id	sid	tid	token	lemma	pos
ijassa-1257	1	1	adv	adv	PROPN
ijassa-1257	1	2	syst	syst	PROPN
ijassa-1257	1	3	sci	sci	PROPN
ijassa-1257	1	4	appl	appl	PROPN
ijassa-1257	1	5	2022	2022	NUM
ijassa-1257	1	6	;	;	PUNCT
ijassa-1257	1	7	02:109–119	02:109–119	NUM
ijassa-1257	1	8	published	publish	VERB
ijassa-1257	1	9	online	online	ADV
ijassa-1257	1	10	at	at	ADP
ijassa-1257	1	11	https://ijassa.ipu.ru	https://ijassa.ipu.ru	ADV
ijassa-1257	1	12	.	.	PUNCT
ijassa-1257	2	1	the	the	DET
ijassa-1257	2	2	optimal	optimal	ADJ
ijassa-1257	2	3	control	control	NOUN
ijassa-1257	2	4	approach	approach	NOUN
ijassa-1257	2	5	in	in	ADP
ijassa-1257	2	6	problems	problem	NOUN
ijassa-1257	2	7	of	of	ADP
ijassa-1257	2	8	the	the	DET
ijassa-1257	2	9	income	income	NOUN
ijassa-1257	2	10	distribution	distribution	NOUN
ijassa-1257	2	11	into	into	ADP
ijassa-1257	2	12	consumed	consume	VERB
ijassa-1257	2	13	and	and	CCONJ
ijassa-1257	2	14	invested	invest	VERB
ijassa-1257	2	15	parts	part	NOUN
ijassa-1257	2	16	alexander	alexander	PROPN
ijassa-1257	3	1	p.	p.	NOUN
ijassa-1257	3	2	chernyaev1	chernyaev1	PROPN
ijassa-1257	4	1	*	*	PUNCT
ijassa-1257	4	2	1moscow	1moscow	NUM
ijassa-1257	4	3	institute	institute	PROPN
ijassa-1257	4	4	of	of	ADP
ijassa-1257	4	5	physics	physics	PROPN
ijassa-1257	4	6	and	and	CCONJ
ijassa-1257	4	7	technology	technology	NOUN
ijassa-1257	4	8	(	(	PUNCT
ijassa-1257	4	9	state	state	NOUN
ijassa-1257	4	10	university	university	NOUN
ijassa-1257	4	11	)	)	PUNCT
ijassa-1257	4	12	,	,	PUNCT
ijassa-1257	4	13	dolgoprudnyi	dolgoprudnyi	PROPN
ijassa-1257	4	14	,	,	PUNCT
ijassa-1257	4	15	russia	russia	PROPN
ijassa-1257	4	16	abstract	abstract	NOUN
ijassa-1257	4	17	:	:	PUNCT
ijassa-1257	4	18	in	in	ADP
ijassa-1257	4	19	this	this	DET
ijassa-1257	4	20	paper	paper	NOUN
ijassa-1257	4	21	,	,	PUNCT
ijassa-1257	4	22	we	we	PRON
ijassa-1257	4	23	investigate	investigate	VERB
ijassa-1257	4	24	dynamic	dynamic	ADJ
ijassa-1257	4	25	problems	problem	NOUN
ijassa-1257	4	26	of	of	ADP
ijassa-1257	4	27	the	the	DET
ijassa-1257	4	28	income	income	NOUN
ijassa-1257	4	29	distribution	distribution	NOUN
ijassa-1257	4	30	into	into	ADP
ijassa-1257	4	31	consumed	consume	VERB
ijassa-1257	4	32	and	and	CCONJ
ijassa-1257	4	33	invested	invest	VERB
ijassa-1257	4	34	parts	part	NOUN
ijassa-1257	4	35	using	use	VERB
ijassa-1257	4	36	optimal	optimal	ADJ
ijassa-1257	4	37	control	control	NOUN
ijassa-1257	4	38	methods	method	NOUN
ijassa-1257	4	39	.	.	PUNCT
ijassa-1257	5	1	here	here	ADV
ijassa-1257	5	2	it	it	PRON
ijassa-1257	5	3	is	be	AUX
ijassa-1257	5	4	assumed	assume	VERB
ijassa-1257	5	5	that	that	SCONJ
ijassa-1257	5	6	the	the	DET
ijassa-1257	5	7	basic	basic	ADJ
ijassa-1257	5	8	economic	economic	ADJ
ijassa-1257	5	9	identity	identity	NOUN
ijassa-1257	5	10	holds	hold	VERB
ijassa-1257	5	11	true	true	ADJ
ijassa-1257	5	12	,	,	PUNCT
ijassa-1257	5	13	i.e.	i.e.	X
ijassa-1257	5	14	,	,	PUNCT
ijassa-1257	5	15	the	the	DET
ijassa-1257	5	16	income	income	NOUN
ijassa-1257	5	17	is	be	AUX
ijassa-1257	5	18	the	the	DET
ijassa-1257	5	19	sum	sum	NOUN
ijassa-1257	5	20	of	of	ADP
ijassa-1257	5	21	the	the	DET
ijassa-1257	5	22	consumption	consumption	NOUN
ijassa-1257	5	23	and	and	CCONJ
ijassa-1257	5	24	the	the	DET
ijassa-1257	5	25	investment	investment	NOUN
ijassa-1257	5	26	.	.	PUNCT
ijassa-1257	6	1	the	the	DET
ijassa-1257	6	2	income	income	NOUN
ijassa-1257	6	3	is	be	AUX
ijassa-1257	6	4	understood	understand	VERB
ijassa-1257	6	5	either	either	CCONJ
ijassa-1257	6	6	in	in	ADP
ijassa-1257	6	7	the	the	DET
ijassa-1257	6	8	pure	pure	ADJ
ijassa-1257	6	9	form	form	NOUN
ijassa-1257	6	10	or	or	CCONJ
ijassa-1257	6	11	the	the	DET
