on	on	ADP
cjfa-35471	603	29	interest	interest	NOUN
cjfa-35471	603	30	rates	rate	NOUN
cjfa-35471	603	31	and	and	CCONJ
cjfa-35471	603	32	a	a	DET
cjfa-35471	603	33	specific	specific	ADJ
cjfa-35471	603	34	form	form	NOUN
cjfa-35471	603	35	of	of	ADP
cjfa-35471	603	36	cost	cost	NOUN
cjfa-35471	603	37	function	function	NOUN
cjfa-35471	603	38	(	(	PUNCT
cjfa-35471	603	39	a	a	DET
cjfa-35471	603	40	cubic	cubic	ADJ
cjfa-35471	603	41	function	function	NOUN
cjfa-35471	603	42	of	of	ADP
cjfa-35471	603	43	level	level	NOUN
cjfa-35471	603	44	of	of	ADP
cjfa-35471	603	45	production	production	NOUN
cjfa-35471	603	46	)	)	PUNCT
cjfa-35471	603	47	.	.	PUNCT
cjfa-35471	604	1	graphs	graph	NOUN
cjfa-35471	604	2	are	be	AUX
cjfa-35471	604	3	produced	produce	VERB
cjfa-35471	604	4	to	to	PART
cjfa-35471	604	5	visualize	visualize	VERB
cjfa-35471	604	6	the	the	DET
cjfa-35471	604	7	impact	impact	NOUN
cjfa-35471	604	8	of	of	ADP
cjfa-35471	604	9	assumptions	assumption	NOUN
cjfa-35471	604	10	about	about	ADP
cjfa-35471	604	11	interest	interest	NOUN
cjfa-35471	604	12	rates	rate	NOUN
cjfa-35471	604	13	,	,	PUNCT
cjfa-35471	604	14	parameters	parameter	NOUN
cjfa-35471	604	15	of	of	ADP
cjfa-35471	604	16	demand	demand	NOUN
cjfa-35471	604	17	function	function	NOUN
cjfa-35471	604	18	,	,	PUNCT
cjfa-35471	604	19	and	and	CCONJ
cjfa-35471	604	20	holding	hold	VERB
cjfa-35471	604	21	cost	cost	NOUN
cjfa-35471	604	22	.	.	PUNCT
cjfa-35471	605	1	research	research	NOUN
cjfa-35471	605	2	process	process	NOUN
cjfa-35471	605	3	the	the	DET
cjfa-35471	605	4	specific	specific	ADJ
cjfa-35471	605	5	cost	cost	NOUN
cjfa-35471	605	6	function	function	NOUN
cjfa-35471	605	7	,	,	PUNCT
cjfa-35471	605	8	in	in	ADP
cjfa-35471	605	9	this	this	DET
cjfa-35471	605	10	example	example	NOUN
cjfa-35471	605	11	,	,	PUNCT
cjfa-35471	605	12	will	will	AUX
cjfa-35471	605	13	be	be	AUX
cjfa-35471	605	14	assumed	assume	VERB
cjfa-35471	605	15	to	to	PART
cjfa-35471	605	16	have	have	VERB
cjfa-35471	605	17	the	the	DET
cjfa-35471	605	18	more	more	ADV
cjfa-35471	605	19	realistic	realistic	ADJ
cjfa-35471	605	20	form	form	NOUN
cjfa-35471	605	21	of	of	ADP
cjfa-35471	605	22	:	:	PUNCT
cjfa-35471	605	23	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	605	24	�	�	PROPN
cjfa-35471	605	25	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	ADJ
cjfa-35471	605	26	�	�	PROPN
cjfa-35471	605	27	=	=	SYM
cjfa-35471	605	28	𝑎𝑎𝑐𝑐	𝑎𝑎𝑐𝑐	PROPN
cjfa-35471	605	29	�	�	PROPN
cjfa-35471	605	30	+	+	CCONJ
cjfa-35471	605	31	𝑏𝑏𝑐𝑐	𝑏𝑏𝑐𝑐	PROPN
cjfa-35471	605	32	�	�	PROPN
cjfa-35471	605	33	+	+	NUM
cjfa-35471	605	34	𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	605	35	+	+	CCONJ
cjfa-35471	605	36	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	605	37	and	and	CCONJ
cjfa-35471	605	38	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	606	1	=	=	SYM
cjfa-35471	606	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	606	3	+	+	CCONJ
cjfa-35471	606	4	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	PROPN
cjfa-35471	606	5	as	as	SCONJ
cjfa-35471	606	6	defined	define	VERB
cjfa-35471	606	7	previously	previously	ADV
cjfa-35471	606	8	where	where	SCONJ
cjfa-35471	606	9	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	606	10	represents	represent	VERB
cjfa-35471	606	11	the	the	DET
cjfa-35471	606	12	periodicity	periodicity	NOUN
cjfa-35471	606	13	of	of	ADP
cjfa-35471	606	14	the	the	DET
cjfa-35471	606	15	demand	demand	NOUN
cjfa-35471	606	16	function	function	NOUN
cjfa-35471	606	17	.	.	PUNCT
cjfa-35471	607	1	in	in	ADP
cjfa-35471	607	2	the	the	DET
cjfa-35471	607	3	examples	example	NOUN
cjfa-35471	607	4	below	below	ADV
cjfa-35471	607	5	,	,	PUNCT
cjfa-35471	607	6	we	we	PRON
cjfa-35471	607	7	will	will	AUX
cjfa-35471	607	8	assume	assume	VERB
cjfa-35471	607	9	that	that	SCONJ
cjfa-35471	607	10	𝑎𝑎	𝑎𝑎	ADJ
cjfa-35471	607	11	=	=	SYM
cjfa-35471	607	12	𝑎𝑎𝑎𝑎	𝑎𝑎𝑎𝑎	NOUN
cjfa-35471	607	13	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	607	14	=	=	PUNCT
cjfa-35471	607	15	𝑎𝑎	𝑎𝑎	NOUN
cjfa-35471	607	16	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	607	17	=	=	PUNCT
cjfa-35471	607	18	𝑎𝑎	𝑎𝑎	VERB
cjfa-35471	607	19	𝑎	𝑎	NOUN
cjfa-35471	607	20	=	=	PUNCT
cjfa-35471	607	21	𝑎𝐴𝐴𝑎	𝑎𝐴𝐴𝑎	NOUN
cjfa-35471	607	22	𝑏𝑏	𝑏𝑏	NOUN
cjfa-35471	607	23	=	=	NOUN
cjfa-35471	607	24	𝑎𝑎𝑎	𝑎𝑎𝑎	VERB
cjfa-35471	607	25	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	608	1	=	=	PUNCT
cjfa-35471	608	2	𝑎	𝑎	NOUN
cjfa-35471	608	3	for	for	ADP
cjfa-35471	608	4	simplicity	simplicity	NOUN
cjfa-35471	608	5	.	.	PUNCT
cjfa-35471	609	1	case	case	NOUN
cjfa-35471	610	1	i	i	PRON
cjfa-35471	610	2	:	:	PUNCT
cjfa-35471	610	3	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	610	4	=	=	SYM
cjfa-35471	610	5	𝑎	𝑎	X
cjfa-35471	610	6	(	(	PUNCT
cjfa-35471	610	7	one	one	NUM
cjfa-35471	610	8	cycle	cycle	NOUN
cjfa-35471	610	9	of	of	ADP
cjfa-35471	610	10	the	the	DET
cjfa-35471	610	11	demand	demand	NOUN
cjfa-35471	610	12	curve	curve	NOUN
cjfa-35471	610	13	in	in	ADP
cjfa-35471	610	14	the	the	DET
cjfa-35471	610	15	planning	planning	NOUN
cjfa-35471	610	16	horizon	horizon	NOUN
cjfa-35471	610	17	of	of	ADP
cjfa-35471	610	18	one	one	NUM
cjfa-35471	610	19	and	and	CCONJ
cjfa-35471	610	20	interest	interest	NOUN
cjfa-35471	610	21	rate	rate	NOUN
cjfa-35471	610	22	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	610	23	=	=	SYM
cjfa-35471	610	24	𝑎.	𝑎.	PROPN
cjfa-35471	610	25	)	)	PUNCT
cjfa-35471	610	26	then	then	ADV
cjfa-35471	610	27	the	the	DET
cjfa-35471	610	28	inequality	inequality	NOUN
cjfa-35471	610	29	(	(	PUNCT
cjfa-35471	610	30	4	4	X
cjfa-35471	610	31	)	)	PUNCT
cjfa-35471	610	32	becomes	become	VERB
cjfa-35471	610	33	:	:	PUNCT
cjfa-35471	610	34	𝑐𝑎𝑎𝑎	𝑐𝑎𝑎𝑎	NOUN
cjfa-35471	610	35	∗	∗	NOUN
cjfa-35471	610	36	3𝑐𝑎	3𝑐𝑎	NOUN
cjfa-35471	611	1	+	+	CCONJ
cjfa-35471	611	2	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	NOUN
cjfa-35471	611	3	𝑎	𝑎	PRON
cjfa-35471	611	4	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	NUM
cjfa-35471	611	5	𝑐	𝑐	PROPN
cjfa-35471	611	6	𝐴𝑎𝑎	𝐴𝑎𝑎	PROPN
cjfa-35471	611	7	(	(	PUNCT
cjfa-35471	611	8	5	5	NUM
cjfa-35471	611	9	)	)	PUNCT
cjfa-35471	611	10	and	and	CCONJ
cjfa-35471	611	11	equation	equation	NOUN
cjfa-35471	611	12	will	will	AUX
cjfa-35471	611	13	be	be	AUX
cjfa-35471	611	14	low	low	ADJ
cjfa-35471	611	15	even	even	ADV
cjfa-35471	611	16	if	if	SCONJ
cjfa-35471	611	17	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	611	18	is	be	AUX
cjfa-35471	611	19	high	high	ADJ
cjfa-35471	611	20	(	(	PUNCT
cjfa-35471	611	21	a	a	DET
cjfa-35471	611	22	firm	firm	NOUN
cjfa-35471	611	23	technologically	technologically	ADV
cjfa-35471	611	24	inefficient	inefficient	ADJ
cjfa-35471	611	25	.	.	PUNCT
cjfa-35471	611	26	)	)	PUNCT
cjfa-35471	611	27	.	.	PUNCT
cjfa-35471	612	1	in	in	ADP
cjfa-35471	612	2	countries	country	NOUN
cjfa-35471	612	3	with	with	ADP
cjfa-35471	612	4	high	high	ADJ
cjfa-35471	612	5	interest	interest	NOUN
cjfa-35471	612	6	rates	rate	NOUN
cjfa-35471	612	7	,	,	PUNCT
cjfa-35471	612	8	the	the	DET
cjfa-35471	612	9	importance	importance	NOUN
cjfa-35471	612	10	of	of	ADP
cjfa-35471	612	11	efficient	efficient	ADJ
cjfa-35471	612	12	technologies	technology	NOUN
cjfa-35471	612	13	is	be	AUX
cjfa-35471	612	14	evident	evident	ADJ
cjfa-35471	612	15	because	because	SCONJ
cjfa-35471	612	16	both	both	DET
cjfa-35471	612	17	terms	term	NOUN
cjfa-35471	612	18	(	(	PUNCT
cjfa-35471	612	19	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	612	20	and	and	CCONJ
cjfa-35471	612	21	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	612	22	are	be	AUX
cjfa-35471	612	23	)	)	PUNCT
cjfa-35471	612	24	large	large	ADJ
cjfa-35471	612	25	.	.	PUNCT
cjfa-35471	613	1	5	5	X
cjfa-35471	613	2	.	.	X
cjfa-35471	613	3	the	the	DET
cjfa-35471	613	4	cyclicality	cyclicality	NOUN
cjfa-35471	613	5	of	of	ADP
cjfa-35471	613	6	demand	demand	NOUN
cjfa-35471	613	7	and	and	CCONJ
cjfa-35471	613	8	the	the	DET
cjfa-35471	613	9	time	time	NOUN
cjfa-35471	613	10	dependency	dependency	NOUN
cjfa-35471	613	11	of	of	ADP
cjfa-35471	613	12	interest	interest	NOUN
cjfa-35471	613	13	rates	rate	NOUN
cjfa-35471	613	14	can	can	AUX
cjfa-35471	613	15	affect	affect	VERB
cjfa-35471	613	16	the	the	DET
cjfa-35471	613	17	producers	producer	NOUN
cjfa-35471	613	18	.	.	PUNCT
cjfa-35471	614	1	producers	producer	NOUN
cjfa-35471	614	2	,	,	PUNCT
cjfa-35471	614	3	facing	face	VERB
cjfa-35471	614	4	cyclical	cyclical	ADJ
cjfa-35471	614	5	demand	demand	NOUN
cjfa-35471	614	6	with	with	ADP
cjfa-35471	614	7	very	very	ADV
cjfa-35471	614	8	high	high	ADJ
cjfa-35471	614	9	periodicity	periodicity	NOUN
cjfa-35471	614	10	will	will	AUX
cjfa-35471	614	11	have	have	VERB
cjfa-35471	614	12	extreme	extreme	ADJ
cjfa-35471	614	13	difficulty	difficulty	NOUN
cjfa-35471	614	14	in	in	ADP
cjfa-35471	614	15	planning	planning	NOUN
cjfa-35471	614	16	and	and	CCONJ
cjfa-35471	614	17	hence	hence	ADV
cjfa-35471	614	18	may	may	AUX
cjfa-35471	614	19	not	not	PART
cjfa-35471	614	20	produce	produce	VERB
cjfa-35471	614	21	for	for	ADP
cjfa-35471	614	22	inventory	inventory	NOUN
cjfa-35471	614	23	buildup	buildup	NOUN
cjfa-35471	614	24	at	at	ADV
cjfa-35471	614	25	all	all	ADV
cjfa-35471	614	26	.	.	PUNCT
cjfa-35471	615	1	cyclicality	cyclicality	NOUN
cjfa-35471	615	2	in	in	ADP
cjfa-35471	615	3	the	the	DET
cjfa-35471	615	4	following	follow	VERB
cjfa-35471	615	5	examples	example	NOUN
cjfa-35471	615	6	is	be	AUX
cjfa-35471	615	7	denoted	denote	VERB
cjfa-35471	615	8	by	by	ADP
cjfa-35471	615	9	the	the	DET
cjfa-35471	615	10	parameter	parameter	NOUN
cjfa-35471	615	11	k.	k.	PROPN
cjfa-35471	616	1	the	the	DET
cjfa-35471	616	2	value	value	NOUN
cjfa-35471	616	3	of	of	ADP
cjfa-35471	616	4	k	k	PROPN
cjfa-35471	616	5	will	will	AUX
cjfa-35471	616	6	be	be	AUX
cjfa-35471	616	7	assumed	assume	VERB
cjfa-35471	616	8	to	to	PART
cjfa-35471	616	9	be	be	AUX
cjfa-35471	616	10	1	1	NUM
cjfa-35471	616	11	in	in	ADP
cjfa-35471	616	12	all	all	DET
cjfa-35471	616	13	cases	case	NOUN
cjfa-35471	616	14	for	for	ADP
cjfa-35471	616	15	simplicity	simplicity	NOUN
cjfa-35471	616	16	.	.	PUNCT
cjfa-35471	617	1	for	for	ADP
cjfa-35471	617	2	higher	high	ADJ
cjfa-35471	617	3	values	value	NOUN
cjfa-35471	617	4	of	of	ADP
cjfa-35471	617	5	k	k	NOUN
cjfa-35471	617	6	,	,	PUNCT
cjfa-35471	617	7	trigonometric	trigonometric	ADJ
cjfa-35471	617	8	functions	function	NOUN
cjfa-35471	617	9	will	will	AUX
cjfa-35471	617	10	complete	complete	VERB
cjfa-35471	617	11	360	360	NUM
cjfa-35471	617	12	-	-	PUNCT
cjfa-35471	617	13	degree	degree	NOUN
cjfa-35471	617	14	cycle	cycle	NOUN
cjfa-35471	617	15	twice	twice	ADV
cjfa-35471	617	16	in	in	ADP
cjfa-35471	617	17	the	the	DET
cjfa-35471	617	18	planning	planning	NOUN
cjfa-35471	617	19	horizon	horizon	NOUN
cjfa-35471	617	20	.	.	PUNCT
cjfa-35471	618	1	the	the	DET
cjfa-35471	618	2	results	result	NOUN
cjfa-35471	618	3	will	will	AUX
cjfa-35471	618	4	not	not	PART
cjfa-35471	618	5	change	change	VERB
cjfa-35471	618	6	except	except	SCONJ
cjfa-35471	618	7	the	the	DET
cjfa-35471	618	8	firms	firm	NOUN
cjfa-35471	618	9	will	will	AUX
cjfa-35471	618	10	stop	stop	VERB
cjfa-35471	618	11	and	and	CCONJ
cjfa-35471	618	12	start	start	VERB
cjfa-35471	618	13	two	two	NUM
cjfa-35471	618	14	times	time	NOUN
cjfa-35471	618	15	in	in	ADP
cjfa-35471	618	16	the	the	DET
cjfa-35471	618	17	planning	planning	NOUN
cjfa-35471	618	18	period	period	NOUN
cjfa-35471	618	19	indicating	indicate	VERB
cjfa-35471	618	20	more	more	ADJ
cjfa-35471	618	21	instability	instability	NOUN
cjfa-35471	618	22	of	of	ADP
cjfa-35471	618	23	demand	demand	NOUN
cjfa-35471	618	24	.	.	PUNCT
cjfa-35471	619	1	6	6	NUM
cjfa-35471	619	2	.	.	NOUN
cjfa-35471	619	3	size	size	NOUN
cjfa-35471	619	4	of	of	ADP
cjfa-35471	619	5	the	the	DET
cjfa-35471	619	6	firms	firm	NOUN
cjfa-35471	619	7	,	,	PUNCT
cjfa-35471	619	8	expressed	express	VERB
cjfa-35471	619	9	as	as	ADP
cjfa-35471	619	10	a	a	DET
cjfa-35471	619	11	constant	constant	ADJ
cjfa-35471	619	12	in	in	ADP
cjfa-35471	619	13	the	the	DET
cjfa-35471	619	14	total	total	ADJ
cjfa-35471	619	15	production	production	NOUN
cjfa-35471	619	16	cost	cost	NOUN
cjfa-35471	619	17	(	(	PUNCT
cjfa-35471	619	18	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	619	19	)	)	PUNCT
cjfa-35471	619	20	,	,	PUNCT
cjfa-35471	619	21	is	be	AUX
cjfa-35471	619	22	irrelevant	irrelevant	ADJ
cjfa-35471	619	23	in	in	ADP
cjfa-35471	619	24	production	production	NOUN
cjfa-35471	619	25	decisions	decision	NOUN
cjfa-35471	619	26	since	since	SCONJ
cjfa-35471	619	27	it	it	PRON
cjfa-35471	619	28	will	will	AUX
cjfa-35471	619	29	not	not	PART
cjfa-35471	619	30	appear	appear	VERB
cjfa-35471	619	31	in	in	ADP
cjfa-35471	619	32	equation	equation	NOUN
cjfa-35471	619	33	(	(	PUNCT
cjfa-35471	619	34	4	4	NUM
cjfa-35471	619	35	)	)	PUNCT
cjfa-35471	619	36	.	.	PUNCT
cjfa-35471	620	1	in	in	ADP
cjfa-35471	620	2	the	the	DET
cjfa-35471	620	3	next	next	ADJ
cjfa-35471	620	4	section	section	NOUN
cjfa-35471	620	5	,	,	PUNCT
cjfa-35471	620	6	the	the	DET
cjfa-35471	620	7	impact	impact	NOUN
cjfa-35471	620	8	of	of	ADP
cjfa-35471	620	9	holding	hold	VERB
cjfa-35471	620	10	cost	cost	NOUN
cjfa-35471	620	11	,	,	PUNCT
cjfa-35471	620	12	technology	technology	NOUN
cjfa-35471	620	13	,	,	PUNCT
cjfa-35471	620	14	and	and	CCONJ
cjfa-35471	620	15	interest	interest	NOUN
cjfa-35471	620	16	rates	rate	NOUN
cjfa-35471	620	17	on	on	ADP
cjfa-35471	620	18	the	the	DET
cjfa-35471	620	19	production	production	NOUN
cjfa-35471	620	20	behavior	behavior	NOUN
cjfa-35471	620	21	of	of	ADP
cjfa-35471	620	22	firms	firm	NOUN
cjfa-35471	620	23	is	be	AUX
cjfa-35471	620	24	analyzed	analyze	VERB
cjfa-35471	620	25	with	with	ADP
cjfa-35471	620	26	different	different	ADJ
cjfa-35471	620	27	assumptions	assumption	NOUN
cjfa-35471	620	28	on	on	ADP
cjfa-35471	620	29	interest	interest	NOUN
cjfa-35471	620	30	rates	rate	NOUN
cjfa-35471	620	31	and	and	CCONJ
cjfa-35471	620	32	a	a	DET
cjfa-35471	620	33	specific	specific	ADJ
cjfa-35471	620	34	form	form	NOUN
cjfa-35471	620	35	of	of	ADP
cjfa-35471	620	36	cost	cost	NOUN
cjfa-35471	620	37	function	function	NOUN
cjfa-35471	620	38	(	(	PUNCT
cjfa-35471	620	39	a	a	DET
cjfa-35471	620	40	cubic	cubic	ADJ
cjfa-35471	620	41	function	function	NOUN
cjfa-35471	620	42	of	of	ADP
cjfa-35471	620	43	level	level	NOUN
cjfa-35471	620	44	of	of	ADP
cjfa-35471	620	45	production	production	NOUN
cjfa-35471	620	46	)	)	PUNCT
cjfa-35471	620	47	.	.	PUNCT
cjfa-35471	621	1	graphs	graph	NOUN
cjfa-35471	621	2	are	be	AUX
cjfa-35471	621	3	produced	produce	VERB
cjfa-35471	621	4	to	to	PART
cjfa-35471	621	5	visualize	visualize	VERB
cjfa-35471	621	6	the	the	DET
cjfa-35471	621	7	impact	impact	NOUN
cjfa-35471	621	8	of	of	ADP
cjfa-35471	621	9	assumptions	assumption	NOUN
cjfa-35471	621	10	about	about	ADP
cjfa-35471	621	11	interest	interest	NOUN
cjfa-35471	621	12	rates	rate	NOUN
cjfa-35471	621	13	,	,	PUNCT
cjfa-35471	621	14	parameters	parameter	NOUN
cjfa-35471	621	15	of	of	ADP
cjfa-35471	621	16	demand	demand	NOUN
cjfa-35471	621	17	function	function	NOUN
cjfa-35471	621	18	,	,	PUNCT
cjfa-35471	621	19	and	and	CCONJ
cjfa-35471	621	20	holding	hold	VERB
cjfa-35471	621	21	cost	cost	NOUN
cjfa-35471	621	22	.	.	PUNCT
cjfa-35471	622	1	research	research	NOUN
cjfa-35471	622	2	process	process	NOUN
cjfa-35471	622	3	the	the	DET
cjfa-35471	622	4	specific	specific	ADJ
cjfa-35471	622	5	cost	cost	NOUN
cjfa-35471	622	6	function	function	NOUN
cjfa-35471	622	7	,	,	PUNCT
cjfa-35471	622	8	in	in	ADP
cjfa-35471	622	9	this	this	DET
cjfa-35471	622	10	example	example	NOUN
cjfa-35471	622	11	,	,	PUNCT
cjfa-35471	622	12	will	will	AUX
cjfa-35471	622	13	be	be	AUX
cjfa-35471	622	14	assumed	assume	VERB
cjfa-35471	622	15	to	to	PART
cjfa-35471	622	16	have	have	VERB
cjfa-35471	622	17	the	the	DET
cjfa-35471	622	18	more	more	ADV
cjfa-35471	622	19	realistic	realistic	ADJ
cjfa-35471	622	20	form	form	NOUN
cjfa-35471	622	21	of	of	ADP
cjfa-35471	622	22	:	:	PUNCT
cjfa-35471	622	23	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	622	24	�	�	PROPN
cjfa-35471	622	25	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	ADJ
cjfa-35471	622	26	�	�	PROPN
cjfa-35471	622	27	=	=	SYM
cjfa-35471	622	28	𝑎𝑎𝑐𝑐	𝑎𝑎𝑐𝑐	PROPN
cjfa-35471	622	29	�	�	PROPN
cjfa-35471	622	30	+	+	CCONJ
cjfa-35471	622	31	𝑏𝑏𝑐𝑐	𝑏𝑏𝑐𝑐	PROPN
cjfa-35471	622	32	�	�	PROPN
cjfa-35471	622	33	+	+	NUM
cjfa-35471	622	34	𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	622	35	+	+	CCONJ
cjfa-35471	622	36	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	622	37	and	and	CCONJ
cjfa-35471	622	38	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	623	1	=	=	SYM
cjfa-35471	623	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	623	3	+	+	CCONJ
cjfa-35471	623	4	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	PROPN
cjfa-35471	623	5	as	as	SCONJ
cjfa-35471	623	6	defined	define	VERB
cjfa-35471	623	7	previously	previously	ADV
cjfa-35471	623	8	where	where	SCONJ
cjfa-35471	623	9	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	623	10	represents	represent	VERB
cjfa-35471	623	11	the	the	DET
cjfa-35471	623	12	periodicity	periodicity	NOUN
cjfa-35471	623	13	of	of	ADP
cjfa-35471	623	14	the	the	DET
cjfa-35471	623	15	demand	demand	NOUN
cjfa-35471	623	16	function	function	NOUN
cjfa-35471	623	17	.	.	PUNCT
cjfa-35471	624	1	in	in	ADP
cjfa-35471	624	2	the	the	DET
cjfa-35471	624	3	examples	example	NOUN
cjfa-35471	624	4	below	below	ADV
cjfa-35471	624	5	,	,	PUNCT
cjfa-35471	624	6	we	we	PRON
cjfa-35471	624	7	will	will	AUX
cjfa-35471	624	8	assume	assume	VERB
cjfa-35471	624	9	that	that	SCONJ
cjfa-35471	624	10	𝑎𝑎	𝑎𝑎	ADJ
cjfa-35471	624	11	=	=	SYM
cjfa-35471	624	12	𝑎𝑎𝑎𝑎	𝑎𝑎𝑎𝑎	NOUN
cjfa-35471	624	13	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	624	14	=	=	PUNCT
cjfa-35471	624	15	𝑎𝑎	𝑎𝑎	NOUN
cjfa-35471	624	16	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	624	17	=	=	PUNCT
cjfa-35471	624	18	𝑎𝑎	𝑎𝑎	VERB
cjfa-35471	624	19	𝑎	𝑎	NOUN
cjfa-35471	624	20	=	=	PUNCT
cjfa-35471	624	21	𝑎𝐴𝐴𝑎	𝑎𝐴𝐴𝑎	NOUN
cjfa-35471	624	22	𝑏𝑏	𝑏𝑏	NOUN
cjfa-35471	624	23	=	=	NOUN
cjfa-35471	624	24	𝑎𝑎𝑎	𝑎𝑎𝑎	VERB
cjfa-35471	624	25	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	625	1	=	=	PUNCT
cjfa-35471	625	2	𝑎	𝑎	NOUN
cjfa-35471	625	3	for	for	ADP
cjfa-35471	625	4	simplicity	simplicity	NOUN
cjfa-35471	625	5	.	.	PUNCT
cjfa-35471	626	1	case	case	NOUN
cjfa-35471	627	1	i	i	PRON
cjfa-35471	627	2	:	:	PUNCT
cjfa-35471	627	3	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	627	4	=	=	SYM
cjfa-35471	627	5	𝑎	𝑎	X
cjfa-35471	627	6	(	(	PUNCT
cjfa-35471	627	7	one	one	NUM
cjfa-35471	627	8	cycle	cycle	NOUN
cjfa-35471	627	9	of	of	ADP
cjfa-35471	627	10	the	the	DET
cjfa-35471	627	11	demand	demand	NOUN
cjfa-35471	627	12	curve	curve	NOUN
cjfa-35471	627	13	in	in	ADP
cjfa-35471	627	14	the	the	DET
cjfa-35471	627	15	planning	planning	NOUN
cjfa-35471	627	16	horizon	horizon	NOUN
cjfa-35471	627	17	of	of	ADP
cjfa-35471	627	18	one	one	NUM
cjfa-35471	627	19	and	and	CCONJ
cjfa-35471	627	20	interest	interest	NOUN
cjfa-35471	627	21	rate	rate	NOUN
cjfa-35471	627	22	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	627	23	=	=	SYM
cjfa-35471	627	24	𝑎.	𝑎.	PROPN
cjfa-35471	627	25	)	)	PUNCT
cjfa-35471	627	26	then	then	ADV
cjfa-35471	627	27	the	the	DET
cjfa-35471	627	28	inequality	inequality	NOUN
cjfa-35471	627	29	(	(	PUNCT
cjfa-35471	627	30	4	4	X
cjfa-35471	627	31	)	)	PUNCT
cjfa-35471	627	32	becomes	become	VERB
cjfa-35471	627	33	:	:	PUNCT
cjfa-35471	627	34	𝑐𝑎𝑎𝑎	𝑐𝑎𝑎𝑎	NOUN
cjfa-35471	627	35	∗	∗	NOUN
cjfa-35471	627	36	3𝑐𝑎	3𝑐𝑎	NOUN
cjfa-35471	628	1	+	+	CCONJ
cjfa-35471	628	2	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	NOUN
cjfa-35471	628	3	𝑎	𝑎	PRON
cjfa-35471	628	4	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	NUM
cjfa-35471	628	5	𝑐	𝑐	PROPN
cjfa-35471	628	6	𝐴𝑎𝑎	𝐴𝑎𝑎	PROPN
cjfa-35471	628	7	(	(	PUNCT
cjfa-35471	628	8	5	5	NUM
cjfa-35471	628	9	)	)	PUNCT
cjfa-35471	628	10	as	as	SCONJ
cjfa-35471	628	11	defined	define	VERB
cjfa-35471	628	12	previously	previously	ADV
cjfa-35471	628	13	where	where	SCONJ
cjfa-35471	628	14	k	k	PROPN
cjfa-35471	628	15	represents	represent	VERB
cjfa-35471	628	16	the	the	DET
cjfa-35471	628	17	periodicity	periodicity	NOUN
cjfa-35471	628	18	of	of	ADP
cjfa-35471	628	19	the	the	DET
cjfa-35471	628	20	demand	demand	NOUN
cjfa-35471	628	21	function	function	NOUN
cjfa-35471	628	22	.	.	PUNCT
cjfa-35471	629	1	in	in	ADP
cjfa-35471	629	2	the	the	DET
cjfa-35471	629	3	examples	example	NOUN
cjfa-35471	629	4	below	below	ADV
cjfa-35471	629	5	,	,	PUNCT
cjfa-35471	629	6	we	we	PRON
cjfa-35471	629	7	will	will	AUX
cjfa-35471	629	8	assume	assume	VERB
cjfa-35471	629	9	that	that	SCONJ
cjfa-35471	629	10	equation	equation	NOUN
cjfa-35471	629	11	will	will	AUX
cjfa-35471	629	12	be	be	AUX
cjfa-35471	629	13	low	low	ADJ
cjfa-35471	629	14	even	even	ADV
cjfa-35471	629	15	if	if	SCONJ
cjfa-35471	629	16	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	629	17	is	be	AUX
cjfa-35471	629	18	high	high	ADJ
cjfa-35471	629	19	(	(	PUNCT
cjfa-35471	629	20	a	a	DET
cjfa-35471	629	21	firm	firm	NOUN
cjfa-35471	629	22	technologically	technologically	ADV
cjfa-35471	629	23	inefficient	inefficient	ADJ
cjfa-35471	629	24	.	.	PUNCT
cjfa-35471	629	25	)	)	PUNCT
cjfa-35471	629	26	.	.	PUNCT
cjfa-35471	630	1	in	in	ADP
cjfa-35471	630	2	countries	country	NOUN
cjfa-35471	630	3	with	with	ADP
cjfa-35471	630	4	high	high	ADJ
cjfa-35471	630	5	interest	interest	NOUN
cjfa-35471	630	6	rates	rate	NOUN
cjfa-35471	630	7	,	,	PUNCT
cjfa-35471	630	8	the	the	DET
cjfa-35471	630	9	importance	importance	NOUN
cjfa-35471	630	10	of	of	ADP
cjfa-35471	630	11	efficient	efficient	ADJ
cjfa-35471	630	12	technologies	technology	NOUN
cjfa-35471	630	13	is	be	AUX
cjfa-35471	630	14	evident	evident	ADJ
cjfa-35471	630	15	because	because	SCONJ
cjfa-35471	630	16	both	both	DET
cjfa-35471	630	17	terms	term	NOUN
cjfa-35471	630	18	(	(	PUNCT
cjfa-35471	630	19	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	630	20	and	and	CCONJ
cjfa-35471	630	21	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	630	22	are	be	AUX
cjfa-35471	630	23	)	)	PUNCT
cjfa-35471	630	24	large	large	ADJ
cjfa-35471	630	25	.	.	PUNCT
cjfa-35471	631	1	5	5	X
cjfa-35471	631	2	.	.	X
cjfa-35471	631	3	the	the	DET
cjfa-35471	631	4	cyclicality	cyclicality	NOUN
cjfa-35471	631	5	of	of	ADP
cjfa-35471	631	6	demand	demand	NOUN
cjfa-35471	631	7	and	and	CCONJ
cjfa-35471	631	8	the	the	DET
cjfa-35471	631	9	time	time	NOUN
cjfa-35471	631	10	dependency	dependency	NOUN
cjfa-35471	631	11	of	of	ADP
cjfa-35471	631	12	interest	interest	NOUN
cjfa-35471	631	13	rates	rate	NOUN
cjfa-35471	631	14	can	can	AUX
cjfa-35471	631	15	affect	affect	VERB
cjfa-35471	631	16	the	the	DET
cjfa-35471	631	17	producers	producer	NOUN
cjfa-35471	631	18	.	.	PUNCT
cjfa-35471	632	1	producers	producer	NOUN
cjfa-35471	632	2	,	,	PUNCT
cjfa-35471	632	3	facing	face	VERB
cjfa-35471	632	4	cyclical	cyclical	ADJ
cjfa-35471	632	5	demand	demand	NOUN
cjfa-35471	632	6	with	with	ADP
cjfa-35471	632	7	very	very	ADV
cjfa-35471	632	8	high	high	ADJ
cjfa-35471	632	9	periodicity	periodicity	NOUN
cjfa-35471	632	10	will	will	AUX
cjfa-35471	632	11	have	have	VERB
cjfa-35471	632	12	extreme	extreme	ADJ
cjfa-35471	632	13	difficulty	difficulty	NOUN
cjfa-35471	632	14	in	in	ADP
cjfa-35471	632	15	planning	planning	NOUN
cjfa-35471	632	16	and	and	CCONJ
cjfa-35471	632	17	hence	hence	ADV
cjfa-35471	632	18	may	may	AUX
cjfa-35471	632	19	not	not	PART
cjfa-35471	632	20	produce	produce	VERB
cjfa-35471	632	21	for	for	ADP
cjfa-35471	632	22	inventory	inventory	NOUN
cjfa-35471	632	23	buildup	buildup	NOUN
cjfa-35471	632	24	at	at	ADV
cjfa-35471	632	25	all	all	ADV
cjfa-35471	632	26	.	.	PUNCT
cjfa-35471	633	1	cyclicality	cyclicality	NOUN
cjfa-35471	633	2	in	in	ADP
cjfa-35471	633	3	the	the	DET
cjfa-35471	633	4	following	follow	VERB
cjfa-35471	633	5	examples	example	NOUN
cjfa-35471	633	6	is	be	AUX
cjfa-35471	633	7	denoted	denote	VERB
cjfa-35471	633	8	by	by	ADP
cjfa-35471	633	9	the	the	DET
cjfa-35471	633	10	parameter	parameter	NOUN
cjfa-35471	633	11	k.	k.	PROPN
cjfa-35471	634	1	the	the	DET
cjfa-35471	634	2	value	value	NOUN
cjfa-35471	634	3	of	of	ADP
cjfa-35471	634	4	k	k	PROPN
cjfa-35471	634	5	will	will	AUX
cjfa-35471	634	6	be	be	AUX
cjfa-35471	634	7	assumed	assume	VERB
cjfa-35471	634	8	to	to	PART
cjfa-35471	634	9	be	be	AUX
cjfa-35471	634	10	1	1	NUM
cjfa-35471	634	11	in	in	ADP
cjfa-35471	634	12	all	all	DET
cjfa-35471	634	13	cases	case	NOUN
cjfa-35471	634	14	for	for	ADP
cjfa-35471	634	15	simplicity	simplicity	NOUN
cjfa-35471	634	16	.	.	PUNCT
cjfa-35471	635	1	for	for	ADP
cjfa-35471	635	2	higher	high	ADJ
cjfa-35471	635	3	values	value	NOUN
cjfa-35471	635	4	of	of	ADP
cjfa-35471	635	5	k	k	NOUN
cjfa-35471	635	6	,	,	PUNCT
cjfa-35471	635	7	trigonometric	trigonometric	ADJ
cjfa-35471	635	8	functions	function	NOUN
cjfa-35471	635	9	will	will	AUX
cjfa-35471	635	10	complete	complete	VERB
cjfa-35471	635	11	360	360	NUM
cjfa-35471	635	12	-	-	PUNCT
cjfa-35471	635	13	degree	degree	NOUN
cjfa-35471	635	14	cycle	cycle	NOUN
cjfa-35471	635	15	twice	twice	ADV
cjfa-35471	635	16	in	in	ADP
cjfa-35471	635	17	the	the	DET
cjfa-35471	635	18	planning	planning	NOUN
cjfa-35471	635	19	horizon	horizon	NOUN
cjfa-35471	635	20	.	.	PUNCT
cjfa-35471	636	1	the	the	DET
cjfa-35471	636	2	results	result	NOUN
cjfa-35471	636	3	will	will	AUX
cjfa-35471	636	4	not	not	PART
cjfa-35471	636	5	change	change	VERB
cjfa-35471	636	6	except	except	SCONJ
cjfa-35471	636	7	the	the	DET
cjfa-35471	636	8	firms	firm	NOUN
cjfa-35471	636	9	will	will	AUX
cjfa-35471	636	10	stop	stop	VERB
cjfa-35471	636	11	and	and	CCONJ
cjfa-35471	636	12	start	start	VERB
cjfa-35471	636	13	two	two	NUM
cjfa-35471	636	14	times	time	NOUN
cjfa-35471	636	15	in	in	ADP
cjfa-35471	636	16	the	the	DET
cjfa-35471	636	17	planning	planning	NOUN
cjfa-35471	636	18	period	period	NOUN
cjfa-35471	636	19	indicating	indicate	VERB
cjfa-35471	636	20	more	more	ADJ
cjfa-35471	636	21	instability	instability	NOUN
cjfa-35471	636	22	of	of	ADP
cjfa-35471	636	23	demand	demand	NOUN
cjfa-35471	636	24	.	.	PUNCT
cjfa-35471	637	1	6	6	NUM
cjfa-35471	637	2	.	.	NOUN
cjfa-35471	637	3	size	size	NOUN
cjfa-35471	637	4	of	of	ADP
cjfa-35471	637	5	the	the	DET
cjfa-35471	637	6	firms	firm	NOUN
cjfa-35471	637	7	,	,	PUNCT
cjfa-35471	637	8	expressed	express	VERB
cjfa-35471	637	9	as	as	ADP
cjfa-35471	637	10	a	a	DET
cjfa-35471	637	11	constant	constant	ADJ
cjfa-35471	637	12	in	in	ADP
cjfa-35471	637	13	the	the	DET
cjfa-35471	637	14	total	total	ADJ
cjfa-35471	637	15	production	production	NOUN
cjfa-35471	637	16	cost	cost	NOUN
cjfa-35471	637	17	(	(	PUNCT
cjfa-35471	637	18	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	637	19	)	)	PUNCT
cjfa-35471	637	20	,	,	PUNCT
cjfa-35471	637	21	is	be	AUX
cjfa-35471	637	22	irrelevant	irrelevant	ADJ
cjfa-35471	637	23	in	in	ADP
cjfa-35471	637	24	production	production	NOUN
cjfa-35471	637	25	decisions	decision	NOUN
cjfa-35471	637	26	since	since	SCONJ
cjfa-35471	637	27	it	it	PRON
cjfa-35471	637	28	will	will	AUX
cjfa-35471	637	29	not	not	PART
cjfa-35471	637	30	appear	appear	VERB
cjfa-35471	637	31	in	in	ADP
cjfa-35471	637	32	equation	equation	NOUN
cjfa-35471	637	33	(	(	PUNCT
cjfa-35471	637	34	4	4	NUM
cjfa-35471	637	35	)	)	PUNCT
cjfa-35471	637	36	.	.	PUNCT
cjfa-35471	638	1	in	in	ADP
cjfa-35471	638	2	the	the	DET
cjfa-35471	638	3	next	next	ADJ
cjfa-35471	638	4	section	section	NOUN
cjfa-35471	638	5	,	,	PUNCT
cjfa-35471	638	6	the	the	DET
cjfa-35471	638	7	impact	impact	NOUN
cjfa-35471	638	8	of	of	ADP
cjfa-35471	638	9	holding	hold	VERB
cjfa-35471	638	10	cost	cost	NOUN
cjfa-35471	638	11	,	,	PUNCT
cjfa-35471	638	12	technology	technology	NOUN
cjfa-35471	638	13	,	,	PUNCT
cjfa-35471	638	14	and	and	CCONJ
cjfa-35471	638	15	interest	interest	NOUN
cjfa-35471	638	16	rates	rate	NOUN
cjfa-35471	638	17	on	on	ADP
cjfa-35471	638	18	the	the	DET
cjfa-35471	638	19	production	production	NOUN
cjfa-35471	638	20	behavior	behavior	NOUN
cjfa-35471	638	21	of	of	ADP
cjfa-35471	638	22	firms	firm	NOUN
cjfa-35471	638	23	is	be	AUX
cjfa-35471	638	24	analyzed	analyze	VERB
cjfa-35471	638	25	with	with	ADP
cjfa-35471	638	26	different	different	ADJ
cjfa-35471	638	27	assumptions	assumption	NOUN
cjfa-35471	638	28	on	on	ADP
cjfa-35471	638	29	interest	interest	NOUN
cjfa-35471	638	30	rates	rate	NOUN
cjfa-35471	638	31	and	and	CCONJ
cjfa-35471	638	32	a	a	DET
cjfa-35471	638	33	specific	specific	ADJ
cjfa-35471	638	34	form	form	NOUN
cjfa-35471	638	35	of	of	ADP
cjfa-35471	638	36	cost	cost	NOUN
cjfa-35471	638	37	function	function	NOUN
cjfa-35471	638	38	(	(	PUNCT
cjfa-35471	638	39	a	a	DET
cjfa-35471	638	40	cubic	cubic	ADJ
cjfa-35471	638	41	function	function	NOUN
cjfa-35471	638	42	of	of	ADP
cjfa-35471	638	43	level	level	NOUN
cjfa-35471	638	44	of	of	ADP
cjfa-35471	638	45	production	production	NOUN
cjfa-35471	638	46	)	)	PUNCT
cjfa-35471	638	47	.	.	PUNCT
cjfa-35471	639	1	graphs	graph	NOUN
cjfa-35471	639	2	are	be	AUX
cjfa-35471	639	3	produced	produce	VERB
cjfa-35471	639	4	to	to	PART
cjfa-35471	639	5	visualize	visualize	VERB
cjfa-35471	639	6	the	the	DET
cjfa-35471	639	7	impact	impact	NOUN
cjfa-35471	639	8	of	of	ADP
cjfa-35471	639	9	assumptions	assumption	NOUN
cjfa-35471	639	10	about	about	ADP
cjfa-35471	639	11	interest	interest	NOUN
cjfa-35471	639	12	rates	rate	NOUN
cjfa-35471	639	13	,	,	PUNCT
cjfa-35471	639	14	parameters	parameter	NOUN
cjfa-35471	639	15	of	of	ADP
cjfa-35471	639	16	demand	demand	NOUN
cjfa-35471	639	17	function	function	NOUN
cjfa-35471	639	18	,	,	PUNCT
cjfa-35471	639	19	and	and	CCONJ
cjfa-35471	639	20	holding	hold	VERB
cjfa-35471	639	21	cost	cost	NOUN
cjfa-35471	639	22	.	.	PUNCT
cjfa-35471	640	1	research	research	NOUN
cjfa-35471	640	2	process	process	NOUN
cjfa-35471	640	3	the	the	DET
cjfa-35471	640	4	specific	specific	ADJ
cjfa-35471	640	5	cost	cost	NOUN
cjfa-35471	640	6	function	function	NOUN
cjfa-35471	640	7	,	,	PUNCT
cjfa-35471	640	8	in	in	ADP
cjfa-35471	640	9	this	this	DET
cjfa-35471	640	10	example	example	NOUN
cjfa-35471	640	11	,	,	PUNCT
cjfa-35471	640	12	will	will	AUX
cjfa-35471	640	13	be	be	AUX
cjfa-35471	640	14	assumed	assume	VERB
cjfa-35471	640	15	to	to	PART
cjfa-35471	640	16	have	have	VERB
cjfa-35471	640	17	the	the	DET
cjfa-35471	640	18	more	more	ADV
cjfa-35471	640	19	realistic	realistic	ADJ
cjfa-35471	640	20	form	form	NOUN
cjfa-35471	640	21	of	of	ADP
cjfa-35471	640	22	:	:	PUNCT
cjfa-35471	640	23	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	640	24	�	�	PROPN
cjfa-35471	640	25	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	ADJ
cjfa-35471	640	26	�	�	PROPN
cjfa-35471	640	27	=	=	SYM
cjfa-35471	640	28	𝑎𝑎𝑐𝑐	𝑎𝑎𝑐𝑐	PROPN
cjfa-35471	640	29	�	�	PROPN
cjfa-35471	640	30	+	+	CCONJ
cjfa-35471	640	31	𝑏𝑏𝑐𝑐	𝑏𝑏𝑐𝑐	PROPN
cjfa-35471	640	32	�	�	PROPN
cjfa-35471	640	33	+	+	NUM
cjfa-35471	640	34	𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	640	35	+	+	CCONJ
cjfa-35471	640	36	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	640	37	and	and	CCONJ
cjfa-35471	640	38	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	641	1	=	=	SYM
cjfa-35471	641	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	641	3	+	+	CCONJ
cjfa-35471	641	4	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	PROPN
cjfa-35471	641	5	as	as	SCONJ
cjfa-35471	641	6	defined	define	VERB
cjfa-35471	641	7	previously	previously	ADV
cjfa-35471	641	8	where	where	SCONJ
cjfa-35471	641	9	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	641	10	represents	represent	VERB
cjfa-35471	641	11	the	the	DET
cjfa-35471	641	12	periodicity	periodicity	NOUN
cjfa-35471	641	13	of	of	ADP
cjfa-35471	641	14	the	the	DET
cjfa-35471	641	15	demand	demand	NOUN
cjfa-35471	641	16	function	function	NOUN
cjfa-35471	641	17	.	.	PUNCT
cjfa-35471	642	1	in	in	ADP
cjfa-35471	642	2	the	the	DET
cjfa-35471	642	3	examples	example	NOUN
cjfa-35471	642	4	below	below	ADV
cjfa-35471	642	5	,	,	PUNCT
cjfa-35471	642	6	we	we	PRON
cjfa-35471	642	7	will	will	AUX
cjfa-35471	642	8	assume	assume	VERB
cjfa-35471	642	9	that	that	SCONJ
cjfa-35471	642	10	𝑎𝑎	𝑎𝑎	ADJ
cjfa-35471	642	11	=	=	SYM
cjfa-35471	642	12	𝑎𝑎𝑎𝑎	𝑎𝑎𝑎𝑎	NOUN
cjfa-35471	642	13	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	642	14	=	=	PUNCT
cjfa-35471	642	15	𝑎𝑎	𝑎𝑎	NOUN
cjfa-35471	642	16	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	642	17	=	=	PUNCT
cjfa-35471	642	18	𝑎𝑎	𝑎𝑎	VERB
cjfa-35471	642	19	𝑎	𝑎	NOUN
cjfa-35471	642	20	=	=	PUNCT
cjfa-35471	642	21	𝑎𝐴𝐴𝑎	𝑎𝐴𝐴𝑎	NOUN
cjfa-35471	642	22	𝑏𝑏	𝑏𝑏	NOUN
cjfa-35471	642	23	=	=	NOUN
cjfa-35471	642	24	𝑎𝑎𝑎	𝑎𝑎𝑎	VERB
cjfa-35471	642	25	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	643	1	=	=	PUNCT
cjfa-35471	643	2	𝑎	𝑎	NOUN
cjfa-35471	643	3	for	for	ADP
cjfa-35471	643	4	simplicity	simplicity	NOUN
cjfa-35471	643	5	.	.	PUNCT
cjfa-35471	644	1	case	case	NOUN
cjfa-35471	645	1	i	i	PRON
cjfa-35471	645	2	:	:	PUNCT
cjfa-35471	645	3	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	645	4	=	=	SYM
cjfa-35471	645	5	𝑎	𝑎	X
cjfa-35471	645	6	(	(	PUNCT
cjfa-35471	645	7	one	one	NUM
cjfa-35471	645	8	cycle	cycle	NOUN
cjfa-35471	645	9	of	of	ADP
cjfa-35471	645	10	the	the	DET
cjfa-35471	645	11	demand	demand	NOUN
cjfa-35471	645	12	curve	curve	NOUN
cjfa-35471	645	13	in	in	ADP
cjfa-35471	645	14	the	the	DET
cjfa-35471	645	15	planning	planning	NOUN
cjfa-35471	645	16	horizon	horizon	NOUN
cjfa-35471	645	17	of	of	ADP
cjfa-35471	645	18	one	one	NUM
cjfa-35471	645	19	and	and	CCONJ
cjfa-35471	645	20	interest	interest	NOUN
cjfa-35471	645	21	rate	rate	NOUN
cjfa-35471	645	22	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	645	23	=	=	SYM
cjfa-35471	645	24	𝑎.	𝑎.	PROPN
cjfa-35471	645	25	)	)	PUNCT
cjfa-35471	645	26	then	then	ADV
cjfa-35471	645	27	the	the	DET
cjfa-35471	645	28	inequality	inequality	NOUN
cjfa-35471	645	29	(	(	PUNCT
cjfa-35471	645	30	4	4	X
cjfa-35471	645	31	)	)	PUNCT
cjfa-35471	645	32	becomes	become	VERB
cjfa-35471	645	33	:	:	PUNCT
cjfa-35471	645	34	𝑐𝑎𝑎𝑎	𝑐𝑎𝑎𝑎	NOUN
cjfa-35471	645	35	∗	∗	NOUN
cjfa-35471	645	36	3𝑐𝑎	3𝑐𝑎	NOUN
cjfa-35471	646	1	+	+	CCONJ
cjfa-35471	646	2	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	NOUN
cjfa-35471	646	3	𝑎	𝑎	PRON
cjfa-35471	646	4	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	NUM
cjfa-35471	646	5	𝑐	𝑐	PROPN
cjfa-35471	646	6	𝐴𝑎𝑎	𝐴𝑎𝑎	PROPN
cjfa-35471	646	7	(	(	PUNCT
cjfa-35471	646	8	5	5	NUM
cjfa-35471	646	9	)	)	PUNCT
cjfa-35471	646	10	equation	equation	NOUN
cjfa-35471	646	11	will	will	AUX
cjfa-35471	646	12	be	be	AUX
cjfa-35471	646	13	low	low	ADJ
cjfa-35471	646	14	even	even	ADV
cjfa-35471	646	15	if	if	SCONJ
cjfa-35471	646	16	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	646	17	is	be	AUX
cjfa-35471	646	18	high	high	ADJ
cjfa-35471	646	19	(	(	PUNCT
cjfa-35471	646	20	a	a	DET
cjfa-35471	646	21	firm	firm	NOUN
cjfa-35471	646	22	technologically	technologically	ADV
cjfa-35471	646	23	inefficient	inefficient	ADJ
cjfa-35471	646	24	.	.	PUNCT
cjfa-35471	646	25	)	)	PUNCT
cjfa-35471	646	26	.	.	PUNCT
cjfa-35471	647	1	in	in	ADP
cjfa-35471	647	2	countries	country	NOUN
cjfa-35471	647	3	with	with	ADP
cjfa-35471	647	4	high	high	ADJ
cjfa-35471	647	5	interest	interest	NOUN
cjfa-35471	647	6	rates	rate	NOUN
cjfa-35471	647	7	,	,	PUNCT
cjfa-35471	647	8	the	the	DET
cjfa-35471	647	9	importance	importance	NOUN
cjfa-35471	647	10	of	of	ADP
cjfa-35471	647	11	efficient	efficient	ADJ
cjfa-35471	647	12	technologies	technology	NOUN
cjfa-35471	647	13	is	be	AUX
cjfa-35471	647	14	evident	evident	ADJ
cjfa-35471	647	15	because	because	SCONJ
cjfa-35471	647	16	both	both	DET
cjfa-35471	647	17	terms	term	NOUN
cjfa-35471	647	18	(	(	PUNCT
cjfa-35471	647	19	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	647	20	and	and	CCONJ
cjfa-35471	647	21	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	647	22	are	be	AUX
cjfa-35471	647	23	)	)	PUNCT
cjfa-35471	647	24	large	large	ADJ
cjfa-35471	647	25	.	.	PUNCT
cjfa-35471	648	1	5	5	X
cjfa-35471	648	2	.	.	X
cjfa-35471	648	3	the	the	DET
cjfa-35471	648	4	cyclicality	cyclicality	NOUN
cjfa-35471	648	5	of	of	ADP
cjfa-35471	648	6	demand	demand	NOUN
cjfa-35471	648	7	and	and	CCONJ
cjfa-35471	648	8	the	the	DET
cjfa-35471	648	9	time	time	NOUN
cjfa-35471	648	10	dependency	dependency	NOUN
cjfa-35471	648	11	of	of	ADP
cjfa-35471	648	12	interest	interest	NOUN
cjfa-35471	648	13	rates	rate	NOUN
cjfa-35471	648	14	can	can	AUX
cjfa-35471	648	15	affect	affect	VERB
cjfa-35471	648	16	the	the	DET
cjfa-35471	648	17	producers	producer	NOUN
cjfa-35471	648	18	.	.	PUNCT
cjfa-35471	649	1	producers	producer	NOUN
cjfa-35471	649	2	,	,	PUNCT
cjfa-35471	649	3	facing	face	VERB
cjfa-35471	649	4	cyclical	cyclical	ADJ
cjfa-35471	649	5	demand	demand	NOUN
cjfa-35471	649	6	with	with	ADP
cjfa-35471	649	7	very	very	ADV
cjfa-35471	649	8	high	high	ADJ
cjfa-35471	649	9	periodicity	periodicity	NOUN
cjfa-35471	649	10	will	will	AUX
cjfa-35471	649	11	have	have	VERB
cjfa-35471	649	12	extreme	extreme	ADJ
cjfa-35471	649	13	difficulty	difficulty	NOUN
cjfa-35471	649	14	in	in	ADP
cjfa-35471	649	15	planning	planning	NOUN
cjfa-35471	649	16	and	and	CCONJ
cjfa-35471	649	17	hence	hence	ADV
cjfa-35471	649	18	may	may	AUX
cjfa-35471	649	19	not	not	PART
cjfa-35471	649	20	produce	produce	VERB
cjfa-35471	649	21	for	for	ADP
cjfa-35471	649	22	inventory	inventory	NOUN
cjfa-35471	649	23	buildup	buildup	NOUN
cjfa-35471	649	24	at	at	ADV
cjfa-35471	649	25	all	all	ADV
cjfa-35471	649	26	.	.	PUNCT
cjfa-35471	650	1	cyclicality	cyclicality	NOUN
cjfa-35471	650	2	in	in	ADP
cjfa-35471	650	3	the	the	DET
cjfa-35471	650	4	following	follow	VERB
cjfa-35471	650	5	examples	example	NOUN
cjfa-35471	650	6	is	be	AUX
cjfa-35471	650	7	denoted	denote	VERB
cjfa-35471	650	8	by	by	ADP
cjfa-35471	650	9	the	the	DET
cjfa-35471	650	10	parameter	parameter	NOUN
cjfa-35471	650	11	k.	k.	PROPN
cjfa-35471	651	1	the	the	DET
cjfa-35471	651	2	value	value	NOUN
cjfa-35471	651	3	of	of	ADP
cjfa-35471	651	4	k	k	PROPN
cjfa-35471	651	5	will	will	AUX
cjfa-35471	651	6	be	be	AUX
cjfa-35471	651	7	assumed	assume	VERB
cjfa-35471	651	8	to	to	PART
cjfa-35471	651	9	be	be	AUX
cjfa-35471	651	10	1	1	NUM
cjfa-35471	651	11	in	in	ADP
cjfa-35471	651	12	all	all	DET
cjfa-35471	651	13	cases	case	NOUN
cjfa-35471	651	14	for	for	ADP
cjfa-35471	651	15	simplicity	simplicity	NOUN
cjfa-35471	651	16	.	.	PUNCT
cjfa-35471	652	1	for	for	ADP
cjfa-35471	652	2	higher	high	ADJ
cjfa-35471	652	3	values	value	NOUN
cjfa-35471	652	4	of	of	ADP
cjfa-35471	652	5	k	k	NOUN
cjfa-35471	652	6	,	,	PUNCT
cjfa-35471	652	7	trigonometric	trigonometric	ADJ
cjfa-35471	652	8	functions	function	NOUN
cjfa-35471	652	9	will	will	AUX
cjfa-35471	652	10	complete	complete	VERB
cjfa-35471	652	11	360	360	NUM
cjfa-35471	652	12	-	-	PUNCT
cjfa-35471	652	13	degree	degree	NOUN
cjfa-35471	652	14	cycle	cycle	NOUN
cjfa-35471	652	15	twice	twice	ADV
cjfa-35471	652	16	in	in	ADP
cjfa-35471	652	17	the	the	DET
cjfa-35471	652	18	planning	planning	NOUN
cjfa-35471	652	19	horizon	horizon	NOUN
cjfa-35471	652	20	.	.	PUNCT
cjfa-35471	653	1	the	the	DET
cjfa-35471	653	2	results	result	NOUN
cjfa-35471	653	3	will	will	AUX
cjfa-35471	653	4	not	not	PART
cjfa-35471	653	5	change	change	VERB
cjfa-35471	653	6	except	except	SCONJ
cjfa-35471	653	7	the	the	DET
cjfa-35471	653	8	firms	firm	NOUN
cjfa-35471	653	9	will	will	AUX
cjfa-35471	653	10	stop	stop	VERB
cjfa-35471	653	11	and	and	CCONJ
cjfa-35471	653	12	start	start	VERB
cjfa-35471	653	13	two	two	NUM
cjfa-35471	653	14	times	time	NOUN
cjfa-35471	653	15	in	in	ADP
cjfa-35471	653	16	the	the	DET
cjfa-35471	653	17	planning	planning	NOUN
cjfa-35471	653	18	period	period	NOUN
cjfa-35471	653	19	indicating	indicate	VERB
cjfa-35471	653	20	more	more	ADJ
cjfa-35471	653	21	instability	instability	NOUN
cjfa-35471	653	22	of	of	ADP
cjfa-35471	653	23	demand	demand	NOUN
cjfa-35471	653	24	.	.	PUNCT
cjfa-35471	654	1	6	6	NUM
cjfa-35471	654	2	.	.	NOUN
cjfa-35471	654	3	size	size	NOUN
cjfa-35471	654	4	of	of	ADP