ijassa-1257	6	12	gross	gross	ADJ
ijassa-1257	6	13	domestic	domestic	ADJ
ijassa-1257	6	14	product	product	NOUN
ijassa-1257	6	15	,	,	PUNCT
ijassa-1257	6	16	or	or	CCONJ
ijassa-1257	6	17	the	the	DET
ijassa-1257	6	18	national	national	ADJ
ijassa-1257	6	19	income	income	NOUN
ijassa-1257	6	20	.	.	PUNCT
ijassa-1257	7	1	the	the	DET
ijassa-1257	7	2	consumption	consumption	NOUN
ijassa-1257	7	3	is	be	AUX
ijassa-1257	7	4	also	also	ADV
ijassa-1257	7	5	understood	understand	VERB
ijassa-1257	7	6	in	in	ADP
ijassa-1257	7	7	different	different	ADJ
ijassa-1257	7	8	ways	way	NOUN
ijassa-1257	7	9	:	:	PUNCT
ijassa-1257	7	10	in	in	ADP
ijassa-1257	7	11	its	its	PRON
ijassa-1257	7	12	pure	pure	ADJ
ijassa-1257	7	13	form	form	NOUN
ijassa-1257	7	14	or	or	CCONJ
ijassa-1257	7	15	the	the	DET
ijassa-1257	7	16	aggregate	aggregate	ADJ
ijassa-1257	7	17	consumption	consumption	NOUN
ijassa-1257	7	18	.	.	PUNCT
ijassa-1257	8	1	we	we	PRON
ijassa-1257	8	2	start	start	VERB
ijassa-1257	8	3	with	with	ADP
ijassa-1257	8	4	the	the	DET
ijassa-1257	8	5	analysis	analysis	NOUN
ijassa-1257	8	6	of	of	ADP
ijassa-1257	8	7	the	the	DET
ijassa-1257	8	8	harrod	harrod	NOUN
ijassa-1257	8	9	–	–	PUNCT
ijassa-1257	8	10	domar	domar	NOUN
ijassa-1257	8	11	macromodel	macromodel	NOUN
ijassa-1257	8	12	with	with	ADP
ijassa-1257	8	13	the	the	DET
ijassa-1257	8	14	capital	capital	NOUN
ijassa-1257	8	15	intensity	intensity	NOUN
ijassa-1257	8	16	of	of	ADP
ijassa-1257	8	17	the	the	DET
ijassa-1257	8	18	income	income	NOUN
ijassa-1257	8	19	growth	growth	NOUN
ijassa-1257	8	20	depending	depend	VERB
ijassa-1257	8	21	on	on	ADP
ijassa-1257	8	22	the	the	DET
ijassa-1257	8	23	continuous	continuous	ADJ
ijassa-1257	8	24	time	time	NOUN
ijassa-1257	8	25	.	.	PUNCT
ijassa-1257	9	1	in	in	ADP
ijassa-1257	9	2	particular	particular	ADJ
ijassa-1257	9	3	,	,	PUNCT
ijassa-1257	9	4	it	it	PRON
ijassa-1257	9	5	is	be	AUX
ijassa-1257	9	6	shown	show	VERB
ijassa-1257	9	7	that	that	SCONJ
ijassa-1257	9	8	the	the	DET
ijassa-1257	9	9	balance	balance	NOUN
ijassa-1257	9	10	equation	equation	NOUN
ijassa-1257	9	11	for	for	ADP
ijassa-1257	9	12	accumulated	accumulate	VERB
ijassa-1257	9	13	household	household	NOUN
ijassa-1257	9	14	savings	saving	NOUN
ijassa-1257	9	15	also	also	ADV
ijassa-1257	9	16	satisfies	satisfy	VERB
ijassa-1257	9	17	the	the	DET
ijassa-1257	9	18	basic	basic	ADJ
ijassa-1257	9	19	economic	economic	ADJ
ijassa-1257	9	20	identity	identity	NOUN
ijassa-1257	9	21	and	and	CCONJ
ijassa-1257	9	22	the	the	DET
ijassa-1257	9	23	capital	capital	NOUN
ijassa-1257	9	24	intensity	intensity	NOUN
ijassa-1257	9	25	of	of	ADP
ijassa-1257	9	26	the	the	DET
ijassa-1257	9	27	income	income	NOUN
ijassa-1257	9	28	growth	growth	NOUN
ijassa-1257	9	29	can	can	AUX
ijassa-1257	9	30	depend	depend	VERB
ijassa-1257	9	31	on	on	ADP
ijassa-1257	9	32	time	time	NOUN
ijassa-1257	9	33	.	.	PUNCT
ijassa-1257	10	1	since	since	SCONJ
ijassa-1257	10	2	households	household	NOUN
ijassa-1257	10	3	are	be	AUX
ijassa-1257	10	4	the	the	DET
ijassa-1257	10	5	best	good	ADJ
ijassa-1257	10	6	savers	saver	NOUN
ijassa-1257	10	7	and	and	CCONJ
ijassa-1257	10	8	they	they	PRON
ijassa-1257	10	9	demonstrate	demonstrate	VERB
ijassa-1257	10	10	the	the	DET
ijassa-1257	10	11	best	good	ADJ
ijassa-1257	10	12	survival	survival	NOUN
ijassa-1257	10	13	,	,	PUNCT
ijassa-1257	10	14	we	we	PRON
ijassa-1257	10	15	modify	modify	VERB
ijassa-1257	10	16	the	the	DET
ijassa-1257	10	17	considered	consider	VERB
ijassa-1257	10	18	macromodels	macromodel	NOUN
ijassa-1257	10	19	replacing	replace	VERB
ijassa-1257	10	20	the	the	DET
ijassa-1257	10	21	given	give	VERB
ijassa-1257	10	22	production	production	NOUN
ijassa-1257	10	23	functions	function	NOUN
ijassa-1257	10	24	with	with	ADP
ijassa-1257	10	25	the	the	DET
ijassa-1257	10	26	problem	problem	NOUN
ijassa-1257	10	27	of	of	ADP
ijassa-1257	10	28	maximizing	maximize	VERB
ijassa-1257	10	29	the	the	DET
ijassa-1257	10	30	integral	integral	ADJ
ijassa-1257	10	31	discounted	discount	VERB
ijassa-1257	10	32	utility	utility	NOUN
ijassa-1257	10	33	of	of	ADP
ijassa-1257	10	34	the	the	DET
ijassa-1257	10	35	consumption	consumption	NOUN
ijassa-1257	10	36	.	.	PUNCT
ijassa-1257	11	1	in	in	ADP
ijassa-1257	11	2	this	this	DET
ijassa-1257	11	3	case	case	NOUN
ijassa-1257	11	4	,	,	PUNCT
ijassa-1257	11	5	the	the	DET
ijassa-1257	11	6	utility	utility	NOUN
ijassa-1257	11	7	function	function	NOUN
ijassa-1257	11	8	satisfies	satisfy	VERB
ijassa-1257	11	9	the	the	DET
ijassa-1257	11	10	arrow	arrow	NOUN
ijassa-1257	11	11	–	–	PUNCT
ijassa-1257	11	12	pratt	pratt	NOUN
ijassa-1257	11	13	condition	condition	NOUN
ijassa-1257	11	14	of	of	ADP
ijassa-1257	11	15	the	the	DET
ijassa-1257	11	16	relative	relative	ADJ
ijassa-1257	11	17	risk	risk	NOUN
ijassa-1257	11	18	aversion	aversion	NOUN
ijassa-1257	11	19	.	.	PUNCT
ijassa-1257	12	1	keywords	keyword	NOUN
ijassa-1257	12	2	:	:	PUNCT
ijassa-1257	12	3	optimal	optimal	ADJ
ijassa-1257	12	4	control	control	NOUN
ijassa-1257	12	5	,	,	PUNCT
ijassa-1257	12	6	income	income	NOUN
ijassa-1257	12	7	,	,	PUNCT
ijassa-1257	12	8	consumption	consumption	NOUN
ijassa-1257	12	9	,	,	PUNCT
ijassa-1257	12	10	investment	investment	NOUN
ijassa-1257	12	11	introduction	introduction	NOUN
ijassa-1257	12	12	throughout	throughout	ADP
ijassa-1257	12	13	the	the	DET
ijassa-1257	12	14	paper	paper	NOUN
ijassa-1257	12	15	,	,	PUNCT
ijassa-1257	12	16	we	we	PRON
ijassa-1257	12	17	assume	assume	VERB
ijassa-1257	12	18	the	the	DET
ijassa-1257	12	19	basic	basic	ADJ
ijassa-1257	12	20	economic	economic	ADJ
ijassa-1257	12	21	identity	identity	NOUN
ijassa-1257	12	22	:	:	PUNCT
ijassa-1257	12	23	the	the	DET
ijassa-1257	12	24	income	income	NOUN
ijassa-1257	12	25	is	be	AUX
ijassa-1257	12	26	equal	equal	ADJ
ijassa-1257	12	27	to	to	ADP
ijassa-1257	12	28	the	the	DET
ijassa-1257	12	29	sum	sum	NOUN
ijassa-1257	12	30	of	of	ADP
ijassa-1257	12	31	the	the	DET
ijassa-1257	12	32	consumption	consumption	NOUN
ijassa-1257	12	33	and	and	CCONJ
ijassa-1257	12	34	the	the	DET
ijassa-1257	12	35	investment	investment	NOUN
ijassa-1257	12	36	[	[	X
ijassa-1257	12	37	1	1	NUM
ijassa-1257	12	38	]	]	PUNCT
ijassa-1257	12	39	.	.	PUNCT
ijassa-1257	13	1	this	this	DET
ijassa-1257	13	2	identity	identity	NOUN
ijassa-1257	13	3	has	have	VERB
ijassa-1257	13	4	many	many	ADJ
ijassa-1257	13	5	various	various	ADJ
ijassa-1257	13	6	applications	application	NOUN
ijassa-1257	13	7	;	;	PUNCT
ijassa-1257	13	8	see	see	VERB
ijassa-1257	13	9	,	,	PUNCT
ijassa-1257	13	10	e.g.	e.g.	ADV
ijassa-1257	13	11	,	,	PUNCT
ijassa-1257	13	12	[	[	X
ijassa-1257	13	13	2	2	NUM
ijassa-1257	13	14	]	]	PUNCT
ijassa-1257	13	15	.	.	PUNCT
ijassa-1257	14	1	for	for	ADP
ijassa-1257	14	2	example	example	NOUN
ijassa-1257	14	3	,	,	PUNCT
ijassa-1257	14	4	this	this	DET
ijassa-1257	14	5	identity	identity	NOUN
ijassa-1257	14	6	holds	hold	VERB
ijassa-1257	14	7	true	true	ADJ
ijassa-1257	14	8	in	in	ADP
ijassa-1257	14	9	the	the	DET
ijassa-1257	14	10	harrod	harrod	NOUN
ijassa-1257	14	11	–	–	PUNCT
ijassa-1257	14	12	domar	domar	PROPN
ijassa-1257	14	13	and	and	CCONJ
ijassa-1257	14	14	the	the	DET
ijassa-1257	14	15	solow	solow	PROPN
ijassa-1257	14	16	macromodels	macromodel	NOUN
ijassa-1257	14	17	[	[	X
ijassa-1257	14	18	3	3	NUM