cjfa-35471	654	5	the	the	DET
cjfa-35471	654	6	firms	firm	NOUN
cjfa-35471	654	7	,	,	PUNCT
cjfa-35471	654	8	expressed	express	VERB
cjfa-35471	654	9	as	as	ADP
cjfa-35471	654	10	a	a	DET
cjfa-35471	654	11	constant	constant	ADJ
cjfa-35471	654	12	in	in	ADP
cjfa-35471	654	13	the	the	DET
cjfa-35471	654	14	total	total	ADJ
cjfa-35471	654	15	production	production	NOUN
cjfa-35471	654	16	cost	cost	NOUN
cjfa-35471	654	17	(	(	PUNCT
cjfa-35471	654	18	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	654	19	)	)	PUNCT
cjfa-35471	654	20	,	,	PUNCT
cjfa-35471	654	21	is	be	AUX
cjfa-35471	654	22	irrelevant	irrelevant	ADJ
cjfa-35471	654	23	in	in	ADP
cjfa-35471	654	24	production	production	NOUN
cjfa-35471	654	25	decisions	decision	NOUN
cjfa-35471	654	26	since	since	SCONJ
cjfa-35471	654	27	it	it	PRON
cjfa-35471	654	28	will	will	AUX
cjfa-35471	654	29	not	not	PART
cjfa-35471	654	30	appear	appear	VERB
cjfa-35471	654	31	in	in	ADP
cjfa-35471	654	32	equation	equation	NOUN
cjfa-35471	654	33	(	(	PUNCT
cjfa-35471	654	34	4	4	NUM
cjfa-35471	654	35	)	)	PUNCT
cjfa-35471	654	36	.	.	PUNCT
cjfa-35471	655	1	in	in	ADP
cjfa-35471	655	2	the	the	DET
cjfa-35471	655	3	next	next	ADJ
cjfa-35471	655	4	section	section	NOUN
cjfa-35471	655	5	,	,	PUNCT
cjfa-35471	655	6	the	the	DET
cjfa-35471	655	7	impact	impact	NOUN
cjfa-35471	655	8	of	of	ADP
cjfa-35471	655	9	holding	hold	VERB
cjfa-35471	655	10	cost	cost	NOUN
cjfa-35471	655	11	,	,	PUNCT
cjfa-35471	655	12	technology	technology	NOUN
cjfa-35471	655	13	,	,	PUNCT
cjfa-35471	655	14	and	and	CCONJ
cjfa-35471	655	15	interest	interest	NOUN
cjfa-35471	655	16	rates	rate	NOUN
cjfa-35471	655	17	on	on	ADP
cjfa-35471	655	18	the	the	DET
cjfa-35471	655	19	production	production	NOUN
cjfa-35471	655	20	behavior	behavior	NOUN
cjfa-35471	655	21	of	of	ADP
cjfa-35471	655	22	firms	firm	NOUN
cjfa-35471	655	23	is	be	AUX
cjfa-35471	655	24	analyzed	analyze	VERB
cjfa-35471	655	25	with	with	ADP
cjfa-35471	655	26	different	different	ADJ
cjfa-35471	655	27	assumptions	assumption	NOUN
cjfa-35471	655	28	on	on	ADP
cjfa-35471	655	29	interest	interest	NOUN
cjfa-35471	655	30	rates	rate	NOUN
cjfa-35471	655	31	and	and	CCONJ
cjfa-35471	655	32	a	a	DET
cjfa-35471	655	33	specific	specific	ADJ
cjfa-35471	655	34	form	form	NOUN
cjfa-35471	655	35	of	of	ADP
cjfa-35471	655	36	cost	cost	NOUN
cjfa-35471	655	37	function	function	NOUN
cjfa-35471	655	38	(	(	PUNCT
cjfa-35471	655	39	a	a	DET
cjfa-35471	655	40	cubic	cubic	ADJ
cjfa-35471	655	41	function	function	NOUN
cjfa-35471	655	42	of	of	ADP
cjfa-35471	655	43	level	level	NOUN
cjfa-35471	655	44	of	of	ADP
cjfa-35471	655	45	production	production	NOUN
cjfa-35471	655	46	)	)	PUNCT
cjfa-35471	655	47	.	.	PUNCT
cjfa-35471	656	1	graphs	graph	NOUN
cjfa-35471	656	2	are	be	AUX
cjfa-35471	656	3	produced	produce	VERB
cjfa-35471	656	4	to	to	PART
cjfa-35471	656	5	visualize	visualize	VERB
cjfa-35471	656	6	the	the	DET
cjfa-35471	656	7	impact	impact	NOUN
cjfa-35471	656	8	of	of	ADP
cjfa-35471	656	9	assumptions	assumption	NOUN
cjfa-35471	656	10	about	about	ADP
cjfa-35471	656	11	interest	interest	NOUN
cjfa-35471	656	12	rates	rate	NOUN
cjfa-35471	656	13	,	,	PUNCT
cjfa-35471	656	14	parameters	parameter	NOUN
cjfa-35471	656	15	of	of	ADP
cjfa-35471	656	16	demand	demand	NOUN
cjfa-35471	656	17	function	function	NOUN
cjfa-35471	656	18	,	,	PUNCT
cjfa-35471	656	19	and	and	CCONJ
cjfa-35471	656	20	holding	hold	VERB
cjfa-35471	656	21	cost	cost	NOUN
cjfa-35471	656	22	.	.	PUNCT
cjfa-35471	657	1	research	research	NOUN
cjfa-35471	657	2	process	process	NOUN
cjfa-35471	657	3	the	the	DET
cjfa-35471	657	4	specific	specific	ADJ
cjfa-35471	657	5	cost	cost	NOUN
cjfa-35471	657	6	function	function	NOUN
cjfa-35471	657	7	,	,	PUNCT
cjfa-35471	657	8	in	in	ADP
cjfa-35471	657	9	this	this	DET
cjfa-35471	657	10	example	example	NOUN
cjfa-35471	657	11	,	,	PUNCT
cjfa-35471	657	12	will	will	AUX
cjfa-35471	657	13	be	be	AUX
cjfa-35471	657	14	assumed	assume	VERB
cjfa-35471	657	15	to	to	PART
cjfa-35471	657	16	have	have	VERB
cjfa-35471	657	17	the	the	DET
cjfa-35471	657	18	more	more	ADV
cjfa-35471	657	19	realistic	realistic	ADJ
cjfa-35471	657	20	form	form	NOUN
cjfa-35471	657	21	of	of	ADP
cjfa-35471	657	22	:	:	PUNCT
cjfa-35471	657	23	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	657	24	�	�	PROPN
cjfa-35471	657	25	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	ADJ
cjfa-35471	657	26	�	�	PROPN
cjfa-35471	657	27	=	=	SYM
cjfa-35471	657	28	𝑎𝑎𝑐𝑐	𝑎𝑎𝑐𝑐	PROPN
cjfa-35471	657	29	�	�	PROPN
cjfa-35471	657	30	+	+	CCONJ
cjfa-35471	657	31	𝑏𝑏𝑐𝑐	𝑏𝑏𝑐𝑐	PROPN
cjfa-35471	657	32	�	�	PROPN
cjfa-35471	657	33	+	+	NUM
cjfa-35471	657	34	𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	657	35	+	+	CCONJ
cjfa-35471	657	36	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	657	37	and	and	CCONJ
cjfa-35471	657	38	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	658	1	=	=	SYM
cjfa-35471	658	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	658	3	+	+	CCONJ
cjfa-35471	658	4	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	PROPN
cjfa-35471	658	5	as	as	SCONJ
cjfa-35471	658	6	defined	define	VERB
cjfa-35471	658	7	previously	previously	ADV
cjfa-35471	658	8	where	where	SCONJ
cjfa-35471	658	9	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	658	10	represents	represent	VERB
cjfa-35471	658	11	the	the	DET
cjfa-35471	658	12	periodicity	periodicity	NOUN
cjfa-35471	658	13	of	of	ADP
cjfa-35471	658	14	the	the	DET
cjfa-35471	658	15	demand	demand	NOUN
cjfa-35471	658	16	function	function	NOUN
cjfa-35471	658	17	.	.	PUNCT
cjfa-35471	659	1	in	in	ADP
cjfa-35471	659	2	the	the	DET
cjfa-35471	659	3	examples	example	NOUN
cjfa-35471	659	4	below	below	ADV
cjfa-35471	659	5	,	,	PUNCT
cjfa-35471	659	6	we	we	PRON
cjfa-35471	659	7	will	will	AUX
cjfa-35471	659	8	assume	assume	VERB
cjfa-35471	659	9	that	that	SCONJ
cjfa-35471	659	10	𝑎𝑎	𝑎𝑎	ADJ
cjfa-35471	659	11	=	=	SYM
cjfa-35471	659	12	𝑎𝑎𝑎𝑎	𝑎𝑎𝑎𝑎	NOUN
cjfa-35471	659	13	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	659	14	=	=	PUNCT
cjfa-35471	659	15	𝑎𝑎	𝑎𝑎	NOUN
cjfa-35471	659	16	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	659	17	=	=	PUNCT
cjfa-35471	659	18	𝑎𝑎	𝑎𝑎	VERB
cjfa-35471	659	19	𝑎	𝑎	NOUN
cjfa-35471	659	20	=	=	PUNCT
cjfa-35471	659	21	𝑎𝐴𝐴𝑎	𝑎𝐴𝐴𝑎	NOUN
cjfa-35471	659	22	𝑏𝑏	𝑏𝑏	NOUN
cjfa-35471	659	23	=	=	NOUN
cjfa-35471	659	24	𝑎𝑎𝑎	𝑎𝑎𝑎	VERB
cjfa-35471	659	25	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	660	1	=	=	PUNCT
cjfa-35471	660	2	𝑎	𝑎	NOUN
cjfa-35471	660	3	for	for	ADP
cjfa-35471	660	4	simplicity	simplicity	NOUN
cjfa-35471	660	5	.	.	PUNCT
cjfa-35471	661	1	case	case	NOUN
cjfa-35471	662	1	i	i	PRON
cjfa-35471	662	2	:	:	PUNCT
cjfa-35471	662	3	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	662	4	=	=	SYM
cjfa-35471	662	5	𝑎	𝑎	X
cjfa-35471	662	6	(	(	PUNCT
cjfa-35471	662	7	one	one	NUM
cjfa-35471	662	8	cycle	cycle	NOUN
cjfa-35471	662	9	of	of	ADP
cjfa-35471	662	10	the	the	DET
cjfa-35471	662	11	demand	demand	NOUN
cjfa-35471	662	12	curve	curve	NOUN
cjfa-35471	662	13	in	in	ADP
cjfa-35471	662	14	the	the	DET
cjfa-35471	662	15	planning	planning	NOUN
cjfa-35471	662	16	horizon	horizon	NOUN
cjfa-35471	662	17	of	of	ADP
cjfa-35471	662	18	one	one	NUM
cjfa-35471	662	19	and	and	CCONJ
cjfa-35471	662	20	interest	interest	NOUN
cjfa-35471	662	21	rate	rate	NOUN
cjfa-35471	662	22	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	662	23	=	=	SYM
cjfa-35471	662	24	𝑎.	𝑎.	PROPN
cjfa-35471	662	25	)	)	PUNCT
cjfa-35471	662	26	then	then	ADV
cjfa-35471	662	27	the	the	DET
cjfa-35471	662	28	inequality	inequality	NOUN
cjfa-35471	662	29	(	(	PUNCT
cjfa-35471	662	30	4	4	X
cjfa-35471	662	31	)	)	PUNCT
cjfa-35471	662	32	becomes	become	VERB
cjfa-35471	662	33	:	:	PUNCT
cjfa-35471	662	34	𝑐𝑎𝑎𝑎	𝑐𝑎𝑎𝑎	NOUN
cjfa-35471	662	35	∗	∗	NOUN
cjfa-35471	662	36	3𝑐𝑎	3𝑐𝑎	NOUN
cjfa-35471	663	1	+	+	CCONJ
cjfa-35471	663	2	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	NOUN
cjfa-35471	663	3	𝑎	𝑎	PRON
cjfa-35471	663	4	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	NUM
cjfa-35471	663	5	𝑐	𝑐	PROPN
cjfa-35471	663	6	𝐴𝑎𝑎	𝐴𝑎𝑎	PROPN
cjfa-35471	663	7	(	(	PUNCT
cjfa-35471	663	8	5	5	NUM
cjfa-35471	663	9	)	)	PUNCT
cjfa-35471	663	10	for	for	ADP
cjfa-35471	663	11	simplicity	simplicity	NOUN
cjfa-35471	663	12	.	.	PUNCT
cjfa-35471	664	1	case	case	NOUN
cjfa-35471	665	1	i	i	PRON
cjfa-35471	665	2	:	:	PUNCT
cjfa-35471	665	3	k	k	X
cjfa-35471	665	4	=	=	SYM
cjfa-35471	665	5	1	1	NUM
cjfa-35471	665	6	(	(	PUNCT
cjfa-35471	665	7	one	one	NUM
cjfa-35471	665	8	cycle	cycle	NOUN
cjfa-35471	665	9	of	of	ADP
cjfa-35471	665	10	the	the	DET
cjfa-35471	665	11	demand	demand	NOUN
cjfa-35471	665	12	curve	curve	NOUN
cjfa-35471	665	13	in	in	ADP
cjfa-35471	665	14	the	the	DET
cjfa-35471	665	15	planning	planning	NOUN
cjfa-35471	665	16	horizon	horizon	NOUN
cjfa-35471	665	17	of	of	ADP
cjfa-35471	665	18	one	one	NUM
cjfa-35471	665	19	and	and	CCONJ
cjfa-35471	665	20	interest	interest	NOUN
cjfa-35471	665	21	rate	rate	NOUN
cjfa-35471	665	22	f(t	f(t	NOUN
cjfa-35471	665	23	)	)	PUNCT
cjfa-35471	665	24	=	=	SYM
cjfa-35471	665	25	0	0	X
cjfa-35471	665	26	.	.	PUNCT
cjfa-35471	665	27	)	)	PUNCT
cjfa-35471	666	1	then	then	ADV
cjfa-35471	666	2	the	the	DET
cjfa-35471	666	3	inequality	inequality	NOUN
cjfa-35471	666	4	(	(	PUNCT
cjfa-35471	666	5	4	4	X
cjfa-35471	666	6	)	)	PUNCT
cjfa-35471	666	7	becomes	become	VERB
cjfa-35471	666	8	:	:	PUNCT
cjfa-35471	666	9	equation	equation	NOUN
cjfa-35471	666	10	will	will	AUX
cjfa-35471	666	11	be	be	AUX
cjfa-35471	666	12	low	low	ADJ
cjfa-35471	666	13	even	even	ADV
cjfa-35471	666	14	if	if	SCONJ
cjfa-35471	666	15	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	666	16	is	be	AUX
cjfa-35471	666	17	high	high	ADJ
cjfa-35471	666	18	(	(	PUNCT
cjfa-35471	666	19	a	a	DET
cjfa-35471	666	20	firm	firm	NOUN
cjfa-35471	666	21	technologically	technologically	ADV
cjfa-35471	666	22	inefficient	inefficient	ADJ
cjfa-35471	666	23	.	.	PUNCT
cjfa-35471	666	24	)	)	PUNCT
cjfa-35471	666	25	.	.	PUNCT
cjfa-35471	667	1	in	in	ADP
cjfa-35471	667	2	countries	country	NOUN
cjfa-35471	667	3	with	with	ADP
cjfa-35471	667	4	high	high	ADJ
cjfa-35471	667	5	interest	interest	NOUN
cjfa-35471	667	6	rates	rate	NOUN
cjfa-35471	667	7	,	,	PUNCT
cjfa-35471	667	8	the	the	DET
cjfa-35471	667	9	importance	importance	NOUN
cjfa-35471	667	10	of	of	ADP
cjfa-35471	667	11	efficient	efficient	ADJ
cjfa-35471	667	12	technologies	technology	NOUN
cjfa-35471	667	13	is	be	AUX
cjfa-35471	667	14	evident	evident	ADJ
cjfa-35471	667	15	because	because	SCONJ
cjfa-35471	667	16	both	both	DET
cjfa-35471	667	17	terms	term	NOUN
cjfa-35471	667	18	(	(	PUNCT
cjfa-35471	667	19	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	667	20	and	and	CCONJ
cjfa-35471	667	21	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	667	22	are	be	AUX
cjfa-35471	667	23	)	)	PUNCT
cjfa-35471	667	24	large	large	ADJ
cjfa-35471	667	25	.	.	PUNCT
cjfa-35471	668	1	5	5	X
cjfa-35471	668	2	.	.	X
cjfa-35471	668	3	the	the	DET
cjfa-35471	668	4	cyclicality	cyclicality	NOUN
cjfa-35471	668	5	of	of	ADP
cjfa-35471	668	6	demand	demand	NOUN
cjfa-35471	668	7	and	and	CCONJ
cjfa-35471	668	8	the	the	DET
cjfa-35471	668	9	time	time	NOUN
cjfa-35471	668	10	dependency	dependency	NOUN
cjfa-35471	668	11	of	of	ADP
cjfa-35471	668	12	interest	interest	NOUN
cjfa-35471	668	13	rates	rate	NOUN
cjfa-35471	668	14	can	can	AUX
cjfa-35471	668	15	affect	affect	VERB
cjfa-35471	668	16	the	the	DET
cjfa-35471	668	17	producers	producer	NOUN
cjfa-35471	668	18	.	.	PUNCT
cjfa-35471	669	1	producers	producer	NOUN
cjfa-35471	669	2	,	,	PUNCT
cjfa-35471	669	3	facing	face	VERB
cjfa-35471	669	4	cyclical	cyclical	ADJ
cjfa-35471	669	5	demand	demand	NOUN
cjfa-35471	669	6	with	with	ADP
cjfa-35471	669	7	very	very	ADV
cjfa-35471	669	8	high	high	ADJ
cjfa-35471	669	9	periodicity	periodicity	NOUN
cjfa-35471	669	10	will	will	AUX
cjfa-35471	669	11	have	have	VERB
cjfa-35471	669	12	extreme	extreme	ADJ
cjfa-35471	669	13	difficulty	difficulty	NOUN
cjfa-35471	669	14	in	in	ADP
cjfa-35471	669	15	planning	planning	NOUN
cjfa-35471	669	16	and	and	CCONJ
cjfa-35471	669	17	hence	hence	ADV
cjfa-35471	669	18	may	may	AUX
cjfa-35471	669	19	not	not	PART
cjfa-35471	669	20	produce	produce	VERB
cjfa-35471	669	21	for	for	ADP
cjfa-35471	669	22	inventory	inventory	NOUN
cjfa-35471	669	23	buildup	buildup	NOUN
cjfa-35471	669	24	at	at	ADV
cjfa-35471	669	25	all	all	ADV
cjfa-35471	669	26	.	.	PUNCT
cjfa-35471	670	1	cyclicality	cyclicality	NOUN
cjfa-35471	670	2	in	in	ADP
cjfa-35471	670	3	the	the	DET
cjfa-35471	670	4	following	follow	VERB
cjfa-35471	670	5	examples	example	NOUN
cjfa-35471	670	6	is	be	AUX
cjfa-35471	670	7	denoted	denote	VERB
cjfa-35471	670	8	by	by	ADP
cjfa-35471	670	9	the	the	DET
cjfa-35471	670	10	parameter	parameter	NOUN
cjfa-35471	670	11	k.	k.	PROPN
cjfa-35471	671	1	the	the	DET
cjfa-35471	671	2	value	value	NOUN
cjfa-35471	671	3	of	of	ADP
cjfa-35471	671	4	k	k	PROPN
cjfa-35471	671	5	will	will	AUX
cjfa-35471	671	6	be	be	AUX
cjfa-35471	671	7	assumed	assume	VERB
cjfa-35471	671	8	to	to	PART
cjfa-35471	671	9	be	be	AUX
cjfa-35471	671	10	1	1	NUM
cjfa-35471	671	11	in	in	ADP
cjfa-35471	671	12	all	all	DET
cjfa-35471	671	13	cases	case	NOUN
cjfa-35471	671	14	for	for	ADP
cjfa-35471	671	15	simplicity	simplicity	NOUN
cjfa-35471	671	16	.	.	PUNCT
cjfa-35471	672	1	for	for	ADP
cjfa-35471	672	2	higher	high	ADJ
cjfa-35471	672	3	values	value	NOUN
cjfa-35471	672	4	of	of	ADP
cjfa-35471	672	5	k	k	NOUN
cjfa-35471	672	6	,	,	PUNCT
cjfa-35471	672	7	trigonometric	trigonometric	ADJ
cjfa-35471	672	8	functions	function	NOUN
cjfa-35471	672	9	will	will	AUX
cjfa-35471	672	10	complete	complete	VERB
cjfa-35471	672	11	360	360	NUM
cjfa-35471	672	12	-	-	PUNCT
cjfa-35471	672	13	degree	degree	NOUN
cjfa-35471	672	14	cycle	cycle	NOUN
cjfa-35471	672	15	twice	twice	ADV
cjfa-35471	672	16	in	in	ADP
cjfa-35471	672	17	the	the	DET
cjfa-35471	672	18	planning	planning	NOUN
cjfa-35471	672	19	horizon	horizon	NOUN
cjfa-35471	672	20	.	.	PUNCT
cjfa-35471	673	1	the	the	DET
cjfa-35471	673	2	results	result	NOUN
cjfa-35471	673	3	will	will	AUX
cjfa-35471	673	4	not	not	PART
cjfa-35471	673	5	change	change	VERB
cjfa-35471	673	6	except	except	SCONJ
cjfa-35471	673	7	the	the	DET
cjfa-35471	673	8	firms	firm	NOUN
cjfa-35471	673	9	will	will	AUX
cjfa-35471	673	10	stop	stop	VERB
cjfa-35471	673	11	and	and	CCONJ
cjfa-35471	673	12	start	start	VERB
cjfa-35471	673	13	two	two	NUM
cjfa-35471	673	14	times	time	NOUN
cjfa-35471	673	15	in	in	ADP
cjfa-35471	673	16	the	the	DET
cjfa-35471	673	17	planning	planning	NOUN
cjfa-35471	673	18	period	period	NOUN
cjfa-35471	673	19	indicating	indicate	VERB
cjfa-35471	673	20	more	more	ADJ
cjfa-35471	673	21	instability	instability	NOUN
cjfa-35471	673	22	of	of	ADP
cjfa-35471	673	23	demand	demand	NOUN
cjfa-35471	673	24	.	.	PUNCT
cjfa-35471	674	1	6	6	NUM
cjfa-35471	674	2	.	.	NOUN
cjfa-35471	674	3	size	size	NOUN
cjfa-35471	674	4	of	of	ADP
cjfa-35471	674	5	the	the	DET
cjfa-35471	674	6	firms	firm	NOUN
cjfa-35471	674	7	,	,	PUNCT
cjfa-35471	674	8	expressed	express	VERB
cjfa-35471	674	9	as	as	ADP
cjfa-35471	674	10	a	a	DET
cjfa-35471	674	11	constant	constant	ADJ
cjfa-35471	674	12	in	in	ADP
cjfa-35471	674	13	the	the	DET
cjfa-35471	674	14	total	total	ADJ
cjfa-35471	674	15	production	production	NOUN
cjfa-35471	674	16	cost	cost	NOUN
cjfa-35471	674	17	(	(	PUNCT
cjfa-35471	674	18	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	674	19	)	)	PUNCT
cjfa-35471	674	20	,	,	PUNCT
cjfa-35471	674	21	is	be	AUX
cjfa-35471	674	22	irrelevant	irrelevant	ADJ
cjfa-35471	674	23	in	in	ADP
cjfa-35471	674	24	production	production	NOUN
cjfa-35471	674	25	decisions	decision	NOUN
cjfa-35471	674	26	since	since	SCONJ
cjfa-35471	674	27	it	it	PRON
cjfa-35471	674	28	will	will	AUX
cjfa-35471	674	29	not	not	PART
cjfa-35471	674	30	appear	appear	VERB
cjfa-35471	674	31	in	in	ADP
cjfa-35471	674	32	equation	equation	NOUN
cjfa-35471	674	33	(	(	PUNCT
cjfa-35471	674	34	4	4	NUM
cjfa-35471	674	35	)	)	PUNCT
cjfa-35471	674	36	.	.	PUNCT
cjfa-35471	675	1	in	in	ADP
cjfa-35471	675	2	the	the	DET
cjfa-35471	675	3	next	next	ADJ
cjfa-35471	675	4	section	section	NOUN
cjfa-35471	675	5	,	,	PUNCT
cjfa-35471	675	6	the	the	DET
cjfa-35471	675	7	impact	impact	NOUN
cjfa-35471	675	8	of	of	ADP
cjfa-35471	675	9	holding	hold	VERB
cjfa-35471	675	10	cost	cost	NOUN
cjfa-35471	675	11	,	,	PUNCT
cjfa-35471	675	12	technology	technology	NOUN
cjfa-35471	675	13	,	,	PUNCT
cjfa-35471	675	14	and	and	CCONJ
cjfa-35471	675	15	interest	interest	NOUN
cjfa-35471	675	16	rates	rate	NOUN
cjfa-35471	675	17	on	on	ADP
cjfa-35471	675	18	the	the	DET
cjfa-35471	675	19	production	production	NOUN
cjfa-35471	675	20	behavior	behavior	NOUN
cjfa-35471	675	21	of	of	ADP
cjfa-35471	675	22	firms	firm	NOUN
cjfa-35471	675	23	is	be	AUX
cjfa-35471	675	24	analyzed	analyze	VERB
cjfa-35471	675	25	with	with	ADP
cjfa-35471	675	26	different	different	ADJ
cjfa-35471	675	27	assumptions	assumption	NOUN
cjfa-35471	675	28	on	on	ADP
cjfa-35471	675	29	interest	interest	NOUN
cjfa-35471	675	30	rates	rate	NOUN
cjfa-35471	675	31	and	and	CCONJ
cjfa-35471	675	32	a	a	DET
cjfa-35471	675	33	specific	specific	ADJ
cjfa-35471	675	34	form	form	NOUN
cjfa-35471	675	35	of	of	ADP
cjfa-35471	675	36	cost	cost	NOUN
cjfa-35471	675	37	function	function	NOUN
cjfa-35471	675	38	(	(	PUNCT
cjfa-35471	675	39	a	a	DET
cjfa-35471	675	40	cubic	cubic	ADJ
cjfa-35471	675	41	function	function	NOUN
cjfa-35471	675	42	of	of	ADP
cjfa-35471	675	43	level	level	NOUN
cjfa-35471	675	44	of	of	ADP
cjfa-35471	675	45	production	production	NOUN
cjfa-35471	675	46	)	)	PUNCT
cjfa-35471	675	47	.	.	PUNCT
cjfa-35471	676	1	graphs	graph	NOUN
cjfa-35471	676	2	are	be	AUX
cjfa-35471	676	3	produced	produce	VERB
cjfa-35471	676	4	to	to	PART
cjfa-35471	676	5	visualize	visualize	VERB
cjfa-35471	676	6	the	the	DET
cjfa-35471	676	7	impact	impact	NOUN
cjfa-35471	676	8	of	of	ADP
cjfa-35471	676	9	assumptions	assumption	NOUN
cjfa-35471	676	10	about	about	ADP
cjfa-35471	676	11	interest	interest	NOUN
cjfa-35471	676	12	rates	rate	NOUN
cjfa-35471	676	13	,	,	PUNCT
cjfa-35471	676	14	parameters	parameter	NOUN
cjfa-35471	676	15	of	of	ADP
cjfa-35471	676	16	demand	demand	NOUN
cjfa-35471	676	17	function	function	NOUN
cjfa-35471	676	18	,	,	PUNCT
cjfa-35471	676	19	and	and	CCONJ
cjfa-35471	676	20	holding	hold	VERB
cjfa-35471	676	21	cost	cost	NOUN
cjfa-35471	676	22	.	.	PUNCT
cjfa-35471	677	1	research	research	NOUN
cjfa-35471	677	2	process	process	NOUN
cjfa-35471	677	3	the	the	DET
cjfa-35471	677	4	specific	specific	ADJ
cjfa-35471	677	5	cost	cost	NOUN
cjfa-35471	677	6	function	function	NOUN
cjfa-35471	677	7	,	,	PUNCT
cjfa-35471	677	8	in	in	ADP
cjfa-35471	677	9	this	this	DET
cjfa-35471	677	10	example	example	NOUN
cjfa-35471	677	11	,	,	PUNCT
cjfa-35471	677	12	will	will	AUX
cjfa-35471	677	13	be	be	AUX
cjfa-35471	677	14	assumed	assume	VERB
cjfa-35471	677	15	to	to	PART
cjfa-35471	677	16	have	have	VERB
cjfa-35471	677	17	the	the	DET
cjfa-35471	677	18	more	more	ADV
cjfa-35471	677	19	realistic	realistic	ADJ
cjfa-35471	677	20	form	form	NOUN
cjfa-35471	677	21	of	of	ADP
cjfa-35471	677	22	:	:	PUNCT
cjfa-35471	677	23	𝑐𝑐	𝑐𝑐	PROPN
cjfa-35471	677	24	�	�	PROPN
cjfa-35471	677	25	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	ADJ
cjfa-35471	677	26	�	�	PROPN
cjfa-35471	677	27	=	=	SYM
cjfa-35471	677	28	𝑎𝑎𝑐𝑐	𝑎𝑎𝑐𝑐	PROPN
cjfa-35471	677	29	�	�	PROPN
cjfa-35471	677	30	+	+	CCONJ
cjfa-35471	677	31	𝑏𝑏𝑐𝑐	𝑏𝑏𝑐𝑐	PROPN
cjfa-35471	677	32	�	�	PROPN
cjfa-35471	677	33	+	+	NUM
cjfa-35471	677	34	𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	677	35	+	+	CCONJ
cjfa-35471	677	36	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	677	37	and	and	CCONJ
cjfa-35471	677	38	𝑐𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	678	1	=	=	SYM
cjfa-35471	678	2	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	678	3	+	+	CCONJ
cjfa-35471	678	4	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐	PROPN
cjfa-35471	678	5	as	as	SCONJ
cjfa-35471	678	6	defined	define	VERB
cjfa-35471	678	7	previously	previously	ADV
cjfa-35471	678	8	where	where	SCONJ
cjfa-35471	678	9	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	678	10	represents	represent	VERB
cjfa-35471	678	11	the	the	DET
cjfa-35471	678	12	periodicity	periodicity	NOUN
cjfa-35471	678	13	of	of	ADP
cjfa-35471	678	14	the	the	DET
cjfa-35471	678	15	demand	demand	NOUN
cjfa-35471	678	16	function	function	NOUN
cjfa-35471	678	17	.	.	PUNCT
cjfa-35471	679	1	in	in	ADP
cjfa-35471	679	2	the	the	DET
cjfa-35471	679	3	examples	example	NOUN
cjfa-35471	679	4	below	below	ADV
cjfa-35471	679	5	,	,	PUNCT
cjfa-35471	679	6	we	we	PRON
cjfa-35471	679	7	will	will	AUX
cjfa-35471	679	8	assume	assume	VERB
cjfa-35471	679	9	that	that	SCONJ
cjfa-35471	679	10	𝑎𝑎	𝑎𝑎	ADJ
cjfa-35471	679	11	=	=	SYM
cjfa-35471	679	12	𝑎𝑎𝑎𝑎	𝑎𝑎𝑎𝑎	NOUN
cjfa-35471	679	13	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	679	14	=	=	PUNCT
cjfa-35471	679	15	𝑎𝑎	𝑎𝑎	NOUN
cjfa-35471	679	16	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	679	17	=	=	PUNCT
cjfa-35471	679	18	𝑎𝑎	𝑎𝑎	VERB
cjfa-35471	679	19	𝑎	𝑎	NOUN
cjfa-35471	679	20	=	=	PUNCT
cjfa-35471	679	21	𝑎𝐴𝐴𝑎	𝑎𝐴𝐴𝑎	NOUN
cjfa-35471	679	22	𝑏𝑏	𝑏𝑏	NOUN
cjfa-35471	679	23	=	=	NOUN
cjfa-35471	679	24	𝑎𝑎𝑎	𝑎𝑎𝑎	VERB
cjfa-35471	679	25	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	680	1	=	=	PUNCT
cjfa-35471	680	2	𝑎	𝑎	NOUN
cjfa-35471	680	3	for	for	ADP
cjfa-35471	680	4	simplicity	simplicity	NOUN
cjfa-35471	680	5	.	.	PUNCT
cjfa-35471	681	1	case	case	NOUN
cjfa-35471	682	1	i	i	PRON
cjfa-35471	682	2	:	:	PUNCT
cjfa-35471	682	3	𝐴𝐴	𝐴𝐴	PROPN
cjfa-35471	682	4	=	=	SYM
cjfa-35471	682	5	𝑎	𝑎	X
cjfa-35471	682	6	(	(	PUNCT
cjfa-35471	682	7	one	one	NUM
cjfa-35471	682	8	cycle	cycle	NOUN
cjfa-35471	682	9	of	of	ADP
cjfa-35471	682	10	the	the	DET
cjfa-35471	682	11	demand	demand	NOUN
cjfa-35471	682	12	curve	curve	NOUN
cjfa-35471	682	13	in	in	ADP
cjfa-35471	682	14	the	the	DET
cjfa-35471	682	15	planning	planning	NOUN
cjfa-35471	682	16	horizon	horizon	NOUN
cjfa-35471	682	17	of	of	ADP
cjfa-35471	682	18	one	one	NUM
cjfa-35471	682	19	and	and	CCONJ
cjfa-35471	682	20	interest	interest	NOUN
cjfa-35471	682	21	rate	rate	NOUN
cjfa-35471	682	22	𝑓𝑓𝑐𝑐𝑐𝑐	𝑓𝑓𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	682	23	=	=	SYM
cjfa-35471	682	24	𝑎.	𝑎.	PROPN
cjfa-35471	682	25	)	)	PUNCT
cjfa-35471	682	26	then	then	ADV
cjfa-35471	682	27	the	the	DET
cjfa-35471	682	28	inequality	inequality	NOUN
cjfa-35471	682	29	(	(	PUNCT
cjfa-35471	682	30	4	4	X
cjfa-35471	682	31	)	)	PUNCT
cjfa-35471	682	32	becomes	become	VERB
cjfa-35471	682	33	:	:	PUNCT
cjfa-35471	682	34	𝑐𝑎𝑎𝑎	𝑐𝑎𝑎𝑎	NOUN
cjfa-35471	682	35	∗	∗	NOUN
cjfa-35471	682	36	3𝑐𝑎	3𝑐𝑎	NOUN
cjfa-35471	683	1	+	+	CCONJ
cjfa-35471	683	2	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝑐𝑐𝑐	NOUN
cjfa-35471	683	3	𝑎	𝑎	PRON
cjfa-35471	683	4	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	𝑎𝑐𝑐𝑐𝑐𝑐𝐴𝐴𝐴𝐴𝐴𝑐𝑐	NUM
cjfa-35471	683	5	𝑐	𝑐	PROPN
cjfa-35471	683	6	𝐴𝑎𝑎	𝐴𝑎𝑎	PROPN
cjfa-35471	683	7	(	(	PUNCT
cjfa-35471	683	8	5	5	NUM
cjfa-35471	683	9	)	)	PUNCT
cjfa-35471	683	10	(	(	PUNCT
cjfa-35471	683	11	5	5	X
cjfa-35471	683	12	)	)	PUNCT
cjfa-35471	683	13	both	both	DET
cjfa-35471	683	14	sides	side	NOUN
cjfa-35471	683	15	of	of	ADP
cjfa-35471	683	16	inequality	inequality	NOUN
cjfa-35471	683	17	in	in	ADP
cjfa-35471	683	18	(	(	PUNCT
cjfa-35471	683	19	5	5	NUM
cjfa-35471	683	20	)	)	PUNCT
cjfa-35471	683	21	is	be	AUX
cjfa-35471	683	22	presented	present	VERB
cjfa-35471	683	23	in	in	ADP
cjfa-35471	683	24	the	the	DET
cjfa-35471	683	25	graph	graph	NOUN
cjfa-35471	683	26	below	below	ADP
cjfa-35471	683	27	produced	produce	VERB
cjfa-35471	683	28	using	use	VERB
cjfa-35471	683	29	arbitrary	arbitrary	ADJ
cjfa-35471	683	30	numbers	number	NOUN
cjfa-35471	683	31	for	for	ADP
cjfa-35471	683	32	relevant	relevant	ADJ
cjfa-35471	683	33	variables	variable	NOUN
cjfa-35471	683	34	(	(	PUNCT
cjfa-35471	683	35	figure	figure	NOUN
cjfa-35471	683	36	1	1	NUM
cjfa-35471	683	37	)	)	PUNCT
cjfa-35471	683	38	.	.	PUNCT
cjfa-35471	684	1	this	this	DET
cjfa-35471	684	2	graph	graph	NOUN
cjfa-35471	684	3	(	(	PUNCT
cjfa-35471	684	4	figure	figure	NOUN
cjfa-35471	684	5	1	1	NUM
cjfa-35471	684	6	)	)	PUNCT
cjfa-35471	684	7	implies	imply	VERB
cjfa-35471	684	8	(	(	PUNCT
cjfa-35471	684	9	notice	notice	VERB
cjfa-35471	684	10	the	the	DET
cjfa-35471	684	11	tip	tip	NOUN
cjfa-35471	684	12	of	of	ADP
cjfa-35471	684	13	arrows	arrow	NOUN
cjfa-35471	684	14	in	in	ADP
cjfa-35471	684	15	the	the	DET
cjfa-35471	684	16	graph	graph	NOUN
cjfa-35471	684	17	shows	show	VERB
cjfa-35471	684	18	the	the	DET
cjfa-35471	684	19	times	times	ADJ
cjfa-35471	684	20	production	production	NOUN
cjfa-35471	684	21	is	be	AUX
cjfa-35471	684	22	stopped	stop	VERB
cjfa-35471	684	23	and	and	CCONJ
cjfa-35471	684	24	started	start	VERB
cjfa-35471	684	25	)	)	PUNCT
cjfa-35471	684	26	that	that	SCONJ
cjfa-35471	684	27	the	the	DET
cjfa-35471	684	28	firm	firm	NOUN
cjfa-35471	684	29	will	will	AUX
cjfa-35471	684	30	stop	stop	VERB
cjfa-35471	684	31	producing	produce	VERB
cjfa-35471	684	32	for	for	ADP
cjfa-35471	684	33	inventories	inventory	NOUN
cjfa-35471	684	34	just	just	ADV
cjfa-35471	684	35	before	before	SCONJ
cjfa-35471	684	36	the	the	DET
cjfa-35471	684	37	demand	demand	NOUN
cjfa-35471	684	38	reaches	reach	VERB
cjfa-35471	684	39	its	its	PRON
cjfa-35471	684	40	maximum	maximum	NOUN
cjfa-35471	684	41	and	and	CCONJ
cjfa-35471	684	42	starts	start	VERB
cjfa-35471	684	43	just	just	ADV
cjfa-35471	684	44	after	after	SCONJ
cjfa-35471	684	45	the	the	DET
cjfa-35471	684	46	demand	demand	NOUN
cjfa-35471	684	47	reaches	reach	VERB
cjfa-35471	684	48	its	its	PRON
cjfa-35471	684	49	minimum	minimum	NOUN
cjfa-35471	684	50	(	(	PUNCT
cjfa-35471	684	51	recall	recall	VERB
cjfa-35471	684	52	that	that	SCONJ
cjfa-35471	684	53	the	the	DET
cjfa-35471	684	54	sinusoidal	sinusoidal	ADJ
cjfa-35471	684	55	demand	demand	NOUN
cjfa-35471	684	56	reaches	reach	VERB
cjfa-35471	684	57	its	its	PRON
cjfa-35471	684	58	maximum	maximum	NOUN
cjfa-35471	684	59	at	at	ADP
cjfa-35471	684	60	t	t	NOUN
cjfa-35471	684	61	=	=	NUM
cjfa-35471	684	62	0.25	0.25	NUM
cjfa-35471	684	63	and	and	CCONJ
cjfa-35471	684	64	its	its	PRON
cjfa-35471	684	65	minimum	minimum	NOUN
cjfa-35471	684	66	at	at	ADP
cjfa-35471	684	67	t	t	NOUN
cjfa-35471	684	68	=	=	PUNCT
cjfa-35471	684	69	0.75	0.75	NUM
cjfa-35471	684	70	)	)	PUNCT
cjfa-35471	684	71	.	.	PUNCT
cjfa-35471	685	1	these	these	DET
cjfa-35471	685	2	points	point	NOUN
cjfa-35471	685	3	are	be	AUX
cjfa-35471	685	4	indicated	indicate	VERB
cjfa-35471	685	5	by	by	ADP
cjfa-35471	685	6	arrows	arrow	NOUN
cjfa-35471	685	7	in	in	ADP
cjfa-35471	685	8	all	all	DET
cjfa-35471	685	9	graphs	graph	NOUN
cjfa-35471	685	10	(	(	PUNCT
cjfa-35471	685	11	the	the	DET
cjfa-35471	685	12	tip	tip	NOUN
cjfa-35471	685	13	of	of	ADP
cjfa-35471	685	14	the	the	DET
cjfa-35471	685	15	arrow	arrow	NOUN
cjfa-35471	685	16	shows	show	VERB
cjfa-35471	685	17	the	the	DET
cjfa-35471	685	18	point	point	NOUN
cjfa-35471	685	19	at	at	ADP
cjfa-35471	685	20	which	which	PRON
cjfa-35471	685	21	the	the	DET
cjfa-35471	685	22	left	left	ADJ
cjfa-35471	685	23	,	,	PUNCT
cjfa-35471	685	24	0.18	0.18	NUM
cjfa-35471	685	25	,	,	PUNCT
cjfa-35471	685	26	and	and	CCONJ
cjfa-35471	685	27	right	right	ADJ
cjfa-35471	685	28	,	,	PUNCT
cjfa-35471	685	29	0.86	0.86	NUM
cjfa-35471	685	30	)	)	PUNCT
cjfa-35471	685	31	hand	hand	NOUN
cjfa-35471	685	32	side	side	NOUN
cjfa-35471	685	33	of	of	ADP
cjfa-35471	685	34	equation	equation	NOUN
cjfa-35471	685	35	4	4	NUM
cjfa-35471	685	36	becomes	become	VERB
cjfa-35471	685	37	equal	equal	ADJ
cjfa-35471	685	38	)	)	PUNCT
cjfa-35471	685	39	.	.	PUNCT
cjfa-35471	686	1	therefore	therefore	ADV
cjfa-35471	686	2	,	,	PUNCT
cjfa-35471	686	3	it	it	PRON
cjfa-35471	686	4	is	be	AUX
cjfa-35471	686	5	only	only	ADV
cjfa-35471	686	6	possible	possible	ADJ
cjfa-35471	686	7	for	for	SCONJ
cjfa-35471	686	8	firms	firm	NOUN
cjfa-35471	686	9	to	to	PART
cjfa-35471	686	10	stop	stop	VERB
cjfa-35471	686	11	producing	produce	VERB
cjfa-35471	686	12	later	later	ADV
cjfa-35471	686	13	and	and	CCONJ
cjfa-35471	686	14	start	start	VERB
cjfa-35471	686	15	producing	produce	VERB
cjfa-35471	686	16	earlier	early	ADV
cjfa-35471	686	17	is	be	AUX
cjfa-35471	686	18	to	to	PART
cjfa-35471	686	19	decrease	decrease	VERB
cjfa-35471	686	20	the	the	DET
cjfa-35471	686	21	holding	holding	NOUN
cjfa-35471	686	22	costs	cost	NOUN
cjfa-35471	686	23	(	(	PUNCT
cjfa-35471	686	24	h	h	NOUN
cjfa-35471	686	25	)	)	PUNCT
cjfa-35471	686	26	as	as	ADV
cjfa-35471	686	27	defined	define	VERB
cjfa-35471	686	28	above	above	ADV
cjfa-35471	686	29	.	.	PUNCT
cjfa-35471	687	1	mustafa	mustafa	PROPN
cjfa-35471	687	2	akan	akan	PROPN
cjfa-35471	687	3	,	,	PUNCT
cjfa-35471	687	4	natalia	natalia	PROPN
cjfa-35471	687	5	konovalova18	konovalova18	PROPN
cjfa-35471	687	6	figure	figure	VERB
cjfa-35471	687	7	1	1	NUM
cjfa-35471	687	8	.	.	PUNCT
cjfa-35471	688	1	graphs	graph	NOUN
cjfa-35471	688	2	of	of	ADP
cjfa-35471	688	3	left	left	NOUN
cjfa-35471	688	4	(	(	PUNCT
cjfa-35471	688	5	f(t	f(t	PROPN
cjfa-35471	688	6	)	)	PUNCT
cjfa-35471	688	7	)	)	PUNCT
cjfa-35471	689	1	and	and	CCONJ
cjfa-35471	689	2	right	right	INTJ
cjfa-35471	689	3	(	(	PUNCT
cjfa-35471	689	4	g(x	g(x	NOUN
cjfa-35471	689	5	)	)	PUNCT
cjfa-35471	689	6	)	)	PUNCT
cjfa-35471	689	7	hand	hand	NOUN
cjfa-35471	689	8	sides	side	NOUN
cjfa-35471	689	9	of	of	ADP
cjfa-35471	689	10	inequality	inequality	NOUN
cjfa-35471	689	11	(	(	PUNCT
cjfa-35471	689	12	5	5	NUM
cjfa-35471	689	13	)	)	PUNCT
cjfa-35471	689	14	and	and	CCONJ
cjfa-35471	689	15	demand	demand	NOUN
cjfa-35471	689	16	function	function	NOUN
cjfa-35471	689	17	(	(	PUNCT
cjfa-35471	689	18	h(x	h(x	PROPN
cjfa-35471	689	19	)	)	PUNCT
cjfa-35471	689	20	=	=	SYM
cjfa-35471	689	21	r(t	r(t	NOUN
cjfa-35471	689	22	)	)	PUNCT
cjfa-35471	689	23	)	)	PUNCT
cjfa-35471	689	24	both	both	DET
cjfa-35471	689	25	sides	side	NOUN
cjfa-35471	689	26	of	of	ADP
cjfa-35471	689	27	inequality	inequality	NOUN
cjfa-35471	689	28	in	in	ADP
cjfa-35471	689	29	(	(	PUNCT
cjfa-35471	689	30	5	5	NUM
cjfa-35471	689	31	)	)	PUNCT
cjfa-35471	689	32	is	be	AUX
cjfa-35471	689	33	presented	present	VERB
cjfa-35471	689	34	in	in	ADP
cjfa-35471	689	35	the	the	DET
cjfa-35471	689	36	graph	graph	NOUN
cjfa-35471	689	37	below	below	ADP
cjfa-35471	689	38	produced	produce	VERB
cjfa-35471	689	39	using	use	VERB
cjfa-35471	689	40	arbitrary	arbitrary	ADJ
cjfa-35471	689	41	numbers	number	NOUN
cjfa-35471	689	42	for	for	ADP
cjfa-35471	689	43	relevant	relevant	ADJ
cjfa-35471	689	44	variables	variable	NOUN
cjfa-35471	689	45	(	(	PUNCT
cjfa-35471	689	46	figure	figure	NOUN
cjfa-35471	689	47	1	1	NUM
cjfa-35471	689	48	)	)	PUNCT
cjfa-35471	689	49	.	.	PUNCT
cjfa-35471	690	1	this	this	DET
cjfa-35471	690	2	graph	graph	NOUN
cjfa-35471	690	3	(	(	PUNCT
cjfa-35471	690	4	figure	figure	NOUN
cjfa-35471	690	5	1	1	NUM
cjfa-35471	690	6	)	)	PUNCT
cjfa-35471	690	7	implies	imply	VERB
cjfa-35471	690	8	(	(	PUNCT
cjfa-35471	690	9	notice	notice	VERB
cjfa-35471	690	10	the	the	DET
cjfa-35471	690	11	tip	tip	NOUN
cjfa-35471	690	12	of	of	ADP
cjfa-35471	690	13	arrows	arrow	NOUN
cjfa-35471	690	14	in	in	ADP
cjfa-35471	690	15	the	the	DET
cjfa-35471	690	16	graph	graph	NOUN
cjfa-35471	690	17	shows	show	VERB
cjfa-35471	690	18	the	the	DET
cjfa-35471	690	19	times	times	ADJ
cjfa-35471	690	20	production	production	NOUN
cjfa-35471	690	21	is	be	AUX
cjfa-35471	690	22	stopped	stop	VERB
cjfa-35471	690	23	and	and	CCONJ
cjfa-35471	690	24	started	start	VERB
cjfa-35471	690	25	)	)	PUNCT
cjfa-35471	690	26	that	that	SCONJ
cjfa-35471	690	27	the	the	DET
cjfa-35471	690	28	firm	firm	NOUN
cjfa-35471	690	29	will	will	AUX
cjfa-35471	690	30	stop	stop	VERB
cjfa-35471	690	31	producing	produce	VERB
cjfa-35471	690	32	for	for	ADP
cjfa-35471	690	33	inventories	inventory	NOUN
cjfa-35471	690	34	just	just	ADV
cjfa-35471	690	35	before	before	SCONJ
cjfa-35471	690	36	the	the	DET
cjfa-35471	690	37	demand	demand	NOUN
cjfa-35471	690	38	reaches	reach	VERB
cjfa-35471	690	39	its	its	PRON
cjfa-35471	690	40	maximum	maximum	NOUN
cjfa-35471	690	41	and	and	CCONJ
cjfa-35471	690	42	starts	start	VERB
cjfa-35471	690	43	just	just	ADV
cjfa-35471	690	44	after	after	SCONJ
cjfa-35471	690	45	the	the	DET
cjfa-35471	690	46	demand	demand	NOUN
cjfa-35471	690	47	reaches	reach	VERB
cjfa-35471	690	48	its	its	PRON
cjfa-35471	690	49	minimum	minimum	NOUN
cjfa-35471	690	50	(	(	PUNCT
cjfa-35471	690	51	recall	recall	VERB
cjfa-35471	690	52	that	that	SCONJ
cjfa-35471	690	53	the	the	DET
cjfa-35471	690	54	sinusoidal	sinusoidal	ADJ
cjfa-35471	690	55	demand	demand	NOUN
cjfa-35471	690	56	reaches	reach	VERB
cjfa-35471	690	57	its	its	PRON
cjfa-35471	690	58	maximum	maximum	NOUN
cjfa-35471	690	59	at	at	ADP
cjfa-35471	690	60	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	690	61	𝑡	𝑡	NOUN
cjfa-35471	690	62	𝑡𝑡𝑡𝑡	𝑡𝑡𝑡𝑡	NOUN
cjfa-35471	690	63	and	and	CCONJ
cjfa-35471	690	64	its	its	PRON
cjfa-35471	690	65	minimum	minimum	NOUN
cjfa-35471	690	66	at	at	ADP
cjfa-35471	690	67	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	690	68	𝑡	𝑡	NOUN
cjfa-35471	690	69	𝑡𝑡𝑡𝑡	𝑡𝑡𝑡𝑡	NOUN
cjfa-35471	690	70	)	)	PUNCT
cjfa-35471	690	71	.	.	PUNCT
cjfa-35471	691	1	these	these	DET
cjfa-35471	691	2	points	point	NOUN
cjfa-35471	691	3	are	be	AUX
cjfa-35471	691	4	indicated	indicate	VERB
cjfa-35471	691	5	by	by	ADP
cjfa-35471	691	6	arrows	arrow	NOUN
cjfa-35471	691	7	in	in	ADP
cjfa-35471	691	8	all	all	DET
cjfa-35471	691	9	graphs	graph	NOUN
cjfa-35471	691	10	(	(	PUNCT
cjfa-35471	691	11	the	the	DET
cjfa-35471	691	12	tip	tip	NOUN
cjfa-35471	691	13	of	of	ADP
cjfa-35471	691	14	the	the	DET
cjfa-35471	691	15	arrow	arrow	NOUN
cjfa-35471	691	16	shows	show	VERB
cjfa-35471	691	17	the	the	DET
cjfa-35471	691	18	point	point	NOUN
cjfa-35471	691	19	at	at	ADP
cjfa-35471	691	20	which	which	PRON
cjfa-35471	691	21	the	the	DET
cjfa-35471	691	22	left	left	NOUN
cjfa-35471	691	23	,	,	PUNCT
cjfa-35471	691	24	𝑡𝑡18	𝑡𝑡18	PROPN
cjfa-35471	691	25	,	,	PUNCT
cjfa-35471	691	26	and	and	CCONJ
cjfa-35471	691	27	right	right	ADJ
cjfa-35471	691	28	,	,	PUNCT
cjfa-35471	691	29	𝑡𝑡86	𝑡𝑡86	PROPN
cjfa-35471	691	30	)	)	PUNCT
cjfa-35471	691	31	hand	hand	NOUN
cjfa-35471	691	32	side	side	NOUN
cjfa-35471	691	33	of	of	ADP
cjfa-35471	691	34	equation	equation	NOUN
cjfa-35471	691	35	4	4	NUM
cjfa-35471	691	36	becomes	become	VERB
cjfa-35471	691	37	equal	equal	ADJ
cjfa-35471	691	38	)	)	PUNCT
cjfa-35471	691	39	.	.	PUNCT
cjfa-35471	692	1	therefore	therefore	ADV
cjfa-35471	692	2	,	,	PUNCT
cjfa-35471	692	3	it	it	PRON
cjfa-35471	692	4	is	be	AUX
cjfa-35471	692	5	only	only	ADV
cjfa-35471	692	6	possible	possible	ADJ
cjfa-35471	692	7	for	for	SCONJ
cjfa-35471	692	8	firms	firm	NOUN
cjfa-35471	692	9	to	to	PART
cjfa-35471	692	10	stop	stop	VERB
cjfa-35471	692	11	producing	produce	VERB
cjfa-35471	692	12	later	later	ADV
cjfa-35471	692	13	and	and	CCONJ
cjfa-35471	692	14	start	start	VERB
cjfa-35471	692	15	producing	produce	VERB
cjfa-35471	692	16	earlier	early	ADV
cjfa-35471	692	17	is	be	AUX
cjfa-35471	692	18	to	to	PART
cjfa-35471	692	19	decrease	decrease	VERB
cjfa-35471	692	20	the	the	DET
cjfa-35471	692	21	holding	holding	NOUN
cjfa-35471	692	22	costs	cost	NOUN
cjfa-35471	692	23	(	(	PUNCT
cjfa-35471	692	24	ℎ	ℎ	NOUN
cjfa-35471	692	25	)	)	PUNCT
cjfa-35471	692	26	as	as	SCONJ
cjfa-35471	692	27	defined	define	VERB
cjfa-35471	692	28	above	above	ADV
cjfa-35471	692	29	.	.	PUNCT
cjfa-35471	693	1	figure	figure	NOUN
cjfa-35471	693	2	1	1	NUM
cjfa-35471	693	3	.	.	PUNCT
cjfa-35471	694	1	graphs	graph	NOUN
cjfa-35471	694	2	of	of	ADP
cjfa-35471	694	3	left	left	ADJ
cjfa-35471	694	4	(	(	PUNCT
cjfa-35471	694	5	𝑓𝑓𝑓𝑡𝑡𝑓𝑓	𝑓𝑓𝑓𝑡𝑡𝑓𝑓	NOUN
cjfa-35471	694	6	and	and	CCONJ
cjfa-35471	694	7	right	right	ADJ
cjfa-35471	694	8	(	(	PUNCT
cjfa-35471	694	9	𝑔𝑔𝑓𝑔𝑔𝑓	𝑔𝑔𝑓𝑔𝑔𝑓	NOUN
cjfa-35471	694	10	)	)	PUNCT
cjfa-35471	694	11	hand	hand	NOUN
cjfa-35471	694	12	sides	side	NOUN
cjfa-35471	694	13	of	of	ADP
cjfa-35471	694	14	inequality	inequality	NOUN
cjfa-35471	694	15	(	(	PUNCT
cjfa-35471	694	16	5	5	NUM
cjfa-35471	694	17	)	)	PUNCT
cjfa-35471	694	18	and	and	CCONJ
cjfa-35471	694	19	demand	demand	NOUN
cjfa-35471	694	20	function	function	NOUN
cjfa-35471	694	21	(	(	PUNCT
cjfa-35471	694	22	ℎ𝑓𝑔𝑔𝑓	ℎ𝑓𝑔𝑔𝑓	PROPN
cjfa-35471	694	23	𝑡	𝑡	PROPN
cjfa-35471	694	24	𝑟𝑟𝑓𝑡𝑡𝑓	𝑟𝑟𝑓𝑡𝑡𝑓	NOUN
cjfa-35471	694	25	)	)	PUNCT
cjfa-35471	694	26	s	s	PART
cjfa-35471	694	27	o	o	NOUN
cjfa-35471	694	28	u	u	NOUN
cjfa-35471	694	29	r	r	NOUN
cjfa-35471	694	30	c	c	NOUN
cjfa-35471	694	31	e	e	NOUN
cjfa-35471	694	32	:	:	PUNCT
cjfa-35471	694	33	constructed	construct	VERB
cjfa-35471	694	34	by	by	ADP
cjfa-35471	694	35	authors	author	NOUN
cjfa-35471	694	36	.	.	PUNCT
cjfa-35471	695	1	case	case	NOUN
cjfa-35471	695	2	ii	ii	NOUN
cjfa-35471	695	3	:	:	PUNCT
cjfa-35471	695	4	k	k	X
cjfa-35471	695	5	=	=	SYM
cjfa-35471	695	6	1	1	NUM
cjfa-35471	695	7	and	and	CCONJ
cjfa-35471	695	8	interest	interest	NOUN
cjfa-35471	695	9	rate	rate	NOUN
cjfa-35471	695	10	f(t	f(t	NOUN
cjfa-35471	695	11	)	)	PUNCT
cjfa-35471	695	12	=	=	SYM
cjfa-35471	695	13	0	0	NUM
cjfa-35471	695	14	and	and	CCONJ
cjfa-35471	695	15	a	a	DET
cjfa-35471	695	16	new	new	ADJ
cjfa-35471	695	17	technology	technology	NOUN
cjfa-35471	695	18	i	i	PRON
cjfa-35471	695	19	introduced	introduce	VERB
cjfa-35471	695	20	.	.	PUNCT
cjfa-35471	696	1	the	the	DET
cjfa-35471	696	2	impact	impact	NOUN
cjfa-35471	696	3	of	of	ADP
cjfa-35471	696	4	new	new	ADJ
cjfa-35471	696	5	technology	technology	NOUN
cjfa-35471	696	6	will	will	AUX
cjfa-35471	696	7	be	be	AUX
cjfa-35471	696	8	analyzed	analyze	VERB
cjfa-35471	696	9	in	in	ADP
cjfa-35471	696	10	three	three	NUM
cjfa-35471	696	11	cases	case	NOUN
cjfa-35471	696	12	:	:	PUNCT
cjfa-35471	696	13	1	1	X
cjfa-35471	696	14	.	.	PUNCT
cjfa-35471	696	15	fixed	fix	VERB
cjfa-35471	696	16	costs	cost	NOUN
cjfa-35471	696	17	(	(	PUNCT
cjfa-35471	696	18	the	the	DET
cjfa-35471	696	19	term	term	NOUN
cjfa-35471	696	20	d	d	NOUN
cjfa-35471	696	21	in	in	ADP
cjfa-35471	696	22	the	the	DET
cjfa-35471	696	23	cost	cost	NOUN
cjfa-35471	696	24	function	function	NOUN
cjfa-35471	696	25	)	)	PUNCT
cjfa-35471	696	26	is	be	AUX
cjfa-35471	696	27	reduced	reduce	VERB
cjfa-35471	696	28	.	.	PUNCT
cjfa-35471	697	1	there	there	PRON
cjfa-35471	697	2	will	will	AUX
cjfa-35471	697	3	be	be	AUX
cjfa-35471	697	4	no	no	DET
cjfa-35471	697	5	impact	impact	NOUN
cjfa-35471	697	6	on	on	ADP
cjfa-35471	697	7	production	production	NOUN
cjfa-35471	697	8	decision	decision	NOUN
cjfa-35471	697	9	since	since	SCONJ
cjfa-35471	697	10	the	the	DET
cjfa-35471	697	11	fixed	fix	VERB
cjfa-35471	697	12	costs	cost	NOUN
cjfa-35471	697	13	are	be	AUX
cjfa-35471	697	14	already	already	ADV
cjfa-35471	697	15	shown	show	VERB
cjfa-35471	697	16	to	to	PART
cjfa-35471	697	17	have	have	VERB
cjfa-35471	697	18	on	on	ADP
cjfa-35471	697	19	impact	impact	NOUN
cjfa-35471	697	20	on	on	ADP
cjfa-35471	697	21	the	the	DET
cjfa-35471	697	22	inequality	inequality	NOUN
cjfa-35471	697	23	(	(	PUNCT
cjfa-35471	697	24	5	5	NUM
cjfa-35471	697	25	)	)	PUNCT
cjfa-35471	697	26	.	.	PUNCT
cjfa-35471	698	1	2	2	X
cjfa-35471	698	2	.	.	X
cjfa-35471	698	3	only	only	ADV
cjfa-35471	698	4	the	the	DET
cjfa-35471	698	5	constant	constant	ADJ
cjfa-35471	698	6	term	term	NOUN
cjfa-35471	698	7	(	(	PUNCT
cjfa-35471	698	8	c	c	NOUN
cjfa-35471	698	9	)	)	PUNCT
cjfa-35471	698	10	in	in	ADP
cjfa-35471	698	11	the	the	DET
cjfa-35471	698	12	marginal	marginal	ADJ
cjfa-35471	698	13	cost	cost	NOUN
cjfa-35471	698	14	,	,	PUNCT
cjfa-35471	698	15	source	source	NOUN
cjfa-35471	698	16	:	:	PUNCT
cjfa-35471	698	17	constructed	construct	VERB
cjfa-35471	698	18	by	by	ADP
cjfa-35471	698	19	authors	author	NOUN
cjfa-35471	698	20	.	.	PUNCT
cjfa-35471	699	1	case	case	NOUN
cjfa-35471	699	2	ii	ii	PROPN
cjfa-35471	699	3	:	:	PUNCT
cjfa-35471	699	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	699	5	𝑘	𝑘	PRON