ijassa-1257	14	19	]	]	PUNCT
ijassa-1257	14	20	–	–	PUNCT
ijassa-1257	14	21	[	[	X
ijassa-1257	14	22	15	15	NUM
ijassa-1257	14	23	]	]	PUNCT
ijassa-1257	14	24	,	,	PUNCT
ijassa-1257	14	25	and	and	CCONJ
ijassa-1257	14	26	also	also	ADV
ijassa-1257	14	27	in	in	ADP
ijassa-1257	14	28	the	the	DET
ijassa-1257	14	29	household	household	NOUN
ijassa-1257	14	30	micromodel	micromodel	NOUN
ijassa-1257	14	31	[	[	X
ijassa-1257	14	32	?	?	X
ijassa-1257	14	33	]	]	X
ijassa-1257	14	34	,	,	PUNCT
ijassa-1257	14	35	[	[	X
ijassa-1257	14	36	19	19	NUM
ijassa-1257	14	37	]	]	PUNCT
ijassa-1257	14	38	.	.	PUNCT
ijassa-1257	15	1	hence	hence	ADV
ijassa-1257	15	2	,	,	PUNCT
ijassa-1257	15	3	these	these	DET
ijassa-1257	15	4	models	model	NOUN
ijassa-1257	15	5	have	have	VERB
ijassa-1257	15	6	some	some	DET
ijassa-1257	15	7	common	common	ADJ
ijassa-1257	15	8	properties	property	NOUN
ijassa-1257	15	9	.	.	PUNCT
ijassa-1257	16	1	one	one	NUM
ijassa-1257	16	2	of	of	ADP
ijassa-1257	16	3	the	the	DET
ijassa-1257	16	4	main	main	ADJ
ijassa-1257	16	5	goals	goal	NOUN
ijassa-1257	16	6	of	of	ADP
ijassa-1257	16	7	the	the	DET
ijassa-1257	16	8	paper	paper	NOUN
ijassa-1257	16	9	is	be	AUX
ijassa-1257	16	10	to	to	PART
ijassa-1257	16	11	establish	establish	VERB
ijassa-1257	16	12	such	such	ADJ
ijassa-1257	16	13	properties	property	NOUN
ijassa-1257	16	14	.	.	PUNCT
ijassa-1257	17	1	it	it	PRON
ijassa-1257	17	2	should	should	AUX
ijassa-1257	17	3	be	be	AUX
ijassa-1257	17	4	noted	note	VERB
ijassa-1257	17	5	that	that	SCONJ
ijassa-1257	17	6	in	in	ADP
ijassa-1257	17	7	these	these	DET
ijassa-1257	17	8	models	model	NOUN
ijassa-1257	17	9	the	the	DET
ijassa-1257	17	10	income	income	NOUN
ijassa-1257	17	11	is	be	AUX
ijassa-1257	17	12	understood	understand	VERB
ijassa-1257	17	13	in	in	ADP
ijassa-1257	17	14	different	different	ADJ
ijassa-1257	17	15	ways	way	NOUN
ijassa-1257	17	16	.	.	PUNCT
ijassa-1257	18	1	the	the	DET
ijassa-1257	18	2	income	income	NOUN
ijassa-1257	18	3	is	be	AUX
ijassa-1257	18	4	understood	understand	VERB
ijassa-1257	18	5	either	either	CCONJ
ijassa-1257	18	6	in	in	ADP
ijassa-1257	18	7	the	the	DET
ijassa-1257	18	8	pure	pure	ADJ
ijassa-1257	18	9	form	form	NOUN
ijassa-1257	18	10	or	or	CCONJ
ijassa-1257	18	11	the	the	DET
ijassa-1257	18	12	gross	gross	ADJ
ijassa-1257	18	13	domestic	domestic	ADJ
ijassa-1257	18	14	product	product	NOUN
ijassa-1257	18	15	,	,	PUNCT
ijassa-1257	18	16	or	or	CCONJ
ijassa-1257	18	17	the	the	DET
ijassa-1257	18	18	national	national	ADJ
ijassa-1257	18	19	income	income	NOUN
ijassa-1257	18	20	.	.	PUNCT
ijassa-1257	19	1	the	the	DET
ijassa-1257	19	2	consumption	consumption	NOUN
ijassa-1257	19	3	is	be	AUX
ijassa-1257	19	4	also	also	ADV
ijassa-1257	19	5	understood	understand	VERB
ijassa-1257	19	6	in	in	ADP
ijassa-1257	19	7	different	different	ADJ
ijassa-1257	19	8	ways	way	NOUN
ijassa-1257	19	9	:	:	PUNCT
ijassa-1257	19	10	in	in	ADP
ijassa-1257	19	11	its	its	PRON
ijassa-1257	19	12	pure	pure	ADJ
ijassa-1257	19	13	form	form	NOUN
ijassa-1257	19	14	or	or	CCONJ
ijassa-1257	19	15	the	the	DET
ijassa-1257	19	16	aggregate	aggregate	ADJ
ijassa-1257	19	17	consumption	consumption	NOUN
ijassa-1257	19	18	.	.	PUNCT
ijassa-1257	20	1	first	first	ADV
ijassa-1257	20	2	,	,	PUNCT
ijassa-1257	20	3	consider	consider	VERB
ijassa-1257	20	4	the	the	DET
ijassa-1257	20	5	harrod	harrod	NOUN
ijassa-1257	20	6	–	–	PUNCT
ijassa-1257	20	7	domar	domar	PROPN
ijassa-1257	20	8	macromodel	macromodel	NOUN
ijassa-1257	20	9	with	with	ADP
ijassa-1257	20	10	time	time	NOUN
ijassa-1257	20	11	-	-	PUNCT
ijassa-1257	20	12	dependent	dependent	ADJ
ijassa-1257	20	13	capital	capital	NOUN