cjfa-35471	699	6	𝑘	𝑘	NOUN
cjfa-35471	699	7	and	and	CCONJ
cjfa-35471	699	8	interest	interest	NOUN
cjfa-35471	699	9	rate	rate	NOUN
cjfa-35471	699	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	699	11	)	)	PUNCT
cjfa-35471	700	1	𝑘	𝑘	ADP
cjfa-35471	700	2	0	0	NUM
cjfa-35471	700	3	and	and	CCONJ
cjfa-35471	700	4	a	a	DET
cjfa-35471	700	5	new	new	ADJ
cjfa-35471	700	6	technology	technology	NOUN
cjfa-35471	700	7	i	i	PRON
cjfa-35471	700	8	introduced	introduce	VERB
cjfa-35471	700	9	.	.	PUNCT
cjfa-35471	701	1	the	the	DET
cjfa-35471	701	2	impact	impact	NOUN
cjfa-35471	701	3	of	of	ADP
cjfa-35471	701	4	new	new	ADJ
cjfa-35471	701	5	technology	technology	NOUN
cjfa-35471	701	6	will	will	AUX
cjfa-35471	701	7	be	be	AUX
cjfa-35471	701	8	analyzed	analyze	VERB
cjfa-35471	701	9	in	in	ADP
cjfa-35471	701	10	three	three	NUM
cjfa-35471	701	11	cases	case	NOUN
cjfa-35471	701	12	:	:	PUNCT
cjfa-35471	701	13	1	1	X
cjfa-35471	701	14	.	.	PUNCT
cjfa-35471	701	15	fixed	fix	VERB
cjfa-35471	701	16	costs	cost	NOUN
cjfa-35471	701	17	(	(	PUNCT
cjfa-35471	701	18	the	the	DET
cjfa-35471	701	19	term	term	NOUN
cjfa-35471	701	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	701	21	in	in	ADP
cjfa-35471	701	22	the	the	DET
cjfa-35471	701	23	cost	cost	NOUN
cjfa-35471	701	24	function	function	NOUN
cjfa-35471	701	25	)	)	PUNCT
cjfa-35471	701	26	is	be	AUX
cjfa-35471	701	27	reduced	reduce	VERB
cjfa-35471	701	28	.	.	PUNCT
cjfa-35471	702	1	there	there	PRON
cjfa-35471	702	2	will	will	AUX
cjfa-35471	702	3	be	be	AUX
cjfa-35471	702	4	no	no	DET
cjfa-35471	702	5	impact	impact	NOUN
cjfa-35471	702	6	on	on	ADP
cjfa-35471	702	7	production	production	NOUN
cjfa-35471	702	8	decision	decision	NOUN
cjfa-35471	702	9	since	since	SCONJ
cjfa-35471	702	10	the	the	DET
cjfa-35471	702	11	fixed	fix	VERB
cjfa-35471	702	12	costs	cost	NOUN
cjfa-35471	702	13	are	be	AUX
cjfa-35471	702	14	already	already	ADV
cjfa-35471	702	15	shown	show	VERB
cjfa-35471	702	16	to	to	PART
cjfa-35471	702	17	have	have	VERB
cjfa-35471	702	18	on	on	ADP
cjfa-35471	702	19	impact	impact	NOUN
cjfa-35471	702	20	on	on	ADP
cjfa-35471	702	21	the	the	DET
cjfa-35471	702	22	inequality	inequality	NOUN
cjfa-35471	702	23	(	(	PUNCT
cjfa-35471	702	24	5	5	NUM
cjfa-35471	702	25	)	)	PUNCT
cjfa-35471	702	26	.	.	PUNCT
cjfa-35471	703	1	2	2	X
cjfa-35471	703	2	.	.	X
cjfa-35471	703	3	only	only	ADV
cjfa-35471	703	4	the	the	DET
cjfa-35471	703	5	constant	constant	ADJ
cjfa-35471	703	6	term	term	NOUN
cjfa-35471	703	7	(	(	PUNCT
cjfa-35471	703	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	703	9	)	)	PUNCT
cjfa-35471	703	10	in	in	ADP
cjfa-35471	703	11	the	the	DET
cjfa-35471	703	12	marginal	marginal	ADJ
cjfa-35471	703	13	cost	cost	NOUN
cjfa-35471	703	14	,	,	PUNCT
cjfa-35471	703	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	703	16	𝑘	𝑘	PRON
cjfa-35471	703	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	703	18	�	�	PROPN
cjfa-35471	703	19	+	+	CCONJ
cjfa-35471	703	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	704	1	+	+	CCONJ
cjfa-35471	704	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	704	3	is	be	AUX
cjfa-35471	704	4	reduced	reduce	VERB
cjfa-35471	704	5	.	.	PUNCT
cjfa-35471	705	1	the	the	DET
cjfa-35471	705	2	left	left	ADJ
cjfa-35471	705	3	-	-	PUNCT
cjfa-35471	705	4	hand	hand	NOUN
cjfa-35471	705	5	side	side	NOUN
cjfa-35471	705	6	of	of	ADP
cjfa-35471	705	7	inequality	inequality	NOUN
cjfa-35471	705	8	(	(	PUNCT
cjfa-35471	705	9	5	5	NUM
cjfa-35471	705	10	)	)	PUNCT
cjfa-35471	705	11	will	will	AUX
cjfa-35471	705	12	not	not	PART
cjfa-35471	705	13	change	change	VERB
cjfa-35471	705	14	since	since	SCONJ
cjfa-35471	705	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	705	16	)	)	PUNCT
cjfa-35471	705	17	does	do	AUX
cjfa-35471	705	18	not	not	PART
cjfa-35471	705	19	depend	depend	VERB
cjfa-35471	705	20	on	on	ADP
cjfa-35471	705	21	the	the	DET
cjfa-35471	705	22	constant	constant	ADJ
cjfa-35471	705	23	term	term	NOUN
cjfa-35471	705	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	705	25	in	in	ADP
cjfa-35471	705	26	the	the	DET
cjfa-35471	705	27	production	production	NOUN
cjfa-35471	705	28	cost	cost	NOUN
cjfa-35471	705	29	function	function	NOUN
cjfa-35471	705	30	.	.	PUNCT
cjfa-35471	706	1	the	the	DET
cjfa-35471	706	2	right	right	ADJ
cjfa-35471	706	3	-	-	PUNCT
cjfa-35471	706	4	hand	hand	NOUN
cjfa-35471	706	5	side	side	NOUN
cjfa-35471	706	6	will	will	AUX
cjfa-35471	706	7	be	be	AUX
cjfa-35471	706	8	lower	low	ADJ
cjfa-35471	706	9	since	since	SCONJ
cjfa-35471	706	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	706	11	is	be	AUX
cjfa-35471	706	12	lower	low	ADJ
cjfa-35471	706	13	.	.	PUNCT
cjfa-35471	707	1	therefore	therefore	ADV
cjfa-35471	707	2	,	,	PUNCT
cjfa-35471	707	3	the	the	DET
cjfa-35471	707	4	decision	decision	NOUN
cjfa-35471	707	5	of	of	ADP
cjfa-35471	707	6	the	the	DET
cjfa-35471	707	7	firm	firm	NOUN
cjfa-35471	707	8	will	will	AUX
cjfa-35471	707	9	depend	depend	VERB
cjfa-35471	707	10	on	on	ADP
cjfa-35471	707	11	how	how	SCONJ
cjfa-35471	707	12	much	much	ADJ
cjfa-35471	707	13	the	the	DET
cjfa-35471	707	14	new	new	ADJ
cjfa-35471	707	15	technology	technology	NOUN
cjfa-35471	707	16	reduces	reduce	VERB
cjfa-35471	707	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	707	18	the	the	DET
cjfa-35471	707	19	firm	firm	NOUN
cjfa-35471	707	20	will	will	AUX
cjfa-35471	707	21	start	start	VERB
cjfa-35471	707	22	to	to	PART
cjfa-35471	707	23	produce	produce	VERB
cjfa-35471	707	24	sooner	soon	ADV
cjfa-35471	707	25	if	if	SCONJ
cjfa-35471	707	26	the	the	DET
cjfa-35471	707	27	reduction	reduction	NOUN
cjfa-35471	707	28	in	in	ADP
cjfa-35471	707	29	c	c	PROPN
cjfa-35471	707	30	is	be	AUX
cjfa-35471	707	31	large	large	ADJ
cjfa-35471	707	32	enough	enough	ADV
cjfa-35471	707	33	to	to	PART
cjfa-35471	707	34	violate	violate	VERB
cjfa-35471	707	35	the	the	DET
cjfa-35471	707	36	inequality	inequality	NOUN
cjfa-35471	707	37	.	.	PUNCT
cjfa-35471	708	1	3	3	X
cjfa-35471	708	2	.	.	X
cjfa-35471	708	3	marginal	marginal	ADJ
cjfa-35471	708	4	cost	cost	NOUN
cjfa-35471	708	5	function	function	NOUN
cjfa-35471	708	6	,	,	PUNCT
cjfa-35471	708	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	708	8	)	)	PUNCT
cjfa-35471	708	9	,	,	PUNCT
cjfa-35471	708	10	is	be	AUX
cjfa-35471	708	11	reduced	reduce	VERB
cjfa-35471	708	12	as	as	ADP
cjfa-35471	708	13	a	a	DET
cjfa-35471	708	14	whole	whole	NOUN
cjfa-35471	708	15	.	.	PUNCT
cjfa-35471	709	1	we	we	PRON
cjfa-35471	709	2	will	will	AUX
cjfa-35471	709	3	consider	consider	VERB
cjfa-35471	709	4	this	this	DET
cjfa-35471	709	5	last	last	ADJ
cjfa-35471	709	6	case	case	NOUN
cjfa-35471	709	7	assuming	assume	VERB
cjfa-35471	709	8	that	that	SCONJ
cjfa-35471	709	9	the	the	DET
cjfa-35471	709	10	new	new	ADJ
cjfa-35471	709	11	technology	technology	NOUN
cjfa-35471	709	12	reduces	reduce	VERB
cjfa-35471	709	13	the	the	DET
cjfa-35471	709	14	marginal	marginal	ADJ
cjfa-35471	709	15	cost	cost	NOUN
cjfa-35471	709	16	by	by	ADP
cjfa-35471	709	17	20	20	NUM
cjfa-35471	709	18	%	%	NOUN
cjfa-35471	709	19	.	.	PUNCT
cjfa-35471	710	1	this	this	PRON
cjfa-35471	710	2	implies	imply	VERB
cjfa-35471	710	3	that	that	SCONJ
cjfa-35471	710	4	the	the	DET
cjfa-35471	710	5	left	left	ADJ
cjfa-35471	710	6	-	-	PUNCT
cjfa-35471	710	7	hand	hand	NOUN
cjfa-35471	710	8	side	side	NOUN
cjfa-35471	710	9	of	of	ADP
cjfa-35471	710	10	inequality	inequality	NOUN
cjfa-35471	710	11	(	(	PUNCT
cjfa-35471	710	12	5	5	NUM
cjfa-35471	710	13	)	)	PUNCT
cjfa-35471	710	14	will	will	AUX
cjfa-35471	710	15	be	be	AUX
cjfa-35471	710	16	multiplies	multiplie	NOUN
cjfa-35471	710	17	by	by	ADP
cjfa-35471	710	18	0.8	0.8	NUM
cjfa-35471	710	19	.	.	PUNCT
cjfa-35471	711	1	then	then	ADV
cjfa-35471	711	2	the	the	DET
cjfa-35471	711	3	inequality	inequality	NOUN
cjfa-35471	711	4	(	(	PUNCT
cjfa-35471	711	5	4	4	X
cjfa-35471	711	6	)	)	PUNCT
cjfa-35471	711	7	becomes	become	VERB
cjfa-35471	711	8	:	:	PUNCT
cjfa-35471	711	9	(	(	PUNCT
cjfa-35471	711	10	0.5	0.5	NUM
cjfa-35471	711	11	∗	∗	NOUN
cjfa-35471	711	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	712	1	+	+	CCONJ
cjfa-35471	712	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	712	3	)	)	PUNCT
cjfa-35471	712	4	−	−	PROPN
cjfa-35471	713	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	713	2	∗	∗	VERB
cjfa-35471	713	3	0.8	0.8	NUM
cjfa-35471	713	4	𝑐	𝑐	PROPN
cjfa-35471	713	5	2.5	2.5	NUM
cjfa-35471	713	6	(	(	PUNCT
cjfa-35471	713	7	6	6	NUM
cjfa-35471	713	8	)	)	PUNCT
cjfa-35471	713	9	therefore	therefore	ADV
cjfa-35471	713	10	,	,	PUNCT
cjfa-35471	713	11	for	for	ADP
cjfa-35471	713	12	the	the	DET
cjfa-35471	713	13	same	same	ADJ
cjfa-35471	713	14	values	value	NOUN
cjfa-35471	713	15	for	for	ADP
cjfa-35471	713	16	the	the	DET
cjfa-35471	713	17	constants	constant	NOUN
cjfa-35471	713	18	,	,	PUNCT
cjfa-35471	713	19	the	the	DET
cjfa-35471	713	20	graphs	graph	NOUN
cjfa-35471	713	21	of	of	ADP
cjfa-35471	713	22	both	both	DET
cjfa-35471	713	23	sides	side	NOUN
cjfa-35471	713	24	of	of	ADP
cjfa-35471	713	25	inequality	inequality	NOUN
cjfa-35471	713	26	above	above	ADV
cjfa-35471	713	27	and	and	CCONJ
cjfa-35471	713	28	the	the	DET
cjfa-35471	713	29	sales	sale	NOUN
cjfa-35471	713	30	are	be	AUX
cjfa-35471	713	31	presented	present	VERB
cjfa-35471	713	32	below	below	ADV
cjfa-35471	713	33	(	(	PUNCT
cjfa-35471	713	34	figure	figure	NOUN
cjfa-35471	713	35	2	2	NUM
cjfa-35471	713	36	)	)	PUNCT
cjfa-35471	713	37	.	.	PUNCT
cjfa-35471	714	1	inequality	inequality	NOUN
cjfa-35471	714	2	(	(	PUNCT
cjfa-35471	714	3	6	6	NUM
cjfa-35471	714	4	)	)	PUNCT
cjfa-35471	714	5	implies	imply	VERB
cjfa-35471	714	6	the	the	DET
cjfa-35471	714	7	same	same	ADJ
cjfa-35471	714	8	type	type	NOUN
cjfa-35471	714	9	of	of	ADP
cjfa-35471	714	10	results	result	NOUN
cjfa-35471	714	11	as	as	ADP
cjfa-35471	714	12	in	in	ADP
cjfa-35471	714	13	the	the	DET
cjfa-35471	714	14	previous	previous	ADJ
cjfa-35471	714	15	case	case	NOUN
cjfa-35471	714	16	.	.	PUNCT
cjfa-35471	715	1	however	however	ADV
cjfa-35471	715	2	,	,	PUNCT
cjfa-35471	715	3	it	it	PRON
cjfa-35471	715	4	is	be	AUX
cjfa-35471	715	5	evident	evident	ADJ
cjfa-35471	715	6	from	from	ADP
cjfa-35471	715	7	the	the	DET
cjfa-35471	715	8	graphs	graph	NOUN
cjfa-35471	715	9	that	that	SCONJ
cjfa-35471	715	10	in	in	ADP
cjfa-35471	715	11	the	the	DET
cjfa-35471	715	12	second	second	ADJ
cjfa-35471	715	13	case	case	NOUN
cjfa-35471	715	14	the	the	DET
cjfa-35471	715	15	firm	firm	NOUN
cjfa-35471	715	16	will	will	AUX
cjfa-35471	715	17	stop	stop	VERB
cjfa-35471	715	18	producing	produce	VERB
cjfa-35471	715	19	sooner	soon	ADV
cjfa-35471	715	20	and	and	CCONJ
cjfa-35471	715	21	start	start	VERB
cjfa-35471	715	22	producing	produce	VERB
cjfa-35471	715	23	later	later	ADV
cjfa-35471	715	24	than	than	ADP
cjfa-35471	715	25	in	in	ADP
cjfa-35471	715	26	the	the	DET
cjfa-35471	715	27	first	first	ADJ
cjfa-35471	715	28	case	case	NOUN
cjfa-35471	715	29	.	.	PUNCT
cjfa-35471	716	1	this	this	PRON
cjfa-35471	716	2	is	be	AUX
cjfa-35471	716	3	an	an	DET
cjfa-35471	716	4	important	important	ADJ
cjfa-35471	716	5	result	result	NOUN
cjfa-35471	716	6	because	because	SCONJ
cjfa-35471	716	7	it	it	PRON
cjfa-35471	716	8	indicates	indicate	VERB
cjfa-35471	716	9	that	that	SCONJ
cjfa-35471	716	10	introduction	introduction	NOUN
cjfa-35471	716	11	of	of	ADP
cjfa-35471	716	12	new	new	ADJ
cjfa-35471	716	13	technologies	technology	NOUN
cjfa-35471	716	14	which	which	PRON
cjfa-35471	716	15	reduces	reduce	VERB
cjfa-35471	716	16	the	the	DET
cjfa-35471	716	17	marginal	marginal	ADJ
cjfa-35471	716	18	costs	cost	NOUN
cjfa-35471	716	19	will	will	AUX
cjfa-35471	716	20	induce	induce	VERB
cjfa-35471	716	21	firms	firm	NOUN
cjfa-35471	716	22	to	to	PART
cjfa-35471	716	23	stop	stop	VERB
cjfa-35471	716	24	production	production	NOUN
cjfa-35471	716	25	sooner	soon	ADV
cjfa-35471	716	26	.	.	PUNCT
cjfa-35471	717	1	case	case	NOUN
cjfa-35471	717	2	iii	iii	X
cjfa-35471	717	3	:	:	PUNCT
cjfa-35471	717	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	717	5	𝑘	𝑘	PRON
cjfa-35471	717	6	𝑘	𝑘	NOUN
cjfa-35471	717	7	and	and	CCONJ
cjfa-35471	717	8	interest	interest	NOUN
cjfa-35471	717	9	rate	rate	NOUN
cjfa-35471	717	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	717	11	)	)	PUNCT
cjfa-35471	718	1	𝑘	𝑘	ADP
cjfa-35471	718	2	0.2	0.2	NUM
cjfa-35471	718	3	the	the	DET
cjfa-35471	718	4	inequality	inequality	NOUN
cjfa-35471	718	5	(	(	PUNCT
cjfa-35471	718	6	4	4	X
cjfa-35471	718	7	)	)	PUNCT
cjfa-35471	718	8	becomes	become	VERB
cjfa-35471	718	9	:	:	PUNCT
cjfa-35471	718	10	(	(	PUNCT
cjfa-35471	718	11	0.5	0.5	NUM
cjfa-35471	718	12	∗	∗	NOUN
cjfa-35471	718	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	719	1	+	+	CCONJ
cjfa-35471	719	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	719	3	)	)	PUNCT
cjfa-35471	719	4	−	−	PROPN
cjfa-35471	720	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	720	2	𝑐	𝑐	PROPN
cjfa-35471	720	3	2.5	2.5	NUM
cjfa-35471	720	4	+	+	CCONJ
cjfa-35471	720	5	0.2	0.2	NUM
cjfa-35471	720	6	�	�	NOUN
cjfa-35471	720	7	0.5	0.5	NUM
cjfa-35471	720	8	∗	∗	NOUN
cjfa-35471	720	9	𝑐	𝑐	PROPN
cjfa-35471	720	10	∗	∗	NOUN
cjfa-35471	720	11	(	(	PUNCT
cjfa-35471	720	12	4	4	NUM
cjfa-35471	720	13	+	+	SYM
cjfa-35471	720	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	720	15	)	)	PUNCT
cjfa-35471	720	16	�	�	PROPN
cjfa-35471	720	17	�	�	PROPN
cjfa-35471	720	18	−	−	NUM
cjfa-35471	720	19	2	2	NUM
cjfa-35471	720	20	∗	∗	NOUN
cjfa-35471	720	21	(	(	PUNCT
cjfa-35471	720	22	4	4	NUM
cjfa-35471	720	23	+	+	NUM
cjfa-35471	720	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	720	25	)	)	PUNCT
cjfa-35471	720	26	+	+	SYM
cjfa-35471	720	27	𝑘	𝑘	X
cjfa-35471	720	28	)	)	PUNCT
cjfa-35471	720	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	720	30	(	(	PUNCT
cjfa-35471	720	31	7	7	X
cjfa-35471	720	32	)	)	PUNCT
cjfa-35471	720	33	is	be	AUX
cjfa-35471	720	34	reduced	reduce	VERB
cjfa-35471	720	35	.	.	PUNCT
cjfa-35471	721	1	the	the	DET
cjfa-35471	721	2	left	left	ADJ
cjfa-35471	721	3	-	-	PUNCT
cjfa-35471	721	4	hand	hand	NOUN
cjfa-35471	721	5	side	side	NOUN
cjfa-35471	721	6	of	of	ADP
cjfa-35471	721	7	inequality	inequality	NOUN
cjfa-35471	721	8	(	(	PUNCT
cjfa-35471	721	9	5	5	NUM
cjfa-35471	721	10	)	)	PUNCT
cjfa-35471	721	11	will	will	AUX
cjfa-35471	721	12	not	not	PART
cjfa-35471	721	13	change	change	VERB
cjfa-35471	721	14	since	since	SCONJ
cjfa-35471	721	15	source	source	NOUN
cjfa-35471	721	16	:	:	PUNCT
cjfa-35471	721	17	constructed	construct	VERB
cjfa-35471	721	18	by	by	ADP
cjfa-35471	721	19	authors	author	NOUN
cjfa-35471	721	20	.	.	PUNCT
cjfa-35471	722	1	case	case	NOUN
cjfa-35471	722	2	ii	ii	PROPN
cjfa-35471	722	3	:	:	PUNCT
cjfa-35471	722	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	722	5	𝑘	𝑘	PRON
cjfa-35471	722	6	𝑘	𝑘	NOUN
cjfa-35471	722	7	and	and	CCONJ
cjfa-35471	722	8	interest	interest	NOUN
cjfa-35471	722	9	rate	rate	NOUN
cjfa-35471	722	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	722	11	)	)	PUNCT
cjfa-35471	723	1	𝑘	𝑘	ADP
cjfa-35471	723	2	0	0	NUM
cjfa-35471	723	3	and	and	CCONJ
cjfa-35471	723	4	a	a	DET
cjfa-35471	723	5	new	new	ADJ
cjfa-35471	723	6	technology	technology	NOUN
cjfa-35471	723	7	i	i	PRON
cjfa-35471	723	8	introduced	introduce	VERB
cjfa-35471	723	9	.	.	PUNCT
cjfa-35471	724	1	the	the	DET
cjfa-35471	724	2	impact	impact	NOUN
cjfa-35471	724	3	of	of	ADP
cjfa-35471	724	4	new	new	ADJ
cjfa-35471	724	5	technology	technology	NOUN
cjfa-35471	724	6	will	will	AUX
cjfa-35471	724	7	be	be	AUX
cjfa-35471	724	8	analyzed	analyze	VERB
cjfa-35471	724	9	in	in	ADP
cjfa-35471	724	10	three	three	NUM
cjfa-35471	724	11	cases	case	NOUN
cjfa-35471	724	12	:	:	PUNCT
cjfa-35471	724	13	1	1	X
cjfa-35471	724	14	.	.	PUNCT
cjfa-35471	724	15	fixed	fix	VERB
cjfa-35471	724	16	costs	cost	NOUN
cjfa-35471	724	17	(	(	PUNCT
cjfa-35471	724	18	the	the	DET
cjfa-35471	724	19	term	term	NOUN
cjfa-35471	724	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	724	21	in	in	ADP
cjfa-35471	724	22	the	the	DET
cjfa-35471	724	23	cost	cost	NOUN
cjfa-35471	724	24	function	function	NOUN
cjfa-35471	724	25	)	)	PUNCT
cjfa-35471	724	26	is	be	AUX
cjfa-35471	724	27	reduced	reduce	VERB
cjfa-35471	724	28	.	.	PUNCT
cjfa-35471	725	1	there	there	PRON
cjfa-35471	725	2	will	will	AUX
cjfa-35471	725	3	be	be	AUX
cjfa-35471	725	4	no	no	DET
cjfa-35471	725	5	impact	impact	NOUN
cjfa-35471	725	6	on	on	ADP
cjfa-35471	725	7	production	production	NOUN
cjfa-35471	725	8	decision	decision	NOUN
cjfa-35471	725	9	since	since	SCONJ
cjfa-35471	725	10	the	the	DET
cjfa-35471	725	11	fixed	fix	VERB
cjfa-35471	725	12	costs	cost	NOUN
cjfa-35471	725	13	are	be	AUX
cjfa-35471	725	14	already	already	ADV
cjfa-35471	725	15	shown	show	VERB
cjfa-35471	725	16	to	to	PART
cjfa-35471	725	17	have	have	VERB
cjfa-35471	725	18	on	on	ADP
cjfa-35471	725	19	impact	impact	NOUN
cjfa-35471	725	20	on	on	ADP
cjfa-35471	725	21	the	the	DET
cjfa-35471	725	22	inequality	inequality	NOUN
cjfa-35471	725	23	(	(	PUNCT
cjfa-35471	725	24	5	5	NUM
cjfa-35471	725	25	)	)	PUNCT
cjfa-35471	725	26	.	.	PUNCT
cjfa-35471	726	1	2	2	X
cjfa-35471	726	2	.	.	X
cjfa-35471	726	3	only	only	ADV
cjfa-35471	726	4	the	the	DET
cjfa-35471	726	5	constant	constant	ADJ
cjfa-35471	726	6	term	term	NOUN
cjfa-35471	726	7	(	(	PUNCT
cjfa-35471	726	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	726	9	)	)	PUNCT
cjfa-35471	726	10	in	in	ADP
cjfa-35471	726	11	the	the	DET
cjfa-35471	726	12	marginal	marginal	ADJ
cjfa-35471	726	13	cost	cost	NOUN
cjfa-35471	726	14	,	,	PUNCT
cjfa-35471	726	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	726	16	𝑘	𝑘	PRON
cjfa-35471	726	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	726	18	�	�	PROPN
cjfa-35471	726	19	+	+	CCONJ
cjfa-35471	726	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	727	1	+	+	CCONJ
cjfa-35471	727	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	727	3	is	be	AUX
cjfa-35471	727	4	reduced	reduce	VERB
cjfa-35471	727	5	.	.	PUNCT
cjfa-35471	728	1	the	the	DET
cjfa-35471	728	2	left	left	ADJ
cjfa-35471	728	3	-	-	PUNCT
cjfa-35471	728	4	hand	hand	NOUN
cjfa-35471	728	5	side	side	NOUN
cjfa-35471	728	6	of	of	ADP
cjfa-35471	728	7	inequality	inequality	NOUN
cjfa-35471	728	8	(	(	PUNCT
cjfa-35471	728	9	5	5	NUM
cjfa-35471	728	10	)	)	PUNCT
cjfa-35471	728	11	will	will	AUX
cjfa-35471	728	12	not	not	PART
cjfa-35471	728	13	change	change	VERB
cjfa-35471	728	14	since	since	SCONJ
cjfa-35471	728	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	728	16	)	)	PUNCT
cjfa-35471	728	17	does	do	AUX
cjfa-35471	728	18	not	not	PART
cjfa-35471	728	19	depend	depend	VERB
cjfa-35471	728	20	on	on	ADP
cjfa-35471	728	21	the	the	DET
cjfa-35471	728	22	constant	constant	ADJ
cjfa-35471	728	23	term	term	NOUN
cjfa-35471	728	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	728	25	in	in	ADP
cjfa-35471	728	26	the	the	DET
cjfa-35471	728	27	production	production	NOUN
cjfa-35471	728	28	cost	cost	NOUN
cjfa-35471	728	29	function	function	NOUN
cjfa-35471	728	30	.	.	PUNCT
cjfa-35471	729	1	the	the	DET
cjfa-35471	729	2	right	right	ADJ
cjfa-35471	729	3	-	-	PUNCT
cjfa-35471	729	4	hand	hand	NOUN
cjfa-35471	729	5	side	side	NOUN
cjfa-35471	729	6	will	will	AUX
cjfa-35471	729	7	be	be	AUX
cjfa-35471	729	8	lower	low	ADJ
cjfa-35471	729	9	since	since	SCONJ
cjfa-35471	729	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	729	11	is	be	AUX
cjfa-35471	729	12	lower	low	ADJ
cjfa-35471	729	13	.	.	PUNCT
cjfa-35471	730	1	therefore	therefore	ADV
cjfa-35471	730	2	,	,	PUNCT
cjfa-35471	730	3	the	the	DET
cjfa-35471	730	4	decision	decision	NOUN
cjfa-35471	730	5	of	of	ADP
cjfa-35471	730	6	the	the	DET
cjfa-35471	730	7	firm	firm	NOUN
cjfa-35471	730	8	will	will	AUX
cjfa-35471	730	9	depend	depend	VERB
cjfa-35471	730	10	on	on	ADP
cjfa-35471	730	11	how	how	SCONJ
cjfa-35471	730	12	much	much	ADJ
cjfa-35471	730	13	the	the	DET
cjfa-35471	730	14	new	new	ADJ
cjfa-35471	730	15	technology	technology	NOUN
cjfa-35471	730	16	reduces	reduce	VERB
cjfa-35471	730	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	730	18	the	the	DET
cjfa-35471	730	19	firm	firm	NOUN
cjfa-35471	730	20	will	will	AUX
cjfa-35471	730	21	start	start	VERB
cjfa-35471	730	22	to	to	PART
cjfa-35471	730	23	produce	produce	VERB
cjfa-35471	730	24	sooner	soon	ADV
cjfa-35471	730	25	if	if	SCONJ
cjfa-35471	730	26	the	the	DET
cjfa-35471	730	27	reduction	reduction	NOUN
cjfa-35471	730	28	in	in	ADP
cjfa-35471	730	29	c	c	PROPN
cjfa-35471	730	30	is	be	AUX
cjfa-35471	730	31	large	large	ADJ
cjfa-35471	730	32	enough	enough	ADV
cjfa-35471	730	33	to	to	PART
cjfa-35471	730	34	violate	violate	VERB
cjfa-35471	730	35	the	the	DET
cjfa-35471	730	36	inequality	inequality	NOUN
cjfa-35471	730	37	.	.	PUNCT
cjfa-35471	731	1	3	3	X
cjfa-35471	731	2	.	.	X
cjfa-35471	731	3	marginal	marginal	ADJ
cjfa-35471	731	4	cost	cost	NOUN
cjfa-35471	731	5	function	function	NOUN
cjfa-35471	731	6	,	,	PUNCT
cjfa-35471	731	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	731	8	)	)	PUNCT
cjfa-35471	731	9	,	,	PUNCT
cjfa-35471	731	10	is	be	AUX
cjfa-35471	731	11	reduced	reduce	VERB
cjfa-35471	731	12	as	as	ADP
cjfa-35471	731	13	a	a	DET
cjfa-35471	731	14	whole	whole	NOUN
cjfa-35471	731	15	.	.	PUNCT
cjfa-35471	732	1	we	we	PRON
cjfa-35471	732	2	will	will	AUX
cjfa-35471	732	3	consider	consider	VERB
cjfa-35471	732	4	this	this	DET
cjfa-35471	732	5	last	last	ADJ
cjfa-35471	732	6	case	case	NOUN
cjfa-35471	732	7	assuming	assume	VERB
cjfa-35471	732	8	that	that	SCONJ
cjfa-35471	732	9	the	the	DET
cjfa-35471	732	10	new	new	ADJ
cjfa-35471	732	11	technology	technology	NOUN
cjfa-35471	732	12	reduces	reduce	VERB
cjfa-35471	732	13	the	the	DET
cjfa-35471	732	14	marginal	marginal	ADJ
cjfa-35471	732	15	cost	cost	NOUN
cjfa-35471	732	16	by	by	ADP
cjfa-35471	732	17	20	20	NUM
cjfa-35471	732	18	%	%	NOUN
cjfa-35471	732	19	.	.	PUNCT
cjfa-35471	733	1	this	this	PRON
cjfa-35471	733	2	implies	imply	VERB
cjfa-35471	733	3	that	that	SCONJ
cjfa-35471	733	4	the	the	DET
cjfa-35471	733	5	left	left	ADJ
cjfa-35471	733	6	-	-	PUNCT
cjfa-35471	733	7	hand	hand	NOUN
cjfa-35471	733	8	side	side	NOUN
cjfa-35471	733	9	of	of	ADP
cjfa-35471	733	10	inequality	inequality	NOUN
cjfa-35471	733	11	(	(	PUNCT
cjfa-35471	733	12	5	5	NUM
cjfa-35471	733	13	)	)	PUNCT
cjfa-35471	733	14	will	will	AUX
cjfa-35471	733	15	be	be	AUX
cjfa-35471	733	16	multiplies	multiplie	NOUN
cjfa-35471	733	17	by	by	ADP
cjfa-35471	733	18	0.8	0.8	NUM
cjfa-35471	733	19	.	.	PUNCT
cjfa-35471	734	1	then	then	ADV
cjfa-35471	734	2	the	the	DET
cjfa-35471	734	3	inequality	inequality	NOUN
cjfa-35471	734	4	(	(	PUNCT
cjfa-35471	734	5	4	4	X
cjfa-35471	734	6	)	)	PUNCT
cjfa-35471	734	7	becomes	become	VERB
cjfa-35471	734	8	:	:	PUNCT
cjfa-35471	734	9	(	(	PUNCT
cjfa-35471	734	10	0.5	0.5	NUM
cjfa-35471	734	11	∗	∗	NOUN
cjfa-35471	734	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	735	1	+	+	CCONJ
cjfa-35471	735	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	735	3	)	)	PUNCT
cjfa-35471	735	4	−	−	PROPN
cjfa-35471	736	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	736	2	∗	∗	VERB
cjfa-35471	736	3	0.8	0.8	NUM
cjfa-35471	736	4	𝑐	𝑐	PROPN
cjfa-35471	736	5	2.5	2.5	NUM
cjfa-35471	736	6	(	(	PUNCT
cjfa-35471	736	7	6	6	NUM
cjfa-35471	736	8	)	)	PUNCT
cjfa-35471	736	9	therefore	therefore	ADV
cjfa-35471	736	10	,	,	PUNCT
cjfa-35471	736	11	for	for	ADP
cjfa-35471	736	12	the	the	DET
cjfa-35471	736	13	same	same	ADJ
cjfa-35471	736	14	values	value	NOUN
cjfa-35471	736	15	for	for	ADP
cjfa-35471	736	16	the	the	DET
cjfa-35471	736	17	constants	constant	NOUN
cjfa-35471	736	18	,	,	PUNCT
cjfa-35471	736	19	the	the	DET
cjfa-35471	736	20	graphs	graph	NOUN
cjfa-35471	736	21	of	of	ADP
cjfa-35471	736	22	both	both	DET
cjfa-35471	736	23	sides	side	NOUN
cjfa-35471	736	24	of	of	ADP
cjfa-35471	736	25	inequality	inequality	NOUN
cjfa-35471	736	26	above	above	ADV
cjfa-35471	736	27	and	and	CCONJ
cjfa-35471	736	28	the	the	DET
cjfa-35471	736	29	sales	sale	NOUN
cjfa-35471	736	30	are	be	AUX
cjfa-35471	736	31	presented	present	VERB
cjfa-35471	736	32	below	below	ADV
cjfa-35471	736	33	(	(	PUNCT
cjfa-35471	736	34	figure	figure	NOUN
cjfa-35471	736	35	2	2	NUM
cjfa-35471	736	36	)	)	PUNCT
cjfa-35471	736	37	.	.	PUNCT
cjfa-35471	737	1	inequality	inequality	NOUN
cjfa-35471	737	2	(	(	PUNCT
cjfa-35471	737	3	6	6	NUM
cjfa-35471	737	4	)	)	PUNCT
cjfa-35471	737	5	implies	imply	VERB
cjfa-35471	737	6	the	the	DET
cjfa-35471	737	7	same	same	ADJ
cjfa-35471	737	8	type	type	NOUN
cjfa-35471	737	9	of	of	ADP
cjfa-35471	737	10	results	result	NOUN
cjfa-35471	737	11	as	as	ADP
cjfa-35471	737	12	in	in	ADP
cjfa-35471	737	13	the	the	DET
cjfa-35471	737	14	previous	previous	ADJ
cjfa-35471	737	15	case	case	NOUN
cjfa-35471	737	16	.	.	PUNCT
cjfa-35471	738	1	however	however	ADV
cjfa-35471	738	2	,	,	PUNCT
cjfa-35471	738	3	it	it	PRON
cjfa-35471	738	4	is	be	AUX
cjfa-35471	738	5	evident	evident	ADJ
cjfa-35471	738	6	from	from	ADP
cjfa-35471	738	7	the	the	DET
cjfa-35471	738	8	graphs	graph	NOUN
cjfa-35471	738	9	that	that	SCONJ
cjfa-35471	738	10	in	in	ADP
cjfa-35471	738	11	the	the	DET
cjfa-35471	738	12	second	second	ADJ
cjfa-35471	738	13	case	case	NOUN
cjfa-35471	738	14	the	the	DET
cjfa-35471	738	15	firm	firm	NOUN
cjfa-35471	738	16	will	will	AUX
cjfa-35471	738	17	stop	stop	VERB
cjfa-35471	738	18	producing	produce	VERB
cjfa-35471	738	19	sooner	soon	ADV
cjfa-35471	738	20	and	and	CCONJ
cjfa-35471	738	21	start	start	VERB
cjfa-35471	738	22	producing	produce	VERB
cjfa-35471	738	23	later	later	ADV
cjfa-35471	738	24	than	than	ADP
cjfa-35471	738	25	in	in	ADP
cjfa-35471	738	26	the	the	DET
cjfa-35471	738	27	first	first	ADJ
cjfa-35471	738	28	case	case	NOUN
cjfa-35471	738	29	.	.	PUNCT
cjfa-35471	739	1	this	this	PRON
cjfa-35471	739	2	is	be	AUX
cjfa-35471	739	3	an	an	DET
cjfa-35471	739	4	important	important	ADJ
cjfa-35471	739	5	result	result	NOUN
cjfa-35471	739	6	because	because	SCONJ
cjfa-35471	739	7	it	it	PRON
cjfa-35471	739	8	indicates	indicate	VERB
cjfa-35471	739	9	that	that	SCONJ
cjfa-35471	739	10	introduction	introduction	NOUN
cjfa-35471	739	11	of	of	ADP
cjfa-35471	739	12	new	new	ADJ
cjfa-35471	739	13	technologies	technology	NOUN
cjfa-35471	739	14	which	which	PRON
cjfa-35471	739	15	reduces	reduce	VERB
cjfa-35471	739	16	the	the	DET
cjfa-35471	739	17	marginal	marginal	ADJ
cjfa-35471	739	18	costs	cost	NOUN
cjfa-35471	739	19	will	will	AUX
cjfa-35471	739	20	induce	induce	VERB
cjfa-35471	739	21	firms	firm	NOUN
cjfa-35471	739	22	to	to	PART
cjfa-35471	739	23	stop	stop	VERB
cjfa-35471	739	24	production	production	NOUN
cjfa-35471	739	25	sooner	soon	ADV
cjfa-35471	739	26	.	.	PUNCT
cjfa-35471	740	1	case	case	NOUN
cjfa-35471	740	2	iii	iii	X
cjfa-35471	740	3	:	:	PUNCT
cjfa-35471	740	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	740	5	𝑘	𝑘	PRON
cjfa-35471	740	6	𝑘	𝑘	NOUN
cjfa-35471	740	7	and	and	CCONJ
cjfa-35471	740	8	interest	interest	NOUN
cjfa-35471	740	9	rate	rate	NOUN
cjfa-35471	740	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	740	11	)	)	PUNCT
cjfa-35471	741	1	𝑘	𝑘	ADP
cjfa-35471	741	2	0.2	0.2	NUM
cjfa-35471	741	3	the	the	DET
cjfa-35471	741	4	inequality	inequality	NOUN
cjfa-35471	741	5	(	(	PUNCT
cjfa-35471	741	6	4	4	X
cjfa-35471	741	7	)	)	PUNCT
cjfa-35471	741	8	becomes	become	VERB
cjfa-35471	741	9	:	:	PUNCT
cjfa-35471	741	10	(	(	PUNCT
cjfa-35471	741	11	0.5	0.5	NUM
cjfa-35471	741	12	∗	∗	NOUN
cjfa-35471	741	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	742	1	+	+	CCONJ
cjfa-35471	742	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	742	3	)	)	PUNCT
cjfa-35471	742	4	−	−	PROPN
cjfa-35471	743	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	743	2	𝑐	𝑐	PROPN
cjfa-35471	743	3	2.5	2.5	NUM
cjfa-35471	743	4	+	+	CCONJ
cjfa-35471	743	5	0.2	0.2	NUM
cjfa-35471	743	6	�	�	NOUN
cjfa-35471	743	7	0.5	0.5	NUM
cjfa-35471	743	8	∗	∗	NOUN
cjfa-35471	743	9	𝑐	𝑐	PROPN
cjfa-35471	743	10	∗	∗	NOUN
cjfa-35471	743	11	(	(	PUNCT
cjfa-35471	743	12	4	4	NUM
cjfa-35471	743	13	+	+	SYM
cjfa-35471	743	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	743	15	)	)	PUNCT
cjfa-35471	743	16	�	�	PROPN
cjfa-35471	743	17	�	�	PROPN
cjfa-35471	743	18	−	−	NUM
cjfa-35471	743	19	2	2	NUM
cjfa-35471	743	20	∗	∗	NOUN
cjfa-35471	743	21	(	(	PUNCT
cjfa-35471	743	22	4	4	NUM
cjfa-35471	743	23	+	+	NUM
cjfa-35471	743	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	743	25	)	)	PUNCT
cjfa-35471	743	26	+	+	SYM
cjfa-35471	743	27	𝑘	𝑘	X
cjfa-35471	743	28	)	)	PUNCT
cjfa-35471	743	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	743	30	(	(	PUNCT
cjfa-35471	743	31	7	7	X
cjfa-35471	743	32	)	)	PUNCT
cjfa-35471	743	33	does	do	AUX
cjfa-35471	743	34	not	not	PART
cjfa-35471	743	35	depend	depend	VERB
cjfa-35471	743	36	on	on	ADP
cjfa-35471	743	37	the	the	DET
cjfa-35471	743	38	constant	constant	ADJ
cjfa-35471	743	39	term	term	NOUN
cjfa-35471	743	40	c	c	NOUN
cjfa-35471	743	41	in	in	ADP
cjfa-35471	743	42	the	the	DET
cjfa-35471	743	43	production	production	NOUN
cjfa-35471	743	44	cost	cost	NOUN
cjfa-35471	743	45	function	function	NOUN
cjfa-35471	743	46	.	.	PUNCT
cjfa-35471	744	1	the	the	DET
cjfa-35471	744	2	right	right	ADJ
cjfa-35471	744	3	-	-	PUNCT
cjfa-35471	744	4	hand	hand	NOUN
cjfa-35471	744	5	side	side	NOUN
cjfa-35471	744	6	will	will	AUX
cjfa-35471	744	7	be	be	AUX
cjfa-35471	744	8	lower	low	ADJ
cjfa-35471	744	9	since	since	SCONJ
cjfa-35471	744	10	c	c	NOUN
cjfa-35471	744	11	is	be	AUX
cjfa-35471	744	12	lower	low	ADJ
cjfa-35471	744	13	.	.	PUNCT
cjfa-35471	745	1	therefore	therefore	ADV
cjfa-35471	745	2	,	,	PUNCT
cjfa-35471	745	3	the	the	DET
cjfa-35471	745	4	decision	decision	NOUN
cjfa-35471	745	5	of	of	ADP
cjfa-35471	745	6	the	the	DET
cjfa-35471	745	7	firm	firm	NOUN
cjfa-35471	745	8	will	will	AUX
cjfa-35471	745	9	depend	depend	VERB
cjfa-35471	745	10	on	on	ADP
cjfa-35471	745	11	how	how	SCONJ
cjfa-35471	745	12	much	much	ADJ
cjfa-35471	745	13	the	the	DET
cjfa-35471	745	14	new	new	ADJ
cjfa-35471	745	15	technology	technology	NOUN
cjfa-35471	745	16	reduces	reduce	VERB
cjfa-35471	745	17	c.	c.	NOUN
cjfa-35471	745	18	the	the	DET
cjfa-35471	745	19	firm	firm	NOUN
cjfa-35471	745	20	will	will	AUX
cjfa-35471	745	21	start	start	VERB
cjfa-35471	745	22	to	to	PART
cjfa-35471	745	23	produce	produce	VERB
cjfa-35471	745	24	sooner	soon	ADV
cjfa-35471	745	25	if	if	SCONJ
cjfa-35471	745	26	the	the	DET
cjfa-35471	745	27	reduction	reduction	NOUN
cjfa-35471	745	28	in	in	ADP
cjfa-35471	745	29	c	c	PROPN
cjfa-35471	745	30	is	be	AUX
cjfa-35471	745	31	large	large	ADJ
cjfa-35471	745	32	enough	enough	ADV
cjfa-35471	745	33	to	to	PART
cjfa-35471	745	34	violate	violate	VERB
cjfa-35471	745	35	the	the	DET
cjfa-35471	745	36	inequality	inequality	NOUN
cjfa-35471	745	37	.	.	PUNCT
cjfa-35471	746	1	optimal	optimal	ADJ
cjfa-35471	746	2	incentives	incentive	NOUN
cjfa-35471	746	3	for	for	ADP
cjfa-35471	746	4	economic	economic	ADJ
cjfa-35471	746	5	growth	growth	NOUN
cjfa-35471	746	6	…	…	PUNCT
cjfa-35471	746	7	19	19	NUM
cjfa-35471	746	8	3	3	NUM
cjfa-35471	746	9	.	.	PUNCT
cjfa-35471	746	10	marginal	marginal	ADJ
cjfa-35471	746	11	cost	cost	NOUN
cjfa-35471	746	12	function	function	NOUN
cjfa-35471	746	13	,	,	PUNCT
cjfa-35471	746	14	source	source	NOUN
cjfa-35471	746	15	:	:	PUNCT
cjfa-35471	746	16	constructed	construct	VERB
cjfa-35471	746	17	by	by	ADP
cjfa-35471	746	18	authors	author	NOUN
cjfa-35471	746	19	.	.	PUNCT
cjfa-35471	747	1	case	case	NOUN
cjfa-35471	747	2	ii	ii	PROPN
cjfa-35471	747	3	:	:	PUNCT
cjfa-35471	747	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	747	5	𝑘	𝑘	PRON
cjfa-35471	747	6	𝑘	𝑘	NOUN
cjfa-35471	747	7	and	and	CCONJ
cjfa-35471	747	8	interest	interest	NOUN
cjfa-35471	747	9	rate	rate	NOUN
cjfa-35471	747	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	747	11	)	)	PUNCT
cjfa-35471	748	1	𝑘	𝑘	ADP
cjfa-35471	748	2	0	0	NUM
cjfa-35471	748	3	and	and	CCONJ
cjfa-35471	748	4	a	a	DET
cjfa-35471	748	5	new	new	ADJ
cjfa-35471	748	6	technology	technology	NOUN
cjfa-35471	748	7	i	i	PRON
cjfa-35471	748	8	introduced	introduce	VERB
cjfa-35471	748	9	.	.	PUNCT
cjfa-35471	749	1	the	the	DET
cjfa-35471	749	2	impact	impact	NOUN
cjfa-35471	749	3	of	of	ADP
cjfa-35471	749	4	new	new	ADJ
cjfa-35471	749	5	technology	technology	NOUN
cjfa-35471	749	6	will	will	AUX
cjfa-35471	749	7	be	be	AUX
cjfa-35471	749	8	analyzed	analyze	VERB
cjfa-35471	749	9	in	in	ADP
cjfa-35471	749	10	three	three	NUM
cjfa-35471	749	11	cases	case	NOUN
cjfa-35471	749	12	:	:	PUNCT
cjfa-35471	749	13	1	1	X
cjfa-35471	749	14	.	.	PUNCT
cjfa-35471	749	15	fixed	fix	VERB
cjfa-35471	749	16	costs	cost	NOUN
cjfa-35471	749	17	(	(	PUNCT
cjfa-35471	749	18	the	the	DET
cjfa-35471	749	19	term	term	NOUN
cjfa-35471	749	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	749	21	in	in	ADP
cjfa-35471	749	22	the	the	DET
cjfa-35471	749	23	cost	cost	NOUN
cjfa-35471	749	24	function	function	NOUN
cjfa-35471	749	25	)	)	PUNCT
cjfa-35471	749	26	is	be	AUX
cjfa-35471	749	27	reduced	reduce	VERB
cjfa-35471	749	28	.	.	PUNCT
cjfa-35471	750	1	there	there	PRON
cjfa-35471	750	2	will	will	AUX
cjfa-35471	750	3	be	be	AUX
cjfa-35471	750	4	no	no	DET
cjfa-35471	750	5	impact	impact	NOUN
cjfa-35471	750	6	on	on	ADP
cjfa-35471	750	7	production	production	NOUN
cjfa-35471	750	8	decision	decision	NOUN
cjfa-35471	750	9	since	since	SCONJ
cjfa-35471	750	10	the	the	DET
cjfa-35471	750	11	fixed	fix	VERB
cjfa-35471	750	12	costs	cost	NOUN
cjfa-35471	750	13	are	be	AUX
cjfa-35471	750	14	already	already	ADV
cjfa-35471	750	15	shown	show	VERB
cjfa-35471	750	16	to	to	PART
cjfa-35471	750	17	have	have	VERB
cjfa-35471	750	18	on	on	ADP
cjfa-35471	750	19	impact	impact	NOUN
cjfa-35471	750	20	on	on	ADP
cjfa-35471	750	21	the	the	DET
cjfa-35471	750	22	inequality	inequality	NOUN
cjfa-35471	750	23	(	(	PUNCT
cjfa-35471	750	24	5	5	NUM
cjfa-35471	750	25	)	)	PUNCT
cjfa-35471	750	26	.	.	PUNCT
cjfa-35471	751	1	2	2	X
cjfa-35471	751	2	.	.	X
cjfa-35471	751	3	only	only	ADV
cjfa-35471	751	4	the	the	DET
cjfa-35471	751	5	constant	constant	ADJ
cjfa-35471	751	6	term	term	NOUN
cjfa-35471	751	7	(	(	PUNCT
cjfa-35471	751	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	751	9	)	)	PUNCT
cjfa-35471	751	10	in	in	ADP
cjfa-35471	751	11	the	the	DET
cjfa-35471	751	12	marginal	marginal	ADJ
cjfa-35471	751	13	cost	cost	NOUN
cjfa-35471	751	14	,	,	PUNCT
cjfa-35471	751	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	751	16	𝑘	𝑘	PRON
cjfa-35471	751	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	751	18	�	�	PROPN
cjfa-35471	751	19	+	+	CCONJ
cjfa-35471	751	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	752	1	+	+	CCONJ
cjfa-35471	752	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	752	3	is	be	AUX
cjfa-35471	752	4	reduced	reduce	VERB
cjfa-35471	752	5	.	.	PUNCT
cjfa-35471	753	1	the	the	DET
cjfa-35471	753	2	left	left	ADJ
cjfa-35471	753	3	-	-	PUNCT
cjfa-35471	753	4	hand	hand	NOUN
cjfa-35471	753	5	side	side	NOUN
cjfa-35471	753	6	of	of	ADP
cjfa-35471	753	7	inequality	inequality	NOUN
cjfa-35471	753	8	(	(	PUNCT
cjfa-35471	753	9	5	5	NUM
cjfa-35471	753	10	)	)	PUNCT
cjfa-35471	753	11	will	will	AUX
cjfa-35471	753	12	not	not	PART
cjfa-35471	753	13	change	change	VERB
cjfa-35471	753	14	since	since	SCONJ
cjfa-35471	753	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	753	16	)	)	PUNCT
cjfa-35471	753	17	does	do	AUX
cjfa-35471	753	18	not	not	PART
cjfa-35471	753	19	depend	depend	VERB
cjfa-35471	753	20	on	on	ADP
cjfa-35471	753	21	the	the	DET
cjfa-35471	753	22	constant	constant	ADJ
cjfa-35471	753	23	term	term	NOUN
cjfa-35471	753	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	753	25	in	in	ADP
cjfa-35471	753	26	the	the	DET
cjfa-35471	753	27	production	production	NOUN
cjfa-35471	753	28	cost	cost	NOUN
cjfa-35471	753	29	function	function	NOUN
cjfa-35471	753	30	.	.	PUNCT
cjfa-35471	754	1	the	the	DET
cjfa-35471	754	2	right	right	ADJ
cjfa-35471	754	3	-	-	PUNCT
cjfa-35471	754	4	hand	hand	NOUN
cjfa-35471	754	5	side	side	NOUN
cjfa-35471	754	6	will	will	AUX
cjfa-35471	754	7	be	be	AUX
cjfa-35471	754	8	lower	low	ADJ
cjfa-35471	754	9	since	since	SCONJ
cjfa-35471	754	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	754	11	is	be	AUX
cjfa-35471	754	12	lower	low	ADJ
cjfa-35471	754	13	.	.	PUNCT
cjfa-35471	755	1	therefore	therefore	ADV
cjfa-35471	755	2	,	,	PUNCT
cjfa-35471	755	3	the	the	DET
cjfa-35471	755	4	decision	decision	NOUN
cjfa-35471	755	5	of	of	ADP
cjfa-35471	755	6	the	the	DET
cjfa-35471	755	7	firm	firm	NOUN
cjfa-35471	755	8	will	will	AUX
cjfa-35471	755	9	depend	depend	VERB
cjfa-35471	755	10	on	on	ADP
cjfa-35471	755	11	how	how	SCONJ
cjfa-35471	755	12	much	much	ADJ
cjfa-35471	755	13	the	the	DET
cjfa-35471	755	14	new	new	ADJ
cjfa-35471	755	15	technology	technology	NOUN
cjfa-35471	755	16	reduces	reduce	VERB
cjfa-35471	755	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	755	18	the	the	DET
cjfa-35471	755	19	firm	firm	NOUN
cjfa-35471	755	20	will	will	AUX
cjfa-35471	755	21	start	start	VERB
cjfa-35471	755	22	to	to	PART
cjfa-35471	755	23	produce	produce	VERB
cjfa-35471	755	24	sooner	soon	ADV
cjfa-35471	755	25	if	if	SCONJ
cjfa-35471	755	26	the	the	DET
cjfa-35471	755	27	reduction	reduction	NOUN
cjfa-35471	755	28	in	in	ADP
cjfa-35471	755	29	c	c	PROPN
cjfa-35471	755	30	is	be	AUX
cjfa-35471	755	31	large	large	ADJ
cjfa-35471	755	32	enough	enough	ADV
cjfa-35471	755	33	to	to	PART
cjfa-35471	755	34	violate	violate	VERB
cjfa-35471	755	35	the	the	DET
cjfa-35471	755	36	inequality	inequality	NOUN
cjfa-35471	755	37	.	.	PUNCT
cjfa-35471	756	1	3	3	X
cjfa-35471	756	2	.	.	X
cjfa-35471	756	3	marginal	marginal	ADJ
cjfa-35471	756	4	cost	cost	NOUN
cjfa-35471	756	5	function	function	NOUN
cjfa-35471	756	6	,	,	PUNCT
cjfa-35471	756	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	756	8	)	)	PUNCT
cjfa-35471	756	9	,	,	PUNCT
cjfa-35471	756	10	is	be	AUX
cjfa-35471	756	11	reduced	reduce	VERB
cjfa-35471	756	12	as	as	ADP
cjfa-35471	756	13	a	a	DET
cjfa-35471	756	14	whole	whole	NOUN
cjfa-35471	756	15	.	.	PUNCT
cjfa-35471	757	1	we	we	PRON
cjfa-35471	757	2	will	will	AUX
cjfa-35471	757	3	consider	consider	VERB
cjfa-35471	757	4	this	this	DET
cjfa-35471	757	5	last	last	ADJ
cjfa-35471	757	6	case	case	NOUN
cjfa-35471	757	7	assuming	assume	VERB
cjfa-35471	757	8	that	that	SCONJ
cjfa-35471	757	9	the	the	DET
cjfa-35471	757	10	new	new	ADJ
cjfa-35471	757	11	technology	technology	NOUN
cjfa-35471	757	12	reduces	reduce	VERB
cjfa-35471	757	13	the	the	DET
cjfa-35471	757	14	marginal	marginal	ADJ
cjfa-35471	757	15	cost	cost	NOUN
cjfa-35471	757	16	by	by	ADP
cjfa-35471	757	17	20	20	NUM
cjfa-35471	757	18	%	%	NOUN
cjfa-35471	757	19	.	.	PUNCT
cjfa-35471	758	1	this	this	PRON
cjfa-35471	758	2	implies	imply	VERB
cjfa-35471	758	3	that	that	SCONJ
cjfa-35471	758	4	the	the	DET
cjfa-35471	758	5	left	left	ADJ
cjfa-35471	758	6	-	-	PUNCT
cjfa-35471	758	7	hand	hand	NOUN
cjfa-35471	758	8	side	side	NOUN
cjfa-35471	758	9	of	of	ADP
cjfa-35471	758	10	inequality	inequality	NOUN
cjfa-35471	758	11	(	(	PUNCT
cjfa-35471	758	12	5	5	NUM
cjfa-35471	758	13	)	)	PUNCT
cjfa-35471	758	14	will	will	AUX
cjfa-35471	758	15	be	be	AUX
cjfa-35471	758	16	multiplies	multiplie	NOUN
cjfa-35471	758	17	by	by	ADP
cjfa-35471	758	18	0.8	0.8	NUM
cjfa-35471	758	19	.	.	PUNCT
cjfa-35471	759	1	then	then	ADV
cjfa-35471	759	2	the	the	DET
cjfa-35471	759	3	inequality	inequality	NOUN
cjfa-35471	759	4	(	(	PUNCT
cjfa-35471	759	5	4	4	X
cjfa-35471	759	6	)	)	PUNCT
cjfa-35471	759	7	becomes	become	VERB
cjfa-35471	759	8	:	:	PUNCT
cjfa-35471	759	9	(	(	PUNCT
cjfa-35471	759	10	0.5	0.5	NUM
cjfa-35471	759	11	∗	∗	NOUN
cjfa-35471	759	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	760	1	+	+	CCONJ
cjfa-35471	760	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	760	3	)	)	PUNCT
cjfa-35471	760	4	−	−	PROPN
cjfa-35471	761	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	761	2	∗	∗	VERB
cjfa-35471	761	3	0.8	0.8	NUM
cjfa-35471	761	4	𝑐	𝑐	PROPN
cjfa-35471	761	5	2.5	2.5	NUM
cjfa-35471	761	6	(	(	PUNCT
cjfa-35471	761	7	6	6	NUM
cjfa-35471	761	8	)	)	PUNCT
cjfa-35471	761	9	therefore	therefore	ADV
cjfa-35471	761	10	,	,	PUNCT
cjfa-35471	761	11	for	for	ADP
cjfa-35471	761	12	the	the	DET
cjfa-35471	761	13	same	same	ADJ
cjfa-35471	761	14	values	value	NOUN
cjfa-35471	761	15	for	for	ADP
cjfa-35471	761	16	the	the	DET
cjfa-35471	761	17	constants	constant	NOUN
cjfa-35471	761	18	,	,	PUNCT
cjfa-35471	761	19	the	the	DET
cjfa-35471	761	20	graphs	graph	NOUN
cjfa-35471	761	21	of	of	ADP
cjfa-35471	761	22	both	both	DET
cjfa-35471	761	23	sides	side	NOUN
cjfa-35471	761	24	of	of	ADP
cjfa-35471	761	25	inequality	inequality	NOUN
cjfa-35471	761	26	above	above	ADV
cjfa-35471	761	27	and	and	CCONJ
cjfa-35471	761	28	the	the	DET
cjfa-35471	761	29	sales	sale	NOUN
cjfa-35471	761	30	are	be	AUX
cjfa-35471	761	31	presented	present	VERB
cjfa-35471	761	32	below	below	ADV
cjfa-35471	761	33	(	(	PUNCT
cjfa-35471	761	34	figure	figure	NOUN
cjfa-35471	761	35	2	2	NUM
cjfa-35471	761	36	)	)	PUNCT
cjfa-35471	761	37	.	.	PUNCT
cjfa-35471	762	1	inequality	inequality	NOUN
cjfa-35471	762	2	(	(	PUNCT
cjfa-35471	762	3	6	6	NUM
cjfa-35471	762	4	)	)	PUNCT
cjfa-35471	762	5	implies	imply	VERB
cjfa-35471	762	6	the	the	DET
cjfa-35471	762	7	same	same	ADJ
cjfa-35471	762	8	type	type	NOUN
cjfa-35471	762	9	of	of	ADP
cjfa-35471	762	10	results	result	NOUN
cjfa-35471	762	11	as	as	ADP
cjfa-35471	762	12	in	in	ADP
cjfa-35471	762	13	the	the	DET
cjfa-35471	762	14	previous	previous	ADJ
cjfa-35471	762	15	case	case	NOUN
cjfa-35471	762	16	.	.	PUNCT
cjfa-35471	763	1	however	however	ADV
cjfa-35471	763	2	,	,	PUNCT
cjfa-35471	763	3	it	it	PRON
cjfa-35471	763	4	is	be	AUX
cjfa-35471	763	5	evident	evident	ADJ
cjfa-35471	763	6	from	from	ADP
cjfa-35471	763	7	the	the	DET
cjfa-35471	763	8	graphs	graph	NOUN
cjfa-35471	763	9	that	that	SCONJ
cjfa-35471	763	10	in	in	ADP
cjfa-35471	763	11	the	the	DET
cjfa-35471	763	12	second	second	ADJ
cjfa-35471	763	13	case	case	NOUN
cjfa-35471	763	14	the	the	DET
cjfa-35471	763	15	firm	firm	NOUN
cjfa-35471	763	16	will	will	AUX
cjfa-35471	763	17	stop	stop	VERB
cjfa-35471	763	18	producing	produce	VERB
cjfa-35471	763	19	sooner	soon	ADV
cjfa-35471	763	20	and	and	CCONJ
cjfa-35471	763	21	start	start	VERB
cjfa-35471	763	22	producing	produce	VERB
cjfa-35471	763	23	later	later	ADV
cjfa-35471	763	24	than	than	ADP
cjfa-35471	763	25	in	in	ADP
cjfa-35471	763	26	the	the	DET
cjfa-35471	763	27	first	first	ADJ
cjfa-35471	763	28	case	case	NOUN
cjfa-35471	763	29	.	.	PUNCT
cjfa-35471	764	1	this	this	PRON
cjfa-35471	764	2	is	be	AUX
cjfa-35471	764	3	an	an	DET
cjfa-35471	764	4	important	important	ADJ
cjfa-35471	764	5	result	result	NOUN
cjfa-35471	764	6	because	because	SCONJ
cjfa-35471	764	7	it	it	PRON
cjfa-35471	764	8	indicates	indicate	VERB
cjfa-35471	764	9	that	that	SCONJ
cjfa-35471	764	10	introduction	introduction	NOUN
cjfa-35471	764	11	of	of	ADP
cjfa-35471	764	12	new	new	ADJ
cjfa-35471	764	13	technologies	technology	NOUN
cjfa-35471	764	14	which	which	PRON
cjfa-35471	764	15	reduces	reduce	VERB
cjfa-35471	764	16	the	the	DET
cjfa-35471	764	17	marginal	marginal	ADJ
cjfa-35471	764	18	costs	cost	NOUN
cjfa-35471	764	19	will	will	AUX
cjfa-35471	764	20	induce	induce	VERB
cjfa-35471	764	21	firms	firm	NOUN
cjfa-35471	764	22	to	to	PART
cjfa-35471	764	23	stop	stop	VERB
cjfa-35471	764	24	production	production	NOUN
cjfa-35471	764	25	sooner	soon	ADV
cjfa-35471	764	26	.	.	PUNCT
cjfa-35471	765	1	case	case	NOUN
cjfa-35471	765	2	iii	iii	X
cjfa-35471	765	3	:	:	PUNCT
cjfa-35471	765	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	765	5	𝑘	𝑘	PRON
cjfa-35471	765	6	𝑘	𝑘	NOUN
cjfa-35471	765	7	and	and	CCONJ
cjfa-35471	765	8	interest	interest	NOUN
cjfa-35471	765	9	rate	rate	NOUN
cjfa-35471	765	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	765	11	)	)	PUNCT
cjfa-35471	766	1	𝑘	𝑘	ADP
cjfa-35471	766	2	0.2	0.2	NUM
cjfa-35471	766	3	the	the	DET
cjfa-35471	766	4	inequality	inequality	NOUN
cjfa-35471	766	5	(	(	PUNCT
cjfa-35471	766	6	4	4	X
cjfa-35471	766	7	)	)	PUNCT
cjfa-35471	766	8	becomes	become	VERB
cjfa-35471	766	9	:	:	PUNCT
cjfa-35471	766	10	(	(	PUNCT
cjfa-35471	766	11	0.5	0.5	NUM
cjfa-35471	766	12	∗	∗	NOUN
cjfa-35471	766	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	767	1	+	+	CCONJ
cjfa-35471	767	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	767	3	)	)	PUNCT
cjfa-35471	767	4	−	−	PROPN
cjfa-35471	768	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	768	2	𝑐	𝑐	PROPN
cjfa-35471	768	3	2.5	2.5	NUM
cjfa-35471	768	4	+	+	CCONJ
cjfa-35471	768	5	0.2	0.2	NUM
cjfa-35471	768	6	�	�	NOUN
cjfa-35471	768	7	0.5	0.5	NUM
cjfa-35471	768	8	∗	∗	NOUN
cjfa-35471	768	9	𝑐	𝑐	PROPN
cjfa-35471	768	10	∗	∗	NOUN
cjfa-35471	768	11	(	(	PUNCT
cjfa-35471	768	12	4	4	NUM
cjfa-35471	768	13	+	+	SYM
cjfa-35471	768	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	768	15	)	)	PUNCT
cjfa-35471	768	16	�	�	PROPN
cjfa-35471	768	17	�	�	PROPN
cjfa-35471	768	18	−	−	NUM
cjfa-35471	768	19	2	2	NUM
cjfa-35471	768	20	∗	∗	NOUN
cjfa-35471	768	21	(	(	PUNCT
cjfa-35471	768	22	4	4	NUM
cjfa-35471	768	23	+	+	NUM
cjfa-35471	768	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	768	25	)	)	PUNCT
cjfa-35471	768	26	+	+	SYM
cjfa-35471	768	27	𝑘	𝑘	X
cjfa-35471	768	28	)	)	PUNCT
cjfa-35471	768	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	768	30	(	(	PUNCT
cjfa-35471	768	31	7	7	X
cjfa-35471	768	32	)	)	PUNCT
cjfa-35471	768	33	is	be	AUX
cjfa-35471	768	34	reduced	reduce	VERB
cjfa-35471	768	35	as	as	ADP
cjfa-35471	768	36	a	a	DET
cjfa-35471	768	37	whole	whole	NOUN
cjfa-35471	768	38	.	.	PUNCT
cjfa-35471	769	1	we	we	PRON
cjfa-35471	769	2	will	will	AUX
cjfa-35471	769	3	consider	consider	VERB
cjfa-35471	769	4	this	this	DET
cjfa-35471	769	5	last	last	ADJ
cjfa-35471	769	6	case	case	NOUN
cjfa-35471	769	7	assuming	assume	VERB
cjfa-35471	769	8	that	that	SCONJ
cjfa-35471	769	9	the	the	DET
cjfa-35471	769	10	new	new	ADJ
cjfa-35471	769	11	technology	technology	NOUN
cjfa-35471	769	12	reduces	reduce	VERB
cjfa-35471	769	13	the	the	DET
cjfa-35471	769	14	marginal	marginal	ADJ
cjfa-35471	769	15	cost	cost	NOUN
cjfa-35471	769	16	by	by	ADP
cjfa-35471	769	17	20	20	NUM
cjfa-35471	769	18	%	%	NOUN
cjfa-35471	769	19	.	.	PUNCT
cjfa-35471	770	1	this	this	PRON
cjfa-35471	770	2	implies	imply	VERB
cjfa-35471	770	3	that	that	SCONJ
cjfa-35471	770	4	the	the	DET
cjfa-35471	770	5	left	left	ADJ
cjfa-35471	770	6	-	-	PUNCT
cjfa-35471	770	7	hand	hand	NOUN
cjfa-35471	770	8	side	side	NOUN
cjfa-35471	770	9	of	of	ADP
cjfa-35471	770	10	inequality	inequality	NOUN
cjfa-35471	770	11	(	(	PUNCT
cjfa-35471	770	12	5	5	NUM
cjfa-35471	770	13	)	)	PUNCT
cjfa-35471	770	14	will	will	AUX
cjfa-35471	770	15	be	be	AUX
cjfa-35471	770	16	multiplies	multiplie	NOUN
cjfa-35471	770	17	by	by	ADP
cjfa-35471	770	18	0,8	0,8	NUM
cjfa-35471	770	19	.	.	PUNCT
cjfa-35471	771	1	then	then	ADV
cjfa-35471	771	2	the	the	DET
cjfa-35471	771	3	inequality	inequality	NOUN
cjfa-35471	771	4	(	(	PUNCT
cjfa-35471	771	5	4	4	X
cjfa-35471	771	6	)	)	PUNCT
cjfa-35471	771	7	becomes	become	VERB
cjfa-35471	771	8	:	:	PUNCT
cjfa-35471	771	9	source	source	NOUN
cjfa-35471	771	10	:	:	PUNCT
cjfa-35471	771	11	constructed	construct	VERB
cjfa-35471	771	12	by	by	ADP
cjfa-35471	771	13	authors	author	NOUN
cjfa-35471	771	14	.	.	PUNCT
cjfa-35471	772	1	case	case	NOUN
cjfa-35471	772	2	ii	ii	PROPN
cjfa-35471	772	3	:	:	PUNCT
cjfa-35471	772	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	772	5	𝑘	𝑘	PRON
cjfa-35471	772	6	𝑘	𝑘	NOUN
cjfa-35471	772	7	and	and	CCONJ
cjfa-35471	772	8	interest	interest	NOUN
cjfa-35471	772	9	rate	rate	NOUN
cjfa-35471	772	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	772	11	)	)	PUNCT
cjfa-35471	773	1	𝑘	𝑘	ADP
cjfa-35471	773	2	0	0	NUM
cjfa-35471	773	3	and	and	CCONJ
cjfa-35471	773	4	a	a	DET
cjfa-35471	773	5	new	new	ADJ
cjfa-35471	773	6	technology	technology	NOUN
cjfa-35471	773	7	i	i	PRON
cjfa-35471	773	8	introduced	introduce	VERB
cjfa-35471	773	9	.	.	PUNCT
cjfa-35471	774	1	the	the	DET
cjfa-35471	774	2	impact	impact	NOUN
cjfa-35471	774	3	of	of	ADP
cjfa-35471	774	4	new	new	ADJ
cjfa-35471	774	5	technology	technology	NOUN
cjfa-35471	774	6	will	will	AUX
cjfa-35471	774	7	be	be	AUX
cjfa-35471	774	8	analyzed	analyze	VERB
cjfa-35471	774	9	in	in	ADP
cjfa-35471	774	10	three	three	NUM
cjfa-35471	774	11	cases	case	NOUN
cjfa-35471	774	12	:	:	PUNCT
cjfa-35471	774	13	1	1	X
cjfa-35471	774	14	.	.	PUNCT
cjfa-35471	774	15	fixed	fix	VERB
cjfa-35471	774	16	costs	cost	NOUN
cjfa-35471	774	17	(	(	PUNCT
cjfa-35471	774	18	the	the	DET
cjfa-35471	774	19	term	term	NOUN
cjfa-35471	774	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	774	21	in	in	ADP
cjfa-35471	774	22	the	the	DET
cjfa-35471	774	23	cost	cost	NOUN
cjfa-35471	774	24	function	function	NOUN
cjfa-35471	774	25	)	)	PUNCT
cjfa-35471	774	26	is	be	AUX
cjfa-35471	774	27	reduced	reduce	VERB
cjfa-35471	774	28	.	.	PUNCT
cjfa-35471	775	1	there	there	PRON
cjfa-35471	775	2	will	will	AUX
cjfa-35471	775	3	be	be	AUX
cjfa-35471	775	4	no	no	DET
cjfa-35471	775	5	impact	impact	NOUN
cjfa-35471	775	6	on	on	ADP
cjfa-35471	775	7	production	production	NOUN
cjfa-35471	775	8	decision	decision	NOUN
cjfa-35471	775	9	since	since	SCONJ
cjfa-35471	775	10	the	the	DET
cjfa-35471	775	11	fixed	fix	VERB
cjfa-35471	775	12	costs	cost	NOUN
cjfa-35471	775	13	are	be	AUX
cjfa-35471	775	14	already	already	ADV
cjfa-35471	775	15	shown	show	VERB
cjfa-35471	775	16	to	to	PART
cjfa-35471	775	17	have	have	VERB
cjfa-35471	775	18	on	on	ADP
cjfa-35471	775	19	impact	impact	NOUN
cjfa-35471	775	20	on	on	ADP
cjfa-35471	775	21	the	the	DET
cjfa-35471	775	22	inequality	inequality	NOUN
cjfa-35471	775	23	(	(	PUNCT
cjfa-35471	775	24	5	5	NUM
cjfa-35471	775	25	)	)	PUNCT
cjfa-35471	775	26	.	.	PUNCT
cjfa-35471	776	1	2	2	X
cjfa-35471	776	2	.	.	X
cjfa-35471	776	3	only	only	ADV
cjfa-35471	776	4	the	the	DET
cjfa-35471	776	5	constant	constant	ADJ
cjfa-35471	776	6	term	term	NOUN
cjfa-35471	776	7	(	(	PUNCT
cjfa-35471	776	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	776	9	)	)	PUNCT
cjfa-35471	776	10	in	in	ADP
cjfa-35471	776	11	the	the	DET
cjfa-35471	776	12	marginal	marginal	ADJ
cjfa-35471	776	13	cost	cost	NOUN
cjfa-35471	776	14	,	,	PUNCT
cjfa-35471	776	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	776	16	𝑘	𝑘	PRON
cjfa-35471	776	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	776	18	�	�	PROPN
cjfa-35471	776	19	+	+	CCONJ
cjfa-35471	776	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	777	1	+	+	CCONJ
cjfa-35471	777	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	777	3	is	be	AUX
cjfa-35471	777	4	reduced	reduce	VERB
cjfa-35471	777	5	.	.	PUNCT
cjfa-35471	778	1	the	the	DET
cjfa-35471	778	2	left	left	ADJ
cjfa-35471	778	3	-	-	PUNCT
cjfa-35471	778	4	hand	hand	NOUN
cjfa-35471	778	5	side	side	NOUN
cjfa-35471	778	6	of	of	ADP
cjfa-35471	778	7	inequality	inequality	NOUN
cjfa-35471	778	8	(	(	PUNCT
cjfa-35471	778	9	5	5	NUM
cjfa-35471	778	10	)	)	PUNCT
cjfa-35471	778	11	will	will	AUX
cjfa-35471	778	12	not	not	PART
cjfa-35471	778	13	change	change	VERB
cjfa-35471	778	14	since	since	SCONJ
cjfa-35471	778	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	778	16	)	)	PUNCT
cjfa-35471	778	17	does	do	AUX
cjfa-35471	778	18	not	not	PART
cjfa-35471	778	19	depend	depend	VERB
cjfa-35471	778	20	on	on	ADP
cjfa-35471	778	21	the	the	DET
cjfa-35471	778	22	constant	constant	ADJ
cjfa-35471	778	23	term	term	NOUN
cjfa-35471	778	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	778	25	in	in	ADP
cjfa-35471	778	26	the	the	DET
cjfa-35471	778	27	production	production	NOUN
cjfa-35471	778	28	cost	cost	NOUN
cjfa-35471	778	29	function	function	NOUN
cjfa-35471	778	30	.	.	PUNCT
cjfa-35471	779	1	the	the	DET
cjfa-35471	779	2	right	right	ADJ
cjfa-35471	779	3	-	-	PUNCT
cjfa-35471	779	4	hand	hand	NOUN
cjfa-35471	779	5	side	side	NOUN
cjfa-35471	779	6	will	will	AUX
cjfa-35471	779	7	be	be	AUX
cjfa-35471	779	8	lower	low	ADJ
cjfa-35471	779	9	since	since	SCONJ
cjfa-35471	779	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	779	11	is	be	AUX
cjfa-35471	779	12	lower	low	ADJ
cjfa-35471	779	13	.	.	PUNCT
cjfa-35471	780	1	therefore	therefore	ADV
cjfa-35471	780	2	,	,	PUNCT
cjfa-35471	780	3	the	the	DET
cjfa-35471	780	4	decision	decision	NOUN
cjfa-35471	780	5	of	of	ADP
cjfa-35471	780	6	the	the	DET
cjfa-35471	780	7	firm	firm	NOUN
cjfa-35471	780	8	will	will	AUX
cjfa-35471	780	9	depend	depend	VERB
cjfa-35471	780	10	on	on	ADP
cjfa-35471	780	11	how	how	SCONJ
cjfa-35471	780	12	much	much	ADJ
cjfa-35471	780	13	the	the	DET
cjfa-35471	780	14	new	new	ADJ
cjfa-35471	780	15	technology	technology	NOUN
cjfa-35471	780	16	reduces	reduce	VERB
cjfa-35471	780	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	780	18	the	the	DET
cjfa-35471	780	19	firm	firm	NOUN
cjfa-35471	780	20	will	will	AUX
cjfa-35471	780	21	start	start	VERB
cjfa-35471	780	22	to	to	PART
cjfa-35471	780	23	produce	produce	VERB
cjfa-35471	780	24	sooner	soon	ADV
cjfa-35471	780	25	if	if	SCONJ
cjfa-35471	780	26	the	the	DET
cjfa-35471	780	27	reduction	reduction	NOUN
cjfa-35471	780	28	in	in	ADP
cjfa-35471	780	29	c	c	PROPN
cjfa-35471	780	30	is	be	AUX
cjfa-35471	780	31	large	large	ADJ
cjfa-35471	780	32	enough	enough	ADV
cjfa-35471	780	33	to	to	PART
cjfa-35471	780	34	violate	violate	VERB
cjfa-35471	780	35	the	the	DET
cjfa-35471	780	36	inequality	inequality	NOUN
cjfa-35471	780	37	.	.	PUNCT
cjfa-35471	781	1	3	3	X
cjfa-35471	781	2	.	.	X
cjfa-35471	781	3	marginal	marginal	ADJ
cjfa-35471	781	4	cost	cost	NOUN
cjfa-35471	781	5	function	function	NOUN
cjfa-35471	781	6	,	,	PUNCT
cjfa-35471	781	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	781	8	)	)	PUNCT
cjfa-35471	781	9	,	,	PUNCT
cjfa-35471	781	10	is	be	AUX
cjfa-35471	781	11	reduced	reduce	VERB
cjfa-35471	781	12	as	as	ADP
cjfa-35471	781	13	a	a	DET
cjfa-35471	781	14	whole	whole	NOUN
cjfa-35471	781	15	.	.	PUNCT
cjfa-35471	782	1	we	we	PRON
cjfa-35471	782	2	will	will	AUX
cjfa-35471	782	3	consider	consider	VERB
cjfa-35471	782	4	this	this	DET
cjfa-35471	782	5	last	last	ADJ
cjfa-35471	782	6	case	case	NOUN
cjfa-35471	782	7	assuming	assume	VERB
cjfa-35471	782	8	that	that	SCONJ
cjfa-35471	782	9	the	the	DET
cjfa-35471	782	10	new	new	ADJ
cjfa-35471	782	11	technology	technology	NOUN
cjfa-35471	782	12	reduces	reduce	VERB
cjfa-35471	782	13	the	the	DET
cjfa-35471	782	14	marginal	marginal	ADJ
cjfa-35471	782	15	cost	cost	NOUN
cjfa-35471	782	16	by	by	ADP
cjfa-35471	782	17	20	20	NUM
cjfa-35471	782	18	%	%	NOUN
cjfa-35471	782	19	.	.	PUNCT
cjfa-35471	783	1	this	this	PRON
cjfa-35471	783	2	implies	imply	VERB
cjfa-35471	783	3	that	that	SCONJ
cjfa-35471	783	4	the	the	DET
cjfa-35471	783	5	left	left	ADJ
cjfa-35471	783	6	-	-	PUNCT
cjfa-35471	783	7	hand	hand	NOUN
cjfa-35471	783	8	side	side	NOUN
cjfa-35471	783	9	of	of	ADP
cjfa-35471	783	10	inequality	inequality	NOUN
cjfa-35471	783	11	(	(	PUNCT
cjfa-35471	783	12	5	5	NUM
cjfa-35471	783	13	)	)	PUNCT
cjfa-35471	783	14	will	will	AUX
cjfa-35471	783	15	be	be	AUX
cjfa-35471	783	16	multiplies	multiplie	NOUN
cjfa-35471	783	17	by	by	ADP
cjfa-35471	783	18	0.8	0.8	NUM
cjfa-35471	783	19	.	.	PUNCT
cjfa-35471	784	1	then	then	ADV
cjfa-35471	784	2	the	the	DET
cjfa-35471	784	3	inequality	inequality	NOUN
cjfa-35471	784	4	(	(	PUNCT
cjfa-35471	784	5	4	4	X
cjfa-35471	784	6	)	)	PUNCT
cjfa-35471	784	7	becomes	become	VERB
cjfa-35471	784	8	:	:	PUNCT
cjfa-35471	784	9	(	(	PUNCT
cjfa-35471	784	10	0.5	0.5	NUM
cjfa-35471	784	11	∗	∗	NOUN
cjfa-35471	784	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	785	1	+	+	CCONJ
cjfa-35471	785	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	785	3	)	)	PUNCT
cjfa-35471	785	4	−	−	PROPN
cjfa-35471	786	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	786	2	∗	∗	VERB
cjfa-35471	786	3	0.8	0.8	NUM
cjfa-35471	786	4	𝑐	𝑐	PROPN
cjfa-35471	786	5	2.5	2.5	NUM
cjfa-35471	786	6	(	(	PUNCT
cjfa-35471	786	7	6	6	NUM
cjfa-35471	786	8	)	)	PUNCT
cjfa-35471	786	9	therefore	therefore	ADV
cjfa-35471	786	10	,	,	PUNCT
cjfa-35471	786	11	for	for	ADP
cjfa-35471	786	12	the	the	DET
cjfa-35471	786	13	same	same	ADJ
cjfa-35471	786	14	values	value	NOUN
cjfa-35471	786	15	for	for	ADP
cjfa-35471	786	16	the	the	DET
cjfa-35471	786	17	constants	constant	NOUN
cjfa-35471	786	18	,	,	PUNCT
cjfa-35471	786	19	the	the	DET
cjfa-35471	786	20	graphs	graph	NOUN
cjfa-35471	786	21	of	of	ADP
cjfa-35471	786	22	both	both	DET
cjfa-35471	786	23	sides	side	NOUN
cjfa-35471	786	24	of	of	ADP
cjfa-35471	786	25	inequality	inequality	NOUN
cjfa-35471	786	26	above	above	ADV
cjfa-35471	786	27	and	and	CCONJ
cjfa-35471	786	28	the	the	DET
cjfa-35471	786	29	sales	sale	NOUN
cjfa-35471	786	30	are	be	AUX
cjfa-35471	786	31	presented	present	VERB
cjfa-35471	786	32	below	below	ADV
cjfa-35471	786	33	(	(	PUNCT
cjfa-35471	786	34	figure	figure	NOUN
cjfa-35471	786	35	2	2	NUM
cjfa-35471	786	36	)	)	PUNCT
cjfa-35471	786	37	.	.	PUNCT
cjfa-35471	787	1	inequality	inequality	NOUN
cjfa-35471	787	2	(	(	PUNCT
cjfa-35471	787	3	6	6	NUM
cjfa-35471	787	4	)	)	PUNCT
cjfa-35471	787	5	implies	imply	VERB
cjfa-35471	787	6	the	the	DET
cjfa-35471	787	7	same	same	ADJ
cjfa-35471	787	8	type	type	NOUN
cjfa-35471	787	9	of	of	ADP
cjfa-35471	787	10	results	result	NOUN
cjfa-35471	787	11	as	as	ADP
cjfa-35471	787	12	in	in	ADP
cjfa-35471	787	13	the	the	DET
cjfa-35471	787	14	previous	previous	ADJ
cjfa-35471	787	15	case	case	NOUN
cjfa-35471	787	16	.	.	PUNCT
cjfa-35471	788	1	however	however	ADV
cjfa-35471	788	2	,	,	PUNCT
cjfa-35471	788	3	it	it	PRON
cjfa-35471	788	4	is	be	AUX
cjfa-35471	788	5	evident	evident	ADJ
cjfa-35471	788	6	from	from	ADP
cjfa-35471	788	7	the	the	DET
cjfa-35471	788	8	graphs	graph	NOUN
cjfa-35471	788	9	that	that	SCONJ
cjfa-35471	788	10	in	in	ADP
cjfa-35471	788	11	the	the	DET
cjfa-35471	788	12	second	second	ADJ
cjfa-35471	788	13	case	case	NOUN
cjfa-35471	788	14	the	the	DET
cjfa-35471	788	15	firm	firm	NOUN
cjfa-35471	788	16	will	will	AUX
cjfa-35471	788	17	stop	stop	VERB
cjfa-35471	788	18	producing	produce	VERB
cjfa-35471	788	19	sooner	soon	ADV
cjfa-35471	788	20	and	and	CCONJ
cjfa-35471	788	21	start	start	VERB
cjfa-35471	788	22	producing	produce	VERB
cjfa-35471	788	23	later	later	ADV
cjfa-35471	788	24	than	than	ADP
cjfa-35471	788	25	in	in	ADP
cjfa-35471	788	26	the	the	DET
cjfa-35471	788	27	first	first	ADJ
cjfa-35471	788	28	case	case	NOUN
cjfa-35471	788	29	.	.	PUNCT
cjfa-35471	789	1	this	this	PRON
cjfa-35471	789	2	is	be	AUX
cjfa-35471	789	3	an	an	DET
cjfa-35471	789	4	important	important	ADJ
cjfa-35471	789	5	result	result	NOUN
cjfa-35471	789	6	because	because	SCONJ
cjfa-35471	789	7	it	it	PRON
cjfa-35471	789	8	indicates	indicate	VERB
cjfa-35471	789	9	that	that	SCONJ
cjfa-35471	789	10	introduction	introduction	NOUN
cjfa-35471	789	11	of	of	ADP
cjfa-35471	789	12	new	new	ADJ
cjfa-35471	789	13	technologies	technology	NOUN
cjfa-35471	789	14	which	which	PRON
cjfa-35471	789	15	reduces	reduce	VERB
cjfa-35471	789	16	the	the	DET
cjfa-35471	789	17	marginal	marginal	ADJ
cjfa-35471	789	18	costs	cost	NOUN
cjfa-35471	789	19	will	will	AUX
cjfa-35471	789	20	induce	induce	VERB
cjfa-35471	789	21	firms	firm	NOUN
cjfa-35471	789	22	to	to	PART
cjfa-35471	789	23	stop	stop	VERB
cjfa-35471	789	24	production	production	NOUN
cjfa-35471	789	25	sooner	soon	ADV
cjfa-35471	789	26	.	.	PUNCT
cjfa-35471	790	1	case	case	NOUN
cjfa-35471	790	2	iii	iii	X
cjfa-35471	790	3	:	:	PUNCT
cjfa-35471	790	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	790	5	𝑘	𝑘	PRON
cjfa-35471	790	6	𝑘	𝑘	NOUN
cjfa-35471	790	7	and	and	CCONJ
cjfa-35471	790	8	interest	interest	NOUN
cjfa-35471	790	9	rate	rate	NOUN
cjfa-35471	790	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	790	11	)	)	PUNCT
cjfa-35471	791	1	𝑘	𝑘	ADP
cjfa-35471	791	2	0.2	0.2	NUM
cjfa-35471	791	3	the	the	DET
cjfa-35471	791	4	inequality	inequality	NOUN
cjfa-35471	791	5	(	(	PUNCT
cjfa-35471	791	6	4	4	X
cjfa-35471	791	7	)	)	PUNCT
cjfa-35471	791	8	becomes	become	VERB
cjfa-35471	791	9	:	:	PUNCT
cjfa-35471	791	10	(	(	PUNCT
cjfa-35471	791	11	0.5	0.5	NUM
cjfa-35471	791	12	∗	∗	NOUN
cjfa-35471	791	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	792	1	+	+	CCONJ
cjfa-35471	792	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	792	3	)	)	PUNCT
cjfa-35471	792	4	−	−	PROPN
cjfa-35471	793	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	793	2	𝑐	𝑐	PROPN
cjfa-35471	793	3	2.5	2.5	NUM
cjfa-35471	793	4	+	+	CCONJ
cjfa-35471	793	5	0.2	0.2	NUM
cjfa-35471	793	6	�	�	NOUN
cjfa-35471	793	7	0.5	0.5	NUM
cjfa-35471	793	8	∗	∗	NOUN
cjfa-35471	793	9	𝑐	𝑐	PROPN
cjfa-35471	793	10	∗	∗	NOUN
cjfa-35471	793	11	(	(	PUNCT
cjfa-35471	793	12	4	4	NUM
cjfa-35471	793	13	+	+	SYM
cjfa-35471	793	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	793	15	)	)	PUNCT
cjfa-35471	793	16	�	�	PROPN
cjfa-35471	793	17	�	�	PROPN
cjfa-35471	793	18	−	−	NUM
cjfa-35471	793	19	2	2	NUM
cjfa-35471	793	20	∗	∗	NOUN
cjfa-35471	793	21	(	(	PUNCT
cjfa-35471	793	22	4	4	NUM
cjfa-35471	793	23	+	+	NUM
cjfa-35471	793	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	793	25	)	)	PUNCT
cjfa-35471	793	26	+	+	SYM
cjfa-35471	793	27	𝑘	𝑘	X
cjfa-35471	793	28	)	)	PUNCT
cjfa-35471	793	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	793	30	(	(	PUNCT
cjfa-35471	793	31	7	7	NUM
cjfa-35471	793	32	)	)	PUNCT
cjfa-35471	793	33	(	(	PUNCT
cjfa-35471	793	34	6	6	NUM
cjfa-35471	793	35	)	)	PUNCT
cjfa-35471	793	36	therefore	therefore	ADV
cjfa-35471	793	37	,	,	PUNCT
cjfa-35471	793	38	for	for	ADP
cjfa-35471	793	39	the	the	DET
cjfa-35471	793	40	same	same	ADJ
cjfa-35471	793	41	values	value	NOUN
cjfa-35471	793	42	for	for	ADP
cjfa-35471	793	43	the	the	DET
cjfa-35471	793	44	constants	constant	NOUN
cjfa-35471	793	45	,	,	PUNCT
cjfa-35471	793	46	the	the	DET
cjfa-35471	793	47	graphs	graph	NOUN
cjfa-35471	793	48	of	of	ADP
cjfa-35471	793	49	both	both	DET
cjfa-35471	793	50	sides	side	NOUN
cjfa-35471	793	51	of	of	ADP
cjfa-35471	793	52	inequality	inequality	NOUN
cjfa-35471	793	53	above	above	ADV
cjfa-35471	793	54	and	and	CCONJ
cjfa-35471	793	55	the	the	DET
cjfa-35471	793	56	sales	sale	NOUN
cjfa-35471	793	57	are	be	AUX
cjfa-35471	793	58	presented	present	VERB
cjfa-35471	793	59	below	below	ADV
cjfa-35471	793	60	(	(	PUNCT
cjfa-35471	793	61	figure	figure	NOUN
cjfa-35471	793	62	2	2	NUM
cjfa-35471	793	63	)	)	PUNCT
cjfa-35471	793	64	.	.	PUNCT
cjfa-35471	794	1	inequality	inequality	NOUN
cjfa-35471	794	2	(	(	PUNCT
cjfa-35471	794	3	6	6	NUM
cjfa-35471	794	4	)	)	PUNCT
cjfa-35471	794	5	implies	imply	VERB
cjfa-35471	794	6	the	the	DET
cjfa-35471	794	7	same	same	ADJ
cjfa-35471	794	8	type	type	NOUN
cjfa-35471	794	9	of	of	ADP
cjfa-35471	794	10	results	result	NOUN
cjfa-35471	794	11	as	as	ADP
cjfa-35471	794	12	in	in	ADP
cjfa-35471	794	13	the	the	DET
cjfa-35471	794	14	previous	previous	ADJ
cjfa-35471	794	15	case	case	NOUN
cjfa-35471	794	16	.	.	PUNCT
cjfa-35471	795	1	however	however	ADV
cjfa-35471	795	2	,	,	PUNCT
cjfa-35471	795	3	it	it	PRON
cjfa-35471	795	4	is	be	AUX
cjfa-35471	795	5	evident	evident	ADJ
cjfa-35471	795	6	from	from	ADP
cjfa-35471	795	7	the	the	DET
cjfa-35471	795	8	graphs	graph	NOUN
cjfa-35471	795	9	that	that	SCONJ
cjfa-35471	795	10	in	in	ADP
cjfa-35471	795	11	the	the	DET
cjfa-35471	795	12	second	second	ADJ
cjfa-35471	795	13	case	case	NOUN
cjfa-35471	795	14	the	the	DET
cjfa-35471	795	15	firm	firm	NOUN
cjfa-35471	795	16	will	will	AUX
cjfa-35471	795	17	stop	stop	VERB
cjfa-35471	795	18	producing	produce	VERB
cjfa-35471	795	19	sooner	soon	ADV
cjfa-35471	795	20	and	and	CCONJ
cjfa-35471	795	21	start	start	VERB
cjfa-35471	795	22	producing	produce	VERB
cjfa-35471	795	23	later	later	ADV
cjfa-35471	795	24	than	than	ADP
cjfa-35471	795	25	in	in	ADP
cjfa-35471	795	26	the	the	DET
cjfa-35471	795	27	first	first	ADJ
cjfa-35471	795	28	case	case	NOUN
cjfa-35471	795	29	.	.	PUNCT
cjfa-35471	796	1	this	this	PRON
cjfa-35471	796	2	is	be	AUX
cjfa-35471	796	3	an	an	DET
cjfa-35471	796	4	important	important	ADJ
cjfa-35471	796	5	result	result	NOUN
cjfa-35471	796	6	because	because	SCONJ
cjfa-35471	796	7	it	it	PRON
cjfa-35471	796	8	indicates	indicate	VERB
cjfa-35471	796	9	that	that	SCONJ
cjfa-35471	796	10	introduction	introduction	NOUN
cjfa-35471	796	11	of	of	ADP
cjfa-35471	796	12	new	new	ADJ
cjfa-35471	796	13	technologies	technology	NOUN
cjfa-35471	796	14	which	which	PRON
cjfa-35471	796	15	reduces	reduce	VERB
cjfa-35471	796	16	the	the	DET
cjfa-35471	796	17	marginal	marginal	ADJ
cjfa-35471	796	18	costs	cost	NOUN
cjfa-35471	796	19	will	will	AUX
cjfa-35471	796	20	induce	induce	VERB
cjfa-35471	796	21	firms	firm	NOUN
cjfa-35471	796	22	to	to	PART
cjfa-35471	796	23	stop	stop	VERB
cjfa-35471	796	24	production	production	NOUN
cjfa-35471	796	25	sooner	soon	ADV
cjfa-35471	796	26	.	.	PUNCT
cjfa-35471	797	1	case	case	NOUN
cjfa-35471	797	2	iii	iii	NOUN
cjfa-35471	797	3	:	:	PUNCT
cjfa-35471	797	4	k	k	NOUN
cjfa-35471	797	5	=	=	SYM
cjfa-35471	797	6	1	1	NUM
cjfa-35471	797	7	and	and	CCONJ
cjfa-35471	797	8	interest	interest	NOUN
cjfa-35471	797	9	rate	rate	NOUN
cjfa-35471	797	10	f(t	f(t	NOUN
cjfa-35471	797	11	)	)	PUNCT
cjfa-35471	797	12	=	=	SYM
cjfa-35471	797	13	0.2	0.2	NUM
cjfa-35471	797	14	the	the	DET
cjfa-35471	797	15	inequality	inequality	NOUN
cjfa-35471	797	16	(	(	PUNCT
cjfa-35471	797	17	4	4	X
cjfa-35471	797	18	)	)	PUNCT
cjfa-35471	797	19	becomes	become	VERB
cjfa-35471	797	20	:	:	PUNCT
cjfa-35471	797	21	source	source	NOUN
cjfa-35471	797	22	:	:	PUNCT
cjfa-35471	797	23	constructed	construct	VERB
cjfa-35471	797	24	by	by	ADP
cjfa-35471	797	25	authors	author	NOUN
cjfa-35471	797	26	.	.	PUNCT
cjfa-35471	798	1	case	case	NOUN
cjfa-35471	798	2	ii	ii	PROPN
cjfa-35471	798	3	:	:	PUNCT
cjfa-35471	798	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	798	5	𝑘	𝑘	PRON
cjfa-35471	798	6	𝑘	𝑘	NOUN
cjfa-35471	798	7	and	and	CCONJ
cjfa-35471	798	8	interest	interest	NOUN
cjfa-35471	798	9	rate	rate	NOUN
cjfa-35471	798	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	798	11	)	)	PUNCT
cjfa-35471	799	1	𝑘	𝑘	ADP
cjfa-35471	799	2	0	0	NUM
cjfa-35471	799	3	and	and	CCONJ
cjfa-35471	799	4	a	a	DET
cjfa-35471	799	5	new	new	ADJ
cjfa-35471	799	6	technology	technology	NOUN
cjfa-35471	799	7	i	i	PRON
cjfa-35471	799	8	introduced	introduce	VERB
cjfa-35471	799	9	.	.	PUNCT
cjfa-35471	800	1	the	the	DET
cjfa-35471	800	2	impact	impact	NOUN
cjfa-35471	800	3	of	of	ADP
cjfa-35471	800	4	new	new	ADJ
cjfa-35471	800	5	technology	technology	NOUN
cjfa-35471	800	6	will	will	AUX
cjfa-35471	800	7	be	be	AUX
cjfa-35471	800	8	analyzed	analyze	VERB
cjfa-35471	800	9	in	in	ADP
cjfa-35471	800	10	three	three	NUM
cjfa-35471	800	11	cases	case	NOUN
cjfa-35471	800	12	:	:	PUNCT
cjfa-35471	800	13	1	1	X
cjfa-35471	800	14	.	.	PUNCT
cjfa-35471	800	15	fixed	fix	VERB
cjfa-35471	800	16	costs	cost	NOUN
cjfa-35471	800	17	(	(	PUNCT
cjfa-35471	800	18	the	the	DET
cjfa-35471	800	19	term	term	NOUN
cjfa-35471	800	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	800	21	in	in	ADP
cjfa-35471	800	22	the	the	DET
cjfa-35471	800	23	cost	cost	NOUN
cjfa-35471	800	24	function	function	NOUN
cjfa-35471	800	25	)	)	PUNCT
cjfa-35471	800	26	is	be	AUX
cjfa-35471	800	27	reduced	reduce	VERB
cjfa-35471	800	28	.	.	PUNCT
cjfa-35471	801	1	there	there	PRON
cjfa-35471	801	2	will	will	AUX
cjfa-35471	801	3	be	be	AUX
cjfa-35471	801	4	no	no	DET
cjfa-35471	801	5	impact	impact	NOUN
cjfa-35471	801	6	on	on	ADP
cjfa-35471	801	7	production	production	NOUN
cjfa-35471	801	8	decision	decision	NOUN
cjfa-35471	801	9	since	since	SCONJ
cjfa-35471	801	10	the	the	DET
cjfa-35471	801	11	fixed	fix	VERB
cjfa-35471	801	12	costs	cost	NOUN
cjfa-35471	801	13	are	be	AUX
cjfa-35471	801	14	already	already	ADV
cjfa-35471	801	15	shown	show	VERB
cjfa-35471	801	16	to	to	PART
cjfa-35471	801	17	have	have	VERB
cjfa-35471	801	18	on	on	ADP
cjfa-35471	801	19	impact	impact	NOUN
cjfa-35471	801	20	on	on	ADP
cjfa-35471	801	21	the	the	DET
cjfa-35471	801	22	inequality	inequality	NOUN
cjfa-35471	801	23	(	(	PUNCT
cjfa-35471	801	24	5	5	NUM
cjfa-35471	801	25	)	)	PUNCT
cjfa-35471	801	26	.	.	PUNCT
cjfa-35471	802	1	2	2	X
cjfa-35471	802	2	.	.	X
cjfa-35471	802	3	only	only	ADV
cjfa-35471	802	4	the	the	DET
cjfa-35471	802	5	constant	constant	ADJ
cjfa-35471	802	6	term	term	NOUN
cjfa-35471	802	7	(	(	PUNCT
cjfa-35471	802	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	802	9	)	)	PUNCT
cjfa-35471	802	10	in	in	ADP
cjfa-35471	802	11	the	the	DET
cjfa-35471	802	12	marginal	marginal	ADJ
cjfa-35471	802	13	cost	cost	NOUN
cjfa-35471	802	14	,	,	PUNCT
cjfa-35471	802	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	802	16	𝑘	𝑘	PRON
cjfa-35471	802	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	802	18	�	�	PROPN
cjfa-35471	802	19	+	+	CCONJ
cjfa-35471	802	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	803	1	+	+	CCONJ
cjfa-35471	803	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	803	3	is	be	AUX
cjfa-35471	803	4	reduced	reduce	VERB
cjfa-35471	803	5	.	.	PUNCT
cjfa-35471	804	1	the	the	DET
cjfa-35471	804	2	left	left	ADJ
cjfa-35471	804	3	-	-	PUNCT
cjfa-35471	804	4	hand	hand	NOUN
cjfa-35471	804	5	side	side	NOUN
cjfa-35471	804	6	of	of	ADP
cjfa-35471	804	7	inequality	inequality	NOUN
cjfa-35471	804	8	(	(	PUNCT
cjfa-35471	804	9	5	5	NUM
cjfa-35471	804	10	)	)	PUNCT
cjfa-35471	804	11	will	will	AUX
cjfa-35471	804	12	not	not	PART
cjfa-35471	804	13	change	change	VERB
cjfa-35471	804	14	since	since	SCONJ
cjfa-35471	804	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	804	16	)	)	PUNCT
cjfa-35471	804	17	does	do	AUX
cjfa-35471	804	18	not	not	PART
cjfa-35471	804	19	depend	depend	VERB
cjfa-35471	804	20	on	on	ADP
cjfa-35471	804	21	the	the	DET
cjfa-35471	804	22	constant	constant	ADJ
cjfa-35471	804	23	term	term	NOUN
cjfa-35471	804	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	804	25	in	in	ADP
cjfa-35471	804	26	the	the	DET
cjfa-35471	804	27	production	production	NOUN
cjfa-35471	804	28	cost	cost	NOUN
cjfa-35471	804	29	function	function	NOUN
cjfa-35471	804	30	.	.	PUNCT
cjfa-35471	805	1	the	the	DET
cjfa-35471	805	2	right	right	ADJ
cjfa-35471	805	3	-	-	PUNCT
cjfa-35471	805	4	hand	hand	NOUN
cjfa-35471	805	5	side	side	NOUN
cjfa-35471	805	6	will	will	AUX
cjfa-35471	805	7	be	be	AUX
cjfa-35471	805	8	lower	low	ADJ
cjfa-35471	805	9	since	since	SCONJ
cjfa-35471	805	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	805	11	is	be	AUX
cjfa-35471	805	12	lower	low	ADJ
cjfa-35471	805	13	.	.	PUNCT
cjfa-35471	806	1	therefore	therefore	ADV
cjfa-35471	806	2	,	,	PUNCT
cjfa-35471	806	3	the	the	DET
cjfa-35471	806	4	decision	decision	NOUN
cjfa-35471	806	5	of	of	ADP
cjfa-35471	806	6	the	the	DET
cjfa-35471	806	7	firm	firm	NOUN
cjfa-35471	806	8	will	will	AUX
cjfa-35471	806	9	depend	depend	VERB
cjfa-35471	806	10	on	on	ADP
cjfa-35471	806	11	how	how	SCONJ
cjfa-35471	806	12	much	much	ADJ
cjfa-35471	806	13	the	the	DET
cjfa-35471	806	14	new	new	ADJ
cjfa-35471	806	15	technology	technology	NOUN
cjfa-35471	806	16	reduces	reduce	VERB
cjfa-35471	806	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	806	18	the	the	DET
cjfa-35471	806	19	firm	firm	NOUN
cjfa-35471	806	20	will	will	AUX
cjfa-35471	806	21	start	start	VERB
cjfa-35471	806	22	to	to	PART
cjfa-35471	806	23	produce	produce	VERB
cjfa-35471	806	24	sooner	soon	ADV
cjfa-35471	806	25	if	if	SCONJ
cjfa-35471	806	26	the	the	DET
cjfa-35471	806	27	reduction	reduction	NOUN
cjfa-35471	806	28	in	in	ADP
cjfa-35471	806	29	c	c	PROPN
cjfa-35471	806	30	is	be	AUX
cjfa-35471	806	31	large	large	ADJ
cjfa-35471	806	32	enough	enough	ADV
cjfa-35471	806	33	to	to	PART
cjfa-35471	806	34	violate	violate	VERB
cjfa-35471	806	35	the	the	DET
cjfa-35471	806	36	inequality	inequality	NOUN
cjfa-35471	806	37	.	.	PUNCT
cjfa-35471	807	1	3	3	X
cjfa-35471	807	2	.	.	X
cjfa-35471	807	3	marginal	marginal	ADJ
cjfa-35471	807	4	cost	cost	NOUN
cjfa-35471	807	5	function	function	NOUN
cjfa-35471	807	6	,	,	PUNCT
cjfa-35471	807	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	807	8	)	)	PUNCT
cjfa-35471	807	9	,	,	PUNCT
cjfa-35471	807	10	is	be	AUX
cjfa-35471	807	11	reduced	reduce	VERB
cjfa-35471	807	12	as	as	ADP
cjfa-35471	807	13	a	a	DET
cjfa-35471	807	14	whole	whole	NOUN
cjfa-35471	807	15	.	.	PUNCT
cjfa-35471	808	1	we	we	PRON
cjfa-35471	808	2	will	will	AUX
cjfa-35471	808	3	consider	consider	VERB
cjfa-35471	808	4	this	this	DET
cjfa-35471	808	5	last	last	ADJ
cjfa-35471	808	6	case	case	NOUN
cjfa-35471	808	7	assuming	assume	VERB
cjfa-35471	808	8	that	that	SCONJ
cjfa-35471	808	9	the	the	DET
cjfa-35471	808	10	new	new	ADJ
cjfa-35471	808	11	technology	technology	NOUN
cjfa-35471	808	12	reduces	reduce	VERB
cjfa-35471	808	13	the	the	DET
cjfa-35471	808	14	marginal	marginal	ADJ
cjfa-35471	808	15	cost	cost	NOUN
cjfa-35471	808	16	by	by	ADP
cjfa-35471	808	17	20	20	NUM
cjfa-35471	808	18	%	%	NOUN
cjfa-35471	808	19	.	.	PUNCT
cjfa-35471	809	1	this	this	PRON
cjfa-35471	809	2	implies	imply	VERB
cjfa-35471	809	3	that	that	SCONJ
cjfa-35471	809	4	the	the	DET
cjfa-35471	809	5	left	left	ADJ
cjfa-35471	809	6	-	-	PUNCT
cjfa-35471	809	7	hand	hand	NOUN
cjfa-35471	809	8	side	side	NOUN
cjfa-35471	809	9	of	of	ADP
cjfa-35471	809	10	inequality	inequality	NOUN
cjfa-35471	809	11	(	(	PUNCT
cjfa-35471	809	12	5	5	NUM
cjfa-35471	809	13	)	)	PUNCT
cjfa-35471	809	14	will	will	AUX
cjfa-35471	809	15	be	be	AUX
cjfa-35471	809	16	multiplies	multiplie	NOUN
cjfa-35471	809	17	by	by	ADP
cjfa-35471	809	18	0.8	0.8	NUM
cjfa-35471	809	19	.	.	PUNCT
cjfa-35471	810	1	then	then	ADV
cjfa-35471	810	2	the	the	DET
cjfa-35471	810	3	inequality	inequality	NOUN
cjfa-35471	810	4	(	(	PUNCT
cjfa-35471	810	5	4	4	X
cjfa-35471	810	6	)	)	PUNCT
cjfa-35471	810	7	becomes	become	VERB
cjfa-35471	810	8	:	:	PUNCT
cjfa-35471	810	9	(	(	PUNCT
cjfa-35471	810	10	0.5	0.5	NUM
cjfa-35471	810	11	∗	∗	NOUN
cjfa-35471	810	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	811	1	+	+	CCONJ
cjfa-35471	811	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	811	3	)	)	PUNCT
cjfa-35471	811	4	−	−	PROPN
cjfa-35471	812	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	812	2	∗	∗	VERB
cjfa-35471	812	3	0.8	0.8	NUM
cjfa-35471	812	4	𝑐	𝑐	PROPN
cjfa-35471	812	5	2.5	2.5	NUM
cjfa-35471	812	6	(	(	PUNCT
cjfa-35471	812	7	6	6	NUM
cjfa-35471	812	8	)	)	PUNCT
cjfa-35471	812	9	therefore	therefore	ADV
cjfa-35471	812	10	,	,	PUNCT
cjfa-35471	812	11	for	for	ADP
cjfa-35471	812	12	the	the	DET
cjfa-35471	812	13	same	same	ADJ
cjfa-35471	812	14	values	value	NOUN
cjfa-35471	812	15	for	for	ADP
cjfa-35471	812	16	the	the	DET
cjfa-35471	812	17	constants	constant	NOUN
cjfa-35471	812	18	,	,	PUNCT
cjfa-35471	812	19	the	the	DET
cjfa-35471	812	20	graphs	graph	NOUN
cjfa-35471	812	21	of	of	ADP
cjfa-35471	812	22	both	both	DET
cjfa-35471	812	23	sides	side	NOUN
cjfa-35471	812	24	of	of	ADP
cjfa-35471	812	25	inequality	inequality	NOUN
cjfa-35471	812	26	above	above	ADV
cjfa-35471	812	27	and	and	CCONJ
cjfa-35471	812	28	the	the	DET
cjfa-35471	812	29	sales	sale	NOUN
cjfa-35471	812	30	are	be	AUX
cjfa-35471	812	31	presented	present	VERB
cjfa-35471	812	32	below	below	ADV
cjfa-35471	812	33	(	(	PUNCT
cjfa-35471	812	34	figure	figure	NOUN
cjfa-35471	812	35	2	2	NUM
cjfa-35471	812	36	)	)	PUNCT
cjfa-35471	812	37	.	.	PUNCT
cjfa-35471	813	1	inequality	inequality	NOUN
cjfa-35471	813	2	(	(	PUNCT
cjfa-35471	813	3	6	6	NUM
cjfa-35471	813	4	)	)	PUNCT
cjfa-35471	813	5	implies	imply	VERB
cjfa-35471	813	6	the	the	DET
cjfa-35471	813	7	same	same	ADJ
cjfa-35471	813	8	type	type	NOUN
cjfa-35471	813	9	of	of	ADP
cjfa-35471	813	10	results	result	NOUN
cjfa-35471	813	11	as	as	ADP
cjfa-35471	813	12	in	in	ADP
cjfa-35471	813	13	the	the	DET
cjfa-35471	813	14	previous	previous	ADJ
cjfa-35471	813	15	case	case	NOUN
cjfa-35471	813	16	.	.	PUNCT
cjfa-35471	814	1	however	however	ADV
cjfa-35471	814	2	,	,	PUNCT
cjfa-35471	814	3	it	it	PRON
cjfa-35471	814	4	is	be	AUX
cjfa-35471	814	5	evident	evident	ADJ
cjfa-35471	814	6	from	from	ADP
cjfa-35471	814	7	the	the	DET
cjfa-35471	814	8	graphs	graph	NOUN
cjfa-35471	814	9	that	that	SCONJ
cjfa-35471	814	10	in	in	ADP
cjfa-35471	814	11	the	the	DET
cjfa-35471	814	12	second	second	ADJ
cjfa-35471	814	13	case	case	NOUN
cjfa-35471	814	14	the	the	DET
cjfa-35471	814	15	firm	firm	NOUN
cjfa-35471	814	16	will	will	AUX
cjfa-35471	814	17	stop	stop	VERB
cjfa-35471	814	18	producing	produce	VERB
cjfa-35471	814	19	sooner	soon	ADV
cjfa-35471	814	20	and	and	CCONJ
cjfa-35471	814	21	start	start	VERB
cjfa-35471	814	22	producing	produce	VERB
cjfa-35471	814	23	later	later	ADV
cjfa-35471	814	24	than	than	ADP
cjfa-35471	814	25	in	in	ADP
cjfa-35471	814	26	the	the	DET
cjfa-35471	814	27	first	first	ADJ
cjfa-35471	814	28	case	case	NOUN
cjfa-35471	814	29	.	.	PUNCT
cjfa-35471	815	1	this	this	PRON
cjfa-35471	815	2	is	be	AUX
cjfa-35471	815	3	an	an	DET
cjfa-35471	815	4	important	important	ADJ
cjfa-35471	815	5	result	result	NOUN
cjfa-35471	815	6	because	because	SCONJ
cjfa-35471	815	7	it	it	PRON
cjfa-35471	815	8	indicates	indicate	VERB
cjfa-35471	815	9	that	that	SCONJ
cjfa-35471	815	10	introduction	introduction	NOUN
cjfa-35471	815	11	of	of	ADP
cjfa-35471	815	12	new	new	ADJ
cjfa-35471	815	13	technologies	technology	NOUN
cjfa-35471	815	14	which	which	PRON
cjfa-35471	815	15	reduces	reduce	VERB
cjfa-35471	815	16	the	the	DET
cjfa-35471	815	17	marginal	marginal	ADJ
cjfa-35471	815	18	costs	cost	NOUN
cjfa-35471	815	19	will	will	AUX
cjfa-35471	815	20	induce	induce	VERB
cjfa-35471	815	21	firms	firm	NOUN
cjfa-35471	815	22	to	to	PART
cjfa-35471	815	23	stop	stop	VERB
cjfa-35471	815	24	production	production	NOUN
cjfa-35471	815	25	sooner	soon	ADV
cjfa-35471	815	26	.	.	PUNCT
cjfa-35471	816	1	case	case	NOUN
cjfa-35471	816	2	iii	iii	X
cjfa-35471	816	3	:	:	PUNCT
cjfa-35471	816	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	816	5	𝑘	𝑘	PRON
cjfa-35471	816	6	𝑘	𝑘	NOUN
cjfa-35471	816	7	and	and	CCONJ
cjfa-35471	816	8	interest	interest	NOUN
cjfa-35471	816	9	rate	rate	NOUN
cjfa-35471	816	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	816	11	)	)	PUNCT
cjfa-35471	817	1	𝑘	𝑘	ADP
cjfa-35471	817	2	0.2	0.2	NUM
cjfa-35471	817	3	the	the	DET
cjfa-35471	817	4	inequality	inequality	NOUN
cjfa-35471	817	5	(	(	PUNCT
cjfa-35471	817	6	4	4	X
cjfa-35471	817	7	)	)	PUNCT
cjfa-35471	817	8	becomes	become	VERB
cjfa-35471	817	9	:	:	PUNCT
cjfa-35471	817	10	(	(	PUNCT
cjfa-35471	817	11	0.5	0.5	NUM
cjfa-35471	817	12	∗	∗	NOUN
cjfa-35471	817	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	818	1	+	+	CCONJ
cjfa-35471	818	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	818	3	)	)	PUNCT
cjfa-35471	818	4	−	−	PROPN
cjfa-35471	819	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	819	2	𝑐	𝑐	PROPN
cjfa-35471	819	3	2.5	2.5	NUM
cjfa-35471	819	4	+	+	CCONJ
cjfa-35471	819	5	0.2	0.2	NUM
cjfa-35471	819	6	�	�	NOUN
cjfa-35471	819	7	0.5	0.5	NUM
cjfa-35471	819	8	∗	∗	NOUN
cjfa-35471	819	9	𝑐	𝑐	PROPN
cjfa-35471	819	10	∗	∗	NOUN
cjfa-35471	819	11	(	(	PUNCT
cjfa-35471	819	12	4	4	NUM
cjfa-35471	819	13	+	+	SYM
cjfa-35471	819	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	819	15	)	)	PUNCT
cjfa-35471	819	16	�	�	PROPN
cjfa-35471	819	17	�	�	PROPN
cjfa-35471	819	18	−	−	NUM
cjfa-35471	819	19	2	2	NUM
cjfa-35471	819	20	∗	∗	NOUN
cjfa-35471	819	21	(	(	PUNCT
cjfa-35471	819	22	4	4	NUM
cjfa-35471	819	23	+	+	NUM
cjfa-35471	819	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	819	25	)	)	PUNCT
cjfa-35471	819	26	+	+	SYM
cjfa-35471	819	27	𝑘	𝑘	X
cjfa-35471	819	28	)	)	PUNCT
cjfa-35471	819	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	819	30	(	(	PUNCT
cjfa-35471	819	31	7	7	X
cjfa-35471	819	32	)	)	PUNCT
cjfa-35471	819	33	source	source	NOUN
cjfa-35471	819	34	:	:	PUNCT
cjfa-35471	819	35	constructed	construct	VERB
cjfa-35471	819	36	by	by	ADP
cjfa-35471	819	37	authors	author	NOUN
cjfa-35471	819	38	.	.	PUNCT
cjfa-35471	820	1	case	case	NOUN
cjfa-35471	820	2	ii	ii	PROPN