ijassa-1257	20	14	intensity	intensity	NOUN
ijassa-1257	20	15	of	of	ADP
ijassa-1257	20	16	the	the	DET
ijassa-1257	20	17	income	income	NOUN
ijassa-1257	20	18	growth	growth	NOUN
ijassa-1257	20	19	.	.	PUNCT
ijassa-1257	21	1	we	we	PRON
ijassa-1257	21	2	also	also	ADV
ijassa-1257	21	3	introduce	introduce	VERB
ijassa-1257	21	4	a	a	DET
ijassa-1257	21	5	new	new	ADJ
ijassa-1257	21	6	variable	variable	NOUN
ijassa-1257	21	7	,	,	PUNCT
ijassa-1257	21	8	namely	namely	ADV
ijassa-1257	21	9	,	,	PUNCT
ijassa-1257	21	10	the	the	DET
ijassa-1257	21	11	relative	relative	ADJ
ijassa-1257	21	12	increase	increase	NOUN
ijassa-1257	21	13	in	in	ADP
ijassa-1257	21	14	the	the	DET
ijassa-1257	21	15	income	income	NOUN
ijassa-1257	21	16	of	of	ADP
ijassa-1257	21	17	the	the	DET
ijassa-1257	21	18	cobb	cobb	PROPN
ijassa-1257	21	19	–	–	PUNCT
ijassa-1257	21	20	douglas	douglas	PROPN
ijassa-1257	21	21	production	production	NOUN
ijassa-1257	21	22	function	function	NOUN
ijassa-1257	21	23	,	,	PUNCT
ijassa-1257	21	24	and	and	CCONJ
ijassa-1257	21	25	consider	consider	VERB
ijassa-1257	21	26	the	the	DET
ijassa-1257	21	27	balance	balance	NOUN
ijassa-1257	21	28	equation	equation	NOUN
ijassa-1257	21	29	for	for	ADP
ijassa-1257	21	30	the	the	DET
ijassa-1257	21	31	capital	capital	NOUN
ijassa-1257	21	32	.	.	PUNCT
ijassa-1257	22	1	as	as	ADP
ijassa-1257	22	2	a	a	DET
ijassa-1257	22	3	result	result	NOUN
ijassa-1257	22	4	,	,	PUNCT
ijassa-1257	22	5	we	we	PRON
ijassa-1257	22	6	establish	establish	VERB
ijassa-1257	22	7	the	the	DET
ijassa-1257	22	8	time	time	NOUN
ijassa-1257	22	9	dependence	dependence	NOUN
ijassa-1257	22	10	for	for	ADP
ijassa-1257	22	11	the	the	DET
ijassa-1257	22	12	capital	capital	NOUN
ijassa-1257	22	13	intensity	intensity	NOUN
ijassa-1257	22	14	of	of	ADP
ijassa-1257	22	15	the	the	DET
ijassa-1257	22	16	income	income	NOUN
ijassa-1257	22	17	growth	growth	NOUN
ijassa-1257	22	18	of	of	ADP
ijassa-1257	22	19	the	the	DET
ijassa-1257	22	20	solow	solow	PROPN
ijassa-1257	22	21	model	model	NOUN
ijassa-1257	22	22	.	.	PUNCT
ijassa-1257	23	1	further	far	ADV
ijassa-1257	23	2	,	,	PUNCT
ijassa-1257	23	3	we	we	PRON
ijassa-1257	23	4	show	show	VERB
ijassa-1257	23	5	that	that	SCONJ
ijassa-1257	23	6	the	the	DET
ijassa-1257	23	7	capital	capital	NOUN
ijassa-1257	23	8	intensity	intensity	NOUN
ijassa-1257	23	9	of	of	ADP
ijassa-1257	23	10	the	the	DET
ijassa-1257	23	11	income	income	NOUN
ijassa-1257	23	12	growth	growth	NOUN
ijassa-1257	23	13	in	in	ADP
ijassa-1257	23	14	the	the	DET
ijassa-1257	23	15	household	household	NOUN
ijassa-1257	23	16	model	model	NOUN
ijassa-1257	23	17	can	can	AUX
ijassa-1257	23	18	also	also	ADV
ijassa-1257	23	19	depend	depend	VERB
ijassa-1257	23	20	on	on	ADP
ijassa-1257	23	21	time	time	NOUN
ijassa-1257	23	22	.	.	PUNCT
ijassa-1257	24	1	since	since	SCONJ
ijassa-1257	24	2	households	household	NOUN
ijassa-1257	24	3	are	be	AUX
ijassa-1257	24	4	the	the	DET
ijassa-1257	24	5	best	good	ADJ
ijassa-1257	24	6	savers	saver	NOUN
ijassa-1257	24	7	and	and	CCONJ
ijassa-1257	24	8	they	they	PRON
ijassa-1257	24	9	demonstrate	demonstrate	VERB
ijassa-1257	24	10	the	the	DET
ijassa-1257	24	11	best	good	ADJ
ijassa-1257	24	12	survival	survival	NOUN
ijassa-1257	24	13	,	,	PUNCT
ijassa-1257	24	14	we	we	PRON
ijassa-1257	24	15	shall	shall	AUX
ijassa-1257	24	16	modify	modify	VERB
ijassa-1257	24	17	the	the	DET
ijassa-1257	24	18	considered	consider	VERB
ijassa-1257	24	19	macromodels	macromodel	NOUN
ijassa-1257	24	20	.	.	PUNCT
ijassa-1257	25	1	namely	namely	ADV
ijassa-1257	25	2	,	,	PUNCT
ijassa-1257	25	3	we	we	PRON
ijassa-1257	25	4	replace	replace	VERB
ijassa-1257	25	5	the	the	DET