cjfa-35471	820	3	:	:	PUNCT
cjfa-35471	820	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	820	5	𝑘	𝑘	PRON
cjfa-35471	820	6	𝑘	𝑘	NOUN
cjfa-35471	820	7	and	and	CCONJ
cjfa-35471	820	8	interest	interest	NOUN
cjfa-35471	820	9	rate	rate	NOUN
cjfa-35471	820	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	820	11	)	)	PUNCT
cjfa-35471	821	1	𝑘	𝑘	ADP
cjfa-35471	821	2	0	0	NUM
cjfa-35471	821	3	and	and	CCONJ
cjfa-35471	821	4	a	a	DET
cjfa-35471	821	5	new	new	ADJ
cjfa-35471	821	6	technology	technology	NOUN
cjfa-35471	821	7	i	i	PRON
cjfa-35471	821	8	introduced	introduce	VERB
cjfa-35471	821	9	.	.	PUNCT
cjfa-35471	822	1	the	the	DET
cjfa-35471	822	2	impact	impact	NOUN
cjfa-35471	822	3	of	of	ADP
cjfa-35471	822	4	new	new	ADJ
cjfa-35471	822	5	technology	technology	NOUN
cjfa-35471	822	6	will	will	AUX
cjfa-35471	822	7	be	be	AUX
cjfa-35471	822	8	analyzed	analyze	VERB
cjfa-35471	822	9	in	in	ADP
cjfa-35471	822	10	three	three	NUM
cjfa-35471	822	11	cases	case	NOUN
cjfa-35471	822	12	:	:	PUNCT
cjfa-35471	822	13	1	1	X
cjfa-35471	822	14	.	.	PUNCT
cjfa-35471	822	15	fixed	fix	VERB
cjfa-35471	822	16	costs	cost	NOUN
cjfa-35471	822	17	(	(	PUNCT
cjfa-35471	822	18	the	the	DET
cjfa-35471	822	19	term	term	NOUN
cjfa-35471	822	20	𝑑𝑑	𝑑𝑑	VERB
cjfa-35471	822	21	in	in	ADP
cjfa-35471	822	22	the	the	DET
cjfa-35471	822	23	cost	cost	NOUN
cjfa-35471	822	24	function	function	NOUN
cjfa-35471	822	25	)	)	PUNCT
cjfa-35471	822	26	is	be	AUX
cjfa-35471	822	27	reduced	reduce	VERB
cjfa-35471	822	28	.	.	PUNCT
cjfa-35471	823	1	there	there	PRON
cjfa-35471	823	2	will	will	AUX
cjfa-35471	823	3	be	be	AUX
cjfa-35471	823	4	no	no	DET
cjfa-35471	823	5	impact	impact	NOUN
cjfa-35471	823	6	on	on	ADP
cjfa-35471	823	7	production	production	NOUN
cjfa-35471	823	8	decision	decision	NOUN
cjfa-35471	823	9	since	since	SCONJ
cjfa-35471	823	10	the	the	DET
cjfa-35471	823	11	fixed	fix	VERB
cjfa-35471	823	12	costs	cost	NOUN
cjfa-35471	823	13	are	be	AUX
cjfa-35471	823	14	already	already	ADV
cjfa-35471	823	15	shown	show	VERB
cjfa-35471	823	16	to	to	PART
cjfa-35471	823	17	have	have	VERB
cjfa-35471	823	18	on	on	ADP
cjfa-35471	823	19	impact	impact	NOUN
cjfa-35471	823	20	on	on	ADP
cjfa-35471	823	21	the	the	DET
cjfa-35471	823	22	inequality	inequality	NOUN
cjfa-35471	823	23	(	(	PUNCT
cjfa-35471	823	24	5	5	NUM
cjfa-35471	823	25	)	)	PUNCT
cjfa-35471	823	26	.	.	PUNCT
cjfa-35471	824	1	2	2	X
cjfa-35471	824	2	.	.	X
cjfa-35471	824	3	only	only	ADV
cjfa-35471	824	4	the	the	DET
cjfa-35471	824	5	constant	constant	ADJ
cjfa-35471	824	6	term	term	NOUN
cjfa-35471	824	7	(	(	PUNCT
cjfa-35471	824	8	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	824	9	)	)	PUNCT
cjfa-35471	824	10	in	in	ADP
cjfa-35471	824	11	the	the	DET
cjfa-35471	824	12	marginal	marginal	ADJ
cjfa-35471	824	13	cost	cost	NOUN
cjfa-35471	824	14	,	,	PUNCT
cjfa-35471	824	15	𝑐𝑐𝑐	𝑐𝑐𝑐	VERB
cjfa-35471	824	16	𝑘	𝑘	PRON
cjfa-35471	824	17	𝑐𝑐𝑐𝑐𝑐	𝑐𝑐𝑐𝑐𝑐	NOUN
cjfa-35471	824	18	�	�	PROPN
cjfa-35471	824	19	+	+	CCONJ
cjfa-35471	824	20	2𝑏𝑏𝑐𝑐	2𝑏𝑏𝑐𝑐	NUM
cjfa-35471	825	1	+	+	CCONJ
cjfa-35471	825	2	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	825	3	is	be	AUX
cjfa-35471	825	4	reduced	reduce	VERB
cjfa-35471	825	5	.	.	PUNCT
cjfa-35471	826	1	the	the	DET
cjfa-35471	826	2	left	left	ADJ
cjfa-35471	826	3	-	-	PUNCT
cjfa-35471	826	4	hand	hand	NOUN
cjfa-35471	826	5	side	side	NOUN
cjfa-35471	826	6	of	of	ADP
cjfa-35471	826	7	inequality	inequality	NOUN
cjfa-35471	826	8	(	(	PUNCT
cjfa-35471	826	9	5	5	NUM
cjfa-35471	826	10	)	)	PUNCT
cjfa-35471	826	11	will	will	AUX
cjfa-35471	826	12	not	not	PART
cjfa-35471	826	13	change	change	VERB
cjfa-35471	826	14	since	since	SCONJ
cjfa-35471	826	15	𝑐𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	826	16	)	)	PUNCT
cjfa-35471	826	17	does	do	AUX
cjfa-35471	826	18	not	not	PART
cjfa-35471	826	19	depend	depend	VERB
cjfa-35471	826	20	on	on	ADP
cjfa-35471	826	21	the	the	DET
cjfa-35471	826	22	constant	constant	ADJ
cjfa-35471	826	23	term	term	NOUN
cjfa-35471	826	24	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	826	25	in	in	ADP
cjfa-35471	826	26	the	the	DET
cjfa-35471	826	27	production	production	NOUN
cjfa-35471	826	28	cost	cost	NOUN
cjfa-35471	826	29	function	function	NOUN
cjfa-35471	826	30	.	.	PUNCT
cjfa-35471	827	1	the	the	DET
cjfa-35471	827	2	right	right	ADJ
cjfa-35471	827	3	-	-	PUNCT
cjfa-35471	827	4	hand	hand	NOUN
cjfa-35471	827	5	side	side	NOUN
cjfa-35471	827	6	will	will	AUX
cjfa-35471	827	7	be	be	AUX
cjfa-35471	827	8	lower	low	ADJ
cjfa-35471	827	9	since	since	SCONJ
cjfa-35471	827	10	𝑐𝑐	𝑐𝑐	NOUN
cjfa-35471	827	11	is	be	AUX
cjfa-35471	827	12	lower	low	ADJ
cjfa-35471	827	13	.	.	PUNCT
cjfa-35471	828	1	therefore	therefore	ADV
cjfa-35471	828	2	,	,	PUNCT
cjfa-35471	828	3	the	the	DET
cjfa-35471	828	4	decision	decision	NOUN
cjfa-35471	828	5	of	of	ADP
cjfa-35471	828	6	the	the	DET
cjfa-35471	828	7	firm	firm	NOUN
cjfa-35471	828	8	will	will	AUX
cjfa-35471	828	9	depend	depend	VERB
cjfa-35471	828	10	on	on	ADP
cjfa-35471	828	11	how	how	SCONJ
cjfa-35471	828	12	much	much	ADJ
cjfa-35471	828	13	the	the	DET
cjfa-35471	828	14	new	new	ADJ
cjfa-35471	828	15	technology	technology	NOUN
cjfa-35471	828	16	reduces	reduce	VERB
cjfa-35471	828	17	𝑐𝑐.	𝑐𝑐.	NOUN
cjfa-35471	828	18	the	the	DET
cjfa-35471	828	19	firm	firm	NOUN
cjfa-35471	828	20	will	will	AUX
cjfa-35471	828	21	start	start	VERB
cjfa-35471	828	22	to	to	PART
cjfa-35471	828	23	produce	produce	VERB
cjfa-35471	828	24	sooner	soon	ADV
cjfa-35471	828	25	if	if	SCONJ
cjfa-35471	828	26	the	the	DET
cjfa-35471	828	27	reduction	reduction	NOUN
cjfa-35471	828	28	in	in	ADP
cjfa-35471	828	29	c	c	PROPN
cjfa-35471	828	30	is	be	AUX
cjfa-35471	828	31	large	large	ADJ
cjfa-35471	828	32	enough	enough	ADV
cjfa-35471	828	33	to	to	PART
cjfa-35471	828	34	violate	violate	VERB
cjfa-35471	828	35	the	the	DET
cjfa-35471	828	36	inequality	inequality	NOUN
cjfa-35471	828	37	.	.	PUNCT
cjfa-35471	829	1	3	3	X
cjfa-35471	829	2	.	.	X
cjfa-35471	829	3	marginal	marginal	ADJ
cjfa-35471	829	4	cost	cost	NOUN
cjfa-35471	829	5	function	function	NOUN
cjfa-35471	829	6	,	,	PUNCT
cjfa-35471	829	7	𝑐𝑐𝑐(𝑐𝑐	𝑐𝑐𝑐(𝑐𝑐	NOUN
cjfa-35471	829	8	)	)	PUNCT
cjfa-35471	829	9	,	,	PUNCT
cjfa-35471	829	10	is	be	AUX
cjfa-35471	829	11	reduced	reduce	VERB
cjfa-35471	829	12	as	as	ADP
cjfa-35471	829	13	a	a	DET
cjfa-35471	829	14	whole	whole	NOUN
cjfa-35471	829	15	.	.	PUNCT
cjfa-35471	830	1	we	we	PRON
cjfa-35471	830	2	will	will	AUX
cjfa-35471	830	3	consider	consider	VERB
cjfa-35471	830	4	this	this	DET
cjfa-35471	830	5	last	last	ADJ
cjfa-35471	830	6	case	case	NOUN
cjfa-35471	830	7	assuming	assume	VERB
cjfa-35471	830	8	that	that	SCONJ
cjfa-35471	830	9	the	the	DET
cjfa-35471	830	10	new	new	ADJ
cjfa-35471	830	11	technology	technology	NOUN
cjfa-35471	830	12	reduces	reduce	VERB
cjfa-35471	830	13	the	the	DET
cjfa-35471	830	14	marginal	marginal	ADJ
cjfa-35471	830	15	cost	cost	NOUN
cjfa-35471	830	16	by	by	ADP
cjfa-35471	830	17	20	20	NUM
cjfa-35471	830	18	%	%	NOUN
cjfa-35471	830	19	.	.	PUNCT
cjfa-35471	831	1	this	this	PRON
cjfa-35471	831	2	implies	imply	VERB
cjfa-35471	831	3	that	that	SCONJ
cjfa-35471	831	4	the	the	DET
cjfa-35471	831	5	left	left	ADJ
cjfa-35471	831	6	-	-	PUNCT
cjfa-35471	831	7	hand	hand	NOUN
cjfa-35471	831	8	side	side	NOUN
cjfa-35471	831	9	of	of	ADP
cjfa-35471	831	10	inequality	inequality	NOUN
cjfa-35471	831	11	(	(	PUNCT
cjfa-35471	831	12	5	5	NUM
cjfa-35471	831	13	)	)	PUNCT
cjfa-35471	831	14	will	will	AUX
cjfa-35471	831	15	be	be	AUX
cjfa-35471	831	16	multiplies	multiplie	NOUN
cjfa-35471	831	17	by	by	ADP
cjfa-35471	831	18	0.8	0.8	NUM
cjfa-35471	831	19	.	.	PUNCT
cjfa-35471	832	1	then	then	ADV
cjfa-35471	832	2	the	the	DET
cjfa-35471	832	3	inequality	inequality	NOUN
cjfa-35471	832	4	(	(	PUNCT
cjfa-35471	832	5	4	4	X
cjfa-35471	832	6	)	)	PUNCT
cjfa-35471	832	7	becomes	become	VERB
cjfa-35471	832	8	:	:	PUNCT
cjfa-35471	832	9	(	(	PUNCT
cjfa-35471	832	10	0.5	0.5	NUM
cjfa-35471	832	11	∗	∗	NOUN
cjfa-35471	832	12	𝑐(4	𝑐(4	PROPN
cjfa-35471	833	1	+	+	CCONJ
cjfa-35471	833	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	833	3	)	)	PUNCT
cjfa-35471	833	4	−	−	PROPN
cjfa-35471	834	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	PROPN
cjfa-35471	834	2	∗	∗	VERB
cjfa-35471	834	3	0.8	0.8	NUM
cjfa-35471	834	4	𝑐	𝑐	PROPN
cjfa-35471	834	5	2.5	2.5	NUM
cjfa-35471	834	6	(	(	PUNCT
cjfa-35471	834	7	6	6	NUM
cjfa-35471	834	8	)	)	PUNCT
cjfa-35471	834	9	therefore	therefore	ADV
cjfa-35471	834	10	,	,	PUNCT
cjfa-35471	834	11	for	for	ADP
cjfa-35471	834	12	the	the	DET
cjfa-35471	834	13	same	same	ADJ
cjfa-35471	834	14	values	value	NOUN
cjfa-35471	834	15	for	for	ADP
cjfa-35471	834	16	the	the	DET
cjfa-35471	834	17	constants	constant	NOUN
cjfa-35471	834	18	,	,	PUNCT
cjfa-35471	834	19	the	the	DET
cjfa-35471	834	20	graphs	graph	NOUN
cjfa-35471	834	21	of	of	ADP
cjfa-35471	834	22	both	both	DET
cjfa-35471	834	23	sides	side	NOUN
cjfa-35471	834	24	of	of	ADP
cjfa-35471	834	25	inequality	inequality	NOUN
cjfa-35471	834	26	above	above	ADV
cjfa-35471	834	27	and	and	CCONJ
cjfa-35471	834	28	the	the	DET
cjfa-35471	834	29	sales	sale	NOUN
cjfa-35471	834	30	are	be	AUX
cjfa-35471	834	31	presented	present	VERB
cjfa-35471	834	32	below	below	ADV
cjfa-35471	834	33	(	(	PUNCT
cjfa-35471	834	34	figure	figure	NOUN
cjfa-35471	834	35	2	2	NUM
cjfa-35471	834	36	)	)	PUNCT
cjfa-35471	834	37	.	.	PUNCT
cjfa-35471	835	1	inequality	inequality	NOUN
cjfa-35471	835	2	(	(	PUNCT
cjfa-35471	835	3	6	6	NUM
cjfa-35471	835	4	)	)	PUNCT
cjfa-35471	835	5	implies	imply	VERB
cjfa-35471	835	6	the	the	DET
cjfa-35471	835	7	same	same	ADJ
cjfa-35471	835	8	type	type	NOUN
cjfa-35471	835	9	of	of	ADP
cjfa-35471	835	10	results	result	NOUN
cjfa-35471	835	11	as	as	ADP
cjfa-35471	835	12	in	in	ADP
cjfa-35471	835	13	the	the	DET
cjfa-35471	835	14	previous	previous	ADJ
cjfa-35471	835	15	case	case	NOUN
cjfa-35471	835	16	.	.	PUNCT
cjfa-35471	836	1	however	however	ADV
cjfa-35471	836	2	,	,	PUNCT
cjfa-35471	836	3	it	it	PRON
cjfa-35471	836	4	is	be	AUX
cjfa-35471	836	5	evident	evident	ADJ
cjfa-35471	836	6	from	from	ADP
cjfa-35471	836	7	the	the	DET
cjfa-35471	836	8	graphs	graph	NOUN
cjfa-35471	836	9	that	that	SCONJ
cjfa-35471	836	10	in	in	ADP
cjfa-35471	836	11	the	the	DET
cjfa-35471	836	12	second	second	ADJ
cjfa-35471	836	13	case	case	NOUN
cjfa-35471	836	14	the	the	DET
cjfa-35471	836	15	firm	firm	NOUN
cjfa-35471	836	16	will	will	AUX
cjfa-35471	836	17	stop	stop	VERB
cjfa-35471	836	18	producing	produce	VERB
cjfa-35471	836	19	sooner	soon	ADV
cjfa-35471	836	20	and	and	CCONJ
cjfa-35471	836	21	start	start	VERB
cjfa-35471	836	22	producing	produce	VERB
cjfa-35471	836	23	later	later	ADV
cjfa-35471	836	24	than	than	ADP
cjfa-35471	836	25	in	in	ADP
cjfa-35471	836	26	the	the	DET
cjfa-35471	836	27	first	first	ADJ
cjfa-35471	836	28	case	case	NOUN
cjfa-35471	836	29	.	.	PUNCT
cjfa-35471	837	1	this	this	PRON
cjfa-35471	837	2	is	be	AUX
cjfa-35471	837	3	an	an	DET
cjfa-35471	837	4	important	important	ADJ
cjfa-35471	837	5	result	result	NOUN
cjfa-35471	837	6	because	because	SCONJ
cjfa-35471	837	7	it	it	PRON
cjfa-35471	837	8	indicates	indicate	VERB
cjfa-35471	837	9	that	that	SCONJ
cjfa-35471	837	10	introduction	introduction	NOUN
cjfa-35471	837	11	of	of	ADP
cjfa-35471	837	12	new	new	ADJ
cjfa-35471	837	13	technologies	technology	NOUN
cjfa-35471	837	14	which	which	PRON
cjfa-35471	837	15	reduces	reduce	VERB
cjfa-35471	837	16	the	the	DET
cjfa-35471	837	17	marginal	marginal	ADJ
cjfa-35471	837	18	costs	cost	NOUN
cjfa-35471	837	19	will	will	AUX
cjfa-35471	837	20	induce	induce	VERB
cjfa-35471	837	21	firms	firm	NOUN
cjfa-35471	837	22	to	to	PART
cjfa-35471	837	23	stop	stop	VERB
cjfa-35471	837	24	production	production	NOUN
cjfa-35471	837	25	sooner	soon	ADV
cjfa-35471	837	26	.	.	PUNCT
cjfa-35471	838	1	case	case	NOUN
cjfa-35471	838	2	iii	iii	X
cjfa-35471	838	3	:	:	PUNCT
cjfa-35471	838	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	838	5	𝑘	𝑘	PRON
cjfa-35471	838	6	𝑘	𝑘	NOUN
cjfa-35471	838	7	and	and	CCONJ
cjfa-35471	838	8	interest	interest	NOUN
cjfa-35471	838	9	rate	rate	NOUN
cjfa-35471	838	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	838	11	)	)	PUNCT
cjfa-35471	839	1	𝑘	𝑘	ADP
cjfa-35471	839	2	0.2	0.2	NUM
cjfa-35471	839	3	the	the	DET
cjfa-35471	839	4	inequality	inequality	NOUN
cjfa-35471	839	5	(	(	PUNCT
cjfa-35471	839	6	4	4	X
cjfa-35471	839	7	)	)	PUNCT
cjfa-35471	839	8	becomes	become	VERB
cjfa-35471	839	9	:	:	PUNCT
cjfa-35471	839	10	(	(	PUNCT
cjfa-35471	839	11	0.5	0.5	NUM
cjfa-35471	839	12	∗	∗	NOUN
cjfa-35471	839	13	𝑐(4	𝑐(4	PROPN
cjfa-35471	840	1	+	+	CCONJ
cjfa-35471	840	2	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑡𝑡	X
cjfa-35471	840	3	)	)	PUNCT
cjfa-35471	840	4	−	−	PROPN
cjfa-35471	841	1	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	𝑘)𝑐𝑐𝑐𝑐𝑠𝑠2𝑠𝑠𝑡𝑡	INTJ
cjfa-35471	841	2	𝑐	𝑐	PROPN
cjfa-35471	841	3	2.5	2.5	NUM
cjfa-35471	841	4	+	+	CCONJ
cjfa-35471	841	5	0.2	0.2	NUM
cjfa-35471	841	6	�	�	NOUN
cjfa-35471	841	7	0.5	0.5	NUM
cjfa-35471	841	8	∗	∗	NOUN
cjfa-35471	841	9	𝑐	𝑐	PROPN
cjfa-35471	841	10	∗	∗	NOUN
cjfa-35471	841	11	(	(	PUNCT
cjfa-35471	841	12	4	4	NUM
cjfa-35471	841	13	+	+	SYM
cjfa-35471	841	14	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	𝑠𝑠𝑠𝑠𝑠𝑠2𝑠𝑠𝑠𝑠	ADJ
cjfa-35471	841	15	)	)	PUNCT
cjfa-35471	841	16	�	�	PROPN
cjfa-35471	841	17	�	�	PROPN
cjfa-35471	841	18	−	−	NUM
cjfa-35471	841	19	2	2	NUM
cjfa-35471	841	20	∗	∗	NOUN
cjfa-35471	841	21	(	(	PUNCT
cjfa-35471	841	22	4	4	NUM
cjfa-35471	841	23	+	+	NUM
cjfa-35471	841	24	sin(2𝑠𝑠𝑠𝑠	sin(2𝑠𝑠𝑠𝑠	NOUN
cjfa-35471	841	25	)	)	PUNCT
cjfa-35471	841	26	+	+	SYM
cjfa-35471	841	27	𝑘	𝑘	X
cjfa-35471	841	28	)	)	PUNCT
cjfa-35471	841	29	/2𝑠𝑠	/2𝑠𝑠	PUNCT
cjfa-35471	841	30	(	(	PUNCT
cjfa-35471	841	31	7	7	NUM
cjfa-35471	841	32	)	)	PUNCT
cjfa-35471	841	33	(	(	PUNCT
cjfa-35471	841	34	7	7	X
cjfa-35471	841	35	)	)	PUNCT
cjfa-35471	841	36	the	the	DET
cjfa-35471	841	37	graphs	graph	NOUN
cjfa-35471	841	38	of	of	ADP
cjfa-35471	841	39	the	the	DET
cjfa-35471	841	40	function	function	NOUN
cjfa-35471	841	41	on	on	ADP
cjfa-35471	841	42	both	both	DET
cjfa-35471	841	43	sides	side	NOUN
cjfa-35471	841	44	of	of	ADP
cjfa-35471	841	45	this	this	DET
cjfa-35471	841	46	inequality	inequality	NOUN
cjfa-35471	841	47	above	above	ADV
cjfa-35471	841	48	are	be	AUX
cjfa-35471	841	49	shown	show	VERB
cjfa-35471	841	50	in	in	ADP
cjfa-35471	841	51	graph	graph	NOUN
cjfa-35471	841	52	iii	iii	PROPN
cjfa-35471	841	53	below	below	ADV
cjfa-35471	841	54	(	(	PUNCT
cjfa-35471	841	55	figure	figure	NOUN
cjfa-35471	841	56	3	3	NUM
cjfa-35471	841	57	)	)	PUNCT
cjfa-35471	841	58	.	.	PUNCT
cjfa-35471	842	1	figure	figure	VERB
cjfa-35471	842	2	3	3	NUM
cjfa-35471	842	3	shows	show	VERB
cjfa-35471	842	4	that	that	PRON
cjfa-35471	842	5	introduction	introduction	NOUN
cjfa-35471	842	6	of	of	ADP
cjfa-35471	842	7	interest	interest	NOUN
cjfa-35471	842	8	rates	rate	NOUN
cjfa-35471	842	9	causes	cause	VERB
cjfa-35471	842	10	the	the	DET
cjfa-35471	842	11	firms	firm	NOUN
cjfa-35471	842	12	to	to	PART
cjfa-35471	842	13	stop	stop	VERB
cjfa-35471	842	14	production	production	NOUN
cjfa-35471	842	15	sooner	soon	ADV
cjfa-35471	842	16	but	but	CCONJ
cjfa-35471	842	17	not	not	PART
cjfa-35471	842	18	very	very	ADV
cjfa-35471	842	19	significantly	significantly	ADV
cjfa-35471	842	20	,	,	PUNCT
cjfa-35471	842	21	from	from	ADP
cjfa-35471	842	22	t	t	PROPN
cjfa-35471	842	23	=	=	SYM
cjfa-35471	842	24	0.18	0.18	NUM
cjfa-35471	842	25	in	in	ADP
cjfa-35471	842	26	graph	graph	NOUN
cjfa-35471	842	27	i	i	PRON
cjfa-35471	842	28	to	to	ADP
cjfa-35471	842	29	about	about	ADV
cjfa-35471	842	30	0.16	0.16	NUM
cjfa-35471	842	31	in	in	ADP
cjfa-35471	842	32	graph	graph	PROPN
cjfa-35471	842	33	iii	iii	PROPN
cjfa-35471	842	34	.	.	PUNCT
cjfa-35471	843	1	this	this	PRON
cjfa-35471	843	2	implies	imply	VERB
cjfa-35471	843	3	that	that	SCONJ
cjfa-35471	843	4	the	the	DET
cjfa-35471	843	5	firms	firm	NOUN
cjfa-35471	843	6	will	will	AUX
cjfa-35471	843	7	start	start	VERB
cjfa-35471	843	8	to	to	PART
cjfa-35471	843	9	produce	produce	VERB
cjfa-35471	843	10	at	at	ADP
cjfa-35471	843	11	about	about	ADV
cjfa-35471	843	12	the	the	DET
cjfa-35471	843	13	same	same	ADJ
cjfa-35471	843	14	time	time	NOUN
cjfa-35471	843	15	as	as	ADP
cjfa-35471	843	16	when	when	SCONJ
cjfa-35471	843	17	interest	interest	NOUN
cjfa-35471	843	18	rate	rate	NOUN
cjfa-35471	843	19	was	be	AUX
cjfa-35471	843	20	zero	zero	NUM
cjfa-35471	843	21	(	(	PUNCT
cjfa-35471	843	22	figure	figure	NOUN
cjfa-35471	843	23	1	1	NUM
cjfa-35471	843	24	)	)	PUNCT
cjfa-35471	843	25	.	.	PUNCT
cjfa-35471	844	1	this	this	PRON
cjfa-35471	844	2	,	,	PUNCT
cjfa-35471	844	3	in	in	ADP
cjfa-35471	844	4	turn	turn	NOUN
cjfa-35471	844	5	,	,	PUNCT
cjfa-35471	844	6	implies	imply	VERB
cjfa-35471	844	7	that	that	SCONJ
cjfa-35471	844	8	firms	firm	NOUN
cjfa-35471	844	9	will	will	AUX
cjfa-35471	844	10	stop	stop	VERB
cjfa-35471	844	11	producing	produce	VERB
cjfa-35471	844	12	later	later	ADV
cjfa-35471	844	13	when	when	SCONJ
cjfa-35471	844	14	interest	interest	NOUN
cjfa-35471	844	15	rates	rate	NOUN
cjfa-35471	844	16	are	be	AUX
cjfa-35471	844	17	lowered	lower	VERB
cjfa-35471	844	18	.	.	PUNCT
cjfa-35471	845	1	however	however	ADV
cjfa-35471	845	2	,	,	PUNCT
cjfa-35471	845	3	they	they	PRON
cjfa-35471	845	4	will	will	AUX
cjfa-35471	845	5	not	not	PART
cjfa-35471	845	6	start	start	VERB
cjfa-35471	845	7	producing	produce	VERB
cjfa-35471	845	8	sooner	soon	ADV
cjfa-35471	845	9	.	.	PUNCT
cjfa-35471	846	1	case	case	NOUN
cjfa-35471	846	2	iv	iv	X
cjfa-35471	846	3	:	:	PUNCT
cjfa-35471	846	4	k	k	NOUN
cjfa-35471	846	5	=	=	SYM
cjfa-35471	846	6	1	1	NUM
cjfa-35471	846	7	and	and	CCONJ
cjfa-35471	846	8	interest	interest	NOUN
cjfa-35471	846	9	rate	rate	NOUN
cjfa-35471	846	10	f(t	f(t	NOUN
cjfa-35471	846	11	)	)	PUNCT
cjfa-35471	846	12	=	=	SYM
cjfa-35471	846	13	0.1	0.1	NUM
cjfa-35471	846	14	,	,	PUNCT
cjfa-35471	846	15	a	a	DET
cjfa-35471	846	16	50	50	NUM
cjfa-35471	846	17	%	%	NOUN
cjfa-35471	846	18	decrease	decrease	NOUN
cjfa-35471	846	19	in	in	ADP
cjfa-35471	846	20	interest	interest	NOUN
cjfa-35471	846	21	rate	rate	NOUN
cjfa-35471	846	22	.	.	PUNCT
cjfa-35471	847	1	in	in	ADP
cjfa-35471	847	2	this	this	PRON
cjfa-35471	847	3	the	the	DET
cjfa-35471	847	4	inequality	inequality	NOUN
cjfa-35471	847	5	(	(	PUNCT
cjfa-35471	847	6	5	5	NUM
cjfa-35471	847	7	)	)	PUNCT
cjfa-35471	847	8	becomes	become	VERB
cjfa-35471	847	9	:	:	PUNCT
cjfa-35471	847	10	the	the	DET
cjfa-35471	847	11	graphs	graph	NOUN
cjfa-35471	847	12	of	of	ADP
cjfa-35471	847	13	the	the	DET
cjfa-35471	847	14	function	function	NOUN
cjfa-35471	847	15	on	on	ADP
cjfa-35471	847	16	both	both	DET
cjfa-35471	847	17	sides	side	NOUN
cjfa-35471	847	18	of	of	ADP
cjfa-35471	847	19	this	this	DET
cjfa-35471	847	20	inequality	inequality	NOUN
cjfa-35471	847	21	above	above	ADV
cjfa-35471	847	22	are	be	AUX
cjfa-35471	847	23	shown	show	VERB
cjfa-35471	847	24	in	in	ADP
cjfa-35471	847	25	graph	graph	NOUN
cjfa-35471	847	26	iii	iii	PROPN
cjfa-35471	847	27	below	below	ADV
cjfa-35471	847	28	(	(	PUNCT
cjfa-35471	847	29	figure	figure	NOUN
cjfa-35471	847	30	3	3	NUM
cjfa-35471	847	31	)	)	PUNCT
cjfa-35471	847	32	.	.	PUNCT
cjfa-35471	848	1	figure	figure	VERB
cjfa-35471	848	2	3	3	NUM
cjfa-35471	848	3	shows	show	VERB
cjfa-35471	848	4	that	that	PRON
cjfa-35471	848	5	introduction	introduction	NOUN
cjfa-35471	848	6	of	of	ADP
cjfa-35471	848	7	interest	interest	NOUN
cjfa-35471	848	8	rates	rate	NOUN
cjfa-35471	848	9	causes	cause	VERB
cjfa-35471	848	10	the	the	DET
cjfa-35471	848	11	firms	firm	NOUN
cjfa-35471	848	12	to	to	PART
cjfa-35471	848	13	stop	stop	VERB
cjfa-35471	848	14	production	production	NOUN
cjfa-35471	848	15	sooner	soon	ADV
cjfa-35471	848	16	but	but	CCONJ
cjfa-35471	848	17	not	not	PART
cjfa-35471	848	18	very	very	ADV
cjfa-35471	848	19	significantly	significantly	ADV
cjfa-35471	848	20	,	,	PUNCT
cjfa-35471	848	21	from	from	ADP
cjfa-35471	848	22	𝑡𝑡	𝑡𝑡	PROPN
cjfa-35471	848	23	𝑡	𝑡	VERB
cjfa-35471	848	24	𝑡𝑡𝑡𝑡	𝑡𝑡𝑡𝑡	NOUN
cjfa-35471	848	25	in	in	ADP
cjfa-35471	848	26	graph	graph	NOUN
cjfa-35471	848	27	i	i	PRON
cjfa-35471	848	28	to	to	ADP
cjfa-35471	848	29	about	about	ADV
cjfa-35471	848	30	0.16	0.16	NUM
cjfa-35471	848	31	in	in	ADP
cjfa-35471	848	32	graph	graph	PROPN
cjfa-35471	848	33	iii	iii	PROPN
cjfa-35471	848	34	.	.	PUNCT
cjfa-35471	849	1	this	this	PRON
cjfa-35471	849	2	implies	imply	VERB
cjfa-35471	849	3	that	that	SCONJ
cjfa-35471	849	4	the	the	DET
cjfa-35471	849	5	firms	firm	NOUN
cjfa-35471	849	6	will	will	AUX
cjfa-35471	849	7	start	start	VERB
cjfa-35471	849	8	to	to	PART
cjfa-35471	849	9	produce	produce	VERB
cjfa-35471	849	10	at	at	ADP
cjfa-35471	849	11	about	about	ADV
cjfa-35471	849	12	the	the	DET
cjfa-35471	849	13	same	same	ADJ
cjfa-35471	849	14	time	time	NOUN
cjfa-35471	849	15	as	as	ADP
cjfa-35471	849	16	when	when	SCONJ
cjfa-35471	849	17	interest	interest	NOUN
cjfa-35471	849	18	rate	rate	NOUN
cjfa-35471	849	19	was	be	AUX
cjfa-35471	849	20	zero	zero	NUM
cjfa-35471	849	21	(	(	PUNCT
cjfa-35471	849	22	figure	figure	NOUN
cjfa-35471	849	23	1	1	NUM
cjfa-35471	849	24	)	)	PUNCT
cjfa-35471	849	25	.	.	PUNCT
cjfa-35471	850	1	this	this	PRON
cjfa-35471	850	2	,	,	PUNCT
cjfa-35471	850	3	in	in	ADP
cjfa-35471	850	4	turn	turn	NOUN
cjfa-35471	850	5	,	,	PUNCT
cjfa-35471	850	6	implies	imply	VERB
cjfa-35471	850	7	that	that	SCONJ
cjfa-35471	850	8	firms	firm	NOUN
cjfa-35471	850	9	will	will	AUX
cjfa-35471	850	10	stop	stop	VERB
cjfa-35471	850	11	producing	produce	VERB
cjfa-35471	850	12	later	later	ADV
cjfa-35471	850	13	when	when	SCONJ
cjfa-35471	850	14	interest	interest	NOUN
cjfa-35471	850	15	rates	rate	NOUN
cjfa-35471	850	16	are	be	AUX
cjfa-35471	850	17	lowered	lower	VERB
cjfa-35471	850	18	.	.	PUNCT
cjfa-35471	851	1	however	however	ADV
cjfa-35471	851	2	,	,	PUNCT
cjfa-35471	851	3	they	they	PRON
cjfa-35471	851	4	will	will	AUX
cjfa-35471	851	5	not	not	PART
cjfa-35471	851	6	start	start	VERB
cjfa-35471	851	7	producing	produce	VERB
cjfa-35471	851	8	sooner	soon	ADV
cjfa-35471	851	9	.	.	PUNCT
cjfa-35471	852	1	case	case	NOUN
cjfa-35471	852	2	iv	iv	X
cjfa-35471	852	3	:	:	PUNCT
cjfa-35471	852	4	𝑘𝑘	𝑘𝑘	NUM
cjfa-35471	852	5	𝑡	𝑡	PROPN
cjfa-35471	852	6	𝑡	𝑡	PROPN
cjfa-35471	852	7	and	and	CCONJ
cjfa-35471	852	8	interest	interest	NOUN
cjfa-35471	852	9	rate	rate	NOUN
cjfa-35471	852	10	𝑓𝑓(𝑡𝑡	𝑓𝑓(𝑡𝑡	NOUN
cjfa-35471	852	11	)	)	PUNCT
cjfa-35471	853	1	𝑡	𝑡	PROPN
cjfa-35471	853	2	𝑡𝑡𝑡	𝑡𝑡𝑡	NOUN
cjfa-35471	853	3	,	,	PUNCT
cjfa-35471	853	4	a	a	DET
cjfa-35471	853	5	5𝑡%	5𝑡%	NUM
cjfa-35471	853	6	decrease	decrease	NOUN
cjfa-35471	853	7	in	in	ADP
cjfa-35471	853	8	interest	interest	NOUN
cjfa-35471	853	9	rate	rate	NOUN
cjfa-35471	853	10	.	.	PUNCT
cjfa-35471	854	1	in	in	ADP
cjfa-35471	854	2	this	this	PRON
cjfa-35471	854	3	the	the	DET
cjfa-35471	854	4	inequality	inequality	NOUN
cjfa-35471	854	5	(	(	PUNCT
cjfa-35471	854	6	5	5	NUM
cjfa-35471	854	7	)	)	PUNCT
cjfa-35471	854	8	becomes	become	VERB
cjfa-35471	854	9	:	:	PUNCT
cjfa-35471	854	10	(	(	PUNCT
cjfa-35471	854	11	𝑡𝑡5	𝑡𝑡5	X
cjfa-35471	854	12	∗	∗	NOUN
cjfa-35471	854	13	3(4	3(4	NUM
cjfa-35471	854	14	+	+	CCONJ
cjfa-35471	854	15	sin(2𝜋𝜋𝑡𝑡	sin(2𝜋𝜋𝑡𝑡	ADJ
cjfa-35471	854	16	)	)	PUNCT
cjfa-35471	854	17	−	−	PRON
cjfa-35471	854	18	𝑡	𝑡	NOUN
cjfa-35471	854	19	)	)	PUNCT
cjfa-35471	854	20	∗	∗	NOUN
cjfa-35471	854	21	𝑐𝑐𝑐𝑐𝑐𝑐2𝜋𝜋𝑡𝑡	𝑐𝑐𝑐𝑐𝑐𝑐2𝜋𝜋𝑡𝑡	PROPN
cjfa-35471	854	22	≤	≤	NOUN
cjfa-35471	854	23	2𝑡5	2𝑡5	NUM
cjfa-35471	855	1	+	+	CCONJ
cjfa-35471	855	2	𝑡𝑡𝑡𝑡	𝑡𝑡𝑡𝑡	NOUN
cjfa-35471	855	3	∗	∗	NOUN
cjfa-35471	855	4	(	(	PUNCT
cjfa-35471	855	5	𝑡𝑡5	𝑡𝑡5	X
cjfa-35471	855	6	∗	∗	NOUN
cjfa-35471	855	7	3	3	NUM
cjfa-35471	855	8	∗	∗	NOUN
cjfa-35471	855	9	(	(	PUNCT
cjfa-35471	855	10	4	4	NUM
cjfa-35471	855	11	+	+	CCONJ
cjfa-35471	855	12	sin(2𝜋𝜋𝜋𝜋	sin(2𝜋𝜋𝜋𝜋	NOUN
cjfa-35471	855	13	)	)	PUNCT
cjfa-35471	855	14	)	)	PUNCT
cjfa-35471	855	15	�	�	PROPN
cjfa-35471	855	16	−	−	NOUN
cjfa-35471	855	17	2	2	NUM
cjfa-35471	855	18	∗	∗	NOUN
cjfa-35471	855	19	(	(	PUNCT
cjfa-35471	855	20	4	4	NUM
cjfa-35471	855	21	+	+	CCONJ
cjfa-35471	855	22	sin(2𝜋𝜋𝜋𝜋	sin(2𝜋𝜋𝜋𝜋	NOUN
cjfa-35471	855	23	)	)	PUNCT
cjfa-35471	856	1	+	+	CCONJ
cjfa-35471	856	2	𝑡)/2𝜋𝜋	𝑡)/2𝜋𝜋	X
cjfa-35471	856	3	(	(	PUNCT
cjfa-35471	856	4	8)	8)	NUM
cjfa-35471	856	5	the	the	DET
cjfa-35471	856	6	graphs	graph	NOUN
cjfa-35471	856	7	of	of	ADP
cjfa-35471	856	8	the	the	DET
cjfa-35471	856	9	functions	function	NOUN
cjfa-35471	856	10	on	on	ADP
cjfa-35471	856	11	both	both	DET
cjfa-35471	856	12	sides	side	NOUN
cjfa-35471	856	13	of	of	ADP
cjfa-35471	856	14	this	this	DET
cjfa-35471	856	15	inequality	inequality	NOUN
cjfa-35471	856	16	are	be	AUX
cjfa-35471	856	17	shown	show	VERB
cjfa-35471	856	18	in	in	ADP
cjfa-35471	856	19	figure	figure	NOUN
cjfa-35471	856	20	4	4	NUM
cjfa-35471	856	21	below	below	ADV
cjfa-35471	856	22	.	.	PUNCT
cjfa-35471	857	1	case	case	NOUN
cjfa-35471	857	2	v	v	ADP
cjfa-35471	857	3	:	:	PUNCT
cjfa-35471	857	4	𝑘𝑘	𝑘𝑘	PROPN
cjfa-35471	857	5	𝑡	𝑡	NOUN
cjfa-35471	857	6	𝑡𝑘	𝑡𝑘	ADV
cjfa-35471	857	7	𝑓𝑓	𝑓𝑓	ADP
cjfa-35471	857	8	𝑡	𝑡	PROPN
cjfa-35471	857	9	5	5	NUM
cjfa-35471	857	10	%	%	NOUN
cjfa-35471	857	11	.	.	PUNCT
cjfa-35471	858	1	reducing	reduce	VERB
cjfa-35471	858	2	the	the	DET
cjfa-35471	858	3	interest	interest	NOUN
cjfa-35471	858	4	rate	rate	NOUN
cjfa-35471	858	5	from	from	ADP
cjfa-35471	858	6	0.10	0.10	NUM
cjfa-35471	858	7	to	to	ADP
cjfa-35471	858	8	0.05	0.05	NUM
cjfa-35471	858	9	,	,	PUNCT
cjfa-35471	858	10	we	we	PRON
cjfa-35471	858	11	get	get	VERB
cjfa-35471	858	12	figure	figure	NOUN
cjfa-35471	858	13	5	5	NUM
cjfa-35471	858	14	.	.	PUNCT
cjfa-35471	859	1	figure	figure	NOUN
cjfa-35471	859	2	2	2	NUM
cjfa-35471	859	3	.	.	PUNCT
cjfa-35471	859	4	graphs	graph	NOUN
cjfa-35471	859	5	of	of	ADP
cjfa-35471	859	6	left	left	ADJ
cjfa-35471	859	7	(	(	PUNCT
cjfa-35471	859	8	𝑓𝑓(𝜋𝜋	𝑓𝑓(𝜋𝜋	NOUN
cjfa-35471	859	9	)	)	PUNCT
cjfa-35471	859	10	)	)	PUNCT
cjfa-35471	860	1	and	and	CCONJ
cjfa-35471	860	2	right	right	INTJ
cjfa-35471	860	3	(	(	PUNCT
cjfa-35471	860	4	𝑔𝑔(𝜋𝜋	𝑔𝑔(𝜋𝜋	NOUN
cjfa-35471	860	5	)	)	PUNCT
cjfa-35471	860	6	)	)	PUNCT
cjfa-35471	860	7	sides	side	NOUN
cjfa-35471	860	8	of	of	ADP
cjfa-35471	860	9	inequality	inequality	NOUN
cjfa-35471	860	10	(	(	PUNCT
cjfa-35471	860	11	6	6	NUM
cjfa-35471	860	12	)	)	PUNCT
cjfa-35471	860	13	and	and	CCONJ
cjfa-35471	860	14	demand	demand	NOUN
cjfa-35471	860	15	function	function	PROPN
cjfa-35471	860	16	�	�	PROPN
cjfa-35471	860	17	�	�	PROPN
cjfa-35471	860	18	(	(	PUNCT
cjfa-35471	860	19	𝜋𝜋	𝜋𝜋	PROPN
cjfa-35471	860	20	)	)	PUNCT
cjfa-35471	860	21	�	�	PROPN
cjfa-35471	860	22	(	(	PUNCT
cjfa-35471	860	23	8)	8)	NUM
cjfa-35471	860	24	mustafa	mustafa	PROPN
cjfa-35471	860	25	akan	akan	PROPN
cjfa-35471	860	26	,	,	PUNCT
cjfa-35471	860	27	natalia	natalia	PROPN
cjfa-35471	860	28	konovalova20	konovalova20	VERB
cjfa-35471	860	29	the	the	DET
cjfa-35471	860	30	graphs	graph	NOUN
cjfa-35471	860	31	of	of	ADP
cjfa-35471	860	32	the	the	DET
cjfa-35471	860	33	functions	function	NOUN
cjfa-35471	860	34	on	on	ADP
cjfa-35471	860	35	both	both	DET
cjfa-35471	860	36	sides	side	NOUN
cjfa-35471	860	37	of	of	ADP
cjfa-35471	860	38	this	this	DET
cjfa-35471	860	39	inequality	inequality	NOUN
cjfa-35471	860	40	are	be	AUX
cjfa-35471	860	41	shown	show	VERB
cjfa-35471	860	42	in	in	ADP
cjfa-35471	860	43	figure	figure	NOUN
cjfa-35471	860	44	4	4	NUM
cjfa-35471	860	45	below	below	ADV
cjfa-35471	860	46	.	.	PUNCT
cjfa-35471	861	1	case	case	NOUN
cjfa-35471	861	2	v	v	ADP
cjfa-35471	861	3	:	:	PUNCT
cjfa-35471	861	4	k	k	NOUN
cjfa-35471	861	5	=	=	SYM
cjfa-35471	861	6	1	1	NUM
cjfa-35471	861	7	,	,	PUNCT
cjfa-35471	861	8	f	f	NOUN
cjfa-35471	861	9	=	=	SYM
cjfa-35471	861	10	50	50	NUM
cjfa-35471	861	11	%	%	NOUN
cjfa-35471	861	12	.	.	PUNCT
cjfa-35471	862	1	reducing	reduce	VERB
cjfa-35471	862	2	the	the	DET
cjfa-35471	862	3	interest	interest	NOUN
cjfa-35471	862	4	rate	rate	NOUN
cjfa-35471	862	5	from	from	ADP
cjfa-35471	862	6	0.10	0.10	NUM
cjfa-35471	862	7	to	to	ADP
cjfa-35471	862	8	0.05	0.05	NUM
cjfa-35471	862	9	,	,	PUNCT
cjfa-35471	862	10	we	we	PRON
cjfa-35471	862	11	get	get	VERB
cjfa-35471	862	12	figure	figure	NOUN
cjfa-35471	862	13	5	5	NUM
cjfa-35471	862	14	.	.	PUNCT
cjfa-35471	863	1	figure	figure	NOUN
cjfa-35471	863	2	2	2	NUM
cjfa-35471	863	3	.	.	PUNCT
cjfa-35471	863	4	graphs	graph	NOUN
cjfa-35471	863	5	of	of	ADP
cjfa-35471	863	6	left	left	ADJ
cjfa-35471	863	7	(	(	PUNCT
cjfa-35471	863	8	f(x	f(x	PROPN
cjfa-35471	863	9	)	)	PUNCT
cjfa-35471	863	10	and	and	CCONJ
cjfa-35471	863	11	right	right	ADJ
cjfa-35471	863	12	(	(	PUNCT
cjfa-35471	863	13	g(x	g(x	NOUN
cjfa-35471	863	14	)	)	PUNCT
cjfa-35471	863	15	)	)	PUNCT
cjfa-35471	863	16	sides	side	NOUN
cjfa-35471	863	17	of	of	ADP
cjfa-35471	863	18	inequality	inequality	NOUN
cjfa-35471	863	19	(	(	PUNCT
cjfa-35471	863	20	6	6	NUM
cjfa-35471	863	21	)	)	PUNCT
cjfa-35471	863	22	and	and	CCONJ
cjfa-35471	863	23	demand	demand	NOUN
cjfa-35471	863	24	function	function	NOUN
cjfa-35471	863	25	(	(	PUNCT
cjfa-35471	863	26	h(x	h(x	PROPN
cjfa-35471	863	27	)	)	PUNCT
cjfa-35471	863	28	)	)	PUNCT
cjfa-35471	864	1	source	source	NOUN
cjfa-35471	864	2	:	:	PUNCT
cjfa-35471	864	3	constructed	construct	VERB
cjfa-35471	864	4	by	by	ADP
cjfa-35471	864	5	authors	author	NOUN
cjfa-35471	864	6	.	.	PUNCT
cjfa-35471	865	1	figure	figure	VERB
cjfa-35471	865	2	3	3	NUM
cjfa-35471	865	3	.	.	PUNCT
cjfa-35471	865	4	graphs	graph	NOUN
cjfa-35471	865	5	of	of	ADP
cjfa-35471	865	6	left	left	NOUN
cjfa-35471	865	7	(	(	PUNCT
cjfa-35471	865	8	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	865	9	and	and	CCONJ
cjfa-35471	865	10	right	right	ADJ
cjfa-35471	865	11	(	(	PUNCT
cjfa-35471	865	12	𝑔𝑔𝑓𝑓𝑓𝑓	𝑔𝑔𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	865	13	)	)	PUNCT
cjfa-35471	865	14	sides	side	NOUN
cjfa-35471	865	15	of	of	ADP
cjfa-35471	865	16	inequality	inequality	NOUN
cjfa-35471	865	17	(	(	PUNCT
cjfa-35471	865	18	7	7	NUM
cjfa-35471	865	19	)	)	PUNCT
cjfa-35471	865	20	and	and	CCONJ
cjfa-35471	865	21	demand	demand	NOUN
cjfa-35471	865	22	function	function	PROPN
cjfa-35471	865	23	�	�	PROPN
cjfa-35471	865	24	�	�	PROPN
cjfa-35471	865	25	𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓	PROPN
cjfa-35471	865	26	�	�	PROPN
cjfa-35471	865	27	s	s	PART
cjfa-35471	865	28	o	o	NOUN
cjfa-35471	865	29	u	u	NOUN
cjfa-35471	865	30	r	r	NOUN
cjfa-35471	865	31	c	c	NOUN
cjfa-35471	865	32	e	e	NOUN
cjfa-35471	865	33	:	:	PUNCT
cjfa-35471	865	34	constructed	construct	VERB
cjfa-35471	865	35	by	by	ADP
cjfa-35471	865	36	authors	author	NOUN
cjfa-35471	865	37	.	.	PUNCT
cjfa-35471	866	1	optimal	optimal	ADJ
cjfa-35471	866	2	incentives	incentive	NOUN
cjfa-35471	866	3	for	for	ADP
cjfa-35471	866	4	economic	economic	ADJ
cjfa-35471	866	5	growth	growth	NOUN
cjfa-35471	866	6	…	…	PUNCT
cjfa-35471	866	7	21	21	NUM
cjfa-35471	866	8	figure	figure	NOUN
cjfa-35471	866	9	3	3	NUM
cjfa-35471	866	10	.	.	PUNCT
cjfa-35471	866	11	graphs	graph	NOUN
cjfa-35471	866	12	of	of	ADP
cjfa-35471	866	13	left	left	ADJ
cjfa-35471	866	14	(	(	PUNCT
cjfa-35471	866	15	f(x	f(x	PROPN
cjfa-35471	866	16	)	)	PUNCT
cjfa-35471	866	17	and	and	CCONJ
cjfa-35471	866	18	right	right	ADJ
cjfa-35471	866	19	(	(	PUNCT
cjfa-35471	866	20	g(x	g(x	NOUN
cjfa-35471	866	21	)	)	PUNCT
cjfa-35471	866	22	)	)	PUNCT
cjfa-35471	866	23	sides	side	NOUN
cjfa-35471	866	24	of	of	ADP
cjfa-35471	866	25	inequality	inequality	NOUN
cjfa-35471	866	26	(	(	PUNCT
cjfa-35471	866	27	7	7	NUM
cjfa-35471	866	28	)	)	PUNCT
cjfa-35471	866	29	and	and	CCONJ
cjfa-35471	866	30	demand	demand	NOUN
cjfa-35471	866	31	function	function	NOUN
cjfa-35471	866	32	(	(	PUNCT
cjfa-35471	866	33	h(x	h(x	PROPN
cjfa-35471	866	34	)	)	PUNCT
cjfa-35471	866	35	)	)	PUNCT
cjfa-35471	867	1	source	source	NOUN
cjfa-35471	867	2	:	:	PUNCT
cjfa-35471	867	3	constructed	construct	VERB
cjfa-35471	867	4	by	by	ADP
cjfa-35471	867	5	authors	author	NOUN
cjfa-35471	867	6	.	.	PUNCT
cjfa-35471	868	1	figure	figure	VERB
cjfa-35471	868	2	4	4	NUM
cjfa-35471	868	3	.	.	PUNCT
cjfa-35471	869	1	graphs	graph	NOUN
cjfa-35471	869	2	of	of	ADP
cjfa-35471	869	3	left	left	NOUN
cjfa-35471	869	4	(	(	PUNCT
cjfa-35471	869	5	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	869	6	and	and	CCONJ
cjfa-35471	869	7	right	right	ADJ
cjfa-35471	869	8	(	(	PUNCT
cjfa-35471	869	9	𝑔𝑔𝑓𝑓𝑓𝑓	𝑔𝑔𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	869	10	)	)	PUNCT
cjfa-35471	869	11	sides	side	NOUN
cjfa-35471	869	12	of	of	ADP
cjfa-35471	869	13	inequality	inequality	NOUN
cjfa-35471	869	14	(	(	PUNCT
cjfa-35471	869	15	8)	8)	NUM
cjfa-35471	869	16	and	and	CCONJ
cjfa-35471	869	17	demand	demand	NOUN
cjfa-35471	869	18	function	function	PROPN
cjfa-35471	869	19	�	�	PROPN
cjfa-35471	869	20	�	�	PROPN
cjfa-35471	869	21	𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓	PROPN
cjfa-35471	869	22	�	�	PROPN
cjfa-35471	869	23	s	s	PART
cjfa-35471	869	24	o	o	NOUN
cjfa-35471	869	25	u	u	NOUN
cjfa-35471	869	26	r	r	NOUN
cjfa-35471	869	27	c	c	NOUN
cjfa-35471	869	28	e	e	NOUN
cjfa-35471	869	29	:	:	PUNCT
cjfa-35471	869	30	constructed	construct	VERB
cjfa-35471	869	31	by	by	ADP
cjfa-35471	869	32	authors	author	NOUN
cjfa-35471	869	33	.	.	PUNCT
cjfa-35471	870	1	mustafa	mustafa	PROPN
cjfa-35471	870	2	akan	akan	PROPN
cjfa-35471	870	3	,	,	PUNCT
cjfa-35471	870	4	natalia	natalia	PROPN
cjfa-35471	870	5	konovalova22	konovalova22	PROPN
cjfa-35471	870	6	figure	figure	NOUN
cjfa-35471	870	7	4	4	NUM
cjfa-35471	870	8	.	.	PUNCT
cjfa-35471	870	9	graphs	graph	NOUN
cjfa-35471	870	10	of	of	ADP
cjfa-35471	870	11	left	left	ADJ
cjfa-35471	870	12	(	(	PUNCT
cjfa-35471	870	13	f(x	f(x	PROPN
cjfa-35471	870	14	)	)	PUNCT
cjfa-35471	870	15	and	and	CCONJ
cjfa-35471	870	16	right	right	ADJ
cjfa-35471	870	17	(	(	PUNCT
cjfa-35471	870	18	g(x	g(x	NOUN
cjfa-35471	870	19	)	)	PUNCT
cjfa-35471	870	20	)	)	PUNCT
cjfa-35471	870	21	sides	side	NOUN
cjfa-35471	870	22	of	of	ADP
cjfa-35471	870	23	inequality	inequality	NOUN
cjfa-35471	870	24	(	(	PUNCT
cjfa-35471	870	25	8)	8)	NUM
cjfa-35471	870	26	and	and	CCONJ
cjfa-35471	870	27	demand	demand	NOUN
cjfa-35471	870	28	function	function	NOUN
cjfa-35471	870	29	(	(	PUNCT
cjfa-35471	870	30	h(x	h(x	PROPN
cjfa-35471	870	31	)	)	PUNCT
cjfa-35471	870	32	)	)	PUNCT
cjfa-35471	870	33	source	source	NOUN
cjfa-35471	870	34	:	:	PUNCT
cjfa-35471	870	35	constructed	construct	VERB
cjfa-35471	870	36	by	by	ADP
cjfa-35471	870	37	authors	author	NOUN
cjfa-35471	870	38	.	.	PUNCT
cjfa-35471	871	1	notice	notice	NOUN
cjfa-35471	871	2	in	in	ADP
cjfa-35471	871	3	this	this	DET
cjfa-35471	871	4	case	case	NOUN
cjfa-35471	871	5	that	that	SCONJ
cjfa-35471	871	6	the	the	DET
cjfa-35471	871	7	firms	firm	NOUN
cjfa-35471	871	8	stop	stop	VERB
cjfa-35471	871	9	and	and	CCONJ
cjfa-35471	871	10	starts	start	VERB
cjfa-35471	871	11	production	production	NOUN
cjfa-35471	871	12	at	at	ADP
cjfa-35471	871	13	about	about	ADV
cjfa-35471	871	14	the	the	DET
cjfa-35471	871	15	same	same	ADJ
cjfa-35471	871	16	time	time	NOUN
cjfa-35471	871	17	as	as	ADP
cjfa-35471	871	18	in	in	ADP
cjfa-35471	871	19	the	the	DET
cjfa-35471	871	20	case	case	NOUN
cjfa-35471	871	21	when	when	SCONJ
cjfa-35471	871	22	interest	interest	NOUN
cjfa-35471	871	23	rate	rate	NOUN
cjfa-35471	871	24	is=20	is=20	PROPN
cjfa-35471	872	1	%	%	NOUN
cjfa-35471	872	2	(	(	PUNCT
cjfa-35471	872	3	previous	previous	ADJ
cjfa-35471	872	4	case	case	NOUN
cjfa-35471	872	5	)	)	PUNCT
cjfa-35471	872	6	implying	imply	VERB
cjfa-35471	872	7	that	that	SCONJ
cjfa-35471	872	8	reduced	reduce	VERB
cjfa-35471	872	9	interest	interest	NOUN
cjfa-35471	872	10	rates	rate	NOUN
cjfa-35471	872	11	do	do	AUX
cjfa-35471	872	12	not	not	PART
cjfa-35471	872	13	affect	affect	VERB
cjfa-35471	872	14	production	production	NOUN
cjfa-35471	872	15	significantly	significantly	ADV
cjfa-35471	872	16	.	.	PUNCT
cjfa-35471	873	1	figure	figure	VERB
cjfa-35471	873	2	5	5	NUM
cjfa-35471	873	3	.	.	PUNCT
cjfa-35471	874	1	graphs	graph	NOUN
cjfa-35471	874	2	of	of	ADP
cjfa-35471	874	3	left	left	NOUN
cjfa-35471	874	4	(	(	PUNCT
cjfa-35471	874	5	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	874	6	and	and	CCONJ
cjfa-35471	874	7	right	right	ADJ
cjfa-35471	874	8	(	(	PUNCT
cjfa-35471	874	9	𝑔𝑔𝑓𝑓𝑓𝑓	𝑔𝑔𝑓𝑓𝑓𝑓	NOUN
cjfa-35471	874	10	)	)	PUNCT
cjfa-35471	874	11	sides	side	NOUN
cjfa-35471	874	12	of	of	ADP
cjfa-35471	874	13	inequality	inequality	NOUN
cjfa-35471	874	14	(	(	PUNCT
cjfa-35471	874	15	8)	8)	NUM
cjfa-35471	874	16	and	and	CCONJ
cjfa-35471	874	17	demand	demand	NOUN
cjfa-35471	874	18	function	function	PROPN
cjfa-35471	874	19	�	�	PROPN
cjfa-35471	874	20	�	�	PROPN
cjfa-35471	874	21	𝑓𝑓𝑓𝑓	𝑓𝑓𝑓𝑓	PROPN
cjfa-35471	874	22	�	�	PROPN
cjfa-35471	874	23	with	with	ADP
cjfa-35471	874	24	𝑓𝑓𝑓𝑡𝑡𝑓	𝑓𝑓𝑓𝑡𝑡𝑓	PROPN
cjfa-35471	874	25	=	=	SYM
cjfa-35471	874	26	5	5	NUM
cjfa-35471	874	27	%	%	NOUN
cjfa-35471	874	28	s	s	PART
cjfa-35471	874	29	o	o	NOUN
cjfa-35471	874	30	u	u	NOUN
cjfa-35471	874	31	r	r	NOUN
cjfa-35471	874	32	c	c	NOUN
cjfa-35471	874	33	e	e	NOUN
cjfa-35471	874	34	:	:	PUNCT
cjfa-35471	874	35	constructed	construct	VERB
cjfa-35471	874	36	by	by	ADP
cjfa-35471	874	37	authors	author	NOUN
cjfa-35471	874	38	.	.	PUNCT
cjfa-35471	875	1	notice	notice	NOUN
cjfa-35471	875	2	in	in	ADP
cjfa-35471	875	3	this	this	DET
cjfa-35471	875	4	case	case	NOUN
cjfa-35471	875	5	that	that	SCONJ
cjfa-35471	875	6	the	the	DET
cjfa-35471	875	7	firms	firm	NOUN
cjfa-35471	875	8	stop	stop	VERB
cjfa-35471	875	9	and	and	CCONJ
cjfa-35471	875	10	starts	start	VERB
cjfa-35471	875	11	production	production	NOUN
cjfa-35471	875	12	at	at	ADP
cjfa-35471	875	13	about	about	ADV
cjfa-35471	875	14	the	the	DET
cjfa-35471	875	15	same	same	ADJ
cjfa-35471	875	16	time	time	NOUN
cjfa-35471	875	17	as	as	ADP
cjfa-35471	875	18	in	in	ADP
cjfa-35471	875	19	the	the	DET
cjfa-35471	875	20	case	case	NOUN
cjfa-35471	875	21	when	when	SCONJ
cjfa-35471	875	22	interest	interest	NOUN
cjfa-35471	875	23	rate	rate	NOUN
cjfa-35471	875	24	is=20	is=20	PROPN
cjfa-35471	876	1	%	%	NOUN
cjfa-35471	876	2	(	(	PUNCT
cjfa-35471	876	3	previous	previous	ADJ
cjfa-35471	876	4	case	case	NOUN
cjfa-35471	876	5	)	)	PUNCT
cjfa-35471	876	6	implying	imply	VERB
cjfa-35471	876	7	that	that	SCONJ
cjfa-35471	876	8	reduced	reduce	VERB
cjfa-35471	876	9	interest	interest	NOUN
cjfa-35471	876	10	rates	rate	NOUN
cjfa-35471	876	11	do	do	AUX
cjfa-35471	876	12	not	not	PART
cjfa-35471	876	13	affect	affect	VERB
cjfa-35471	876	14	production	production	NOUN
cjfa-35471	876	15	significantly	significantly	ADV
cjfa-35471	876	16	.	.	PUNCT
cjfa-35471	877	1	optimal	optimal	ADJ
cjfa-35471	877	2	incentives	incentive	NOUN
cjfa-35471	877	3	for	for	ADP
cjfa-35471	877	4	economic	economic	ADJ
cjfa-35471	877	5	growth	growth	NOUN
cjfa-35471	877	6	…	…	PUNCT
cjfa-35471	877	7	23	23	NUM
cjfa-35471	877	8	figure	figure	NOUN
cjfa-35471	877	9	5	5	NUM
cjfa-35471	877	10	.	.	PUNCT
cjfa-35471	877	11	graphs	graph	NOUN
cjfa-35471	877	12	of	of	ADP
cjfa-35471	877	13	left	left	ADJ
cjfa-35471	877	14	(	(	PUNCT
cjfa-35471	877	15	f(x	f(x	PROPN
cjfa-35471	877	16	)	)	PUNCT
cjfa-35471	877	17	and	and	CCONJ
cjfa-35471	877	18	right	right	ADJ
cjfa-35471	877	19	(	(	PUNCT
cjfa-35471	877	20	g(x	g(x	NOUN
cjfa-35471	877	21	)	)	PUNCT
cjfa-35471	877	22	)	)	PUNCT
cjfa-35471	877	23	sides	side	NOUN
cjfa-35471	877	24	of	of	ADP
cjfa-35471	877	25	inequality	inequality	NOUN
cjfa-35471	877	26	(	(	PUNCT
cjfa-35471	877	27	8)	8)	NUM
cjfa-35471	877	28	and	and	CCONJ
cjfa-35471	877	29	demand	demand	NOUN
cjfa-35471	877	30	function	function	NOUN
cjfa-35471	877	31	(	(	PUNCT
cjfa-35471	877	32	h(x	h(x	PROPN
cjfa-35471	877	33	)	)	PUNCT
cjfa-35471	877	34	)	)	PUNCT
cjfa-35471	877	35	with	with	ADP
cjfa-35471	877	36	f(t	f(t	NOUN
cjfa-35471	877	37	)	)	PUNCT
cjfa-35471	877	38	=	=	SYM
cjfa-35471	877	39	5	5	NUM
cjfa-35471	877	40	%	%	NOUN
cjfa-35471	877	41	source	source	NOUN
cjfa-35471	877	42	:	:	PUNCT
cjfa-35471	877	43	constructed	construct	VERB
cjfa-35471	877	44	by	by	ADP
cjfa-35471	877	45	authors	author	NOUN