ijassa-1257	25	6	production	production	NOUN
ijassa-1257	25	7	functions	function	NOUN
ijassa-1257	25	8	given	give	VERB
ijassa-1257	25	9	a	a	DET
ijassa-1257	25	10	priori	priori	NOUN
ijassa-1257	25	11	with	with	ADP
ijassa-1257	25	12	the	the	DET
ijassa-1257	25	13	problem	problem	NOUN
ijassa-1257	25	14	of	of	ADP
ijassa-1257	25	15	maximizing	maximize	VERB
ijassa-1257	25	16	the	the	DET
ijassa-1257	25	17	integral	integral	ADJ
ijassa-1257	25	18	discounted	discount	VERB
ijassa-1257	25	19	utility	utility	NOUN
ijassa-1257	25	20	of	of	ADP
ijassa-1257	25	21	the	the	DET
ijassa-1257	25	22	consumption	consumption	NOUN
ijassa-1257	25	23	,	,	PUNCT
ijassa-1257	25	24	as	as	ADP
ijassa-1257	25	25	∗corresponding	∗corresponde	VERB
ijassa-1257	25	26	author	author	NOUN
ijassa-1257	25	27	:	:	PUNCT
ijassa-1257	25	28	chernyaev49@yandex.ru	chernyaev49@yandex.ru	NUM
ijassa-1257	25	29	110	110	NUM
ijassa-1257	25	30	a.p	a.p	PROPN
ijassa-1257	25	31	.	.	PROPN
ijassa-1257	25	32	chernyaev	chernyaev	PROPN
ijassa-1257	25	33	households	household	NOUN
ijassa-1257	25	34	usually	usually	ADV
ijassa-1257	25	35	do	do	VERB
ijassa-1257	25	36	.	.	PUNCT
ijassa-1257	26	1	moreover	moreover	ADV
ijassa-1257	26	2	,	,	PUNCT
ijassa-1257	26	3	in	in	ADP
ijassa-1257	26	4	all	all	DET
ijassa-1257	26	5	these	these	DET
ijassa-1257	26	6	models	model	NOUN
ijassa-1257	26	7	the	the	DET
ijassa-1257	26	8	utility	utility	NOUN
ijassa-1257	26	9	function	function	NOUN
ijassa-1257	26	10	satisfies	satisfy	VERB
ijassa-1257	26	11	the	the	DET
ijassa-1257	26	12	arrow	arrow	NOUN
ijassa-1257	26	13	–	–	PUNCT
ijassa-1257	26	14	pratt	pratt	NOUN
ijassa-1257	26	15	condition	condition	NOUN
ijassa-1257	26	16	of	of	ADP
ijassa-1257	26	17	the	the	DET
ijassa-1257	26	18	relative	relative	ADJ
ijassa-1257	26	19	risk	risk	NOUN
ijassa-1257	26	20	aversion	aversion	NOUN
ijassa-1257	26	21	;	;	PUNCT
ijassa-1257	26	22	see	see	VERB
ijassa-1257	26	23	[	[	X
ijassa-1257	26	24	1	1	NUM
ijassa-1257	26	25	,	,	PUNCT
ijassa-1257	26	26	2	2	NUM
ijassa-1257	26	27	,	,	PUNCT
ijassa-1257	26	28	13	13	NUM
ijassa-1257	26	29	,	,	PUNCT
ijassa-1257	26	30	14	14	NUM
ijassa-1257	26	31	]	]	PUNCT
ijassa-1257	26	32	.	.	PUNCT
ijassa-1257	27	1	1	1	X
ijassa-1257	27	2	.	.	PUNCT
ijassa-1257	28	1	the	the	DET
ijassa-1257	28	2	preliminary	preliminary	ADJ
ijassa-1257	28	3	results	result	NOUN
ijassa-1257	28	4	1.1	1.1	NUM
ijassa-1257	28	5	.	.	PUNCT
ijassa-1257	29	1	the	the	DET
ijassa-1257	29	2	main	main	ADJ
ijassa-1257	29	3	economic	economic	ADJ
ijassa-1257	29	4	identity	identity	NOUN
ijassa-1257	29	5	in	in	ADP
ijassa-1257	29	6	this	this	DET
ijassa-1257	29	7	paper	paper	NOUN
ijassa-1257	29	8	,	,	PUNCT
ijassa-1257	29	9	we	we	PRON
ijassa-1257	29	10	shall	shall	AUX
ijassa-1257	29	11	always	always	ADV
ijassa-1257	29	12	assume	assume	VERB
ijassa-1257	29	13	that	that	SCONJ
ijassa-1257	29	14	the	the	DET
ijassa-1257	29	15	main	main	ADJ
ijassa-1257	29	16	economic	economic	ADJ
ijassa-1257	29	17	identity	identity	NOUN
ijassa-1257	29	18	holds	hold	VERB
ijassa-1257	29	19	true	true	ADJ
ijassa-1257	29	20	:	:	PUNCT
ijassa-1257	29	21	y	y	PROPN
ijassa-1257	29	22	(	(	PUNCT
ijassa-1257	29	23	t	t	PROPN
ijassa-1257	29	24	)	)	PUNCT
ijassa-1257	29	25	=	=	SYM
ijassa-1257	29	26	c(t	c(t	PROPN
ijassa-1257	29	27	)	)	PUNCT
ijassa-1257	29	28	+	+	NUM
ijassa-1257	29	29	i(t	i(t	NOUN
ijassa-1257	29	30	)	)	PUNCT
ijassa-1257	29	31	,	,	PUNCT
ijassa-1257	29	32	(	(	PUNCT
ijassa-1257	29	33	1.1	1.1	NUM
ijassa-1257	29	34	)	)	PUNCT
ijassa-1257	29	35	where	where	SCONJ
ijassa-1257	29	36	t	t	PROPN
ijassa-1257	29	37	means	mean	VERB
ijassa-1257	29	38	the	the	DET