cjfa-35471	877	46	.	.	PUNCT
cjfa-35471	878	1	notice	notice	VERB
cjfa-35471	878	2	that	that	SCONJ
cjfa-35471	878	3	the	the	DET
cjfa-35471	878	4	times	time	NOUN
cjfa-35471	878	5	at	at	ADP
cjfa-35471	878	6	which	which	PRON
cjfa-35471	878	7	production	production	NOUN
cjfa-35471	878	8	stopped	stop	VERB
cjfa-35471	878	9	and	and	CCONJ
cjfa-35471	878	10	restarted	restart	VERB
cjfa-35471	878	11	are	be	AUX
cjfa-35471	878	12	the	the	DET
cjfa-35471	878	13	same	same	ADJ
cjfa-35471	878	14	as	as	ADP
cjfa-35471	878	15	in	in	ADP
cjfa-35471	878	16	the	the	DET
cjfa-35471	878	17	case	case	NOUN
cjfa-35471	878	18	when	when	SCONJ
cjfa-35471	878	19	interest	interest	NOUN
cjfa-35471	878	20	rate	rate	NOUN
cjfa-35471	878	21	was	be	AUX
cjfa-35471	878	22	10	10	NUM
cjfa-35471	878	23	%	%	NOUN
cjfa-35471	878	24	.	.	PUNCT
cjfa-35471	879	1	this	this	PRON
cjfa-35471	879	2	is	be	AUX
cjfa-35471	879	3	an	an	DET
cjfa-35471	879	4	important	important	ADJ
cjfa-35471	879	5	result	result	NOUN
cjfa-35471	879	6	since	since	SCONJ
cjfa-35471	879	7	it	it	PRON
cjfa-35471	879	8	helps	help	VERB
cjfa-35471	879	9	to	to	PART
cjfa-35471	879	10	explain	explain	VERB
cjfa-35471	879	11	why	why	SCONJ
cjfa-35471	879	12	low	low	ADJ
cjfa-35471	879	13	interest	interest	NOUN
cjfa-35471	879	14	rates	rate	NOUN
cjfa-35471	879	15	are	be	AUX
cjfa-35471	879	16	no	no	ADV
cjfa-35471	879	17	longer	long	ADV
cjfa-35471	879	18	effective	effective	ADJ
cjfa-35471	879	19	to	to	PART
cjfa-35471	879	20	induce	induce	VERB
cjfa-35471	879	21	growth	growth	NOUN
cjfa-35471	879	22	.	.	PUNCT
cjfa-35471	880	1	research	research	NOUN
cjfa-35471	880	2	results	result	NOUN
cjfa-35471	880	3	and	and	CCONJ
cjfa-35471	880	4	conclusions	conclusion	NOUN
cjfa-35471	880	5	general	general	ADJ
cjfa-35471	880	6	results	result	NOUN
cjfa-35471	880	7	and	and	CCONJ
cjfa-35471	880	8	conclusions	conclusion	NOUN
cjfa-35471	880	9	:	:	PUNCT
cjfa-35471	880	10	based	base	VERB
cjfa-35471	880	11	on	on	ADP
cjfa-35471	880	12	the	the	DET
cjfa-35471	880	13	study	study	NOUN
cjfa-35471	880	14	of	of	ADP
cjfa-35471	880	15	cases	case	NOUN
cjfa-35471	880	16	i	i	NOUN
cjfa-35471	880	17	-	-	PUNCT
cjfa-35471	880	18	v	v	NOUN
cjfa-35471	880	19	and	and	CCONJ
cjfa-35471	880	20	the	the	DET
cjfa-35471	880	21	graphs	graph	NOUN
cjfa-35471	880	22	associated	associate	VERB
cjfa-35471	880	23	with	with	ADP
cjfa-35471	880	24	these	these	DET
cjfa-35471	880	25	cases	case	NOUN
cjfa-35471	880	26	,	,	PUNCT
cjfa-35471	880	27	following	follow	VERB
cjfa-35471	880	28	results	result	NOUN
cjfa-35471	880	29	and	and	CCONJ
cjfa-35471	880	30	their	their	PRON
cjfa-35471	880	31	policy	policy	NOUN
cjfa-35471	880	32	implications	implication	NOUN
cjfa-35471	880	33	can	can	AUX
cjfa-35471	880	34	be	be	AUX
cjfa-35471	880	35	summarized	summarize	VERB
cjfa-35471	880	36	as	as	ADP
cjfa-35471	880	37	:	:	PUNCT
cjfa-35471	880	38	1	1	NUM
cjfa-35471	880	39	.	.	X
cjfa-35471	880	40	high	high	ADJ
cjfa-35471	880	41	holding	holding	NOUN
cjfa-35471	880	42	costs	cost	NOUN
cjfa-35471	880	43	affect	affect	VERB
cjfa-35471	880	44	the	the	DET
cjfa-35471	880	45	production	production	NOUN
cjfa-35471	880	46	decisions	decision	NOUN
cjfa-35471	880	47	negatively	negatively	ADV
cjfa-35471	880	48	.	.	PUNCT
cjfa-35471	881	1	2	2	X
cjfa-35471	881	2	.	.	X
cjfa-35471	881	3	the	the	DET
cjfa-35471	881	4	impact	impact	NOUN
cjfa-35471	881	5	of	of	ADP
cjfa-35471	881	6	new	new	ADJ
cjfa-35471	881	7	technologies	technology	NOUN
cjfa-35471	881	8	depends	depend	VERB
cjfa-35471	881	9	on	on	ADP
cjfa-35471	881	10	the	the	DET
cjfa-35471	881	11	efficiencies	efficiency	NOUN
cjfa-35471	881	12	brought	bring	VERB
cjfa-35471	881	13	about	about	ADP
cjfa-35471	881	14	by	by	ADP
cjfa-35471	881	15	the	the	DET
cjfa-35471	881	16	new	new	ADJ
cjfa-35471	881	17	technology	technology	NOUN
cjfa-35471	881	18	.	.	PUNCT
cjfa-35471	882	1	new	new	ADJ
cjfa-35471	882	2	technology	technology	NOUN
cjfa-35471	882	3	has	have	VERB
cjfa-35471	882	4	no	no	DET
cjfa-35471	882	5	impact	impact	NOUN
cjfa-35471	882	6	on	on	ADP
cjfa-35471	882	7	production	production	NOUN
cjfa-35471	882	8	decision	decision	NOUN
cjfa-35471	882	9	if	if	SCONJ
cjfa-35471	882	10	it	it	PRON
cjfa-35471	882	11	reduces	reduce	VERB
cjfa-35471	882	12	the	the	DET
cjfa-35471	882	13	fixed	fix	VERB
cjfa-35471	882	14	s	s	NOUN
cjfa-35471	882	15	o	o	NOUN
cjfa-35471	882	16	u	u	NOUN
cjfa-35471	882	17	r	r	NOUN
cjfa-35471	882	18	c	c	NOUN
cjfa-35471	882	19	e	e	NOUN
cjfa-35471	882	20	:	:	PUNCT
cjfa-35471	882	21	constructed	construct	VERB
cjfa-35471	882	22	by	by	ADP
cjfa-35471	882	23	authors	author	NOUN
cjfa-35471	882	24	.	.	PUNCT
cjfa-35471	883	1	notice	notice	VERB
cjfa-35471	883	2	that	that	SCONJ
cjfa-35471	883	3	the	the	DET
cjfa-35471	883	4	times	time	NOUN
cjfa-35471	883	5	at	at	ADP
cjfa-35471	883	6	which	which	PRON
cjfa-35471	883	7	production	production	NOUN
cjfa-35471	883	8	stopped	stop	VERB
cjfa-35471	883	9	and	and	CCONJ
cjfa-35471	883	10	restarted	restart	VERB
cjfa-35471	883	11	are	be	AUX
cjfa-35471	883	12	the	the	DET
cjfa-35471	883	13	same	same	ADJ
cjfa-35471	883	14	as	as	ADP
cjfa-35471	883	15	in	in	ADP
cjfa-35471	883	16	the	the	DET
cjfa-35471	883	17	case	case	NOUN
cjfa-35471	883	18	when	when	SCONJ
cjfa-35471	883	19	interest	interest	NOUN
cjfa-35471	883	20	rate	rate	NOUN
cjfa-35471	883	21	was	be	AUX
cjfa-35471	883	22	10	10	NUM
cjfa-35471	883	23	%	%	NOUN
cjfa-35471	883	24	.	.	PUNCT
cjfa-35471	884	1	this	this	PRON
cjfa-35471	884	2	is	be	AUX
cjfa-35471	884	3	an	an	DET
cjfa-35471	884	4	important	important	ADJ
cjfa-35471	884	5	result	result	NOUN
cjfa-35471	884	6	since	since	SCONJ
cjfa-35471	884	7	it	it	PRON
cjfa-35471	884	8	helps	help	VERB
cjfa-35471	884	9	to	to	PART
cjfa-35471	884	10	explain	explain	VERB
cjfa-35471	884	11	why	why	SCONJ
cjfa-35471	884	12	low	low	ADJ
cjfa-35471	884	13	interest	interest	NOUN
cjfa-35471	884	14	rates	rate	NOUN
cjfa-35471	884	15	are	be	AUX
cjfa-35471	884	16	no	no	ADV
cjfa-35471	884	17	longer	long	ADV
cjfa-35471	884	18	effective	effective	ADJ
cjfa-35471	884	19	to	to	PART
cjfa-35471	884	20	induce	induce	VERB
cjfa-35471	884	21	growth	growth	NOUN
cjfa-35471	884	22	.	.	PUNCT
cjfa-35471	885	1	mustafa	mustafa	PROPN
cjfa-35471	885	2	akan	akan	PROPN
cjfa-35471	885	3	,	,	PUNCT
cjfa-35471	885	4	natalia	natalia	PROPN
cjfa-35471	885	5	konovalova24	konovalova24	PROPN
cjfa-35471	885	6	research	research	PROPN
cjfa-35471	885	7	results	result	NOUN
cjfa-35471	885	8	and	and	CCONJ
cjfa-35471	885	9	conclusions	conclusion	NOUN
cjfa-35471	885	10	general	general	ADJ
cjfa-35471	885	11	results	result	NOUN
cjfa-35471	885	12	and	and	CCONJ
cjfa-35471	885	13	conclusions	conclusion	NOUN
cjfa-35471	885	14	:	:	PUNCT
cjfa-35471	885	15	based	base	VERB
cjfa-35471	885	16	on	on	ADP
cjfa-35471	885	17	the	the	DET
cjfa-35471	885	18	study	study	NOUN
cjfa-35471	885	19	of	of	ADP
cjfa-35471	885	20	cases	case	NOUN
cjfa-35471	885	21	i	i	NOUN
cjfa-35471	885	22	-	-	PUNCT
cjfa-35471	885	23	v	v	NOUN
cjfa-35471	885	24	and	and	CCONJ
cjfa-35471	885	25	the	the	DET
cjfa-35471	885	26	graphs	graph	NOUN
cjfa-35471	885	27	associated	associate	VERB
cjfa-35471	885	28	with	with	ADP
cjfa-35471	885	29	these	these	DET
cjfa-35471	885	30	cases	case	NOUN
cjfa-35471	885	31	,	,	PUNCT
cjfa-35471	885	32	following	follow	VERB
cjfa-35471	885	33	results	result	NOUN
cjfa-35471	885	34	and	and	CCONJ
cjfa-35471	885	35	their	their	PRON
cjfa-35471	885	36	policy	policy	NOUN
cjfa-35471	885	37	implications	implication	NOUN
cjfa-35471	885	38	can	can	AUX
cjfa-35471	885	39	be	be	AUX
cjfa-35471	885	40	summarized	summarize	VERB
cjfa-35471	885	41	as	as	ADP
cjfa-35471	885	42	:	:	PUNCT
cjfa-35471	885	43	1	1	NUM
cjfa-35471	885	44	.	.	X
cjfa-35471	885	45	high	high	ADJ
cjfa-35471	885	46	holding	holding	NOUN
cjfa-35471	885	47	costs	cost	NOUN
cjfa-35471	885	48	affect	affect	VERB
cjfa-35471	885	49	the	the	DET
cjfa-35471	885	50	production	production	NOUN
cjfa-35471	885	51	decisions	decision	NOUN
cjfa-35471	885	52	negatively	negatively	ADV
cjfa-35471	885	53	.	.	PUNCT
cjfa-35471	886	1	2	2	X
cjfa-35471	886	2	.	.	X
cjfa-35471	886	3	the	the	DET
cjfa-35471	886	4	impact	impact	NOUN
cjfa-35471	886	5	of	of	ADP
cjfa-35471	886	6	new	new	ADJ
cjfa-35471	886	7	technologies	technology	NOUN
cjfa-35471	886	8	depends	depend	VERB
cjfa-35471	886	9	on	on	ADP
cjfa-35471	886	10	the	the	DET
cjfa-35471	886	11	efficiencies	efficiency	NOUN
cjfa-35471	886	12	brought	bring	VERB
cjfa-35471	886	13	about	about	ADP
cjfa-35471	886	14	by	by	ADP
cjfa-35471	886	15	the	the	DET
cjfa-35471	886	16	new	new	ADJ
cjfa-35471	886	17	technology	technology	NOUN
cjfa-35471	886	18	.	.	PUNCT
cjfa-35471	887	1	new	new	ADJ
cjfa-35471	887	2	technology	technology	NOUN
cjfa-35471	887	3	has	have	VERB
cjfa-35471	887	4	no	no	DET
cjfa-35471	887	5	impact	impact	NOUN
cjfa-35471	887	6	on	on	ADP
cjfa-35471	887	7	production	production	NOUN
cjfa-35471	887	8	decision	decision	NOUN
cjfa-35471	887	9	if	if	SCONJ
cjfa-35471	887	10	it	it	PRON
cjfa-35471	887	11	reduces	reduce	VERB
cjfa-35471	887	12	the	the	DET
cjfa-35471	887	13	fixed	fix	VERB
cjfa-35471	887	14	costs	cost	NOUN
cjfa-35471	887	15	only	only	ADV
cjfa-35471	887	16	or	or	CCONJ
cjfa-35471	887	17	the	the	DET
cjfa-35471	887	18	fixed	fix	VERB
cjfa-35471	887	19	part	part	NOUN
cjfa-35471	887	20	of	of	ADP
cjfa-35471	887	21	the	the	DET
cjfa-35471	887	22	marginal	marginal	ADJ
cjfa-35471	887	23	cost	cost	NOUN
cjfa-35471	887	24	.	.	PUNCT
cjfa-35471	888	1	the	the	DET
cjfa-35471	888	2	firm	firm	NOUN
cjfa-35471	888	3	will	will	AUX
cjfa-35471	888	4	stop	stop	VERB
cjfa-35471	888	5	producing	produce	VERB
cjfa-35471	888	6	sooner	soon	ADV
cjfa-35471	888	7	and	and	CCONJ
cjfa-35471	888	8	start	start	VERB
cjfa-35471	888	9	producing	produce	VERB
cjfa-35471	888	10	later	later	ADV
cjfa-35471	888	11	if	if	SCONJ
cjfa-35471	888	12	the	the	DET
cjfa-35471	888	13	new	new	ADJ
cjfa-35471	888	14	technology	technology	NOUN
cjfa-35471	888	15	reduces	reduce	VERB
cjfa-35471	888	16	the	the	DET
cjfa-35471	888	17	total	total	ADJ
cjfa-35471	888	18	marginal	marginal	ADJ
cjfa-35471	888	19	costs	cost	NOUN
cjfa-35471	888	20	.	.	PUNCT
cjfa-35471	889	1	this	this	PRON
cjfa-35471	889	2	is	be	AUX
cjfa-35471	889	3	a	a	DET
cjfa-35471	889	4	perplexing	perplexing	ADJ
cjfa-35471	889	5	result	result	NOUN
cjfa-35471	889	6	since	since	SCONJ
cjfa-35471	889	7	common	common	ADJ
cjfa-35471	889	8	sense	sense	NOUN
cjfa-35471	889	9	would	would	AUX
cjfa-35471	889	10	dictate	dictate	VERB
cjfa-35471	889	11	otherwise	otherwise	ADV
cjfa-35471	889	12	.	.	PUNCT
cjfa-35471	890	1	3	3	X
cjfa-35471	890	2	.	.	X
cjfa-35471	890	3	changes	change	NOUN
cjfa-35471	890	4	in	in	ADP
cjfa-35471	890	5	interest	interest	NOUN
cjfa-35471	890	6	rates	rate	NOUN
cjfa-35471	890	7	(	(	PUNCT
cjfa-35471	890	8	with	with	ADP
cjfa-35471	890	9	the	the	DET
cjfa-35471	890	10	assumed	assumed	ADJ
cjfa-35471	890	11	value	value	NOUN
cjfa-35471	890	12	of	of	ADP
cjfa-35471	890	13	the	the	DET
cjfa-35471	890	14	parameters	parameter	NOUN
cjfa-35471	890	15	)	)	PUNCT
cjfa-35471	890	16	do	do	AUX
cjfa-35471	890	17	not	not	PART
cjfa-35471	890	18	affect	affect	VERB
cjfa-35471	890	19	production	production	NOUN
cjfa-35471	890	20	.	.	PUNCT
cjfa-35471	891	1	4	4	X
cjfa-35471	891	2	.	.	X
cjfa-35471	891	3	cyclicality	cyclicality	NOUN
cjfa-35471	891	4	of	of	ADP
cjfa-35471	891	5	demand	demand	NOUN
cjfa-35471	891	6	will	will	AUX
cjfa-35471	891	7	affect	affect	VERB
cjfa-35471	891	8	production	production	NOUN
cjfa-35471	891	9	plans	plan	NOUN
cjfa-35471	891	10	.	.	PUNCT
cjfa-35471	892	1	extreme	extreme	ADJ
cjfa-35471	892	2	periodicity	periodicity	NOUN
cjfa-35471	892	3	(	(	PUNCT
cjfa-35471	892	4	cyclicality	cyclicality	NOUN
cjfa-35471	892	5	)	)	PUNCT
cjfa-35471	892	6	of	of	ADP
cjfa-35471	892	7	demand	demand	NOUN
cjfa-35471	892	8	may	may	AUX
cjfa-35471	892	9	result	result	VERB
cjfa-35471	892	10	in	in	ADP
cjfa-35471	892	11	firms	firm	NOUN
cjfa-35471	892	12	never	never	ADV
cjfa-35471	892	13	producing	produce	VERB
cjfa-35471	892	14	for	for	ADP
cjfa-35471	892	15	inventories	inventory	NOUN
cjfa-35471	892	16	.	.	PUNCT
cjfa-35471	893	1	in	in	ADP
cjfa-35471	893	2	case	case	NOUN
cjfa-35471	893	3	of	of	ADP
cjfa-35471	893	4	higher	high	ADJ
cjfa-35471	893	5	cyclicality	cyclicality	NOUN
cjfa-35471	893	6	,	,	PUNCT
cjfa-35471	893	7	both	both	CCONJ
cjfa-35471	893	8	the	the	DET
cjfa-35471	893	9	demand	demand	NOUN
cjfa-35471	893	10	and	and	CCONJ
cjfa-35471	893	11	the	the	DET
cjfa-35471	893	12	cost	cost	NOUN
cjfa-35471	893	13	functions	function	NOUN
cjfa-35471	893	14	will	will	AUX
cjfa-35471	893	15	fluctuate	fluctuate	VERB
cjfa-35471	893	16	as	as	ADV
cjfa-35471	893	17	many	many	ADJ
cjfa-35471	893	18	times	time	NOUN
cjfa-35471	893	19	as	as	ADP
cjfa-35471	893	20	the	the	DET
cjfa-35471	893	21	cyclicality	cyclicality	NOUN
cjfa-35471	893	22	in	in	ADP
cjfa-35471	893	23	a	a	DET
cjfa-35471	893	24	given	give	VERB
cjfa-35471	893	25	time	time	NOUN
cjfa-35471	893	26	horizon	horizon	NOUN
cjfa-35471	893	27	(	(	PUNCT
cjfa-35471	893	28	assumed	assume	VERB
cjfa-35471	893	29	to	to	PART
cjfa-35471	893	30	be	be	AUX
cjfa-35471	893	31	1	1	NUM
cjfa-35471	893	32	here	here	ADV
cjfa-35471	893	33	)	)	PUNCT
cjfa-35471	893	34	which	which	PRON
cjfa-35471	893	35	will	will	AUX
cjfa-35471	893	36	imply	imply	VERB
cjfa-35471	893	37	that	that	SCONJ
cjfa-35471	893	38	the	the	DET
cjfa-35471	893	39	firm	firm	NOUN
cjfa-35471	893	40	will	will	AUX
cjfa-35471	893	41	start	start	VERB
cjfa-35471	893	42	and	and	CCONJ
cjfa-35471	893	43	stop	stop	VERB
cjfa-35471	893	44	production	production	NOUN
cjfa-35471	893	45	many	many	ADJ
cjfa-35471	893	46	times	time	NOUN
cjfa-35471	893	47	which	which	PRON
cjfa-35471	893	48	is	be	AUX
cjfa-35471	893	49	not	not	PART
cjfa-35471	893	50	a	a	DET
cjfa-35471	893	51	conducive	conducive	ADJ
cjfa-35471	893	52	situation	situation	NOUN
cjfa-35471	893	53	for	for	ADP
cjfa-35471	893	54	investment	investment	NOUN
cjfa-35471	893	55	.	.	PUNCT
cjfa-35471	894	1	5	5	X
cjfa-35471	894	2	.	.	X
cjfa-35471	894	3	firm	firm	ADJ
cjfa-35471	894	4	size	size	NOUN
cjfa-35471	894	5	(	(	PUNCT
cjfa-35471	894	6	as	as	SCONJ
cjfa-35471	894	7	expressed	express	VERB
cjfa-35471	894	8	by	by	ADP
cjfa-35471	894	9	the	the	DET
cjfa-35471	894	10	constant	constant	ADJ
cjfa-35471	894	11	d	d	NOUN
cjfa-35471	894	12	in	in	ADP
cjfa-35471	894	13	the	the	DET
cjfa-35471	894	14	expression	expression	NOUN
cjfa-35471	894	15	of	of	ADP
cjfa-35471	894	16	cost	cost	NOUN
cjfa-35471	894	17	function	function	NOUN
cjfa-35471	894	18	)	)	PUNCT
cjfa-35471	894	19	has	have	VERB
cjfa-35471	894	20	no	no	DET
cjfa-35471	894	21	impact	impact	NOUN
cjfa-35471	894	22	on	on	ADP
cjfa-35471	894	23	the	the	DET
cjfa-35471	894	24	production	production	NOUN
cjfa-35471	894	25	decisions	decision	NOUN
cjfa-35471	894	26	.	.	PUNCT
cjfa-35471	895	1	hence	hence	ADV
cjfa-35471	895	2	,	,	PUNCT
cjfa-35471	895	3	no	no	DET
cjfa-35471	895	4	differentiation	differentiation	NOUN
cjfa-35471	895	5	should	should	AUX
cjfa-35471	895	6	be	be	AUX
cjfa-35471	895	7	made	make	VERB
cjfa-35471	895	8	between	between	ADP
cjfa-35471	895	9	small	small	ADJ
cjfa-35471	895	10	and	and	CCONJ
cjfa-35471	895	11	large	large	ADJ
cjfa-35471	895	12	firms	firm	NOUN
cjfa-35471	895	13	when	when	SCONJ
cjfa-35471	895	14	incentives	incentive	VERB
cjfa-35471	895	15	to	to	PART
cjfa-35471	895	16	induce	induce	VERB
cjfa-35471	895	17	firms	firm	NOUN
cjfa-35471	895	18	to	to	PART
cjfa-35471	895	19	produce	produce	VERB
cjfa-35471	895	20	for	for	SCONJ
cjfa-35471	895	21	inventories	inventory	NOUN
cjfa-35471	895	22	are	be	AUX
cjfa-35471	895	23	considered	consider	VERB
cjfa-35471	895	24	.	.	PUNCT
cjfa-35471	896	1	6	6	X
cjfa-35471	896	2	.	.	PUNCT
cjfa-35471	896	3	effects	effect	NOUN
cjfa-35471	896	4	of	of	ADP
cjfa-35471	896	5	changes	change	NOUN
cjfa-35471	896	6	in	in	ADP
cjfa-35471	896	7	interest	interest	NOUN
cjfa-35471	896	8	rates	rate	NOUN
cjfa-35471	896	9	are	be	AUX
cjfa-35471	896	10	especially	especially	ADV
cjfa-35471	896	11	ineffective	ineffective	ADJ
cjfa-35471	896	12	if	if	SCONJ
cjfa-35471	896	13	the	the	DET
cjfa-35471	896	14	interest	interest	NOUN
cjfa-35471	896	15	rate	rate	NOUN
cjfa-35471	896	16	is	be	AUX
cjfa-35471	896	17	already	already	ADV
cjfa-35471	896	18	small	small	ADJ
cjfa-35471	896	19	.	.	PUNCT
cjfa-35471	897	1	7	7	X
cjfa-35471	897	2	.	.	X
cjfa-35471	897	3	tax	tax	NOUN
cjfa-35471	897	4	incentives	incentive	NOUN
cjfa-35471	897	5	have	have	VERB
cjfa-35471	897	6	no	no	DET
cjfa-35471	897	7	impact	impact	NOUN
cjfa-35471	897	8	on	on	ADP
cjfa-35471	897	9	production	production	NOUN
cjfa-35471	897	10	since	since	SCONJ
cjfa-35471	897	11	equation	equation	NOUN
cjfa-35471	897	12	(	(	PUNCT
cjfa-35471	897	13	4	4	X
cjfa-35471	897	14	)	)	PUNCT
cjfa-35471	897	15	does	do	AUX
cjfa-35471	897	16	not	not	PART
cjfa-35471	897	17	involve	involve	VERB
cjfa-35471	897	18	any	any	DET
cjfa-35471	897	19	tax	tax	NOUN
cjfa-35471	897	20	parameter	parameter	NOUN
cjfa-35471	897	21	.	.	PUNCT
cjfa-35471	898	1	therefore	therefore	ADV
cjfa-35471	898	2	:	:	PUNCT
cjfa-35471	898	3	incentives	incentive	NOUN
cjfa-35471	898	4	for	for	SCONJ
cjfa-35471	898	5	firms	firm	NOUN
cjfa-35471	898	6	to	to	PART
cjfa-35471	898	7	lower	lower	VERB
cjfa-35471	898	8	their	their	PRON
cjfa-35471	898	9	holding	holding	NOUN
cjfa-35471	898	10	costs	cost	NOUN
cjfa-35471	898	11	are	be	AUX
cjfa-35471	898	12	an	an	DET
cjfa-35471	898	13	effective	effective	ADJ
cjfa-35471	898	14	method	method	NOUN
cjfa-35471	898	15	to	to	PART
cjfa-35471	898	16	induce	induce	VERB
cjfa-35471	898	17	firms	firm	NOUN
cjfa-35471	898	18	to	to	PART
cjfa-35471	898	19	keep	keep	VERB
cjfa-35471	898	20	production	production	NOUN
cjfa-35471	898	21	above	above	ADP
cjfa-35471	898	22	demand	demand	NOUN
cjfa-35471	898	23	.	.	PUNCT
cjfa-35471	899	1	these	these	PRON
cjfa-35471	899	2	may	may	AUX
cjfa-35471	899	3	include	include	VERB
cjfa-35471	899	4	lower	low	ADJ
cjfa-35471	899	5	prices	price	NOUN
cjfa-35471	899	6	for	for	ADP
cjfa-35471	899	7	electricity	electricity	NOUN
cjfa-35471	899	8	,	,	PUNCT
cjfa-35471	899	9	oil	oil	NOUN
cjfa-35471	899	10	,	,	PUNCT
cjfa-35471	899	11	and	and	CCONJ
cjfa-35471	899	12	gas	gas	NOUN
cjfa-35471	899	13	,	,	PUNCT
cjfa-35471	899	14	lower	low	ADJ
cjfa-35471	899	15	property	property	NOUN
cjfa-35471	899	16	insurance	insurance	NOUN
cjfa-35471	899	17	rates	rate	NOUN
cjfa-35471	899	18	,	,	PUNCT
cjfa-35471	899	19	and	and	CCONJ
cjfa-35471	899	20	lower	low	ADJ
cjfa-35471	899	21	insurance	insurance	NOUN
cjfa-35471	899	22	premiums	premium	NOUN
cjfa-35471	899	23	for	for	ADP
cjfa-35471	899	24	labor	labor	NOUN
cjfa-35471	899	25	to	to	PART
cjfa-35471	899	26	reduce	reduce	VERB
cjfa-35471	899	27	holding	hold	VERB
cjfa-35471	899	28	costs	cost	NOUN
cjfa-35471	899	29	.	.	PUNCT
cjfa-35471	900	1	incentives	incentive	NOUN
cjfa-35471	900	2	for	for	ADP
cjfa-35471	900	3	introducing	introduce	VERB
cjfa-35471	900	4	optimal	optimal	ADJ
cjfa-35471	900	5	incentives	incentive	NOUN
cjfa-35471	900	6	for	for	ADP
cjfa-35471	900	7	economic	economic	ADJ
cjfa-35471	900	8	growth	growth	NOUN
cjfa-35471	900	9	…	…	PUNCT
cjfa-35471	900	10	25	25	NUM
cjfa-35471	900	11	new	new	ADJ
cjfa-35471	900	12	technologies	technology	NOUN
cjfa-35471	900	13	may	may	AUX
cjfa-35471	900	14	be	be	AUX
cjfa-35471	900	15	only	only	ADV
cjfa-35471	900	16	effective	effective	ADJ
cjfa-35471	900	17	if	if	SCONJ
cjfa-35471	900	18	they	they	PRON
cjfa-35471	900	19	are	be	AUX
cjfa-35471	900	20	carefully	carefully	ADV
cjfa-35471	900	21	chosen	choose	VERB
cjfa-35471	900	22	.	.	PUNCT
cjfa-35471	901	1	incentives	incentive	NOUN
cjfa-35471	901	2	to	to	PART
cjfa-35471	901	3	reduce	reduce	VERB
cjfa-35471	901	4	marginal	marginal	ADJ
cjfa-35471	901	5	costs	cost	NOUN
cjfa-35471	901	6	will	will	AUX
cjfa-35471	901	7	not	not	PART
cjfa-35471	901	8	be	be	AUX
cjfa-35471	901	9	effective	effective	ADJ
cjfa-35471	901	10	.	.	PUNCT
cjfa-35471	902	1	implications	implication	NOUN
cjfa-35471	902	2	for	for	ADP
cjfa-35471	902	3	central	central	ADJ
cjfa-35471	902	4	and	and	CCONJ
cjfa-35471	902	5	eastern	eastern	ADJ
cjfa-35471	902	6	european	european	ADJ
cjfa-35471	902	7	countries	country	NOUN
cjfa-35471	902	8	the	the	DET
cjfa-35471	902	9	model	model	NOUN
cjfa-35471	902	10	above	above	ADV
cjfa-35471	902	11	was	be	AUX
cjfa-35471	902	12	developed	develop	VERB
cjfa-35471	902	13	for	for	ADP
cjfa-35471	902	14	a	a	DET
cjfa-35471	902	15	company	company	NOUN
cjfa-35471	902	16	operating	operate	VERB
cjfa-35471	902	17	in	in	ADP
cjfa-35471	902	18	a	a	DET
cjfa-35471	902	19	competitive	competitive	ADJ
cjfa-35471	902	20	sector	sector	NOUN
cjfa-35471	902	21	.	.	PUNCT
cjfa-35471	903	1	the	the	DET
cjfa-35471	903	2	model	model	NOUN
cjfa-35471	903	3	was	be	AUX
cjfa-35471	903	4	not	not	PART
cjfa-35471	903	5	intended	intend	VERB
cjfa-35471	903	6	to	to	PART
cjfa-35471	903	7	identify	identify	VERB
cjfa-35471	903	8	proper	proper	ADJ
cjfa-35471	903	9	incentives	incentive	NOUN
cjfa-35471	903	10	for	for	ADP
cjfa-35471	903	11	growth	growth	NOUN
cjfa-35471	903	12	in	in	ADP
cjfa-35471	903	13	extraordinary	extraordinary	ADJ
cjfa-35471	903	14	times	time	NOUN
cjfa-35471	903	15	like	like	ADP
cjfa-35471	903	16	covit-19	covit-19	PROPN
cjfa-35471	903	17	crisis	crisis	NOUN
cjfa-35471	903	18	the	the	DET
cjfa-35471	903	19	whole	whole	ADJ
cjfa-35471	903	20	world	world	NOUN
cjfa-35471	903	21	is	be	AUX
cjfa-35471	903	22	facing	face	VERB
cjfa-35471	903	23	or	or	CCONJ
cjfa-35471	903	24	2008	2008	NUM
cjfa-35471	903	25	financial	financial	ADJ
cjfa-35471	903	26	crisis	crisis	NOUN
cjfa-35471	903	27	.	.	PUNCT
cjfa-35471	904	1	the	the	DET
cjfa-35471	904	2	model	model	NOUN
cjfa-35471	904	3	was	be	AUX
cjfa-35471	904	4	not	not	PART
cjfa-35471	904	5	intended	intend	VERB
cjfa-35471	904	6	to	to	PART
cjfa-35471	904	7	address	address	VERB
cjfa-35471	904	8	incentives	incentive	NOUN
cjfa-35471	904	9	directed	direct	VERB
cjfa-35471	904	10	to	to	ADP
cjfa-35471	904	11	attracting	attract	VERB
cjfa-35471	904	12	foreign	foreign	ADJ
cjfa-35471	904	13	investment	investment	NOUN
cjfa-35471	904	14	either	either	ADV
cjfa-35471	904	15	.	.	PUNCT
cjfa-35471	905	1	tax	tax	NOUN
cjfa-35471	905	2	incentives	incentive	NOUN
cjfa-35471	905	3	are	be	AUX
cjfa-35471	905	4	not	not	PART
cjfa-35471	905	5	addressed	address	VERB
cjfa-35471	905	6	since	since	SCONJ
cjfa-35471	905	7	a	a	DET
cjfa-35471	905	8	firm	firm	NOUN
cjfa-35471	905	9	operating	operate	VERB
cjfa-35471	905	10	in	in	ADP
cjfa-35471	905	11	a	a	DET
cjfa-35471	905	12	perfectly	perfectly	ADV
cjfa-35471	905	13	competitive	competitive	ADJ
cjfa-35471	905	14	sector	sector	NOUN
cjfa-35471	905	15	tries	try	VERB
cjfa-35471	905	16	only	only	ADV
cjfa-35471	905	17	to	to	PART
cjfa-35471	905	18	minimize	minimize	VERB
cjfa-35471	905	19	its	its	PRON
cjfa-35471	905	20	costs	cost	NOUN
cjfa-35471	905	21	.	.	PUNCT
cjfa-35471	906	1	three	three	NUM
cjfa-35471	906	2	important	important	ADJ
cjfa-35471	906	3	factors	factor	NOUN
cjfa-35471	906	4	are	be	AUX
cjfa-35471	906	5	relevant	relevant	ADJ
cjfa-35471	906	6	in	in	ADP
cjfa-35471	906	7	the	the	DET
cjfa-35471	906	8	context	context	NOUN
cjfa-35471	906	9	of	of	ADP
cjfa-35471	906	10	the	the	DET
cjfa-35471	906	11	paper	paper	NOUN
cjfa-35471	906	12	.	.	PUNCT
cjfa-35471	907	1	they	they	PRON
cjfa-35471	907	2	are	be	AUX
cjfa-35471	907	3	the	the	DET
cjfa-35471	907	4	interest	interest	NOUN
cjfa-35471	907	5	rates	rate	NOUN
cjfa-35471	907	6	,	,	PUNCT
cjfa-35471	907	7	the	the	DET
cjfa-35471	907	8	production	production	NOUN
cjfa-35471	907	9	technology	technology	NOUN
cjfa-35471	907	10	,	,	PUNCT
cjfa-35471	907	11	and	and	CCONJ
cjfa-35471	907	12	the	the	DET
cjfa-35471	907	13	holding	hold	VERB
cjfa-35471	907	14	cost	cost	NOUN
cjfa-35471	907	15	of	of	ADP
cjfa-35471	907	16	inventories	inventory	NOUN
cjfa-35471	907	17	.	.	PUNCT
cjfa-35471	908	1	thus	thus	ADV
cjfa-35471	908	2	,	,	PUNCT
cjfa-35471	908	3	the	the	DET
cjfa-35471	908	4	implications	implication	NOUN
cjfa-35471	908	5	for	for	ADP
cjfa-35471	908	6	the	the	DET
cjfa-35471	908	7	central	central	ADJ
cjfa-35471	908	8	and	and	CCONJ
cjfa-35471	908	9	eastern	eastern	ADJ
cjfa-35471	908	10	european	european	ADJ
cjfa-35471	908	11	countries	country	NOUN
cjfa-35471	908	12	will	will	AUX
cjfa-35471	908	13	be	be	AUX
cjfa-35471	908	14	analyzed	analyze	VERB
cjfa-35471	908	15	based	base	VERB
cjfa-35471	908	16	on	on	ADP
cjfa-35471	908	17	these	these	DET
cjfa-35471	908	18	factors	factor	NOUN
cjfa-35471	908	19	.	.	PUNCT
cjfa-35471	909	1	there	there	PRON
cjfa-35471	909	2	are	be	VERB
cjfa-35471	909	3	many	many	ADJ
cjfa-35471	909	4	classifications	classification	NOUN
cjfa-35471	909	5	of	of	ADP
cjfa-35471	909	6	central	central	ADJ
cjfa-35471	909	7	and	and	CCONJ
cjfa-35471	909	8	eastern	eastern	ADJ
cjfa-35471	909	9	european	european	ADJ
cjfa-35471	909	10	countries	country	NOUN
cjfa-35471	909	11	.	.	PUNCT
cjfa-35471	910	1	central	central	ADJ
cjfa-35471	910	2	and	and	CCONJ
cjfa-35471	910	3	eastern	eastern	ADJ
cjfa-35471	910	4	european	european	ADJ
cjfa-35471	910	5	countries	country	NOUN
cjfa-35471	910	6	(	(	PUNCT
cjfa-35471	910	7	ceecs	ceec	NOUN
cjfa-35471	910	8	)	)	PUNCT
cjfa-35471	910	9	is	be	AUX
cjfa-35471	910	10	an	an	DET
cjfa-35471	910	11	oecd	oecd	ADJ
cjfa-35471	910	12	term	term	NOUN
cjfa-35471	910	13	for	for	ADP
cjfa-35471	910	14	the	the	DET
cjfa-35471	910	15	group	group	NOUN
cjfa-35471	910	16	of	of	ADP
cjfa-35471	910	17	countries	country	NOUN
cjfa-35471	910	18	comprising	comprise	VERB
cjfa-35471	910	19	albania	albania	PROPN
cjfa-35471	910	20	,	,	PUNCT
cjfa-35471	910	21	bulgaria	bulgaria	PROPN
cjfa-35471	910	22	,	,	PUNCT
cjfa-35471	910	23	croatia	croatia	PROPN
cjfa-35471	910	24	,	,	PUNCT
cjfa-35471	910	25	the	the	DET
cjfa-35471	910	26	czech	czech	PROPN
cjfa-35471	910	27	republic	republic	NOUN
cjfa-35471	910	28	,	,	PUNCT
cjfa-35471	910	29	hungary	hungary	PROPN
cjfa-35471	910	30	,	,	PUNCT
cjfa-35471	910	31	poland	poland	PROPN
cjfa-35471	910	32	,	,	PUNCT
cjfa-35471	910	33	romania	romania	PROPN
cjfa-35471	910	34	,	,	PUNCT
cjfa-35471	910	35	the	the	DET
cjfa-35471	910	36	slovak	slovak	PROPN
cjfa-35471	910	37	republic	republic	NOUN
cjfa-35471	910	38	,	,	PUNCT
cjfa-35471	910	39	slovenia	slovenia	PROPN
cjfa-35471	910	40	,	,	PUNCT
cjfa-35471	910	41	and	and	CCONJ
cjfa-35471	910	42	the	the	DET
cjfa-35471	910	43	three	three	NUM
cjfa-35471	910	44	baltic	baltic	ADJ
cjfa-35471	910	45	states	state	NOUN
cjfa-35471	910	46	:	:	PUNCT
cjfa-35471	910	47	estonia	estonia	PROPN
cjfa-35471	910	48	,	,	PUNCT
cjfa-35471	910	49	latvia	latvia	PROPN
cjfa-35471	910	50	and	and	CCONJ
cjfa-35471	910	51	lithuania	lithuania	PROPN
cjfa-35471	910	52	(	(	PUNCT
cjfa-35471	910	53	oecd	oecd	PROPN
cjfa-35471	910	54	,	,	PUNCT
cjfa-35471	910	55	2001	2001	NUM
cjfa-35471	910	56	)	)	PUNCT
cjfa-35471	910	57	.	.	PUNCT
cjfa-35471	911	1	according	accord	VERB
cjfa-35471	911	2	to	to	ADP
cjfa-35471	911	3	the	the	DET
cjfa-35471	911	4	national	national	PROPN
cjfa-35471	911	5	institute	institute	PROPN
cjfa-35471	911	6	of	of	ADP
cjfa-35471	911	7	statistics	statistic	NOUN
cjfa-35471	911	8	and	and	CCONJ
cjfa-35471	911	9	economic	economic	ADJ
cjfa-35471	911	10	research	research	NOUN
cjfa-35471	911	11	of	of	ADP
cjfa-35471	911	12	france	france	PROPN
cjfa-35471	911	13	(	(	PUNCT
cjfa-35471	911	14	insee	insee	PROPN
cjfa-35471	911	15	,	,	PUNCT
cjfa-35471	911	16	2020	2020	NUM
cjfa-35471	911	17	)	)	PUNCT
cjfa-35471	911	18	,	,	PUNCT
cjfa-35471	911	19	the	the	DET
cjfa-35471	911	20	central	central	ADJ
cjfa-35471	911	21	european	european	ADJ
cjfa-35471	911	22	countries	country	NOUN
cjfa-35471	911	23	defined	define	VERB
cjfa-35471	911	24	are	be	AUX
cjfa-35471	911	25	bulgaria	bulgaria	PROPN
cjfa-35471	911	26	,	,	PUNCT
cjfa-35471	911	27	croatia	croatia	PROPN
cjfa-35471	911	28	,	,	PUNCT
cjfa-35471	911	29	estonia	estonia	PROPN
cjfa-35471	911	30	,	,	PUNCT
cjfa-35471	911	31	hungary	hungary	PROPN
cjfa-35471	911	32	,	,	PUNCT
cjfa-35471	911	33	latvia	latvia	PROPN
cjfa-35471	911	34	,	,	PUNCT
cjfa-35471	911	35	lithuania	lithuania	PROPN
cjfa-35471	911	36	,	,	PUNCT
cjfa-35471	911	37	poland	poland	PROPN
cjfa-35471	911	38	,	,	PUNCT
cjfa-35471	911	39	romania	romania	PROPN
cjfa-35471	911	40	,	,	PUNCT
cjfa-35471	911	41	slovenia	slovenia	PROPN
cjfa-35471	911	42	,	,	PUNCT
cjfa-35471	911	43	slovakia	slovakia	PROPN
cjfa-35471	911	44	,	,	PUNCT
cjfa-35471	911	45	czech	czech	PROPN
cjfa-35471	911	46	republic	republic	NOUN
cjfa-35471	911	47	.	.	PUNCT
cjfa-35471	912	1	authors	author	NOUN
cjfa-35471	912	2	use	use	VERB
cjfa-35471	912	3	both	both	PRON
cjfa-35471	912	4	above	above	ADP
cjfa-35471	912	5	mentioned	mention	VERB
cjfa-35471	912	6	classifications	classification	NOUN
cjfa-35471	912	7	and	and	CCONJ
cjfa-35471	912	8	chose	choose	VERB
cjfa-35471	912	9	the	the	DET
cjfa-35471	912	10	following	follow	VERB
cjfa-35471	912	11	11	11	NUM
cjfa-35471	912	12	countries	country	NOUN
cjfa-35471	912	13	of	of	ADP
cjfa-35471	912	14	central	central	ADJ
cjfa-35471	912	15	and	and	CCONJ
cjfa-35471	912	16	eastern	eastern	ADJ
cjfa-35471	912	17	europe	europe	PROPN
cjfa-35471	912	18	according	accord	VERB
cjfa-35471	912	19	to	to	ADP
cjfa-35471	912	20	in	in	SCONJ
cjfa-35471	912	21	see	see	VERB
cjfa-35471	912	22	classification	classification	NOUN
cjfa-35471	912	23	for	for	ADP
cjfa-35471	912	24	demonstration	demonstration	NOUN
cjfa-35471	912	25	of	of	ADP
cjfa-35471	912	26	implications	implication	NOUN
cjfa-35471	912	27	of	of	ADP
cjfa-35471	912	28	economic	economic	ADJ
cjfa-35471	912	29	incentives	incentive	NOUN
cjfa-35471	912	30	on	on	ADP
cjfa-35471	912	31	growth	growth	NOUN
cjfa-35471	912	32	.	.	PUNCT
cjfa-35471	913	1	the	the	DET
cjfa-35471	913	2	interest	interest	NOUN
cjfa-35471	913	3	rates	rate	NOUN
cjfa-35471	913	4	in	in	ADP
cjfa-35471	913	5	these	these	DET
cjfa-35471	913	6	countries	country	NOUN
cjfa-35471	913	7	are	be	AUX
cjfa-35471	913	8	shown	show	VERB
cjfa-35471	913	9	in	in	ADP
cjfa-35471	913	10	table	table	NOUN
cjfa-35471	913	11	1	1	NUM
cjfa-35471	913	12	.	.	PUNCT
cjfa-35471	913	13	table	table	NOUN
cjfa-35471	913	14	1	1	NUM
cjfa-35471	913	15	.	.	PUNCT
cjfa-35471	913	16	interest	interest	NOUN
cjfa-35471	913	17	rates	rate	NOUN
cjfa-35471	913	18	in	in	ADP
cjfa-35471	913	19	central	central	ADJ
cjfa-35471	913	20	and	and	CCONJ
cjfa-35471	913	21	eastern	eastern	ADJ
cjfa-35471	913	22	european	european	ADJ
cjfa-35471	913	23	countries	country	NOUN
cjfa-35471	913	24	(	(	PUNCT
cjfa-35471	913	25	%	%	INTJ
cjfa-35471	913	26	)	)	PUNCT
cjfa-35471	913	27	countries	country	NOUN
cjfa-35471	913	28	last	last	ADJ
cjfa-35471	913	29	previous	previous	ADJ
cjfa-35471	913	30	dates	date	NOUN
cjfa-35471	913	31	croatia	croatia	PROPN
cjfa-35471	913	32	2.50	2.50	NUM
cjfa-35471	913	33	2.50	2.50	NUM
cjfa-35471	913	34	may/20	may/20	PROPN
cjfa-35471	913	35	romania	romania	NOUN
cjfa-35471	913	36	1.75	1.75	NUM
cjfa-35471	913	37	1.75	1.75	NUM
cjfa-35471	913	38	jun/20	jun/20	PROPN
cjfa-35471	913	39	hungary	hungary	PROPN
cjfa-35471	914	1	0.60	0.60	NUM
cjfa-35471	914	2	0.75	0.75	NUM
cjfa-35471	915	1	jul/20	jul/20	PROPN
cjfa-35471	915	2	czech	czech	PROPN
cjfa-35471	915	3	republic	republic	NOUN
cjfa-35471	915	4	0.25	0.25	NUM
cjfa-35471	915	5	0.25	0.25	NUM
cjfa-35471	916	1	jun/20	jun/20	PROPN
cjfa-35471	916	2	mustafa	mustafa	PROPN
cjfa-35471	916	3	akan	akan	PROPN
cjfa-35471	916	4	,	,	PUNCT
cjfa-35471	916	5	natalia	natalia	PROPN
cjfa-35471	916	6	konovalova26	konovalova26	PROPN
cjfa-35471	916	7	countries	country	NOUN
cjfa-35471	916	8	last	last	ADJ
cjfa-35471	916	9	previous	previous	ADJ
cjfa-35471	916	10	dates	date	VERB
cjfa-35471	916	11	poland	poland	PROPN
cjfa-35471	916	12	0.10	0.10	NUM
cjfa-35471	916	13	0.10	0.10	NUM
cjfa-35471	916	14	jul/20	jul/20	PROPN
cjfa-35471	916	15	bulgaria	bulgaria	PROPN
cjfa-35471	916	16	0.00	0.00	NUM
cjfa-35471	916	17	0.00	0.00	NUM
cjfa-35471	916	18	jul/20	jul/20	PROPN
cjfa-35471	916	19	estonia	estonia	PROPN
cjfa-35471	916	20	0.00	0.00	NUM
cjfa-35471	916	21	0.00	0.00	NUM
cjfa-35471	916	22	jul/20	jul/20	PROPN
cjfa-35471	916	23	latvia	latvia	PROPN
cjfa-35471	916	24	0.00	0.00	NUM
cjfa-35471	916	25	0.00	0.00	NUM
cjfa-35471	916	26	jul/20	jul/20	PROPN
cjfa-35471	916	27	lithuania	lithuania	PROPN
cjfa-35471	916	28	0.00	0.00	NUM
cjfa-35471	916	29	0.00	0.00	NUM
cjfa-35471	916	30	jul/20	jul/20	PROPN
cjfa-35471	916	31	slovakia	slovakia	PROPN
cjfa-35471	916	32	0.00	0.00	NUM
cjfa-35471	916	33	0.00	0.00	NUM
cjfa-35471	916	34	jul/20	jul/20	PROPN
cjfa-35471	916	35	slovenia	slovenia	PROPN
cjfa-35471	916	36	0.00	0.00	NUM
cjfa-35471	916	37	0.00	0.00	NUM
cjfa-35471	916	38	jul/20	jul/20	PROPN
cjfa-35471	916	39	s	s	PART
cjfa-35471	916	40	o	o	NOUN
cjfa-35471	916	41	u	u	NOUN
cjfa-35471	916	42	r	r	NOUN
cjfa-35471	916	43	c	c	NOUN
cjfa-35471	916	44	e	e	NOUN
cjfa-35471	916	45	:	:	PUNCT
cjfa-35471	916	46	trading	trade	VERB
cjfa-35471	916	47	economics	economic	NOUN
cjfa-35471	916	48	(	(	PUNCT
cjfa-35471	916	49	2020	2020	NUM
cjfa-35471	916	50	)	)	PUNCT
cjfa-35471	916	51	.	.	PUNCT
cjfa-35471	917	1	thus	thus	ADV
cjfa-35471	917	2	,	,	PUNCT
cjfa-35471	917	3	the	the	DET
cjfa-35471	917	4	first	first	ADJ
cjfa-35471	917	5	implication	implication	NOUN
cjfa-35471	917	6	of	of	ADP
cjfa-35471	917	7	the	the	DET
cjfa-35471	917	8	outcome	outcome	NOUN
cjfa-35471	917	9	of	of	ADP
cjfa-35471	917	10	the	the	DET
cjfa-35471	917	11	results	result	NOUN
cjfa-35471	917	12	of	of	ADP
cjfa-35471	917	13	this	this	DET
cjfa-35471	917	14	paper	paper	NOUN
cjfa-35471	917	15	is	be	AUX
cjfa-35471	917	16	that	that	SCONJ
cjfa-35471	917	17	reducing	reduce	VERB
cjfa-35471	917	18	interest	interest	NOUN
cjfa-35471	917	19	rates	rate	NOUN
cjfa-35471	917	20	will	will	AUX
cjfa-35471	917	21	not	not	PART
cjfa-35471	917	22	induce	induce	VERB
cjfa-35471	917	23	growth	growth	NOUN
cjfa-35471	917	24	significantly	significantly	ADV
cjfa-35471	917	25	except	except	SCONJ
cjfa-35471	917	26	perhaps	perhaps	ADV
cjfa-35471	917	27	in	in	ADP
cjfa-35471	917	28	croatia	croatia	PROPN
cjfa-35471	917	29	and	and	CCONJ
cjfa-35471	917	30	romania	romania	PROPN
cjfa-35471	917	31	where	where	SCONJ
cjfa-35471	917	32	interest	interest	NOUN
cjfa-35471	917	33	rates	rate	NOUN
cjfa-35471	917	34	are	be	AUX
cjfa-35471	917	35	relatively	relatively	ADV
cjfa-35471	917	36	high	high	ADJ
cjfa-35471	917	37	.	.	PUNCT
cjfa-35471	918	1	the	the	DET
cjfa-35471	918	2	second	second	ADJ
cjfa-35471	918	3	factor	factor	NOUN
cjfa-35471	918	4	influencing	influence	VERB
cjfa-35471	918	5	growth	growth	NOUN
cjfa-35471	918	6	positively	positively	ADV
cjfa-35471	918	7	was	be	AUX
cjfa-35471	918	8	the	the	DET
cjfa-35471	918	9	production	production	NOUN
cjfa-35471	918	10	technology	technology	NOUN
cjfa-35471	918	11	(	(	PUNCT
cjfa-35471	918	12	production	production	NOUN
cjfa-35471	918	13	function	function	NOUN
cjfa-35471	918	14	)	)	PUNCT
cjfa-35471	918	15	.	.	PUNCT
cjfa-35471	919	1	however	however	ADV
cjfa-35471	919	2	,	,	PUNCT
cjfa-35471	919	3	each	each	DET
cjfa-35471	919	4	firm	firm	NOUN
cjfa-35471	919	5	operating	operate	VERB
cjfa-35471	919	6	in	in	ADP
cjfa-35471	919	7	any	any	DET
cjfa-35471	919	8	economy	economy	NOUN
cjfa-35471	919	9	where	where	SCONJ
cjfa-35471	919	10	free	free	ADJ
cjfa-35471	919	11	market	market	NOUN
cjfa-35471	919	12	economy	economy	NOUN
cjfa-35471	919	13	is	be	AUX
cjfa-35471	919	14	practiced	practice	VERB
cjfa-35471	919	15	has	have	VERB
cjfa-35471	919	16	a	a	DET
cjfa-35471	919	17	different	different	ADJ
cjfa-35471	919	18	technology	technology	NOUN
cjfa-35471	919	19	.	.	PUNCT
cjfa-35471	920	1	it	it	PRON
cjfa-35471	920	2	is	be	AUX
cjfa-35471	920	3	not	not	PART
cjfa-35471	920	4	possible	possible	ADJ
cjfa-35471	920	5	to	to	PART
cjfa-35471	920	6	suggest	suggest	VERB
cjfa-35471	920	7	incentives	incentive	NOUN
cjfa-35471	920	8	concerning	concern	VERB
cjfa-35471	920	9	technology	technology	NOUN
cjfa-35471	920	10	for	for	ADP
cjfa-35471	920	11	each	each	DET
cjfa-35471	920	12	firm	firm	NOUN
cjfa-35471	920	13	in	in	ADP
cjfa-35471	920	14	an	an	DET
cjfa-35471	920	15	economy	economy	NOUN
cjfa-35471	920	16	.	.	PUNCT
cjfa-35471	921	1	however	however	ADV
cjfa-35471	921	2	,	,	PUNCT
cjfa-35471	921	3	it	it	PRON
cjfa-35471	921	4	is	be	AUX
cjfa-35471	921	5	possible	possible	ADJ
cjfa-35471	921	6	to	to	PART
cjfa-35471	921	7	make	make	VERB
cjfa-35471	921	8	a	a	DET
cjfa-35471	921	9	general	general	ADJ
cjfa-35471	921	10	statement	statement	NOUN
cjfa-35471	921	11	on	on	ADP
cjfa-35471	921	12	incentives	incentive	NOUN
cjfa-35471	921	13	to	to	PART
cjfa-35471	921	14	invest	invest	VERB
cjfa-35471	921	15	in	in	ADP
cjfa-35471	921	16	better	well	ADJ
cjfa-35471	921	17	production	production	NOUN
cjfa-35471	921	18	technologies	technology	NOUN
cjfa-35471	921	19	for	for	ADP
cjfa-35471	921	20	a	a	DET
cjfa-35471	921	21	country	country	NOUN
cjfa-35471	921	22	.	.	PUNCT
cjfa-35471	922	1	results	result	NOUN
cjfa-35471	922	2	of	of	ADP
cjfa-35471	922	3	a	a	DET
cjfa-35471	922	4	ranking	rank	VERB
cjfa-35471	922	5	study	study	NOUN
cjfa-35471	922	6	by	by	ADP
cjfa-35471	922	7	schwab	schwab	PROPN
cjfa-35471	922	8	(	(	PUNCT
cjfa-35471	922	9	2019	2019	NUM
cjfa-35471	922	10	)	)	PUNCT
cjfa-35471	922	11	on	on	ADP
cjfa-35471	922	12	competitiveness	competitiveness	NOUN
cjfa-35471	922	13	index	index	NOUN
cjfa-35471	922	14	of	of	ADP
cjfa-35471	922	15	central	central	ADJ
cjfa-35471	922	16	european	european	ADJ
cjfa-35471	922	17	countries	country	NOUN
cjfa-35471	922	18	among	among	ADP
cjfa-35471	922	19	141	141	NUM
cjfa-35471	922	20	countries	country	NOUN
cjfa-35471	922	21	are	be	AUX
cjfa-35471	922	22	shown	show	VERB
cjfa-35471	922	23	in	in	ADP
cjfa-35471	922	24	the	the	DET
cjfa-35471	922	25	column	column	NOUN
cjfa-35471	922	26	(	(	PUNCT
cjfa-35471	922	27	1	1	NUM
cjfa-35471	922	28	)	)	PUNCT
cjfa-35471	922	29	on	on	ADP
cjfa-35471	922	30	table	table	NOUN
cjfa-35471	922	31	2	2	NUM
cjfa-35471	922	32	.	.	PUNCT
cjfa-35471	922	33	results	result	NOUN
cjfa-35471	922	34	of	of	ADP
cjfa-35471	922	35	another	another	DET
cjfa-35471	922	36	ranking	rank	VERB
cjfa-35471	922	37	study	study	NOUN
cjfa-35471	922	38	by	by	ADP
cjfa-35471	922	39	getzoff	getzoff	PROPN
cjfa-35471	922	40	(	(	PUNCT
cjfa-35471	922	41	2020	2020	NUM
cjfa-35471	922	42	)	)	PUNCT
cjfa-35471	922	43	on	on	ADP
cjfa-35471	922	44	the	the	DET
cjfa-35471	922	45	most	most	ADV
cjfa-35471	922	46	technologically	technologically	ADV
cjfa-35471	922	47	advanced	advanced	ADJ
cjfa-35471	922	48	countries	country	NOUN
cjfa-35471	922	49	(	(	PUNCT
cjfa-35471	922	50	among	among	ADP
cjfa-35471	922	51	67	67	NUM
cjfa-35471	922	52	)	)	PUNCT
cjfa-35471	922	53	are	be	AUX
cjfa-35471	922	54	shown	show	VERB
cjfa-35471	922	55	on	on	ADP
cjfa-35471	922	56	column	column	NOUN
cjfa-35471	922	57	(	(	PUNCT
cjfa-35471	922	58	2	2	NUM
cjfa-35471	922	59	)	)	PUNCT
cjfa-35471	922	60	on	on	ADP
cjfa-35471	922	61	the	the	DET
cjfa-35471	922	62	same	same	ADJ
cjfa-35471	922	63	table	table	NOUN
cjfa-35471	922	64	.	.	PUNCT
cjfa-35471	923	1	ourworldindata.org	ourworldindata.org	X
cjfa-35471	923	2	(	(	PUNCT
cjfa-35471	923	3	2021	2021	NUM
cjfa-35471	923	4	)	)	PUNCT
cjfa-35471	923	5	has	have	AUX
cjfa-35471	923	6	produced	produce	VERB
cjfa-35471	923	7	data	datum	NOUN
cjfa-35471	923	8	on	on	ADP
cjfa-35471	923	9	labor	labor	NOUN
cjfa-35471	923	10	productivity	productivity	NOUN
cjfa-35471	923	11	in	in	ADP
cjfa-35471	923	12	all	all	DET
cjfa-35471	923	13	countires	countire	NOUN
cjfa-35471	923	14	on	on	ADP
cjfa-35471	923	15	the	the	DET
cjfa-35471	923	16	basis	basis	NOUN
cjfa-35471	923	17	of	of	ADP
cjfa-35471	923	18	feenstra	feenstra	NOUN
cjfa-35471	923	19	,	,	PUNCT
cjfa-35471	923	20	inklaar	inklaar	NOUN
cjfa-35471	923	21	and	and	CCONJ
cjfa-35471	923	22	timmer	timmer	PROPN
cjfa-35471	923	23	(	(	PUNCT
cjfa-35471	923	24	2015	2015	NUM
cjfa-35471	923	25	)	)	PUNCT
cjfa-35471	923	26	.	.	PUNCT
cjfa-35471	924	1	the	the	DET
cjfa-35471	924	2	data	datum	NOUN
cjfa-35471	924	3	for	for	ADP
cjfa-35471	924	4	central	central	ADJ
cjfa-35471	924	5	and	and	CCONJ
cjfa-35471	924	6	eastern	eastern	ADJ
cjfa-35471	924	7	european	european	ADJ
cjfa-35471	924	8	countires	countire	NOUN
cjfa-35471	924	9	are	be	AUX
cjfa-35471	924	10	produced	produce	VERB
cjfa-35471	924	11	in	in	ADP
cjfa-35471	924	12	column	column	NOUN
cjfa-35471	924	13	3	3	NUM
cjfa-35471	924	14	of	of	ADP
cjfa-35471	924	15	table	table	NOUN
cjfa-35471	924	16	2	2	NUM
cjfa-35471	924	17	also	also	ADV
cjfa-35471	924	18	.	.	PUNCT
cjfa-35471	925	1	table	table	NOUN
cjfa-35471	925	2	2	2	NUM
cjfa-35471	925	3	indicates	indicate	VERB
cjfa-35471	925	4	that	that	SCONJ
cjfa-35471	925	5	estonia	estonia	PROPN
cjfa-35471	925	6	,	,	PUNCT
cjfa-35471	925	7	czech	czech	PROPN
cjfa-35471	925	8	republic	republic	NOUN
cjfa-35471	925	9	,	,	PUNCT
cjfa-35471	925	10	slovenia	slovenia	PROPN
cjfa-35471	925	11	,	,	PUNCT
cjfa-35471	925	12	and	and	CCONJ
cjfa-35471	925	13	poland	poland	PROPN
cjfa-35471	925	14	are	be	AUX
cjfa-35471	925	15	already	already	ADV
cjfa-35471	925	16	quite	quite	ADV
cjfa-35471	925	17	advanced	advanced	ADJ
cjfa-35471	925	18	in	in	ADP
cjfa-35471	925	19	production	production	NOUN
cjfa-35471	925	20	technology	technology	NOUN
cjfa-35471	925	21	.	.	PUNCT
cjfa-35471	926	1	thus	thus	ADV
cjfa-35471	926	2	,	,	PUNCT
cjfa-35471	926	3	incentives	incentive	NOUN
cjfa-35471	926	4	regarding	regard	VERB
cjfa-35471	926	5	investment	investment	NOUN
cjfa-35471	926	6	in	in	ADP
cjfa-35471	926	7	production	production	NOUN
cjfa-35471	926	8	technologies	technology	NOUN
cjfa-35471	926	9	in	in	ADP
cjfa-35471	926	10	these	these	DET
cjfa-35471	926	11	countries	country	NOUN
cjfa-35471	926	12	will	will	AUX
cjfa-35471	926	13	have	have	VERB
cjfa-35471	926	14	less	less	ADJ
cjfa-35471	926	15	impact	impact	NOUN
cjfa-35471	926	16	on	on	ADP
cjfa-35471	926	17	growth	growth	NOUN
cjfa-35471	926	18	than	than	SCONJ
cjfa-35471	926	19	they	they	PRON
cjfa-35471	926	20	will	will	AUX
cjfa-35471	926	21	have	have	VERB
cjfa-35471	926	22	in	in	ADP
cjfa-35471	926	23	other	other	ADJ
cjfa-35471	926	24	countries	country	NOUN
cjfa-35471	926	25	in	in	ADP
cjfa-35471	926	26	the	the	DET
cjfa-35471	926	27	region	region	NOUN
cjfa-35471	926	28	especially	especially	ADV
cjfa-35471	926	29	in	in	ADP
cjfa-35471	926	30	bulgaria	bulgaria	PROPN
cjfa-35471	926	31	,	,	PUNCT
cjfa-35471	926	32	hungary	hungary	NOUN
cjfa-35471	926	33	,	,	PUNCT
cjfa-35471	926	34	and	and	CCONJ
cjfa-35471	926	35	croatia	croatia	PROPN
cjfa-35471	926	36	.	.	PUNCT
cjfa-35471	927	1	table	table	NOUN
cjfa-35471	927	2	1	1	NUM
cjfa-35471	927	3	.	.	PUNCT
cjfa-35471	928	1	interest	interest	NOUN
cjfa-35471	928	2	…	…	PUNCT
cjfa-35471	928	3	https://ourworldindata.org/economic-growth	https://ourworldindata.org/economic-growth	NOUN
cjfa-35471	928	4	https://ourworldindata.org/economic-growth	https://ourworldindata.org/economic-growth	VERB
cjfa-35471	928	5	optimal	optimal	ADJ
cjfa-35471	928	6	incentives	incentive	NOUN
cjfa-35471	928	7	for	for	ADP
cjfa-35471	928	8	economic	economic	ADJ
cjfa-35471	928	9	growth	growth	NOUN
cjfa-35471	928	10	…	…	PUNCT
cjfa-35471	928	11	27	27	NUM
cjfa-35471	928	12	incentives	incentive	NOUN
cjfa-35471	928	13	to	to	PART
cjfa-35471	928	14	increase	increase	VERB
cjfa-35471	928	15	the	the	DET
cjfa-35471	928	16	labor	labor	NOUN
cjfa-35471	928	17	productivity	productivity	NOUN
cjfa-35471	928	18	in	in	ADP
cjfa-35471	928	19	hungary	hungary	PROPN
cjfa-35471	928	20	,	,	PUNCT
cjfa-35471	928	21	bulgaria	bulgaria	PROPN
cjfa-35471	928	22	,	,	PUNCT
cjfa-35471	928	23	estonia	estonia	PROPN
cjfa-35471	928	24	,	,	PUNCT
cjfa-35471	928	25	latvia	latvia	PROPN
cjfa-35471	928	26	,	,	PUNCT
cjfa-35471	928	27	and	and	CCONJ
cjfa-35471	928	28	lithunia	lithunia	NOUN
cjfa-35471	928	29	will	will	AUX
cjfa-35471	928	30	have	have	VERB
cjfa-35471	928	31	more	more	ADJ
cjfa-35471	928	32	impact	impact	NOUN
cjfa-35471	928	33	on	on	ADP
cjfa-35471	928	34	growth	growth	NOUN
cjfa-35471	928	35	than	than	ADP
cjfa-35471	928	36	in	in	ADP
cjfa-35471	928	37	other	other	ADJ
cjfa-35471	928	38	countries	country	NOUN
cjfa-35471	928	39	in	in	ADP
cjfa-35471	928	40	the	the	DET
cjfa-35471	928	41	region	region	NOUN
cjfa-35471	928	42	since	since	SCONJ
cjfa-35471	928	43	labor	labor	NOUN
cjfa-35471	928	44	productivity	productivity	NOUN
cjfa-35471	928	45	is	be	AUX
cjfa-35471	928	46	relatively	relatively	ADV
cjfa-35471	928	47	low	low	ADJ
cjfa-35471	928	48	in	in	ADP
cjfa-35471	928	49	these	these	DET
cjfa-35471	928	50	countries	country	NOUN
cjfa-35471	928	51	.	.	PUNCT
cjfa-35471	929	1	table	table	NOUN
cjfa-35471	929	2	2	2	NUM
cjfa-35471	929	3	.	.	X
cjfa-35471	930	1	competitivity	competitivity	NOUN
cjfa-35471	930	2	,	,	PUNCT
cjfa-35471	930	3	advancement	advancement	NOUN
cjfa-35471	930	4	,	,	PUNCT
cjfa-35471	930	5	and	and	CCONJ
cjfa-35471	930	6	labor	labor	NOUN
cjfa-35471	930	7	productivity	productivity	NOUN
cjfa-35471	930	8	in	in	ADP
cjfa-35471	930	9	central	central	ADJ
cjfa-35471	930	10	and	and	CCONJ
cjfa-35471	930	11	eastern	eastern	ADJ
cjfa-35471	930	12	europe	europe	PROPN
cjfa-35471	930	13	countries	country	NOUN
cjfa-35471	930	14	1	1	NUM
cjfa-35471	930	15	(	(	PUNCT
cjfa-35471	930	16	competitiveness	competitiveness	NOUN
cjfa-35471	930	17	)	)	PUNCT
cjfa-35471	930	18	2	2	NUM
cjfa-35471	930	19	(	(	PUNCT
cjfa-35471	930	20	advanced	advanced	ADJ
cjfa-35471	930	21	)	)	PUNCT
cjfa-35471	930	22	3	3	NUM
cjfa-35471	930	23	(	(	PUNCT
cjfa-35471	930	24	productivity	productivity	NOUN
cjfa-35471	930	25	)	)	PUNCT
cjfa-35471	930	26	(	(	PUNCT
cjfa-35471	930	27	gdp$/hour	gdp$/hour	NOUN
cjfa-35471	930	28	,	,	PUNCT
cjfa-35471	930	29	2017	2017	NUM
cjfa-35471	930	30	)	)	PUNCT
cjfa-35471	930	31	croatia	croatia	PROPN
cjfa-35471	930	32	63	63	NUM
cjfa-35471	930	33	39	39	NUM
cjfa-35471	930	34	34.25	34.25	NUM
cjfa-35471	930	35	romania	romania	NOUN
cjfa-35471	930	36	51	51	NUM
cjfa-35471	930	37	48	48	NUM
cjfa-35471	930	38	33.25	33.25	NUM
cjfa-35471	930	39	hungary	hungary	NOUN
cjfa-35471	931	1	47	47	NUM
cjfa-35471	931	2	35	35	NUM
cjfa-35471	931	3	25.32	25.32	NUM
cjfa-35471	931	4	czech	czech	PROPN
cjfa-35471	931	5	republic	republic	NOUN
cjfa-35471	931	6	32	32	NUM
cjfa-35471	931	7	28	28	NUM
cjfa-35471	931	8	34.76	34.76	NUM
cjfa-35471	931	9	poland	poland	NOUN
cjfa-35471	931	10	37	37	NUM
cjfa-35471	931	11	34	34	NUM
cjfa-35471	931	12	31.06	31.06	NUM
cjfa-35471	931	13	bulgaria	bulgaria	NOUN
cjfa-35471	931	14	49	49	NUM
cjfa-35471	931	15	51	51	NUM
cjfa-35471	931	16	23.26	23.26	NUM
cjfa-35471	931	17	estonia	estonia	NOUN
cjfa-35471	931	18	31	31	NUM
cjfa-35471	931	19	20	20	NUM
cjfa-35471	931	20	28.03	28.03	NUM
cjfa-35471	931	21	latvia	latvia	PROPN
cjfa-35471	931	22	41	41	NUM
cjfa-35471	931	23	30	30	NUM
cjfa-35471	931	24	28.09	28.09	NUM
cjfa-35471	931	25	lithuania	lithuania	PROPN
cjfa-35471	931	26	39	39	NUM
cjfa-35471	931	27	27	27	NUM
cjfa-35471	931	28	29.46	29.46	NUM
cjfa-35471	931	29	slovakia	slovakia	NOUN
cjfa-35471	931	30	42	42	NUM
cjfa-35471	931	31	41	41	NUM
cjfa-35471	931	32	32.73	32.73	NUM
cjfa-35471	931	33	slovenia	slovenia	NOUN
cjfa-35471	931	34	35	35	NUM
cjfa-35471	931	35	33	33	NUM
cjfa-35471	931	36	35.63	35.63	NUM
cjfa-35471	931	37	s	s	NOUN
cjfa-35471	931	38	o	o	NOUN
cjfa-35471	931	39	u	u	NOUN
cjfa-35471	931	40	r	r	NOUN
cjfa-35471	931	41	c	c	NOUN
cjfa-35471	931	42	e	e	NOUN
cjfa-35471	931	43	:	:	PUNCT
cjfa-35471	931	44	constructed	construct	VERB
cjfa-35471	931	45	by	by	ADP
cjfa-35471	931	46	authors	author	NOUN
cjfa-35471	931	47	based	base	VERB
cjfa-35471	931	48	on	on	ADP
cjfa-35471	931	49	:	:	PUNCT
cjfa-35471	931	50	data	datum	NOUN
cjfa-35471	931	51	trading	trading	NOUN
cjfa-35471	931	52	economics	economic	NOUN
cjfa-35471	931	53	(	(	PUNCT
cjfa-35471	931	54	2020	2020	NUM
cjfa-35471	931	55	)	)	PUNCT
cjfa-35471	931	56	;	;	PUNCT
cjfa-35471	931	57	ourworldindata	ourworldindata	ADJ
cjfa-35471	931	58	.	.	PUNCT
cjfa-35471	931	59	org	org	NOUN
cjfa-35471	931	60	(	(	PUNCT
cjfa-35471	931	61	2021	2021	NUM
cjfa-35471	931	62	)	)	PUNCT
cjfa-35471	931	63	.	.	PUNCT
cjfa-35471	932	1	skorupinska	skorupinska	NOUN
cjfa-35471	932	2	and	and	CCONJ
cjfa-35471	932	3	torrent	torrent	NOUN
cjfa-35471	932	4	-	-	PUNCT
cjfa-35471	932	5	sellens	sellen	NOUN
cjfa-35471	932	6	(	(	PUNCT
cjfa-35471	932	7	2015	2015	NUM
cjfa-35471	932	8	)	)	PUNCT
cjfa-35471	932	9	analyses	analyse	VERB
cjfa-35471	932	10	stage	stage	NOUN
cjfa-35471	932	11	of	of	ADP
cjfa-35471	932	12	transition	transition	NOUN
cjfa-35471	932	13	to	to	ADP
cjfa-35471	932	14	knowledge	knowledge	NOUN
cjfa-35471	932	15	economy	economy	NOUN
cjfa-35471	932	16	in	in	ADP
cjfa-35471	932	17	cee	cee	NOUN
cjfa-35471	932	18	countries	country	NOUN
cjfa-35471	932	19	and	and	CCONJ
cjfa-35471	932	20	shows	show	VERB
cjfa-35471	932	21	that	that	SCONJ
cjfa-35471	932	22	there	there	PRON
cjfa-35471	932	23	is	be	VERB
cjfa-35471	932	24	considerable	considerable	ADJ
cjfa-35471	932	25	gab	gab	NOUN
cjfa-35471	932	26	between	between	ADP
cjfa-35471	932	27	cee	cee	PROPN
cjfa-35471	932	28	and	and	CCONJ
cjfa-35471	932	29	eu	eu	PROPN
cjfa-35471	932	30	countries	country	NOUN
cjfa-35471	932	31	in	in	ADP
cjfa-35471	932	32	human	human	ADJ
cjfa-35471	932	33	capital	capital	NOUN
cjfa-35471	932	34	,	,	PUNCT
cjfa-35471	932	35	infrastructure	infrastructure	NOUN
cjfa-35471	932	36	,	,	PUNCT
cjfa-35471	932	37	innovation	innovation	NOUN
cjfa-35471	932	38	capacity	capacity	NOUN
cjfa-35471	932	39	and	and	CCONJ
cjfa-35471	932	40	quality	quality	NOUN
cjfa-35471	932	41	institutions	institution	NOUN
cjfa-35471	932	42	.	.	PUNCT
cjfa-35471	933	1	a	a	DET
cjfa-35471	933	2	summary	summary	NOUN
cjfa-35471	933	3	of	of	ADP
cjfa-35471	933	4	a	a	DET
cjfa-35471	933	5	study	study	NOUN
cjfa-35471	933	6	by	by	ADP
cjfa-35471	933	7	radosevic	radosevic	ADJ
cjfa-35471	933	8	(	(	PUNCT
cjfa-35471	933	9	2017	2017	NUM
cjfa-35471	933	10	)	)	PUNCT
cjfa-35471	933	11	on	on	ADP
cjfa-35471	933	12	technology	technology	NOUN
cjfa-35471	933	13	in	in	ADP
cjfa-35471	933	14	central	central	ADJ
cjfa-35471	933	15	and	and	CCONJ
cjfa-35471	933	16	eastern	eastern	ADJ
cjfa-35471	933	17	european	european	ADJ
cjfa-35471	933	18	economies	economy	NOUN
cjfa-35471	933	19	is	be	AUX
cjfa-35471	933	20	presented	present	VERB
cjfa-35471	933	21	below	below	ADV
cjfa-35471	933	22	.	.	PUNCT
cjfa-35471	934	1	coupling	couple	VERB
cjfa-35471	934	2	domestic	domestic	ADJ
cjfa-35471	934	3	technology	technology	NOUN
cjfa-35471	934	4	efforts	effort	NOUN
cjfa-35471	934	5	with	with	ADP
cjfa-35471	934	6	the	the	DET
cjfa-35471	934	7	import	import	NOUN
cjfa-35471	934	8	of	of	ADP
cjfa-35471	934	9	new	new	ADJ
cjfa-35471	934	10	equipment	equipment	NOUN
cjfa-35471	934	11	and	and	CCONJ
cjfa-35471	934	12	management	management	NOUN
cjfa-35471	934	13	practices	practice	NOUN
cjfa-35471	934	14	could	could	AUX
cjfa-35471	934	15	help	help	VERB
cjfa-35471	934	16	promote	promote	VERB
cjfa-35471	934	17	technology	technology	NOUN
cjfa-35471	934	18	upgrading	upgrading	NOUN
cjfa-35471	934	19	.	.	PUNCT
cjfa-35471	935	1	mustafa	mustafa	PROPN
cjfa-35471	935	2	akan	akan	PROPN
cjfa-35471	935	3	,	,	PUNCT
cjfa-35471	935	4	natalia	natalia	PROPN
cjfa-35471	935	5	konovalova28	konovalova28	PROPN
cjfa-35471	935	6	production	production	NOUN
cjfa-35471	935	7	capability	capability	NOUN
cjfa-35471	935	8	and	and	CCONJ
cjfa-35471	935	9	engineering	engineering	NOUN
cjfa-35471	935	10	,	,	PUNCT
cjfa-35471	935	11	in	in	ADP
cjfa-35471	935	12	addition	addition	NOUN
cjfa-35471	935	13	to	to	ADP
cjfa-35471	935	14	research	research	NOUN
cjfa-35471	935	15	,	,	PUNCT
cjfa-35471	935	16	are	be	AUX
cjfa-35471	935	17	important	important	ADJ
cjfa-35471	935	18	antecedents	antecedent	NOUN
cjfa-35471	935	19	to	to	ADP
cjfa-35471	935	20	development	development	NOUN
cjfa-35471	935	21	and	and	CCONJ
cjfa-35471	935	22	innovation	innovation	NOUN
cjfa-35471	935	23	.	.	PUNCT
cjfa-35471	936	1	production	production	NOUN
cjfa-35471	936	2	capability	capability	NOUN
cjfa-35471	936	3	is	be	AUX
cjfa-35471	936	4	the	the	DET
cjfa-35471	936	5	most	most	ADV
cjfa-35471	936	6	significant	significant	ADJ
cjfa-35471	936	7	driver	driver	NOUN
cjfa-35471	936	8	of	of	ADP
cjfa-35471	936	9	productivity	productivity	NOUN
cjfa-35471	936	10	growth	growth	NOUN
cjfa-35471	936	11	.	.	PUNCT
cjfa-35471	937	1	innovation	innovation	NOUN
cjfa-35471	937	2	policy	policy	NOUN
cjfa-35471	937	3	in	in	ADP
cjfa-35471	937	4	cee	cee	PROPN
cjfa-35471	937	5	is	be	AUX
cjfa-35471	937	6	based	base	VERB
cjfa-35471	937	7	solely	solely	ADV
cjfa-35471	937	8	on	on	ADP
cjfa-35471	937	9	r&d	r&d	NOUN
cjfa-35471	937	10	,	,	PUNCT
cjfa-35471	937	11	imitating	imitate	VERB
cjfa-35471	937	12	best	good	ADJ
cjfa-35471	937	13	practices	practice	NOUN
cjfa-35471	937	14	in	in	ADP
cjfa-35471	937	15	northern	northern	ADJ
cjfa-35471	937	16	europe	europe	PROPN
cjfa-35471	937	17	,	,	PUNCT
cjfa-35471	937	18	instead	instead	ADV
cjfa-35471	937	19	of	of	ADP
cjfa-35471	937	20	addressing	address	VERB
cjfa-35471	937	21	regionally	regionally	ADV
cjfa-35471	937	22	specific	specific	ADJ
cjfa-35471	937	23	challenges	challenge	NOUN
cjfa-35471	937	24	.	.	PUNCT
cjfa-35471	938	1	cee	cee	NOUN
cjfa-35471	938	2	economies	economy	NOUN
cjfa-35471	938	3	over	over	ADP
cjfa-35471	938	4	-	-	PUNCT
cjfa-35471	938	5	prioritize	prioritize	AUX
cjfa-35471	938	6	attracting	attract	VERB
cjfa-35471	938	7	foreign	foreign	ADJ
cjfa-35471	938	8	direct	direct	ADJ
cjfa-35471	938	9	investment	investment	NOUN
cjfa-35471	938	10	and	and	CCONJ
cjfa-35471	938	11	do	do	AUX
cjfa-35471	938	12	not	not	PART
cjfa-35471	938	13	place	place	VERB
cjfa-35471	938	14	enough	enough	ADJ
cjfa-35471	938	15	emphasis	emphasis	NOUN
cjfa-35471	938	16	on	on	ADP
cjfa-35471	938	17	the	the	DET
cjfa-35471	938	18	quality	quality	NOUN
cjfa-35471	938	19	of	of	ADP
cjfa-35471	938	20	subsidiary	subsidiary	ADJ
cjfa-35471	938	21	developments	development	NOUN
cjfa-35471	938	22	.	.	PUNCT
cjfa-35471	939	1	radosevic	radosevic	PROPN
cjfa-35471	939	2	’s	’s	PART
cjfa-35471	939	3	conclusions	conclusion	NOUN
cjfa-35471	939	4	,	,	PUNCT
cjfa-35471	939	5	from	from	ADP
cjfa-35471	939	6	a	a	DET
cjfa-35471	939	7	macro	macro	ADJ
cjfa-35471	939	8	point	point	NOUN
cjfa-35471	939	9	of	of	ADP
cjfa-35471	939	10	view	view	NOUN
cjfa-35471	939	11	,	,	PUNCT
cjfa-35471	939	12	support	support	VERB
cjfa-35471	939	13	the	the	DET
cjfa-35471	939	14	same	same	ADJ
cjfa-35471	939	15	conclusions	conclusion	NOUN
cjfa-35471	939	16	we	we	PRON
cjfa-35471	939	17	derived	derive	VERB
cjfa-35471	939	18	in	in	ADP
cjfa-35471	939	19	our	our	PRON
cjfa-35471	939	20	micro	micro	ADJ
cjfa-35471	939	21	study	study	NOUN
cjfa-35471	939	22	from	from	ADP
cjfa-35471	939	23	technology	technology	NOUN
cjfa-35471	939	24	point	point	NOUN
cjfa-35471	939	25	of	of	ADP
cjfa-35471	939	26	view	view	NOUN
cjfa-35471	939	27	.	.	PUNCT
cjfa-35471	940	1	the	the	DET
cjfa-35471	940	2	third	third	ADJ
cjfa-35471	940	3	implication	implication	NOUN
cjfa-35471	940	4	of	of	ADP
cjfa-35471	940	5	our	our	PRON
cjfa-35471	940	6	results	result	NOUN
cjfa-35471	940	7	was	be	AUX
cjfa-35471	940	8	that	that	SCONJ
cjfa-35471	940	9	the	the	DET
cjfa-35471	940	10	inventory	inventory	NOUN
cjfa-35471	940	11	holding	hold	VERB
cjfa-35471	940	12	costs	cost	NOUN
cjfa-35471	940	13	were	be	AUX
cjfa-35471	940	14	important	important	ADJ
cjfa-35471	940	15	in	in	ADP
cjfa-35471	940	16	inducing	induce	VERB
cjfa-35471	940	17	growth	growth	NOUN
cjfa-35471	940	18	.	.	PUNCT
cjfa-35471	941	1	however	however	ADV
cjfa-35471	941	2	,	,	PUNCT
cjfa-35471	941	3	it	it	PRON
cjfa-35471	941	4	is	be	AUX
cjfa-35471	941	5	not	not	PART
cjfa-35471	941	6	possible	possible	ADJ
cjfa-35471	941	7	to	to	PART
cjfa-35471	941	8	make	make	VERB
cjfa-35471	941	9	generalizations	generalization	NOUN
cjfa-35471	941	10	concerning	concern	VERB
cjfa-35471	941	11	these	these	DET
cjfa-35471	941	12	costs	cost	NOUN
cjfa-35471	941	13	with	with	ADP
cjfa-35471	941	14	regards	regard	NOUN
cjfa-35471	941	15	to	to	ADP
cjfa-35471	941	16	a	a	DET
cjfa-35471	941	17	whole	whole	ADJ
cjfa-35471	941	18	region	region	NOUN
cjfa-35471	941	19	other	other	ADJ
cjfa-35471	941	20	than	than	ADP
cjfa-35471	941	21	the	the	DET
cjfa-35471	941	22	recommendations	recommendation	NOUN
cjfa-35471	941	23	made	make	VERB
cjfa-35471	941	24	in	in	ADP
cjfa-35471	941	25	the	the	DET
cjfa-35471	941	26	previous	previous	ADJ
cjfa-35471	941	27	section	section	NOUN
cjfa-35471	941	28	.	.	PUNCT
cjfa-35471	942	1	incentives	incentive	NOUN
cjfa-35471	942	2	in	in	ADP
cjfa-35471	942	3	terms	term	NOUN
cjfa-35471	942	4	of	of	ADP
cjfa-35471	942	5	holding	hold	VERB
cjfa-35471	942	6	costs	cost	NOUN
cjfa-35471	942	7	should	should	AUX
cjfa-35471	942	8	be	be	AUX
cjfa-35471	942	9	based	base	VERB
cjfa-35471	942	10	on	on	ADP
cjfa-35471	942	11	sectors	sector	NOUN
cjfa-35471	942	12	.	.	PUNCT
cjfa-35471	943	1	companies	company	NOUN
cjfa-35471	943	2	producing	produce	VERB
cjfa-35471	943	3	very	very	ADV
cjfa-35471	943	4	high	high	ADJ
cjfa-35471	943	5	value	value	NOUN
cjfa-35471	943	6	products	product	NOUN
cjfa-35471	943	7	such	such	ADJ
cjfa-35471	943	8	as	as	ADP
cjfa-35471	943	9	cars	car	NOUN
cjfa-35471	943	10	,	,	PUNCT
cjfa-35471	943	11	computers	computer	NOUN
cjfa-35471	943	12	,	,	PUNCT
cjfa-35471	943	13	planes	plane	NOUN
cjfa-35471	943	14	should	should	AUX
cjfa-35471	943	15	get	get	VERB
cjfa-35471	943	16	better	well	ADJ
cjfa-35471	943	17	incentives	incentive	NOUN
cjfa-35471	943	18	since	since	SCONJ
cjfa-35471	943	19	they	they	PRON
cjfa-35471	943	20	are	be	AUX
cjfa-35471	943	21	more	more	ADV
cjfa-35471	943	22	likely	likely	ADJ
cjfa-35471	943	23	to	to	PART
cjfa-35471	943	24	have	have	VERB
cjfa-35471	943	25	higher	high	ADJ
cjfa-35471	943	26	holding	hold	VERB
cjfa-35471	943	27	costs	cost	NOUN
cjfa-35471	943	28	.	.	PUNCT
cjfa-35471	944	1	the	the	DET
cjfa-35471	944	2	general	general	ADJ
cjfa-35471	944	3	conclusions	conclusion	NOUN
cjfa-35471	944	4	on	on	ADP
cjfa-35471	944	5	central	central	ADJ
cjfa-35471	944	6	european	european	ADJ
cjfa-35471	944	7	countries	country	NOUN
cjfa-35471	944	8	are	be	AUX
cjfa-35471	944	9	:	:	PUNCT
cjfa-35471	944	10	1	1	X
cjfa-35471	944	11	.	.	X
cjfa-35471	944	12	lowering	lower	VERB
cjfa-35471	944	13	interest	interest	NOUN
cjfa-35471	944	14	rates	rate	NOUN
cjfa-35471	944	15	will	will	AUX
cjfa-35471	944	16	not	not	PART
cjfa-35471	944	17	have	have	VERB
cjfa-35471	944	18	an	an	DET
cjfa-35471	944	19	appreciable	appreciable	ADJ
cjfa-35471	944	20	effect	effect	NOUN
cjfa-35471	944	21	on	on	ADP
cjfa-35471	944	22	growth	growth	NOUN
cjfa-35471	944	23	.	.	PUNCT
cjfa-35471	945	1	2	2	X
cjfa-35471	945	2	.	.	X
cjfa-35471	945	3	incentives	incentive	NOUN
cjfa-35471	945	4	regarding	regard	VERB
cjfa-35471	945	5	improvement	improvement	NOUN
cjfa-35471	945	6	of	of	ADP
cjfa-35471	945	7	production	production	NOUN
cjfa-35471	945	8	technology	technology	NOUN
cjfa-35471	945	9	will	will	AUX
cjfa-35471	945	10	be	be	AUX
cjfa-35471	945	11	effective	effective	ADJ
cjfa-35471	945	12	.	.	PUNCT
cjfa-35471	946	1	3	3	X
cjfa-35471	946	2	.	.	X
cjfa-35471	946	3	incentives	incentive	NOUN
cjfa-35471	946	4	regarding	regard	VERB
cjfa-35471	946	5	holding	hold	VERB
cjfa-35471	946	6	costs	cost	NOUN
cjfa-35471	946	7	should	should	AUX
cjfa-35471	946	8	be	be	AUX
cjfa-35471	946	9	instituted	institute	VERB
cjfa-35471	946	10	on	on	ADP
cjfa-35471	946	11	sectorial	sectorial	ADJ
cjfa-35471	946	12	basis	basis	NOUN
cjfa-35471	946	13	.	.	PUNCT
cjfa-35471	947	1	the	the	DET
cjfa-35471	947	2	incentives	incentive	NOUN
cjfa-35471	947	3	related	relate	VERB
cjfa-35471	947	4	to	to	ADP
cjfa-35471	947	5	points	point	NOUN
cjfa-35471	947	6	1	1	NUM
cjfa-35471	947	7	and	and	CCONJ
cjfa-35471	947	8	above	above	ADV
cjfa-35471	947	9	are	be	AUX
cjfa-35471	947	10	relatively	relatively	ADV
cjfa-35471	947	11	easy	easy	ADJ
cjfa-35471	947	12	to	to	PART
cjfa-35471	947	13	institute	institute	VERB
cjfa-35471	947	14	.	.	PUNCT
cjfa-35471	948	1	however	however	ADV
cjfa-35471	948	2	,	,	PUNCT
cjfa-35471	948	3	the	the	DET
cjfa-35471	948	4	incentives	incentive	NOUN
cjfa-35471	948	5	regarding	regard	VERB
cjfa-35471	948	6	point	point	NOUN
cjfa-35471	948	7	2	2	NUM
cjfa-35471	948	8	will	will	AUX
cjfa-35471	948	9	take	take	VERB
cjfa-35471	948	10	a	a	DET
cjfa-35471	948	11	longer	long	ADJ
cjfa-35471	948	12	time	time	NOUN
cjfa-35471	948	13	to	to	PART
cjfa-35471	948	14	make	make	VERB
cjfa-35471	948	15	a	a	DET
cjfa-35471	948	16	significant	significant	ADJ
cjfa-35471	948	17	difference	difference	NOUN
cjfa-35471	948	18	in	in	ADP
cjfa-35471	948	19	spurring	spur	VERB
cjfa-35471	948	20	growth	growth	NOUN
cjfa-35471	948	21	.	.	PUNCT
cjfa-35471	949	1	in	in	ADP
cjfa-35471	949	2	the	the	DET
cjfa-35471	949	3	short	short	ADJ
cjfa-35471	949	4	run	run	NOUN
cjfa-35471	949	5	,	,	PUNCT
cjfa-35471	949	6	the	the	DET
cjfa-35471	949	7	governments	government	NOUN
cjfa-35471	949	8	of	of	ADP
cjfa-35471	949	9	the	the	DET
cjfa-35471	949	10	region	region	NOUN
cjfa-35471	949	11	can	can	AUX
cjfa-35471	949	12	institute	institute	VERB
cjfa-35471	949	13	incentives	incentive	NOUN
cjfa-35471	949	14	to	to	PART
cjfa-35471	949	15	lower	lower	VERB
cjfa-35471	949	16	the	the	DET
cjfa-35471	949	17	marginal	marginal	ADJ
cjfa-35471	949	18	cost	cost	NOUN
cjfa-35471	949	19	of	of	ADP
cjfa-35471	949	20	production	production	NOUN
cjfa-35471	949	21	for	for	ADP
cjfa-35471	949	22	all	all	DET
cjfa-35471	949	23	sectors	sector	NOUN
cjfa-35471	949	24	to	to	PART
cjfa-35471	949	25	reduce	reduce	VERB
cjfa-35471	949	26	the	the	DET
cjfa-35471	949	27	cost	cost	NOUN
cjfa-35471	949	28	of	of	ADP
cjfa-35471	949	29	inputs	input	NOUN
cjfa-35471	949	30	to	to	ADP
cjfa-35471	949	31	the	the	DET
cjfa-35471	949	32	production	production	NOUN
cjfa-35471	949	33	process	process	NOUN
cjfa-35471	949	34	such	such	ADJ
cjfa-35471	949	35	as	as	ADP
cjfa-35471	949	36	cost	cost	NOUN
cjfa-35471	949	37	of	of	ADP
cjfa-35471	949	38	energy	energy	NOUN
cjfa-35471	949	39	(	(	PUNCT
cjfa-35471	949	40	lower	low	ADJ
cjfa-35471	949	41	taxes	taxis	NOUN
cjfa-35471	949	42	on	on	ADP
cjfa-35471	949	43	energy	energy	NOUN
cjfa-35471	949	44	,	,	PUNCT
cjfa-35471	949	45	sell	sell	VERB
cjfa-35471	949	46	energy	energy	NOUN
cjfa-35471	949	47	at	at	ADP
cjfa-35471	949	48	a	a	DET
cjfa-35471	949	49	lower	low	ADJ
cjfa-35471	949	50	price	price	NOUN
cjfa-35471	949	51	)	)	PUNCT
cjfa-35471	949	52	,	,	PUNCT
cjfa-35471	949	53	water	water	NOUN
cjfa-35471	949	54	,	,	PUNCT
cjfa-35471	949	55	labor	labor	NOUN
cjfa-35471	949	56	(	(	PUNCT
cjfa-35471	949	57	reduce	reduce	VERB
cjfa-35471	949	58	social	social	ADJ
cjfa-35471	949	59	security	security	NOUN
cjfa-35471	949	60	premiums	premium	NOUN
cjfa-35471	949	61	paid	pay	VERB
cjfa-35471	949	62	by	by	ADP
cjfa-35471	949	63	the	the	DET
cjfa-35471	949	64	employee	employee	NOUN
cjfa-35471	949	65	)	)	PUNCT
cjfa-35471	949	66	,	,	PUNCT
cjfa-35471	949	67	taxes	taxis	NOUN
cjfa-35471	949	68	on	on	ADP
cjfa-35471	949	69	raw	raw	ADJ
cjfa-35471	949	70	materials	material	NOUN
cjfa-35471	949	71	.	.	PUNCT
cjfa-35471	950	1	the	the	DET
cjfa-35471	950	2	analysis	analysis	NOUN
cjfa-35471	950	3	above	above	ADV
cjfa-35471	950	4	is	be	AUX
cjfa-35471	950	5	only	only	ADV
cjfa-35471	950	6	for	for	ADP
cjfa-35471	950	7	firms	firm	NOUN
cjfa-35471	950	8	competing	compete	VERB
cjfa-35471	950	9	in	in	ADP
cjfa-35471	950	10	a	a	DET
cjfa-35471	950	11	perfect	perfect	ADJ
cjfa-35471	950	12	market	market	NOUN
cjfa-35471	950	13	facing	face	VERB
cjfa-35471	950	14	a	a	DET
cjfa-35471	950	15	deterministic	deterministic	ADJ
cjfa-35471	950	16	time	time	NOUN
cjfa-35471	950	17	dependent	dependent	ADJ
cjfa-35471	950	18	function	function	NOUN
cjfa-35471	950	19	.	.	PUNCT
cjfa-35471	951	1	a	a	DET
cjfa-35471	951	2	natural	natural	ADJ
cjfa-35471	951	3	extension	extension	NOUN
cjfa-35471	951	4	of	of	ADP
cjfa-35471	951	5	this	this	DET
cjfa-35471	951	6	model	model	NOUN
cjfa-35471	951	7	is	be	AUX
cjfa-35471	951	8	to	to	PART
cjfa-35471	951	9	make	make	VERB
cjfa-35471	951	10	the	the	DET
cjfa-35471	951	11	demand	demand	NOUN
cjfa-35471	951	12	stochastic	stochastic	NOUN
cjfa-35471	951	13	in	in	ADP
cjfa-35471	951	14	other	other	ADJ
cjfa-35471	951	15	market	market	NOUN
cjfa-35471	951	16	forms	form	NOUN
cjfa-35471	951	17	such	such	ADJ
cjfa-35471	951	18	as	as	ADP
cjfa-35471	951	19	monopolistic	monopolistic	ADJ
cjfa-35471	951	20	or	or	CCONJ
cjfa-35471	951	21	oligopolistic	oligopolistic	ADJ
cjfa-35471	951	22	markets	market	NOUN
cjfa-35471	951	23	.	.	PUNCT
cjfa-35471	952	1	optimal	optimal	ADJ
cjfa-35471	952	2	incentives	incentive	NOUN
cjfa-35471	952	3	for	for	ADP
cjfa-35471	952	4	economic	economic	ADJ
cjfa-35471	952	5	growth	growth	NOUN
cjfa-35471	952	6	…	…	PUNCT
cjfa-35471	952	7	29	29	NUM
cjfa-35471	952	8	 	 	SPACE
cjfa-35471	952	9	references	reference	NOUN
cjfa-35471	952	10	afp	afp	NOUN
cjfa-35471	952	11	(	(	PUNCT
cjfa-35471	952	12	2020	2020	NUM
cjfa-35471	952	13	)	)	PUNCT
cjfa-35471	952	14	.	.	PUNCT
cjfa-35471	953	1	coronavirus	coronavirus	NOUN
cjfa-35471	953	2	could	could	AUX
cjfa-35471	953	3	damage	damage	VERB
cjfa-35471	953	4	global	global	ADJ
cjfa-35471	953	5	growth	growth	NOUN
cjfa-35471	953	6	in	in	ADP
cjfa-35471	953	7	2020	2020	NUM
cjfa-35471	953	8	:	:	PUNCT
cjfa-35471	954	1	imf	imf	PROPN
cjfa-35471	954	2	.	.	PROPN
cjfa-35471	954	3	bangkok	bangkok	PROPN
cjfa-35471	954	4	post	post	PROPN
cjfa-35471	954	5	,	,	PUNCT
cjfa-35471	954	6	https://www.bangkokpost.com/world/1859319/coronavirus-could-damage-globalgrowth-in-2020-imf	https://www.bangkokpost.com/world/1859319/coronavirus-could-damage-globalgrowth-in-2020-imf	PROPN
cjfa-35471	954	7	(	(	PUNCT
cjfa-35471	954	8	accessed	access	VERB
cjfa-35471	954	9	:	:	PUNCT
cjfa-35471	954	10	17.02.2020	17.02.2020	NUM
cjfa-35471	954	11	)	)	PUNCT
cjfa-35471	954	12	.	.	PUNCT
cjfa-35471	955	1	bryson	bryson	PROPN
cjfa-35471	955	2	,	,	PUNCT
cjfa-35471	955	3	a.	a.	PROPN
cjfa-35471	955	4	,	,	PUNCT
cjfa-35471	955	5	denham	denham	PROPN
cjfa-35471	955	6	,	,	PUNCT
cjfa-35471	955	7	w.	w.	PROPN
cjfa-35471	955	8	,	,	PUNCT
cjfa-35471	955	9	&	&	CCONJ
cjfa-35471	955	10	dreyfus	dreyfus	PROPN
cjfa-35471	955	11	,	,	PUNCT
cjfa-35471	955	12	s.	s.	PROPN
cjfa-35471	955	13	(	(	PUNCT
cjfa-35471	955	14	1963	1963	NUM
cjfa-35471	955	15	)	)	PUNCT
cjfa-35471	955	16	.	.	PUNCT
cjfa-35471	956	1	optimal	optimal	ADJ
cjfa-35471	956	2	programming	programming	NOUN
cjfa-35471	956	3	with	with	ADP
cjfa-35471	956	4	inequality	inequality	NOUN
cjfa-35471	956	5	constraints	constraint	NOUN
cjfa-35471	956	6	.	.	PUNCT
cjfa-35471	957	1	aiaa	aiaa	PROPN
cjfa-35471	957	2	journal	journal	PROPN
cjfa-35471	957	3	,	,	PUNCT
cjfa-35471	957	4	1(11	1(11	NUM
cjfa-35471	957	5	)	)	PUNCT
cjfa-35471	957	6	,	,	PUNCT
cjfa-35471	957	7	2544	2544	NUM
cjfa-35471	957	8	-	-	SYM
cjfa-35471	957	9	2550	2550	NUM
cjfa-35471	957	10	.	.	PUNCT
cjfa-35471	958	1	http://dx.doi.org/10.2514/3.2107	http://dx.doi.org/10.2514/3.2107	PROPN
cjfa-35471	958	2	.	.	PUNCT
cjfa-35471	959	1	bryson	bryson	PROPN
cjfa-35471	959	2	,	,	PUNCT
cjfa-35471	959	3	a.e	a.e	PROPN
cjfa-35471	959	4	.	.	PROPN
cjfa-35471	959	5	,	,	PUNCT
cjfa-35471	959	6	jr	jr	PROPN
cjfa-35471	959	7	.	.	PROPN
cjfa-35471	959	8	,	,	PUNCT
cjfa-35471	959	9	&	&	CCONJ
cjfa-35471	959	10	ho	ho	PROPN
cjfa-35471	959	11	,	,	PUNCT
cjfa-35471	959	12	y.-c	y.-c	NOUN
cjfa-35471	959	13	.	.	PUNCT
cjfa-35471	960	1	(	(	PUNCT
cjfa-35471	960	2	1975	1975	NUM
cjfa-35471	960	3	)	)	PUNCT
cjfa-35471	960	4	.	.	PUNCT
cjfa-35471	961	1	applied	apply	VERB
cjfa-35471	961	2	optimal	optimal	ADJ
cjfa-35471	961	3	control	control	NOUN
cjfa-35471	961	4	.	.	PUNCT
cjfa-35471	962	1	washington	washington	PROPN
cjfa-35471	962	2	:	:	PUNCT
cjfa-35471	962	3	hemisphere	hemisphere	PROPN
cjfa-35471	962	4	publishing	publishing	PROPN
cjfa-35471	962	5	co.	co.	PROPN
cjfa-35471	962	6	bundrick	bundrick	PROPN
cjfa-35471	962	7	,	,	PUNCT
cjfa-35471	962	8	j.	j.	PROPN
cjfa-35471	962	9	(	(	PUNCT
cjfa-35471	962	10	2016	2016	NUM
cjfa-35471	962	11	)	)	PUNCT
cjfa-35471	962	12	.	.	PUNCT
cjfa-35471	963	1	tax	tax	NOUN
cjfa-35471	963	2	incentives	incentive	NOUN
cjfa-35471	963	3	and	and	CCONJ
cjfa-35471	963	4	subsidies	subsidy	NOUN
cjfa-35471	963	5	:	:	PUNCT
cjfa-35471	963	6	two	two	NUM
cjfa-35471	963	7	stables	stable	NOUN
cjfa-35471	963	8	of	of	ADP
cjfa-35471	963	9	economic	economic	ADJ
cjfa-35471	963	10	development	development	NOUN
cjfa-35471	963	11	.	.	PUNCT
cjfa-35471	964	1	arkansas	arkansa	NOUN
cjfa-35471	964	2	center	center	PROPN
cjfa-35471	964	3	for	for	ADP
cjfa-35471	964	4	research	research	NOUN
cjfa-35471	964	5	in	in	ADP
cjfa-35471	964	6	economics	economic	NOUN
cjfa-35471	964	7	,	,	PUNCT
cjfa-35471	964	8	university	university	NOUN
cjfa-35471	964	9	of	of	ADP
cjfa-35471	964	10	central	central	ADJ
cjfa-35471	964	11	arkansas	arkansas	PROPN
cjfa-35471	964	12	.	.	PUNCT
cjfa-35471	965	1	buss	buss	PROPN
cjfa-35471	965	2	,	,	PUNCT
cjfa-35471	965	3	f.t	f.t	PROPN
cjfa-35471	965	4	.	.	PUNCT
cjfa-35471	965	5	(	(	PUNCT
cjfa-35471	965	6	2001	2001	NUM
cjfa-35471	965	7	)	)	PUNCT
cjfa-35471	965	8	.	.	PUNCT
cjfa-35471	966	1	the	the	DET
cjfa-35471	966	2	effect	effect	NOUN
cjfa-35471	966	3	of	of	ADP
cjfa-35471	966	4	state	state	NOUN
cjfa-35471	966	5	tax	tax	NOUN
cjfa-35471	966	6	incentives	incentive	NOUN
cjfa-35471	966	7	on	on	ADP
cjfa-35471	966	8	economic	economic	ADJ
cjfa-35471	966	9	growth	growth	NOUN
cjfa-35471	966	10	and	and	CCONJ
cjfa-35471	966	11	firm	firm	ADJ
cjfa-35471	966	12	location	location	NOUN
cjfa-35471	966	13	decisions	decision	NOUN
cjfa-35471	966	14	:	:	PUNCT
cjfa-35471	966	15	an	an	DET
cjfa-35471	966	16	overview	overview	NOUN
cjfa-35471	966	17	of	of	ADP
cjfa-35471	966	18	the	the	DET
cjfa-35471	966	19	literature	literature	NOUN
cjfa-35471	966	20	.	.	PUNCT
cjfa-35471	967	1	economic	economic	ADJ
cjfa-35471	967	2	development	development	PROPN
cjfa-35471	967	3	quarterly	quarterly	PROPN
cjfa-35471	967	4	,	,	PUNCT
cjfa-35471	967	5	15(1	15(1	NUM
cjfa-35471	967	6	)	)	PUNCT
cjfa-35471	967	7	,	,	PUNCT
cjfa-35471	967	8	90	90	NUM
cjfa-35471	967	9	-	-	SYM
cjfa-35471	967	10	105	105	NUM
cjfa-35471	967	11	.	.	PUNCT
cjfa-35471	968	1	http://dx.doi.org/10.1177/089124240101500108	http://dx.doi.org/10.1177/089124240101500108	PROPN
cjfa-35471	968	2	.	.	PUNCT
cjfa-35471	969	1	carlianne	carlianne	PROPN
cjfa-35471	969	2	,	,	PUNCT
cjfa-35471	969	3	p.	p.	NOUN
cjfa-35471	969	4	(	(	PUNCT
cjfa-35471	969	5	2014	2014	NUM
cjfa-35471	969	6	)	)	PUNCT
cjfa-35471	969	7	.	.	PUNCT
cjfa-35471	970	1	does	do	AUX
cjfa-35471	970	2	increasing	increase	VERB
cjfa-35471	970	3	available	available	ADJ
cjfa-35471	970	4	non	non	ADJ
cjfa-35471	970	5	-	-	ADJ
cjfa-35471	970	6	tax	tax	ADJ
cjfa-35471	970	7	economic	economic	ADJ
cjfa-35471	970	8	development	development	NOUN
cjfa-35471	970	9	incentives	incentive	NOUN
cjfa-35471	970	10	result	result	VERB
cjfa-35471	970	11	in	in	ADP
cjfa-35471	970	12	more	more	ADJ
cjfa-35471	970	13	jobs	job	NOUN
cjfa-35471	970	14	?	?	PUNCT
cjfa-35471	971	1	national	national	ADJ
cjfa-35471	971	2	tax	tax	PROPN
cjfa-35471	971	3	journal	journal	PROPN
cjfa-35471	971	4	,	,	PUNCT
cjfa-35471	971	5	67(2	67(2	NUM
cjfa-35471	971	6	)	)	PUNCT
cjfa-35471	971	7	,	,	PUNCT
cjfa-35471	971	8	351	351	NUM
cjfa-35471	971	9	-	-	SYM
cjfa-35471	971	10	386	386	NUM
cjfa-35471	971	11	.	.	PUNCT
cjfa-35471	972	1	christian	christian	PROPN
cjfa-35471	972	2	,	,	PUNCT
cjfa-35471	972	3	g.	g.	PROPN
cjfa-35471	972	4	,	,	PUNCT
cjfa-35471	972	5	karlin	karlin	PROPN
cjfa-35471	972	6	,	,	PUNCT
cjfa-35471	972	7	m.	m.	NOUN
cjfa-35471	972	8	,	,	PUNCT
cjfa-35471	972	9	schaff	schaff	PROPN
cjfa-35471	972	10	,	,	PUNCT
cjfa-35471	972	11	r.	r.	PROPN
cjfa-35471	972	12	,	,	PUNCT
cjfa-35471	972	13	&	&	CCONJ
cjfa-35471	972	14	tucker	tucker	PROPN
cjfa-35471	972	15	-	-	PUNCT
cjfa-35471	972	16	roy	roy	PROPN
cjfa-35471	972	17	,	,	PUNCT
cjfa-35471	972	18	s.	s.	PROPN
cjfa-35471	972	19	(	(	PUNCT
cjfa-35471	972	20	2019	2019	NUM
cjfa-35471	972	21	)	)	PUNCT
cjfa-35471	972	22	.	.	PUNCT
cjfa-35471	973	1	how	how	SCONJ
cjfa-35471	973	2	state	state	NOUN
cjfa-35471	973	3	and	and	CCONJ
cjfa-35471	973	4	local	local	ADJ
cjfa-35471	973	5	governments	government	NOUN
cjfa-35471	973	6	win	win	VERB
cjfa-35471	973	7	at	at	ADP
cjfa-35471	973	8	attracting	attract	VERB
cjfa-35471	973	9	companies	company	NOUN
cjfa-35471	973	10	?	?	PUNCT
cjfa-35471	973	11	.	.	PUNCT
cjfa-35471	974	1	mckinsey	mckinsey	NOUN
cjfa-35471	974	2	and	and	CCONJ
cjfa-35471	974	3	company	company	NOUN
cjfa-35471	974	4	,	,	PUNCT
cjfa-35471	974	5	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governmentswin-at-attracting-companies	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governmentswin-at-attracting-companie	NOUN
cjfa-35471	974	6	.	.	PUNCT
cjfa-35471	975	1	conroy	conroy	PROPN
cjfa-35471	975	2	,	,	PUNCT
cjfa-35471	975	3	c.m	c.m	PROPN
cjfa-35471	975	4	.	.	PROPN
cjfa-35471	975	5	(	(	PUNCT
cjfa-35471	975	6	2019	2019	NUM
cjfa-35471	975	7	)	)	PUNCT
cjfa-35471	975	8	.	.	PUNCT
cjfa-35471	976	1	do	do	AUX
cjfa-35471	976	2	economic	economic	ADJ
cjfa-35471	976	3	incentives	incentive	NOUN
cjfa-35471	976	4	work	work	VERB
cjfa-35471	976	5	?	?	PUNCT
cjfa-35471	977	1	evaluating	evaluate	VERB
cjfa-35471	977	2	the	the	DET
cjfa-35471	977	3	effect	effect	NOUN
cjfa-35471	977	4	of	of	ADP
cjfa-35471	977	5	incentives	incentive	NOUN
cjfa-35471	977	6	designed	design	VERB
cjfa-35471	977	7	to	to	PART
cjfa-35471	977	8	attract	attract	VERB
cjfa-35471	977	9	investment	investment	NOUN
cjfa-35471	977	10	on	on	ADP
cjfa-35471	977	11	a	a	DET
cjfa-35471	977	12	stat	stat	NOUN
cjfa-35471	977	13	.	.	PUNCT
cjfa-35471	978	1	master	master	NOUN
cjfa-35471	978	2	of	of	ADP
cjfa-35471	978	3	public	public	ADJ
cjfa-35471	978	4	policy	policy	NOUN
cjfa-35471	978	5	.	.	PUNCT
cjfa-35471	979	1	georgetown	georgetown	PROPN
cjfa-35471	979	2	university	university	PROPN
cjfa-35471	979	3	.	.	PUNCT
cjfa-35471	980	1	washington	washington	PROPN
cjfa-35471	980	2	d.c	d.c	PROPN
cjfa-35471	980	3	.	.	PROPN
cjfa-35471	980	4	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	PROPN
cjfa-35471	980	5	.	.	PUNCT
cjfa-35471	981	1	crespi	crespi	PROPN
cjfa-35471	981	2	,	,	PUNCT
cjfa-35471	981	3	c.	c.	PROPN
cjfa-35471	981	4	,	,	PUNCT
cjfa-35471	981	5	guiliodori	guiliodori	ADV
cjfa-35471	981	6	,	,	PUNCT
cjfa-35471	981	7	d.	d.	PROPN
cjfa-35471	981	8	,	,	PUNCT
cjfa-35471	981	9	guiliodori	guiliodori	ADV
cjfa-35471	981	10	,	,	PUNCT
cjfa-35471	981	11	r.	r.	PROPN
cjfa-35471	981	12	,	,	PUNCT
cjfa-35471	981	13	&	&	CCONJ
cjfa-35471	981	14	rodriguez	rodriguez	PROPN
cjfa-35471	981	15	,	,	PUNCT
cjfa-35471	981	16	a.	a.	NOUN
cjfa-35471	981	17	(	(	PUNCT
cjfa-35471	981	18	2016	2016	NUM
cjfa-35471	981	19	)	)	PUNCT
cjfa-35471	981	20	.	.	PUNCT
cjfa-35471	982	1	the	the	DET
cjfa-35471	982	2	effectiveness	effectiveness	NOUN
cjfa-35471	982	3	of	of	ADP
cjfa-35471	982	4	tax	tax	NOUN
cjfa-35471	982	5	incentives	incentive	NOUN
cjfa-35471	982	6	for	for	ADP
cjfa-35471	982	7	r&d	r&d	NOUN
cjfa-35471	982	8	in	in	ADP
cjfa-35471	982	9	developing	develop	VERB
cjfa-35471	982	10	countries	country	NOUN
cjfa-35471	982	11	:	:	PUNCT
cjfa-35471	982	12	the	the	DET
cjfa-35471	982	13	case	case	NOUN
cjfa-35471	982	14	of	of	ADP
cjfa-35471	982	15	argentina	argentina	PROPN
cjfa-35471	982	16	.	.	PUNCT
cjfa-35471	983	1	research	research	NOUN
cjfa-35471	983	2	policy	policy	NOUN
cjfa-35471	983	3	:	:	PUNCT
cjfa-35471	983	4	policy	policy	NOUN
cjfa-35471	983	5	,	,	PUNCT
cjfa-35471	983	6	management	management	NOUN
cjfa-35471	983	7	and	and	CCONJ
cjfa-35471	983	8	economic	economic	ADJ
cjfa-35471	983	9	studies	study	NOUN
cjfa-35471	983	10	of	of	ADP
cjfa-35471	983	11	science	science	NOUN
cjfa-35471	983	12	,	,	PUNCT
cjfa-35471	983	13	technology	technology	NOUN
cjfa-35471	983	14	and	and	CCONJ
cjfa-35471	983	15	innovation	innovation	NOUN
cjfa-35471	983	16	,	,	PUNCT
cjfa-35471	983	17	45(10	45(10	NUM
cjfa-35471	983	18	)	)	PUNCT
cjfa-35471	983	19	,	,	PUNCT
cjfa-35471	983	20	2023	2023	NUM
cjfa-35471	983	21	-	-	SYM
cjfa-35471	983	22	2035	2035	NUM
cjfa-35471	983	23	.	.	PUNCT
cjfa-35471	984	1	dpme	dpme	PROPN
cjfa-35471	984	2	/	/	SYM
cjfa-35471	984	3	dsbd	dsbd	NOUN
cjfa-35471	984	4	(	(	PUNCT
cjfa-35471	984	5	2018	2018	NUM
cjfa-35471	984	6	)	)	PUNCT
cjfa-35471	984	7	.	.	PUNCT
cjfa-35471	985	1	evaluation	evaluation	NOUN
cjfa-35471	985	2	of	of	ADP
cjfa-35471	985	3	government	government	NOUN
cjfa-35471	985	4	business	business	NOUN
cjfa-35471	985	5	incentives	incentive	VERB
cjfa-35471	985	6	report	report	NOUN
cjfa-35471	985	7	.	.	PUNCT
cjfa-35471	986	1	pretoria	pretoria	PROPN
cjfa-35471	986	2	:	:	PUNCT
cjfa-35471	986	3	department	department	NOUN
cjfa-35471	986	4	of	of	ADP
cjfa-35471	986	5	planning	planning	NOUN
cjfa-35471	986	6	,	,	PUNCT
cjfa-35471	986	7	monitoring	monitoring	NOUN
cjfa-35471	986	8	and	and	CCONJ
cjfa-35471	986	9	evaluation	evaluation	NOUN
cjfa-35471	986	10	,	,	PUNCT
cjfa-35471	986	11	https://www.dpme.gov.za/publications/reports%20and%20other%20information%20products/business%20	https://www.dpme.gov.za/publications/reports%20and%20other%20information%20products/business%20	PROPN
cjfa-35471	986	12	incentives%20draft%20full%20report%20v7%2005112018%20stc.pdf	incentives%20draft%20full%20report%20v7%2005112018%20stc.pdf	PROPN
cjfa-35471	986	13	.	.	PUNCT
cjfa-35471	986	14	feenstra	feenstra	PROPN
cjfa-35471	986	15	,	,	PUNCT
cjfa-35471	986	16	r.c	r.c	PROPN
cjfa-35471	986	17	.	.	PROPN
cjfa-35471	986	18	,	,	PUNCT
cjfa-35471	986	19	inklaar	inklaar	NOUN
cjfa-35471	986	20	,	,	PUNCT
cjfa-35471	986	21	r.	r.	PROPN
cjfa-35471	986	22	,	,	PUNCT
cjfa-35471	986	23	&	&	CCONJ
cjfa-35471	986	24	timmer	timmer	PROPN
cjfa-35471	986	25	,	,	PUNCT
cjfa-35471	986	26	m.p	m.p	PROPN
cjfa-35471	986	27	.	.	PROPN
cjfa-35471	986	28	(	(	PUNCT
cjfa-35471	986	29	2015	2015	NUM
cjfa-35471	986	30	)	)	PUNCT
cjfa-35471	986	31	.	.	PUNCT
cjfa-35471	987	1	the	the	DET
cjfa-35471	987	2	next	next	ADJ
cjfa-35471	987	3	generation	generation	NOUN
cjfa-35471	987	4	of	of	ADP
cjfa-35471	987	5	the	the	DET
cjfa-35471	987	6	penn	penn	PROPN
cjfa-35471	987	7	world	world	PROPN
cjfa-35471	987	8	table	table	NOUN
cjfa-35471	987	9	.	.	PUNCT
cjfa-35471	988	1	american	american	ADJ
cjfa-35471	988	2	economic	economic	PROPN
cjfa-35471	988	3	review	review	PROPN
cjfa-35471	988	4	,	,	PUNCT
cjfa-35471	988	5	105(10	105(10	NUM
cjfa-35471	988	6	)	)	PUNCT
cjfa-35471	988	7	,	,	PUNCT
cjfa-35471	988	8	3150	3150	NUM
cjfa-35471	988	9	-	-	SYM
cjfa-35471	988	10	3182	3182	NUM
cjfa-35471	988	11	.	.	PUNCT
cjfa-35471	989	1	http://dx.doi.org/10.1257/	http://dx.doi.org/10.1257/	ADJ
cjfa-35471	989	2	aer.20130954	aer.20130954	PROPN
cjfa-35471	989	3	.	.	PUNCT
cjfa-35471	989	4	getzoff	getzoff	PROPN
cjfa-35471	989	5	,	,	PUNCT
cjfa-35471	989	6	m.	m.	NOUN
cjfa-35471	989	7	(	(	PUNCT
cjfa-35471	989	8	2020	2020	NUM
cjfa-35471	989	9	)	)	PUNCT
cjfa-35471	989	10	.	.	PUNCT
cjfa-35471	990	1	most	most	ADV
cjfa-35471	990	2	technologically	technologically	ADV
cjfa-35471	990	3	advanced	advanced	ADJ
cjfa-35471	990	4	countries	country	NOUN
cjfa-35471	990	5	in	in	ADP
cjfa-35471	990	6	the	the	DET
cjfa-35471	990	7	world	world	NOUN
cjfa-35471	990	8	,	,	PUNCT
cjfa-35471	990	9	global	global	ADJ
cjfa-35471	990	10	finance	finance	NOUN
cjfa-35471	990	11	.	.	PUNCT
cjfa-35471	991	1	giles	gile	NOUN
cjfa-35471	991	2	,	,	PUNCT
cjfa-35471	991	3	g.	g.	PROPN
cjfa-35471	991	4	,	,	PUNCT
cjfa-35471	991	5	arnold	arnold	PROPN
cjfa-35471	991	6	,	,	PUNCT
cjfa-35471	991	7	m.	m.	NOUN
cjfa-35471	991	8	,	,	PUNCT
cjfa-35471	991	9	&	&	CCONJ
cjfa-35471	991	10	greely	greely	PROPN
cjfa-35471	991	11	,	,	PUNCT
cjfa-35471	991	12	b.	b.	PROPN
cjfa-35471	991	13	(	(	PUNCT
cjfa-35471	991	14	2020	2020	NUM