ijassa-1257	29	39	continuous	continuous	ADJ
ijassa-1257	29	40	time	time	NOUN
ijassa-1257	29	41	,	,	PUNCT
ijassa-1257	29	42	y	y	PROPN
ijassa-1257	29	43	(	(	PUNCT
ijassa-1257	29	44	t	t	PROPN
ijassa-1257	29	45	)	)	PUNCT
ijassa-1257	29	46	is	be	AUX
ijassa-1257	29	47	the	the	DET
ijassa-1257	29	48	net	net	ADJ
ijassa-1257	29	49	income	income	NOUN
ijassa-1257	29	50	or	or	CCONJ
ijassa-1257	29	51	the	the	DET
ijassa-1257	29	52	gross	gross	ADJ
ijassa-1257	29	53	domestic	domestic	ADJ
ijassa-1257	29	54	product	product	NOUN
ijassa-1257	29	55	or	or	CCONJ
ijassa-1257	29	56	the	the	DET
ijassa-1257	29	57	national	national	ADJ
ijassa-1257	29	58	income	income	NOUN
ijassa-1257	29	59	,	,	PUNCT
ijassa-1257	29	60	c(t	c(t	PROPN
ijassa-1257	29	61	)	)	PUNCT
ijassa-1257	29	62	is	be	AUX
ijassa-1257	29	63	the	the	DET
ijassa-1257	29	64	consumption	consumption	NOUN
ijassa-1257	29	65	or	or	CCONJ
ijassa-1257	29	66	the	the	DET
ijassa-1257	29	67	total	total	ADJ
ijassa-1257	29	68	consumption	consumption	NOUN
ijassa-1257	29	69	,	,	PUNCT
ijassa-1257	29	70	i(t	i(t	PROPN
ijassa-1257	29	71	)	)	PUNCT
ijassa-1257	29	72	is	be	AUX
ijassa-1257	29	73	the	the	DET
ijassa-1257	29	74	general	general	ADJ
ijassa-1257	29	75	investment	investment	NOUN
ijassa-1257	29	76	.	.	PUNCT
ijassa-1257	30	1	1.2	1.2	NUM
ijassa-1257	30	2	.	.	PUNCT
ijassa-1257	31	1	the	the	DET
ijassa-1257	31	2	dependence	dependence	NOUN
ijassa-1257	31	3	of	of	ADP
ijassa-1257	31	4	the	the	DET
ijassa-1257	31	5	income	income	NOUN
ijassa-1257	31	6	on	on	ADP
ijassa-1257	31	7	the	the	DET
ijassa-1257	31	8	consumption	consumption	NOUN
ijassa-1257	31	9	in	in	ADP
ijassa-1257	31	10	the	the	DET
ijassa-1257	31	11	harrod	harrod	NOUN
ijassa-1257	31	12	–	–	PUNCT
ijassa-1257	31	13	domar	domar	NOUN
ijassa-1257	31	14	model	model	NOUN
ijassa-1257	31	15	with	with	ADP
ijassa-1257	31	16	varying	vary	VERB
ijassa-1257	31	17	capital	capital	NOUN
ijassa-1257	31	18	intensity	intensity	NOUN
ijassa-1257	31	19	of	of	ADP
ijassa-1257	31	20	the	the	DET
ijassa-1257	31	21	income	income	NOUN
ijassa-1257	31	22	growth	growth	NOUN
ijassa-1257	31	23	the	the	DET
ijassa-1257	31	24	main	main	ADJ
ijassa-1257	31	25	assumption	assumption	NOUN
ijassa-1257	31	26	in	in	ADP
ijassa-1257	31	27	the	the	DET
ijassa-1257	31	28	harrod	harrod	NOUN
ijassa-1257	31	29	–	–	PUNCT
ijassa-1257	31	30	domar	domar	NOUN
ijassa-1257	31	31	model	model	NOUN
ijassa-1257	31	32	is	be	AUX
ijassa-1257	31	33	that	that	SCONJ
ijassa-1257	31	34	the	the	DET
ijassa-1257	31	35	investment	investment	NOUN
ijassa-1257	31	36	linearly	linearly	ADV
ijassa-1257	31	37	depends	depend	VERB
ijassa-1257	31	38	on	on	ADP
ijassa-1257	31	39	the	the	DET
ijassa-1257	31	40	derivative	derivative	NOUN
ijassa-1257	31	41	of	of	ADP
ijassa-1257	31	42	the	the	DET
ijassa-1257	31	43	income	income	NOUN
ijassa-1257	31	44	by	by	ADP
ijassa-1257	31	45	t	t	PROPN
ijassa-1257	31	46	,	,	PUNCT
ijassa-1257	31	47	that	that	ADV
ijassa-1257	31	48	is	is	ADV
ijassa-1257	31	49	,	,	PUNCT
ijassa-1257	31	50	i(t	i(t	PROPN
ijassa-1257	31	51	)	)	PUNCT
ijassa-1257	31	52	=	=	PUNCT
ijassa-1257	31	53	by	by	ADP
ijassa-1257	31	54	′(t	′(t	NOUN
ijassa-1257	31	55	)	)	PUNCT
ijassa-1257	31	56	;	;	PUNCT
ijassa-1257	31	57	see	see	VERB
ijassa-1257	31	58	[	[	X
ijassa-1257	31	59	1,15	1,15	NUM
ijassa-1257	31	60	]	]	X
ijassa-1257	31	61	.	.	PUNCT
ijassa-1257	32	1	here	here	ADV
ijassa-1257	32	2	the	the	DET
ijassa-1257	32	3	coefficient	coefficient	NOUN
ijassa-1257	32	4	b	b	PROPN
ijassa-1257	32	5	is	be	AUX
ijassa-1257	32	6	a	a	DET
ijassa-1257	32	7	positive	positive	ADJ
ijassa-1257	32	8	constant	constant	NOUN
ijassa-1257	32	9	.	.	PUNCT