cjfa-35471	991	15	)	)	PUNCT
cjfa-35471	991	16	.	.	PUNCT
cjfa-35471	992	1	oecd	oecd	PROPN
cjfa-35471	992	2	warns	warn	VERB
cjfa-35471	992	3	that	that	SCONJ
cjfa-35471	992	4	coronavirus	coronavirus	NOUN
cjfa-35471	992	5	could	could	AUX
cjfa-35471	992	6	halve	halve	VERB
cjfa-35471	992	7	global	global	ADJ
cjfa-35471	992	8	growth	growth	NOUN
cjfa-35471	992	9	.	.	PUNCT
cjfa-35471	993	1	france24	france24	PROPN
cjfa-35471	993	2	tv	tv	PROPN
cjfa-35471	993	3	,	,	PUNCT
cjfa-35471	993	4	https://www.ft.com/content/1356af8c-5c6c-11ea8033-fa40a0d65a98	https://www.ft.com/content/1356af8c-5c6c-11ea8033-fa40a0d65a98	PRON
cjfa-35471	993	5	(	(	PUNCT
cjfa-35471	993	6	accessed	access	VERB
cjfa-35471	993	7	:	:	PUNCT
cjfa-35471	993	8	3.03.2020	3.03.2020	NUM
cjfa-35471	993	9	)	)	PUNCT
cjfa-35471	993	10	.	.	PUNCT
cjfa-35471	994	1	hestenes	hestene	NOUN
cjfa-35471	994	2	,	,	PUNCT
cjfa-35471	994	3	m.r	m.r	PROPN
cjfa-35471	994	4	.	.	PROPN
cjfa-35471	994	5	(	(	PUNCT
cjfa-35471	994	6	1966	1966	NUM
cjfa-35471	994	7	)	)	PUNCT
cjfa-35471	994	8	.	.	PUNCT
cjfa-35471	995	1	calculus	calculus	NOUN
cjfa-35471	995	2	of	of	ADP
cjfa-35471	995	3	variations	variation	NOUN
cjfa-35471	995	4	and	and	CCONJ
cjfa-35471	995	5	optimal	optimal	ADJ
cjfa-35471	995	6	control	control	NOUN
cjfa-35471	995	7	theory	theory	NOUN
cjfa-35471	995	8	.	.	PUNCT
cjfa-35471	996	1	new	new	PROPN
cjfa-35471	996	2	york	york	PROPN
cjfa-35471	996	3	:	:	PUNCT
cjfa-35471	996	4	john	john	PROPN
cjfa-35471	996	5	wiley	wiley	PROPN
cjfa-35471	996	6	&	&	CCONJ
cjfa-35471	996	7	sons	son	NOUN
cjfa-35471	996	8	.	.	PUNCT
cjfa-35471	997	1	imf	imf	PROPN
cjfa-35471	997	2	(	(	PUNCT
cjfa-35471	997	3	2019	2019	NUM
cjfa-35471	997	4	)	)	PUNCT
cjfa-35471	997	5	.	.	PUNCT
cjfa-35471	998	1	world	world	PROPN
cjfa-35471	998	2	economic	economic	ADJ
cjfa-35471	998	3	outlook	outlook	NOUN
cjfa-35471	998	4	,	,	PUNCT
cjfa-35471	998	5	https://www.imf.org/external/datamapper/	https://www.imf.org/external/datamapper/	PROPN
cjfa-35471	998	6	ngdp_rpch@weo	ngdp_rpch@weo	NOUN
cjfa-35471	998	7	/	/	SYM
cjfa-35471	998	8	oemdc	oemdc	NOUN
cjfa-35471	998	9	/	/	SYM
cjfa-35471	998	10	advec	advec	PROPN
cjfa-35471	998	11	/	/	SYM
cjfa-35471	998	12	weoworld.9.10.2018	weoworld.9.10.2018	NOUN
cjfa-35471	998	13	-	-	PUNCT
cjfa-35471	998	14	2019	2019	NUM
cjfa-35471	998	15	.	.	PUNCT
cjfa-35471	999	1	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companies	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companie	NOUN
cjfa-35471	999	2	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companies	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companie	NOUN
cjfa-35471	999	3	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companies	https://www.mckinsey.com/industries/public-sector/our-insights/how-state-and-local-governments-win-at-attracting-companie	NOUN
cjfa-35471	999	4	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	PROPN
cjfa-35471	999	5	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	https://repository.library.georgetown.edu/bitstream/handle/10822/1055104/conroy_georgetown_0076m_14267.pdf?sequence=1	PROPN
cjfa-35471	999	6	https://www.dpme.gov.za/publications/reports	https://www.dpme.gov.za/publications/report	NOUN
cjfa-35471	999	7	and	and	CCONJ
cjfa-35471	999	8	other	other	ADJ
cjfa-35471	999	9	information	information	NOUN
cjfa-35471	999	10	products	product	NOUN
cjfa-35471	999	11	/	/	SYM
cjfa-35471	999	12	business	business	NOUN
cjfa-35471	999	13	incentives	incentive	NOUN
cjfa-35471	999	14	draft	draft	VERB
cjfa-35471	999	15	full	full	ADJ
cjfa-35471	999	16	report	report	NOUN
cjfa-35471	999	17	v7	v7	VERB
cjfa-35471	999	18	05112018	05112018	NUM
cjfa-35471	999	19	stc.pdf	stc.pdf	ADJ
cjfa-35471	999	20	https://www.dpme.gov.za/publications/reports	https://www.dpme.gov.za/publications/report	NOUN
cjfa-35471	999	21	and	and	CCONJ
cjfa-35471	999	22	other	other	ADJ
cjfa-35471	999	23	information	information	NOUN
cjfa-35471	999	24	products	product	NOUN
cjfa-35471	999	25	/	/	SYM
cjfa-35471	999	26	business	business	NOUN
cjfa-35471	999	27	incentives	incentive	NOUN
cjfa-35471	999	28	draft	draft	VERB
cjfa-35471	999	29	full	full	ADJ
cjfa-35471	999	30	report	report	NOUN
cjfa-35471	999	31	v7	v7	VERB
cjfa-35471	999	32	05112018	05112018	NUM
cjfa-35471	999	33	stc.pdf	stc.pdf	ADJ
cjfa-35471	999	34	https://www.dpme.gov.za/publications/reports	https://www.dpme.gov.za/publications/report	NOUN
cjfa-35471	999	35	and	and	CCONJ
cjfa-35471	999	36	other	other	ADJ
cjfa-35471	999	37	information	information	NOUN
cjfa-35471	999	38	products	product	NOUN
cjfa-35471	999	39	/	/	SYM
cjfa-35471	999	40	business	business	NOUN
cjfa-35471	999	41	incentives	incentive	NOUN
cjfa-35471	999	42	draft	draft	VERB
cjfa-35471	999	43	full	full	ADJ
cjfa-35471	999	44	report	report	NOUN
cjfa-35471	999	45	v7	v7	VERB
cjfa-35471	999	46	05112018	05112018	NUM
cjfa-35471	1000	1	stc.pdf	stc.pdf	PROPN
cjfa-35471	1000	2	https://www.ft.com/content/1356af8c-5c6c-11ea-8033-fa40a0d65a98	https://www.ft.com/content/1356af8c-5c6c-11ea-8033-fa40a0d65a98	PUNCT
cjfa-35471	1000	3	https://www.ft.com/content/1356af8c-5c6c-11ea-8033-fa40a0d65a98	https://www.ft.com/content/1356af8c-5c6c-11ea-8033-fa40a0d65a98	PROPN
cjfa-35471	1000	4	mustafa	mustafa	PROPN
cjfa-35471	1000	5	akan	akan	PROPN
cjfa-35471	1000	6	,	,	PUNCT
cjfa-35471	1000	7	natalia	natalia	PROPN
cjfa-35471	1000	8	konovalova30	konovalova30	PROPN
cjfa-35471	1000	9	institut	institut	PROPN
cjfa-35471	1000	10	national	national	PROPN
cjfa-35471	1000	11	de	de	X
cjfa-35471	1000	12	la	la	X
cjfa-35471	1000	13	statistique	statistique	X
cjfa-35471	1000	14	et	et	PROPN
cjfa-35471	1000	15	des	des	PROPN
cjfa-35471	1000	16	études	études	PROPN
cjfa-35471	1000	17	économiques	économiques	X
cjfa-35471	1000	18	(	(	PUNCT
cjfa-35471	1000	19	insee	insee	PROPN
cjfa-35471	1000	20	)	)	PUNCT
cjfa-35471	1000	21	(	(	PUNCT
cjfa-35471	1000	22	2020	2020	NUM
cjfa-35471	1000	23	)	)	PUNCT
cjfa-35471	1000	24	.	.	PUNCT
cjfa-35471	1001	1	https://	https://	PROPN
cjfa-35471	1001	2	www.insee.fr/en/metadonnees/definition/c2055	www.insee.fr/en/metadonnees/definition/c2055	PROPN
cjfa-35471	1001	3	(	(	PUNCT
cjfa-35471	1001	4	accessed	access	VERB
cjfa-35471	1001	5	29.07.2020	29.07.2020	NUM
cjfa-35471	1001	6	)	)	PUNCT
cjfa-35471	1001	7	.	.	PUNCT
cjfa-35471	1002	1	jacobson	jacobson	PROPN
cjfa-35471	1002	2	,	,	PUNCT
cjfa-35471	1002	3	d.h	d.h	PROPN
cjfa-35471	1002	4	.	.	PROPN
cjfa-35471	1002	5	,	,	PUNCT
cjfa-35471	1002	6	&	&	CCONJ
cjfa-35471	1002	7	lele	lele	PROPN
cjfa-35471	1002	8	,	,	PUNCT
cjfa-35471	1002	9	m.m	m.m	PROPN
cjfa-35471	1002	10	.	.	PROPN
cjfa-35471	1002	11	(	(	PUNCT
cjfa-35471	1002	12	1969	1969	NUM
cjfa-35471	1002	13	)	)	PUNCT
cjfa-35471	1002	14	.	.	PUNCT
cjfa-35471	1003	1	a	a	DET
cjfa-35471	1003	2	transformation	transformation	NOUN
cjfa-35471	1003	3	technique	technique	NOUN
cjfa-35471	1003	4	for	for	ADP
cjfa-35471	1003	5	optimality	optimality	NOUN
cjfa-35471	1003	6	for	for	ADP
cjfa-35471	1003	7	control	control	NOUN
cjfa-35471	1003	8	problems	problem	NOUN
cjfa-35471	1003	9	with	with	ADP
cjfa-35471	1003	10	state	state	NOUN
cjfa-35471	1003	11	variable	variable	ADJ
cjfa-35471	1003	12	inequality	inequality	NOUN
cjfa-35471	1003	13	constraint	constraint	NOUN
cjfa-35471	1003	14	.	.	PUNCT
cjfa-35471	1004	1	ieee	ieee	NOUN
cjfa-35471	1004	2	transactions	transaction	NOUN
cjfa-35471	1004	3	on	on	ADP
cjfa-35471	1004	4	automatic	automatic	ADJ
cjfa-35471	1004	5	control	control	NOUN
cjfa-35471	1004	6	,	,	PUNCT
cjfa-35471	1004	7	ac-14(5	ac-14(5	PROPN
cjfa-35471	1004	8	)	)	PUNCT
cjfa-35471	1004	9	,	,	PUNCT
cjfa-35471	1004	10	457	457	NUM
cjfa-35471	1004	11	-	-	SYM
cjfa-35471	1004	12	464	464	NUM
cjfa-35471	1004	13	.	.	PUNCT
cjfa-35471	1005	1	jacobson	jacobson	PROPN
cjfa-35471	1005	2	,	,	PUNCT
cjfa-35471	1005	3	d.h	d.h	PROPN
cjfa-35471	1005	4	.	.	PROPN
cjfa-35471	1005	5	,	,	PUNCT
cjfa-35471	1005	6	lele	lele	PROPN
cjfa-35471	1005	7	,	,	PUNCT
cjfa-35471	1005	8	m.m	m.m	PROPN
cjfa-35471	1005	9	.	.	PROPN
cjfa-35471	1005	10	,	,	PUNCT
cjfa-35471	1005	11	&	&	CCONJ
cjfa-35471	1005	12	speyer	speyer	PROPN
cjfa-35471	1005	13	,	,	PUNCT
cjfa-35471	1005	14	j.l	j.l	PROPN
cjfa-35471	1005	15	.	.	PROPN
cjfa-35471	1005	16	(	(	PUNCT
cjfa-35471	1005	17	1971	1971	NUM
cjfa-35471	1005	18	)	)	PUNCT
cjfa-35471	1005	19	.	.	PUNCT
cjfa-35471	1006	1	new	new	ADJ
cjfa-35471	1006	2	necessary	necessary	ADJ
cjfa-35471	1006	3	conditions	condition	NOUN
cjfa-35471	1006	4	of	of	ADP
cjfa-35471	1006	5	optimal	optimal	ADJ
cjfa-35471	1006	6	control	control	NOUN
cjfa-35471	1006	7	problems	problem	NOUN
cjfa-35471	1006	8	with	with	ADP
cjfa-35471	1006	9	state	state	NOUN
cjfa-35471	1006	10	variable	variable	ADJ
cjfa-35471	1006	11	inequality	inequality	NOUN
cjfa-35471	1006	12	constraints	constraint	NOUN
cjfa-35471	1006	13	.	.	PUNCT
cjfa-35471	1007	1	journal	journal	PROPN
cjfa-35471	1007	2	of	of	ADP
cjfa-35471	1007	3	mathematical	mathematical	ADJ
cjfa-35471	1007	4	analysis	analysis	NOUN
cjfa-35471	1007	5	and	and	CCONJ
cjfa-35471	1007	6	applications	application	NOUN
cjfa-35471	1007	7	,	,	PUNCT
cjfa-35471	1007	8	35(2	35(2	NUM
cjfa-35471	1007	9	)	)	PUNCT
cjfa-35471	1007	10	,	,	PUNCT
cjfa-35471	1007	11	255	255	NUM
cjfa-35471	1007	12	-	-	SYM
cjfa-35471	1007	13	284	284	NUM
cjfa-35471	1007	14	.	.	PUNCT
cjfa-35471	1008	1	http://dx.doi.org/10.1016/0022247x(71)90219-8	http://dx.doi.org/10.1016/0022247x(71)90219-8	NOUN
cjfa-35471	1008	2	.	.	PUNCT
cjfa-35471	1008	3	kamien	kamien	NOUN
cjfa-35471	1008	4	,	,	PUNCT
cjfa-35471	1008	5	m.	m.	NOUN
cjfa-35471	1008	6	,	,	PUNCT
cjfa-35471	1008	7	&	&	CCONJ
cjfa-35471	1008	8	schwartz	schwartz	PROPN
cjfa-35471	1008	9	,	,	PUNCT
cjfa-35471	1008	10	n.	n.	PROPN
cjfa-35471	1008	11	(	(	PUNCT
cjfa-35471	1008	12	2012	2012	NUM
cjfa-35471	1008	13	)	)	PUNCT
cjfa-35471	1008	14	.	.	PUNCT
cjfa-35471	1009	1	dynamic	dynamic	ADJ
cjfa-35471	1009	2	optimization	optimization	NOUN
cjfa-35471	1009	3	.	.	PUNCT
cjfa-35471	1010	1	amsterdam	amsterdam	PROPN
cjfa-35471	1010	2	:	:	PUNCT
cjfa-35471	1010	3	elsevier	elsevier	PROPN
cjfa-35471	1010	4	.	.	PUNCT
cjfa-35471	1011	1	klemm	klemm	PROPN
cjfa-35471	1011	2	,	,	PUNCT
cjfa-35471	1011	3	a.	a.	PROPN
cjfa-35471	1011	4	,	,	PUNCT
cjfa-35471	1011	5	&	&	CCONJ
cjfa-35471	1011	6	van	van	PROPN
cjfa-35471	1011	7	parys	parys	PROPN
cjfa-35471	1011	8	,	,	PUNCT
cjfa-35471	1011	9	s.	s.	PROPN
cjfa-35471	1011	10	(	(	PUNCT
cjfa-35471	1011	11	2012	2012	NUM
cjfa-35471	1011	12	)	)	PUNCT
cjfa-35471	1011	13	.	.	PUNCT
cjfa-35471	1012	1	empirical	empirical	ADJ
cjfa-35471	1012	2	evidence	evidence	NOUN
cjfa-35471	1012	3	on	on	ADP
cjfa-35471	1012	4	the	the	DET
cjfa-35471	1012	5	effects	effect	NOUN
cjfa-35471	1012	6	of	of	ADP
cjfa-35471	1012	7	tax	tax	NOUN
cjfa-35471	1012	8	incentives	incentive	NOUN
cjfa-35471	1012	9	.	.	PUNCT
cjfa-35471	1013	1	international	international	ADJ
cjfa-35471	1013	2	tax	tax	NOUN
cjfa-35471	1013	3	and	and	CCONJ
cjfa-35471	1013	4	public	public	ADJ
cjfa-35471	1013	5	finance	finance	NOUN
cjfa-35471	1013	6	,	,	PUNCT
cjfa-35471	1013	7	19(3	19(3	NUM
cjfa-35471	1013	8	)	)	PUNCT
cjfa-35471	1013	9	,	,	PUNCT
cjfa-35471	1013	10	393	393	NUM
cjfa-35471	1013	11	-	-	SYM
cjfa-35471	1013	12	423	423	NUM
cjfa-35471	1013	13	.	.	PUNCT
cjfa-35471	1014	1	http://dx.doi.org/10.1007/	http://dx.doi.org/10.1007/	NOUN
cjfa-35471	1014	2	s10797	s10797	PROPN
cjfa-35471	1014	3	-	-	PUNCT
cjfa-35471	1014	4	011	011	NUM
cjfa-35471	1014	5	-	-	PUNCT
cjfa-35471	1014	6	9194	9194	NUM
cjfa-35471	1014	7	-	-	PUNCT
cjfa-35471	1014	8	8	8	NUM
cjfa-35471	1014	9	.	.	PUNCT
cjfa-35471	1015	1	kosonen	kosonen	NOUN
cjfa-35471	1015	2	,	,	PUNCT
cjfa-35471	1015	3	t.	t.	PROPN
cjfa-35471	1015	4	(	(	PUNCT
cjfa-35471	1015	5	2012	2012	NUM
cjfa-35471	1015	6	)	)	PUNCT
cjfa-35471	1015	7	.	.	PUNCT
cjfa-35471	1016	1	the	the	DET
cjfa-35471	1016	2	impact	impact	NOUN
cjfa-35471	1016	3	of	of	ADP
cjfa-35471	1016	4	tax	tax	NOUN
cjfa-35471	1016	5	incentives	incentive	NOUN
cjfa-35471	1016	6	on	on	ADP
cjfa-35471	1016	7	the	the	DET
cjfa-35471	1016	8	economic	economic	ADJ
cjfa-35471	1016	9	activity	activity	NOUN
cjfa-35471	1016	10	of	of	ADP
cjfa-35471	1016	11	entrepreneurs	entrepreneur	NOUN
cjfa-35471	1016	12	.	.	PUNCT
cjfa-35471	1017	1	nber	nber	PROPN
cjfa-35471	1017	2	working	working	PROPN
cjfa-35471	1017	3	paper	paper	NOUN
cjfa-35471	1017	4	,	,	PUNCT
cjfa-35471	1017	5	18442	18442	NUM
cjfa-35471	1017	6	,	,	PUNCT
cjfa-35471	1017	7	1	1	NUM
cjfa-35471	1017	8	-	-	SYM
cjfa-35471	1017	9	48	48	NUM
cjfa-35471	1017	10	.	.	PUNCT
cjfa-35471	1018	1	http://dx.doi.org/10.3386/w18442	http://dx.doi.org/10.3386/w18442	PROPN
cjfa-35471	1018	2	.	.	PUNCT
cjfa-35471	1019	1	mcintyre	mcintyre	PROPN
cjfa-35471	1019	2	,	,	PUNCT
cjfa-35471	1019	3	j.mc	j.mc	PROPN
cjfa-35471	1019	4	.	.	PROPN
cjfa-35471	1019	5	,	,	PUNCT
cjfa-35471	1019	6	&	&	CCONJ
cjfa-35471	1019	7	paiewonsky	paiewonsky	PROPN
cjfa-35471	1019	8	,	,	PUNCT
cjfa-35471	1019	9	b.	b.	PROPN
cjfa-35471	1019	10	(	(	PUNCT
cjfa-35471	1019	11	1967	1967	NUM
cjfa-35471	1019	12	)	)	PUNCT
cjfa-35471	1019	13	.	.	PUNCT
cjfa-35471	1020	1	on	on	ADP
cjfa-35471	1020	2	optimal	optimal	ADJ
cjfa-35471	1020	3	control	control	NOUN
cjfa-35471	1020	4	with	with	ADP
cjfa-35471	1020	5	bounded	bounded	ADJ
cjfa-35471	1020	6	state	state	NOUN
cjfa-35471	1020	7	variables	variable	NOUN
cjfa-35471	1020	8	.	.	PUNCT
cjfa-35471	1021	1	in	in	ADP
cjfa-35471	1021	2	c.	c.	PROPN
cjfa-35471	1021	3	leondes	leondes	PROPN
cjfa-35471	1021	4	(	(	PUNCT
cjfa-35471	1021	5	ed	ed	NOUN
cjfa-35471	1021	6	.	.	PUNCT
cjfa-35471	1021	7	)	)	PUNCT
cjfa-35471	1021	8	.	.	PUNCT
cjfa-35471	1022	1	advances	advance	NOUN
cjfa-35471	1022	2	in	in	ADP
cjfa-35471	1022	3	control	control	NOUN
cjfa-35471	1022	4	systems	system	NOUN
cjfa-35471	1022	5	.	.	PUNCT
cjfa-35471	1023	1	new	new	PROPN
cjfa-35471	1023	2	york	york	PROPN
cjfa-35471	1023	3	:	:	PUNCT
cjfa-35471	1023	4	academic	academic	ADJ
cjfa-35471	1023	5	press	press	NOUN
cjfa-35471	1023	6	.	.	PUNCT
cjfa-35471	1024	1	miller	miller	PROPN
cjfa-35471	1024	2	,	,	PUNCT
cjfa-35471	1024	3	b.	b.	PROPN
cjfa-35471	1024	4	,	,	PUNCT
cjfa-35471	1024	5	&	&	CCONJ
cjfa-35471	1024	6	atkinson	atkinson	PROPN
cjfa-35471	1024	7	,	,	PUNCT
cjfa-35471	1024	8	r.d	r.d	PROPN
cjfa-35471	1024	9	.	.	PROPN
cjfa-35471	1024	10	(	(	PUNCT
cjfa-35471	1024	11	2014	2014	NUM
cjfa-35471	1024	12	)	)	PUNCT
cjfa-35471	1024	13	.	.	PUNCT
cjfa-35471	1025	1	raising	raise	VERB
cjfa-35471	1025	2	european	european	ADJ
cjfa-35471	1025	3	productivity	productivity	NOUN
cjfa-35471	1025	4	growth	growth	NOUN
cjfa-35471	1025	5	through	through	ADP
cjfa-35471	1025	6	ict	ict	PROPN
cjfa-35471	1025	7	.	.	PUNCT
cjfa-35471	1025	8	information	information	PROPN
cjfa-35471	1025	9	technology	technology	PROPN
cjfa-35471	1025	10	and	and	CCONJ
cjfa-35471	1025	11	innovation	innovation	NOUN
cjfa-35471	1025	12	foundation	foundation	NOUN
cjfa-35471	1025	13	,	,	PUNCT
cjfa-35471	1025	14	1	1	NUM
cjfa-35471	1025	15	-	-	SYM
cjfa-35471	1025	16	43	43	NUM
cjfa-35471	1025	17	.	.	PUNCT
cjfa-35471	1026	1	http://dx.doi.org/10.2139/	http://dx.doi.org/10.2139/	PUNCT
cjfa-35471	1026	2	ssrn.3079844	ssrn.3079844	PROPN
cjfa-35471	1026	3	.	.	PROPN
cjfa-35471	1026	4	mitschell	mitschell	PROPN
cjfa-35471	1026	5	,	,	PUNCT
cjfa-35471	1026	6	m.	m.	NOUN
cjfa-35471	1026	7	(	(	PUNCT
cjfa-35471	1026	8	2019	2019	NUM
cjfa-35471	1026	9	)	)	PUNCT
cjfa-35471	1026	10	.	.	PUNCT
cjfa-35471	1027	1	do	do	AUX
cjfa-35471	1027	2	targeted	target	VERB
cjfa-35471	1027	3	economic	economic	ADJ
cjfa-35471	1027	4	development	development	NOUN
cjfa-35471	1027	5	deals	deal	NOUN
cjfa-35471	1027	6	work	work	VERB
cjfa-35471	1027	7	as	as	SCONJ
cjfa-35471	1027	8	advertised	advertise	VERB
cjfa-35471	1027	9	.	.	PUNCT
cjfa-35471	1028	1	mercatus	mercatus	PROPN
cjfa-35471	1028	2	center	center	PROPN
cjfa-35471	1028	3	at	at	ADP
cjfa-35471	1028	4	george	george	PROPN
cjfa-35471	1028	5	mason	mason	PROPN
cjfa-35471	1028	6	university	university	PROPN
cjfa-35471	1028	7	.	.	PUNCT
cjfa-35471	1029	1	https://neighbourhoodeffects.mercato	https://neighbourhoodeffects.mercato	PROPN
cjfa-35471	1029	2	.	.	PUNCT
cjfa-35471	1030	1	org/2013/05/21	org/2013/05/21	NOUN
cjfa-35471	1030	2	/	/	SYM
cjfa-35471	1030	3	do	do	AUX
cjfa-35471	1030	4	-	-	PUNCT
cjfa-35471	1030	5	targeted	target	VERB
cjfa-35471	1030	6	-	-	PUNCT
cjfa-35471	1030	7	economic	economic	ADJ
cjfa-35471	1030	8	-	-	PUNCT
cjfa-35471	1030	9	development	development	NOUN
cjfa-35471	1030	10	-	-	PUNCT
cjfa-35471	1030	11	delas	dela	NOUN
cjfa-35471	1030	12	-	-	PUNCT
cjfa-35471	1030	13	work	work	NOUN
cjfa-35471	1030	14	-	-	PUNCT
cjfa-35471	1030	15	as	as	ADP
cjfa-35471	1030	16	-	-	PUNCT
cjfa-35471	1030	17	advertised	advertised	ADJ
cjfa-35471	1030	18	.	.	PUNCT
cjfa-35471	1031	1	organisation	organisation	NOUN
cjfa-35471	1031	2	for	for	ADP
cjfa-35471	1031	3	economic	economic	ADJ
cjfa-35471	1031	4	co	co	NOUN
cjfa-35471	1031	5	-	-	NOUN
cjfa-35471	1031	6	operation	operation	NOUN
cjfa-35471	1031	7	and	and	CCONJ
cjfa-35471	1031	8	development	development	NOUN
cjfa-35471	1031	9	(	(	PUNCT
cjfa-35471	1031	10	oecd	oecd	PROPN
cjfa-35471	1031	11	)	)	PUNCT
cjfa-35471	1031	12	(	(	PUNCT
cjfa-35471	1031	13	2001	2001	NUM
cjfa-35471	1031	14	)	)	PUNCT
cjfa-35471	1031	15	.	.	PUNCT
cjfa-35471	1032	1	https://www	https://www	PROPN
cjfa-35471	1032	2	.	.	PUNCT
cjfa-35471	1032	3	oecd.org/	oecd.org/	NOUN
cjfa-35471	1032	4	,	,	PUNCT
cjfa-35471	1032	5	https://stats.oecd.org/glossary/detail.asp?id=303#:~:text=central%20	https://stats.oecd.org/glossary/detail.asp?id=303#:~:text=central%20	PROPN
cjfa-35471	1032	6	and%20eastern%20european%20countries%20(ceecs)%20is%20an%20	and%20eastern%20european%20countries%20(ceecs)%20is%20an%20	PROPN
cjfa-35471	1032	7	oecd%20term,%3a%20estonia%2c%20latvia%20and%20lithuania	oecd%20term,%3a%20estonia%2c%20latvia%20and%20lithuania	PROPN
cjfa-35471	1032	8	.	.	PROPN
cjfa-35471	1032	9	osario	osario	PROPN
cjfa-35471	1032	10	,	,	PUNCT
cjfa-35471	1032	11	c.	c.	PROPN
cjfa-35471	1032	12	,	,	PUNCT
cjfa-35471	1032	13	&	&	CCONJ
cjfa-35471	1032	14	florida	florida	PROPN
cjfa-35471	1032	15	,	,	PUNCT
cjfa-35471	1032	16	a.p.r	a.p.r	ADV
cjfa-35471	1032	17	.	.	PUNCT
cjfa-35471	1032	18	(	(	PUNCT
cjfa-35471	1032	19	2017	2017	NUM
cjfa-35471	1032	20	)	)	PUNCT
cjfa-35471	1032	21	.	.	PUNCT
cjfa-35471	1033	1	business	business	NOUN
cjfa-35471	1033	2	incentives	incentive	NOUN
cjfa-35471	1033	3	are	be	AUX
cjfa-35471	1033	4	ineffective	ineffective	ADJ
cjfa-35471	1033	5	and	and	CCONJ
cjfa-35471	1033	6	wasteful	wasteful	ADJ
cjfa-35471	1033	7	,	,	PUNCT
cjfa-35471	1033	8	https://www.citylab.com/life/2017/03/business	https://www.citylab.com/life/2017/03/business	PROPN
cjfa-35471	1033	9	tax	tax	NOUN
cjfa-35471	1033	10	-	-	PUNCT
cjfa-35471	1033	11	incentives	incentive	NOUN
cjfa-35471	1033	12	-	-	PUNCT
cjfa-35471	1033	13	waste/518754	waste/518754	NOUN
cjfa-35471	1033	14	(	(	PUNCT
cjfa-35471	1033	15	accessed	access	VERB
cjfa-35471	1033	16	:	:	PUNCT
cjfa-35471	1033	17	7.03.2017	7.03.2017	NUM
cjfa-35471	1033	18	)	)	PUNCT
cjfa-35471	1033	19	.	.	PUNCT
cjfa-35471	1034	1	ourworldindata.org	ourworldindata.org	X
cjfa-35471	1034	2	(	(	PUNCT
cjfa-35471	1034	3	2021	2021	NUM
cjfa-35471	1034	4	)	)	PUNCT
cjfa-35471	1034	5	.	.	PUNCT
cjfa-35471	1035	1	groningen	groningen	PROPN
cjfa-35471	1035	2	growth	growth	PROPN
cjfa-35471	1035	3	and	and	CCONJ
cjfa-35471	1035	4	development	development	NOUN
cjfa-35471	1035	5	centre	centre	NOUN
cjfa-35471	1035	6	,	,	PUNCT
cjfa-35471	1035	7	https://	https://	PROPN
cjfa-35471	1035	8	www.rug.nl/ggdc/productivity/pwt	www.rug.nl/ggdc/productivity/pwt	PROPN
cjfa-35471	1035	9	.	.	PUNCT
cjfa-35471	1035	10	peters	peters	PROPN
cjfa-35471	1035	11	,	,	PUNCT
cjfa-35471	1035	12	a.	a.	PROPN
cjfa-35471	1035	13	,	,	PUNCT
cjfa-35471	1035	14	&	&	CCONJ
cjfa-35471	1035	15	fisher	fisher	PROPN
cjfa-35471	1035	16	,	,	PUNCT
cjfa-35471	1035	17	p.	p.	NOUN
cjfa-35471	1035	18	(	(	PUNCT
cjfa-35471	1035	19	2004	2004	NUM
cjfa-35471	1035	20	)	)	PUNCT
cjfa-35471	1035	21	.	.	PUNCT
cjfa-35471	1036	1	failures	failure	NOUN
cjfa-35471	1036	2	of	of	ADP
cjfa-35471	1036	3	economic	economic	ADJ
cjfa-35471	1036	4	incentives	incentive	NOUN
cjfa-35471	1036	5	.	.	PUNCT
cjfa-35471	1037	1	journal	journal	NOUN
cjfa-35471	1037	2	of	of	ADP
cjfa-35471	1037	3	american	american	PROPN
cjfa-35471	1037	4	planning	planning	PROPN
cjfa-35471	1037	5	association	association	PROPN
cjfa-35471	1037	6	,	,	PUNCT
cjfa-35471	1037	7	70(1	70(1	NOUN
cjfa-35471	1037	8	)	)	PUNCT
cjfa-35471	1037	9	,	,	PUNCT
cjfa-35471	1037	10	27	27	NUM
cjfa-35471	1037	11	-	-	SYM
cjfa-35471	1037	12	37	37	NUM
cjfa-35471	1037	13	.	.	PUNCT
cjfa-35471	1038	1	http://dx.doi.org/10.1080/01944360408976336	http://dx.doi.org/10.1080/01944360408976336	PROPN
cjfa-35471	1038	2	.	.	PUNCT
cjfa-35471	1039	1	petrin	petrin	PROPN
cjfa-35471	1039	2	,	,	PUNCT
cjfa-35471	1039	3	t.	t.	PROPN
cjfa-35471	1039	4	(	(	PUNCT
cjfa-35471	1039	5	2018	2018	NUM
cjfa-35471	1039	6	)	)	PUNCT
cjfa-35471	1039	7	.	.	PUNCT
cjfa-35471	1040	1	a	a	DET
cjfa-35471	1040	2	literature	literature	NOUN
cjfa-35471	1040	3	review	review	NOUN
cjfa-35471	1040	4	on	on	ADP
cjfa-35471	1040	5	the	the	DET
cjfa-35471	1040	6	impact	impact	NOUN
cjfa-35471	1040	7	and	and	CCONJ
cjfa-35471	1040	8	effectiveness	effectiveness	NOUN
cjfa-35471	1040	9	of	of	ADP
cjfa-35471	1040	10	government	government	NOUN
cjfa-35471	1040	11	support	support	NOUN
cjfa-35471	1040	12	for	for	ADP
cjfa-35471	1040	13	r	r	NOUN
cjfa-35471	1040	14	/	/	SYM
cjfa-35471	1040	15	d	d	NOUN
cjfa-35471	1040	16	and	and	CCONJ
cjfa-35471	1040	17	innovation	innovation	NOUN
cjfa-35471	1040	18	.	.	PUNCT
cjfa-35471	1041	1	working	work	VERB
cjfa-35471	1041	2	paper	paper	NOUN
cjfa-35471	1041	3	at	at	ADP
cjfa-35471	1041	4	faculty	faculty	NOUN
cjfa-35471	1041	5	of	of	ADP
cjfa-35471	1041	6	economics	economic	NOUN
cjfa-35471	1041	7	:	:	PUNCT
cjfa-35471	1041	8	university	university	NOUN
cjfa-35471	1041	9	of	of	ADP
cjfa-35471	1041	10	ljubljana	ljubljana	PROPN
cjfa-35471	1041	11	.	.	PUNCT
cjfa-35471	1042	1	http://www.isigrowth.eu/2018/02/14/a-literature-review-on-the-impact-and-effectiveness-of-government-support-for-rd-and-innovation	http://www.isigrowth.eu/2018/02/14/a-literature-review-on-the-impact-and-effectiveness-of-government-support-for-rd-and-innovation	PROPN
cjfa-35471	1042	2	.	.	PUNCT
cjfa-35471	1043	1	pew	pew	NOUN
cjfa-35471	1043	2	(	(	PUNCT
cjfa-35471	1043	3	2019	2019	NUM
cjfa-35471	1043	4	)	)	PUNCT
cjfa-35471	1043	5	.	.	PUNCT
cjfa-35471	1044	1	what	what	PRON
cjfa-35471	1044	2	makes	make	VERB
cjfa-35471	1044	3	an	an	DET
cjfa-35471	1044	4	economic	economic	ADJ
cjfa-35471	1044	5	incentive	incentive	NOUN
cjfa-35471	1044	6	effective	effective	ADJ
cjfa-35471	1044	7	?	?	PUNCT
cjfa-35471	1045	1	https://www.pewtrusts	https://www.pewtrust	NOUN
cjfa-35471	1045	2	.	.	PUNCT
cjfa-35471	1046	1	org	org	ADJ
cjfa-35471	1046	2	/	/	SYM
cjfa-35471	1046	3	en	en	NOUN
cjfa-35471	1046	4	/	/	SYM
cjfa-35471	1046	5	research	research	NOUN
cjfa-35471	1046	6	-	-	PUNCT
cjfa-35471	1046	7	and	and	CCONJ
cjfa-35471	1046	8	-	-	PUNCT
cjfa-35471	1046	9	analysis	analysis	NOUN
cjfa-35471	1046	10	/	/	SYM
cjfa-35471	1046	11	data	data	NOUN
cjfa-35471	1046	12	-	-	PUNCT
cjfa-35471	1046	13	visualizations/2019	visualizations/2019	NOUN
cjfa-35471	1046	14	/	/	SYM
cjfa-35471	1046	15	what	what	PRON
cjfa-35471	1046	16	-	-	PUNCT
cjfa-35471	1046	17	makes	make	VERB
cjfa-35471	1046	18	-	-	PUNCT
cjfa-35471	1046	19	an	an	DET
cjfa-35471	1046	20	-	-	PUNCT
cjfa-35471	1046	21	economic	economic	ADJ
cjfa-35471	1046	22	-	-	PUNCT
cjfa-35471	1046	23	development	development	NOUN
cjfa-35471	1046	24	-	-	PUNCT
cjfa-35471	1046	25	incentive	incentive	NOUN
cjfa-35471	1046	26	-	-	PUNCT
cjfa-35471	1046	27	effective	effective	ADJ
cjfa-35471	1046	28	.	.	PUNCT
cjfa-35471	1047	1	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	ADJ
cjfa-35471	1047	2	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	ADJ
cjfa-35471	1047	3	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	https://www.pewtrusts.org/en/research-and-analysis/data-visualizations/2019/what-makes-an-economic-development-incentive-effective	ADJ
cjfa-35471	1047	4	optimal	optimal	ADJ
cjfa-35471	1047	5	incentives	incentive	NOUN
cjfa-35471	1047	6	for	for	ADP
cjfa-35471	1047	7	economic	economic	ADJ
cjfa-35471	1047	8	growth	growth	NOUN
cjfa-35471	1047	9	…	…	PUNCT
cjfa-35471	1047	10	31	31	NUM
cjfa-35471	1047	11	pontryagin	pontryagin	NOUN
cjfa-35471	1047	12	,	,	PUNCT
cjfa-35471	1047	13	l.l	l.l	PROPN
cjfa-35471	1047	14	,	,	PUNCT
cjfa-35471	1047	15	boltyanskii	boltyanskii	ADJ
cjfa-35471	1047	16	,	,	PUNCT
cjfa-35471	1047	17	v.g	v.g	PROPN
cjfa-35471	1047	18	.	.	PROPN
cjfa-35471	1047	19	,	,	PUNCT
cjfa-35471	1047	20	gamkrelidze	gamkrelidze	PROPN
cjfa-35471	1047	21	,	,	PUNCT
cjfa-35471	1047	22	r.v	r.v	PROPN
cjfa-35471	1047	23	,	,	PUNCT
cjfa-35471	1047	24	&	&	CCONJ
cjfa-35471	1047	25	mishechenko	mishechenko	PROPN
cjfa-35471	1047	26	,	,	PUNCT
cjfa-35471	1047	27	e.f	e.f	PROPN
cjfa-35471	1047	28	.	.	PROPN
cjfa-35471	1047	29	(	(	PUNCT
cjfa-35471	1047	30	1962	1962	NUM
cjfa-35471	1047	31	)	)	PUNCT
cjfa-35471	1047	32	.	.	PUNCT
cjfa-35471	1048	1	the	the	DET
cjfa-35471	1048	2	mathematical	mathematical	ADJ
cjfa-35471	1048	3	theory	theory	NOUN
cjfa-35471	1048	4	of	of	ADP
cjfa-35471	1048	5	optimal	optimal	ADJ
cjfa-35471	1048	6	processes	process	NOUN
cjfa-35471	1048	7	.	.	PUNCT
cjfa-35471	1049	1	new	new	PROPN
cjfa-35471	1049	2	york	york	PROPN
cjfa-35471	1049	3	:	:	PUNCT
cjfa-35471	1049	4	john	john	PROPN
cjfa-35471	1049	5	wiley	wiley	PROPN
cjfa-35471	1049	6	&	&	CCONJ
cjfa-35471	1049	7	sons	son	NOUN
cjfa-35471	1049	8	.	.	PUNCT
cjfa-35471	1050	1	http://	http://	PROPN
cjfa-35471	1050	2	dx.doi.org/10.1002/zamm.19630431023	dx.doi.org/10.1002/zamm.19630431023	PROPN
cjfa-35471	1050	3	.	.	PUNCT
cjfa-35471	1050	4	prillaman	prillaman	PROPN
cjfa-35471	1050	5	,	,	PUNCT
cjfa-35471	1050	6	s.a	s.a	PROPN
cjfa-35471	1050	7	.	.	PROPN
cjfa-35471	1050	8	,	,	PUNCT
cjfa-35471	1050	9	&	&	CCONJ
cjfa-35471	1050	10	meier	meier	PROPN
cjfa-35471	1050	11	,	,	PUNCT
cjfa-35471	1050	12	k.j	k.j	PROPN
cjfa-35471	1050	13	.	.	PROPN
cjfa-35471	1050	14	(	(	PUNCT
cjfa-35471	1050	15	2014	2014	NUM
cjfa-35471	1050	16	)	)	PUNCT
cjfa-35471	1050	17	.	.	PUNCT
cjfa-35471	1051	1	taxes	taxis	NOUN
cjfa-35471	1051	2	,	,	PUNCT
cjfa-35471	1051	3	incentives	incentive	NOUN
cjfa-35471	1051	4	,	,	PUNCT
cjfa-35471	1051	5	and	and	CCONJ
cjfa-35471	1051	6	economic	economic	ADJ
cjfa-35471	1051	7	growth	growth	NOUN
cjfa-35471	1051	8	:	:	PUNCT
cjfa-35471	1051	9	assessing	assess	VERB
cjfa-35471	1051	10	the	the	DET
cjfa-35471	1051	11	impact	impact	NOUN
cjfa-35471	1051	12	of	of	ADP
cjfa-35471	1051	13	pro	pro	ADJ
cjfa-35471	1051	14	-	-	ADJ
cjfa-35471	1051	15	business	business	ADJ
cjfa-35471	1051	16	taxes	taxis	NOUN
cjfa-35471	1051	17	on	on	ADP
cjfa-35471	1051	18	u.s	u.s	PROPN
cjfa-35471	1051	19	.	.	PROPN
cjfa-35471	1051	20	state	state	NOUN
cjfa-35471	1051	21	economies	economy	NOUN
cjfa-35471	1051	22	.	.	PUNCT
cjfa-35471	1052	1	journal	journal	PROPN
cjfa-35471	1052	2	of	of	ADP
cjfa-35471	1052	3	politics	politic	NOUN
cjfa-35471	1052	4	,	,	PUNCT
cjfa-35471	1052	5	76(2	76(2	NUM
cjfa-35471	1052	6	)	)	PUNCT
cjfa-35471	1052	7	,	,	PUNCT
cjfa-35471	1052	8	364	364	NUM
cjfa-35471	1052	9	-	-	SYM
cjfa-35471	1052	10	379	379	NUM
cjfa-35471	1052	11	.	.	PUNCT
cjfa-35471	1053	1	http://dx.doi.org/10.1017/s0022381613001345	http://dx.doi.org/10.1017/s0022381613001345	X
cjfa-35471	1053	2	.	.	PUNCT
cjfa-35471	1054	1	radosevic	radosevic	ADJ
cjfa-35471	1054	2	,	,	PUNCT
cjfa-35471	1054	3	s.	s.	PROPN
cjfa-35471	1054	4	(	(	PUNCT
cjfa-35471	1054	5	2017	2017	NUM
cjfa-35471	1054	6	)	)	PUNCT
cjfa-35471	1054	7	.	.	PUNCT
cjfa-35471	1055	1	upgrading	upgrade	VERB
cjfa-35471	1055	2	technology	technology	NOUN
cjfa-35471	1055	3	in	in	ADP
cjfa-35471	1055	4	central	central	ADJ
cjfa-35471	1055	5	and	and	CCONJ
cjfa-35471	1055	6	eastern	eastern	ADJ
cjfa-35471	1055	7	european	european	ADJ
cjfa-35471	1055	8	economies	economy	NOUN
cjfa-35471	1055	9	.	.	PUNCT
cjfa-35471	1056	1	iza	iza	PROPN
cjfa-35471	1056	2	world	world	PROPN
cjfa-35471	1056	3	of	of	ADP
cjfa-35471	1056	4	labor	labor	NOUN
cjfa-35471	1056	5	,	,	PUNCT
cjfa-35471	1056	6	338	338	NUM
cjfa-35471	1056	7	.	.	PUNCT
cjfa-35471	1057	1	http://dx.doi.org/10.15185/izawol.338	http://dx.doi.org/10.15185/izawol.338	PROPN
cjfa-35471	1057	2	.	.	PUNCT
cjfa-35471	1058	1	schwab	schwab	PROPN
cjfa-35471	1058	2	,	,	PUNCT
cjfa-35471	1058	3	k.	k.	PROPN
cjfa-35471	1058	4	(	(	PUNCT
cjfa-35471	1058	5	2019	2019	NUM
cjfa-35471	1058	6	)	)	PUNCT
cjfa-35471	1058	7	.	.	PUNCT
cjfa-35471	1059	1	the	the	DET
cjfa-35471	1059	2	global	global	ADJ
cjfa-35471	1059	3	competitiveness	competitiveness	NOUN
cjfa-35471	1059	4	report	report	NOUN
cjfa-35471	1059	5	2019	2019	NUM
cjfa-35471	1059	6	.	.	PUNCT
cjfa-35471	1060	1	cologny	cologny	NOUN
cjfa-35471	1060	2	:	:	PUNCT
cjfa-35471	1060	3	world	world	PROPN
cjfa-35471	1060	4	economic	economic	PROPN
cjfa-35471	1060	5	forum	forum	PROPN
cjfa-35471	1060	6	.	.	PUNCT
cjfa-35471	1061	1	schwartz	schwartz	PROPN
cjfa-35471	1061	2	,	,	PUNCT
cjfa-35471	1061	3	a.	a.	NOUN
cjfa-35471	1061	4	(	(	PUNCT
cjfa-35471	1061	5	2018	2018	NUM
cjfa-35471	1061	6	)	)	PUNCT
cjfa-35471	1061	7	.	.	PUNCT
cjfa-35471	1062	1	the	the	DET
cjfa-35471	1062	2	realities	reality	NOUN
cjfa-35471	1062	3	of	of	ADP
cjfa-35471	1062	4	economic	economic	ADJ
cjfa-35471	1062	5	development	development	NOUN
cjfa-35471	1062	6	subsidies	subsidy	NOUN
cjfa-35471	1062	7	.	.	PUNCT
cjfa-35471	1063	1	washington	washington	PROPN
cjfa-35471	1063	2	:	:	PUNCT
cjfa-35471	1063	3	center	center	NOUN
cjfa-35471	1063	4	for	for	ADP
cjfa-35471	1063	5	american	american	ADJ
cjfa-35471	1063	6	progress	progress	NOUN
cjfa-35471	1063	7	.	.	PUNCT
cjfa-35471	1064	1	https://www.americanprogress.org/issues/economy/	https://www.americanprogress.org/issues/economy/	PROPN
cjfa-35471	1064	2	reports/2018/11/01/457771	reports/2018/11/01/457771	ADJ
cjfa-35471	1064	3	/	/	SYM
cjfa-35471	1064	4	realities	reality	NOUN
cjfa-35471	1064	5	-	-	PUNCT
cjfa-35471	1064	6	economic	economic	ADJ
cjfa-35471	1064	7	-	-	PUNCT
cjfa-35471	1064	8	development	development	NOUN
cjfa-35471	1064	9	-	-	PUNCT
cjfa-35471	1064	10	subsidies	subsidy	NOUN
cjfa-35471	1064	11	.	.	PUNCT
cjfa-35471	1065	1	skorupinska	skorupinska	PROPN
cjfa-35471	1065	2	,	,	PUNCT
cjfa-35471	1065	3	a.	a.	PROPN
cjfa-35471	1065	4	,	,	PUNCT
cjfa-35471	1065	5	&	&	CCONJ
cjfa-35471	1065	6	torrent	torrent	PROPN
cjfa-35471	1065	7	-	-	PUNCT
cjfa-35471	1065	8	sellers	seller	NOUN
cjfa-35471	1065	9	,	,	PUNCT
cjfa-35471	1065	10	j.	j.	PROPN
cjfa-35471	1065	11	(	(	PUNCT
cjfa-35471	1065	12	2015	2015	NUM
cjfa-35471	1065	13	)	)	PUNCT
cjfa-35471	1065	14	.	.	PUNCT
cjfa-35471	1066	1	the	the	DET
cjfa-35471	1066	2	role	role	NOUN
cjfa-35471	1066	3	of	of	ADP
cjfa-35471	1066	4	ict	ict	NOUN
cjfa-35471	1066	5	in	in	ADP
cjfa-35471	1066	6	the	the	DET
cjfa-35471	1066	7	productivity	productivity	NOUN
cjfa-35471	1066	8	of	of	ADP
cjfa-35471	1066	9	central	central	ADJ
cjfa-35471	1066	10	and	and	CCONJ
cjfa-35471	1066	11	eastern	eastern	ADJ
cjfa-35471	1066	12	european	european	ADJ
cjfa-35471	1066	13	countries	country	NOUN
cjfa-35471	1066	14	:	:	PUNCT
cjfa-35471	1066	15	cross	cross	VERB
cjfa-35471	1066	16	country	country	PROPN
cjfa-35471	1066	17	comparison	comparison	PROPN
cjfa-35471	1066	18	.	.	PUNCT
cjfa-35471	1067	1	reviste	reviste	PROPN
cjfa-35471	1067	2	de	de	X
cjfa-35471	1067	3	economia	economia	X
cjfa-35471	1067	4	mundial	mundial	ADJ
cjfa-35471	1067	5	,	,	PUNCT
cjfa-35471	1067	6	39	39	NUM
cjfa-35471	1067	7	,	,	PUNCT
cjfa-35471	1067	8	201	201	NUM
cjfa-35471	1067	9	-	-	SYM
cjfa-35471	1067	10	221	221	NUM
cjfa-35471	1067	11	.	.	PUNCT
cjfa-35471	1068	1	sprzeuzkouski	sprzeuzkouski	PROPN
cjfa-35471	1068	2	,	,	PUNCT
cjfa-35471	1068	3	a.	a.	NOUN
cjfa-35471	1068	4	(	(	PUNCT
cjfa-35471	1068	5	1967	1967	NUM
cjfa-35471	1068	6	)	)	PUNCT
cjfa-35471	1068	7	.	.	PUNCT
cjfa-35471	1069	1	a	a	DET
cjfa-35471	1069	2	problem	problem	NOUN
cjfa-35471	1069	3	in	in	ADP
cjfa-35471	1069	4	optimal	optimal	ADJ
cjfa-35471	1069	5	stock	stock	NOUN
cjfa-35471	1069	6	control	control	NOUN
cjfa-35471	1069	7	management	management	PROPN
cjfa-35471	1069	8	.	.	PUNCT
cjfa-35471	1070	1	journal	journal	NOUN
cjfa-35471	1070	2	of	of	ADP
cjfa-35471	1070	3	optimization	optimization	NOUN
cjfa-35471	1070	4	theory	theory	NOUN
cjfa-35471	1070	5	applications	application	NOUN
cjfa-35471	1070	6	,	,	PUNCT
cjfa-35471	1070	7	1(3	1(3	NUM
cjfa-35471	1070	8	)	)	PUNCT
cjfa-35471	1070	9	,	,	PUNCT
cjfa-35471	1070	10	232	232	NUM
cjfa-35471	1070	11	-	-	SYM
cjfa-35471	1070	12	241	241	NUM
cjfa-35471	1070	13	.	.	PUNCT
cjfa-35471	1071	1	http://dx.doi.org/10.1007/	http://dx.doi.org/10.1007/	PROPN
cjfa-35471	1071	2	bf00926065	bf00926065	PROPN
cjfa-35471	1071	3	.	.	PUNCT
cjfa-35471	1072	1	tadesse	tadesse	ADJ
cjfa-35471	1072	2	,	,	PUNCT
cjfa-35471	1072	3	t.	t.	PROPN
cjfa-35471	1072	4	,	,	PUNCT
cjfa-35471	1072	5	&	&	CCONJ
cjfa-35471	1072	6	melaku	melaku	PROPN
cjfa-35471	1072	7	,	,	PUNCT
cjfa-35471	1072	8	t.	t.	NOUN
cjfa-35471	1072	9	(	(	PUNCT
cjfa-35471	1072	10	2019	2019	NUM
cjfa-35471	1072	11	)	)	PUNCT
cjfa-35471	1072	12	.	.	PUNCT
cjfa-35471	1073	1	analysis	analysis	NOUN
cjfa-35471	1073	2	of	of	ADP
cjfa-35471	1073	3	the	the	DET
cjfa-35471	1073	4	relative	relative	ADJ
cjfa-35471	1073	5	impact	impact	NOUN
cjfa-35471	1073	6	of	of	ADP
cjfa-35471	1073	7	monetary	monetary	ADJ
cjfa-35471	1073	8	and	and	CCONJ
cjfa-35471	1073	9	fiscal	fiscal	ADJ
cjfa-35471	1073	10	policies	policy	NOUN
cjfa-35471	1073	11	on	on	ADP
cjfa-35471	1073	12	economic	economic	ADJ
cjfa-35471	1073	13	growth	growth	NOUN
cjfa-35471	1073	14	in	in	ADP
cjfa-35471	1073	15	ethiopia	ethiopia	PROPN
cjfa-35471	1073	16	using	use	VERB
cjfa-35471	1073	17	ardl	ardl	NOUN
cjfa-35471	1073	18	approach	approach	NOUN
cjfa-35471	1073	19	to	to	ADP
cjfa-35471	1073	20	co	co	NOUN
cjfa-35471	1073	21	-	-	NOUN
cjfa-35471	1073	22	integration	integration	NOUN
cjfa-35471	1073	23	:	:	PUNCT
cjfa-35471	1073	24	which	which	DET
cjfa-35471	1073	25	policy	policy	NOUN
cjfa-35471	1073	26	is	be	AUX
cjfa-35471	1073	27	more	more	ADV
cjfa-35471	1073	28	important	important	ADJ
cjfa-35471	1073	29	?	?	PUNCT
cjfa-35471	1074	1	copernicus	copernicus	PROPN
cjfa-35471	1074	2	journal	journal	PROPN
cjfa-35471	1074	3	of	of	ADP
cjfa-35471	1074	4	finance	finance	PROPN
cjfa-35471	1074	5	&	&	CCONJ
cjfa-35471	1074	6	accounting	accounting	PROPN
cjfa-35471	1074	7	,	,	PUNCT
cjfa-35471	1074	8	8(2	8(2	NUM
cjfa-35471	1074	9	)	)	PUNCT
cjfa-35471	1074	10	,	,	PUNCT
cjfa-35471	1074	11	87	87	NUM
cjfa-35471	1074	12	-	-	SYM
cjfa-35471	1074	13	115	115	NUM
cjfa-35471	1074	14	.	.	PUNCT
cjfa-35471	1075	1	http://dx.doi.org/10.12775/cjfa.2019.010	http://dx.doi.org/10.12775/cjfa.2019.010	PROPN
cjfa-35471	1075	2	.	.	PUNCT
cjfa-35471	1076	1	taylor	taylor	PROPN
cjfa-35471	1076	2	,	,	PUNCT
cjfa-35471	1076	3	j.g	j.g	PROPN
cjfa-35471	1076	4	.	.	PROPN
cjfa-35471	1076	5	(	(	PUNCT
cjfa-35471	1076	6	1972	1972	NUM
cjfa-35471	1076	7	)	)	PUNCT
cjfa-35471	1076	8	.	.	PUNCT
cjfa-35471	1077	1	comments	comment	NOUN
cjfa-35471	1077	2	on	on	ADP
cjfa-35471	1077	3	multiplier	multipli	ADJ
cjfa-35471	1077	4	condition	condition	NOUN
cjfa-35471	1077	5	for	for	ADP
cjfa-35471	1077	6	problems	problem	NOUN
cjfa-35471	1077	7	with	with	ADP
cjfa-35471	1077	8	state	state	NOUN
cjfa-35471	1077	9	variable	variable	ADJ
cjfa-35471	1077	10	inequality	inequality	NOUN
cjfa-35471	1077	11	constraints	constraint	NOUN
cjfa-35471	1077	12	.	.	PUNCT
cjfa-35471	1078	1	ieee	ieee	NOUN
cjfa-35471	1078	2	transactions	transaction	NOUN
cjfa-35471	1078	3	on	on	ADP
cjfa-35471	1078	4	automatic	automatic	ADJ
cjfa-35471	1078	5	control	control	NOUN
cjfa-35471	1078	6	,	,	PUNCT
cjfa-35471	1078	7	17(5	17(5	NUM
cjfa-35471	1078	8	)	)	PUNCT
cjfa-35471	1078	9	,	,	PUNCT
cjfa-35471	1078	10	743	743	NUM
cjfa-35471	1078	11	-	-	SYM
cjfa-35471	1078	12	744	744	NUM
cjfa-35471	1078	13	.	.	PUNCT
cjfa-35471	1079	1	trading	trade	VERB
cjfa-35471	1079	2	economics	economic	NOUN
cjfa-35471	1079	3	(	(	PUNCT
cjfa-35471	1079	4	2020	2020	NUM
cjfa-35471	1079	5	)	)	PUNCT
cjfa-35471	1079	6	.	.	PUNCT
cjfa-35471	1080	1	trading	trade	VERB
cjfa-35471	1080	2	economics	economic	NOUN
cjfa-35471	1080	3	,	,	PUNCT
cjfa-35471	1080	4	https://tradingeconomics.com/	https://tradingeconomics.com/	NOUN
cjfa-35471	1080	5	country	country	NOUN
cjfa-35471	1080	6	-	-	PUNCT
cjfa-35471	1080	7	list	list	NOUN
cjfa-35471	1080	8	/	/	SYM
cjfa-35471	1080	9	interest	interest	NOUN
cjfa-35471	1080	10	-	-	PUNCT
cjfa-35471	1080	11	rate?continent	rate?continent	NOUN
cjfa-35471	1080	12	=	=	NOUN
cjfa-35471	1080	13	europe	europe	NOUN
cjfa-35471	1080	14	(	(	PUNCT
cjfa-35471	1080	15	accessed	access	VERB
cjfa-35471	1080	16	29.07.2020	29.07.2020	NUM
cjfa-35471	1080	17	)	)	PUNCT
cjfa-35471	1080	18	.	.	PUNCT
cjfa-35471	1081	1	world	world	PROPN
cjfa-35471	1081	2	bank	bank	PROPN
cjfa-35471	1081	3	(	(	PUNCT
cjfa-35471	1081	4	1999	1999	NUM
cjfa-35471	1081	5	)	)	PUNCT
cjfa-35471	1081	6	.	.	PUNCT
cjfa-35471	1082	1	how	how	SCONJ
cjfa-35471	1082	2	tax	tax	NOUN
cjfa-35471	1082	3	policy	policy	NOUN
cjfa-35471	1082	4	and	and	CCONJ
cjfa-35471	1082	5	incentives	incentive	NOUN
cjfa-35471	1082	6	affect	affect	VERB
cjfa-35471	1082	7	foreign	foreign	ADJ
cjfa-35471	1082	8	direct	direct	ADJ
cjfa-35471	1082	9	investment	investment	NOUN
cjfa-35471	1082	10	:	:	PUNCT
cjfa-35471	1082	11	a	a	DET
cjfa-35471	1082	12	review	review	NOUN
cjfa-35471	1082	13	.	.	PUNCT
cjfa-35471	1083	1	policy	policy	NOUN
cjfa-35471	1083	2	research	research	NOUN
cjfa-35471	1083	3	working	working	NOUN
cjfa-35471	1083	4	papers	paper	NOUN
cjfa-35471	1083	5	.	.	PUNCT
cjfa-35471	1084	1	http://dx.doi.org/10.1596/1813-94502509	http://dx.doi.org/10.1596/1813-94502509	NUM
cjfa-35471	1084	2	.	.	PUNCT
cjfa-35471	1085	1	zee	zee	PROPN
cjfa-35471	1085	2	,	,	PUNCT
cjfa-35471	1085	3	h.	h.	PROPN
cjfa-35471	1085	4	,	,	PUNCT
cjfa-35471	1085	5	stotsky	stotsky	NOUN
cjfa-35471	1085	6	,	,	PUNCT
cjfa-35471	1085	7	j.g	j.g	PROPN
cjfa-35471	1085	8	.	.	PROPN
cjfa-35471	1085	9	,	,	PUNCT
cjfa-35471	1085	10	&	&	CCONJ
cjfa-35471	1085	11	ley	ley	PROPN
cjfa-35471	1085	12	,	,	PUNCT
cjfa-35471	1085	13	e.	e.	PROPN
cjfa-35471	1085	14	(	(	PUNCT
cjfa-35471	1085	15	2002	2002	NUM
cjfa-35471	1085	16	)	)	PUNCT
cjfa-35471	1085	17	.	.	PUNCT
cjfa-35471	1086	1	tax	tax	NOUN
cjfa-35471	1086	2	incentives	incentive	NOUN
cjfa-35471	1086	3	for	for	ADP
cjfa-35471	1086	4	business	business	NOUN
cjfa-35471	1086	5	investment	investment	NOUN
cjfa-35471	1086	6	:	:	PUNCT
cjfa-35471	1086	7	a	a	DET
cjfa-35471	1086	8	primer	primer	NOUN
cjfa-35471	1086	9	for	for	ADP
cjfa-35471	1086	10	policy	policy	NOUN
cjfa-35471	1086	11	makers	maker	NOUN
cjfa-35471	1086	12	in	in	ADP
cjfa-35471	1086	13	developing	develop	VERB
cjfa-35471	1086	14	countries	country	NOUN
cjfa-35471	1086	15	.	.	PUNCT
cjfa-35471	1087	1	world	world	NOUN
cjfa-35471	1087	2	development	development	PROPN
cjfa-35471	1087	3	,	,	PUNCT
cjfa-35471	1087	4	30(9	30(9	NOUN
cjfa-35471	1087	5	)	)	PUNCT
cjfa-35471	1087	6	,	,	PUNCT
cjfa-35471	1087	7	1497	1497	NUM
cjfa-35471	1087	8	-	-	SYM
cjfa-35471	1087	9	1516	1516	NUM
cjfa-35471	1087	10	.	.	PUNCT
cjfa-35471	1088	1	https://www.sciencedirect.com/science/journal/0305750x	https://www.sciencedirect.com/science/journal/0305750x	PROPN
cjfa-35471	1088	2	_	_	PROPN
cjfa-35471	1088	3	hlk76415562	hlk76415562	ADJ
cjfa-35471	1088	4	_	_	PRON
cjfa-35471	1088	5	hlk47948596	hlk47948596	ADJ
cjfa-35471	1088	6	_	_	PUNCT
cjfa-35471	1088	7	hlk47948343	hlk47948343	NOUN