ijassa-1257	33	1	assuming	assume	VERB
ijassa-1257	33	2	that	that	SCONJ
ijassa-1257	33	3	b	b	NOUN
ijassa-1257	33	4	depends	depend	VERB
ijassa-1257	33	5	on	on	ADP
ijassa-1257	33	6	t	t	PROPN
ijassa-1257	33	7	,	,	PUNCT
ijassa-1257	33	8	we	we	PRON
ijassa-1257	33	9	have	have	VERB
ijassa-1257	33	10	:	:	PUNCT
ijassa-1257	34	1	y	y	PROPN
ijassa-1257	34	2	(	(	PUNCT
ijassa-1257	34	3	t	t	PROPN
ijassa-1257	34	4	)	)	PUNCT
ijassa-1257	34	5	=	=	SYM
ijassa-1257	34	6	c(t	c(t	PROPN
ijassa-1257	34	7	)	)	PUNCT
ijassa-1257	35	1	+	+	NOUN
ijassa-1257	35	2	b(t)y	b(t)y	PROPN
ijassa-1257	35	3	′(t	′(t	NOUN
ijassa-1257	35	4	)	)	PUNCT
ijassa-1257	35	5	,	,	PUNCT
ijassa-1257	35	6	(	(	PUNCT
ijassa-1257	35	7	1.2	1.2	NUM
ijassa-1257	35	8	)	)	PUNCT
ijassa-1257	35	9	where	where	SCONJ
ijassa-1257	35	10	b(t	b(t	NOUN
ijassa-1257	35	11	)	)	PUNCT
ijassa-1257	35	12	is	be	AUX
ijassa-1257	35	13	the	the	DET
ijassa-1257	35	14	capital	capital	NOUN
ijassa-1257	35	15	intensity	intensity	NOUN
ijassa-1257	35	16	of	of	ADP
ijassa-1257	35	17	the	the	DET
ijassa-1257	35	18	income	income	NOUN
ijassa-1257	35	19	growth	growth	NOUN
ijassa-1257	35	20	.	.	PUNCT
ijassa-1257	36	1	setting	set	VERB
ijassa-1257	36	2	for	for	ADP
ijassa-1257	36	3	(	(	PUNCT
ijassa-1257	36	4	1.2	1.2	NUM
ijassa-1257	36	5	)	)	PUNCT
ijassa-1257	36	6	the	the	DET
ijassa-1257	36	7	initial	initial	ADJ
ijassa-1257	36	8	condition	condition	NOUN
ijassa-1257	36	9	y	y	PROPN
ijassa-1257	36	10	(	(	PUNCT
ijassa-1257	36	11	t0	t0	PROPN
ijassa-1257	36	12	)	)	PUNCT
ijassa-1257	36	13	=	=	PUNCT
ijassa-1257	36	14	y0	y0	VERB
ijassa-1257	36	15	>	>	X
ijassa-1257	36	16	0	0	NUM
ijassa-1257	36	17	,	,	PUNCT
ijassa-1257	36	18	(	(	PUNCT
ijassa-1257	36	19	1.3	1.3	NUM
ijassa-1257	36	20	)	)	PUNCT
ijassa-1257	36	21	we	we	PRON
ijassa-1257	36	22	obtain	obtain	VERB
ijassa-1257	36	23	the	the	DET
ijassa-1257	36	24	cauchy	cauchy	ADJ
ijassa-1257	36	25	problem	problem	NOUN
ijassa-1257	36	26	,	,	PUNCT
ijassa-1257	36	27	whose	whose	DET
ijassa-1257	36	28	solution	solution	NOUN
ijassa-1257	36	29	is	be	AUX
ijassa-1257	36	30	given	give	VERB
ijassa-1257	36	31	by	by	ADP
ijassa-1257	36	32	the	the	DET
ijassa-1257	36	33	following	follow	VERB
ijassa-1257	36	34	formula	formula	NOUN
ijassa-1257	36	35	(	(	PUNCT
ijassa-1257	36	36	see	see	VERB
ijassa-1257	36	37	,	,	PUNCT
ijassa-1257	36	38	e.g.	e.g.	ADV
ijassa-1257	36	39	,	,	PUNCT
ijassa-1257	36	40	[	[	X
ijassa-1257	36	41	1	1	NUM
ijassa-1257	36	42	,	,	PUNCT
ijassa-1257	36	43	8	8	NUM
ijassa-1257	36	44	]	]	PUNCT
ijassa-1257	36	45	):	):	PUNCT
ijassa-1257	36	46	y	y	PROPN
ijassa-1257	36	47	(	(	PUNCT
ijassa-1257	36	48	t	t	PROPN
ijassa-1257	36	49	)	)	PUNCT
ijassa-1257	36	50	=	=	SYM
ijassa-1257	36	51	exp	exp	X
ijassa-1257	36	52	{	{	PUNCT
ijassa-1257	36	53	∫	∫	PROPN
ijassa-1257	36	54	t	t	PROPN
ijassa-1257	36	55	t0	t0	PROPN
ijassa-1257	36	56	ds	ds	PRON
ijassa-1257	36	57	b(s	b(	NOUN
ijassa-1257	36	58	)	)	PUNCT
ijassa-1257	36	59	}	}	PUNCT
ijassa-1257	36	60	(	(	PUNCT
ijassa-1257	36	61	y0	y0	NOUN
ijassa-1257	36	62	−	−	NOUN
ijassa-1257	36	63	∫	∫	PROPN
ijassa-1257	36	64	t	t	PROPN
ijassa-1257	36	65	t0	t0	PROPN
ijassa-1257	36	66	c(τ	c(τ	PROPN
ijassa-1257	36	67	)	)	PUNCT
ijassa-1257	36	68	b(τ	b(τ	PROPN
ijassa-1257	36	69	)	)	PUNCT
ijassa-1257	36	70	exp	exp	NOUN
ijassa-1257	36	71	{	{	PUNCT
ijassa-1257	36	72	−	−	PROPN
ijassa-1257	36	73	∫	∫	PROPN
ijassa-1257	36	74	τ	τ	PROPN
ijassa-1257	36	75	t0	t0	PROPN
ijassa-1257	36	76	ds	ds	PRON
ijassa-1257	36	77	b(s	b(	NOUN
ijassa-1257	36	78	)	)	PUNCT
ijassa-1257	36	79	}	}	PUNCT
ijassa-1257	36	80	dτ	dτ	NOUN
ijassa-1257	36	81	)	)	PUNCT
ijassa-1257	36	82	.	.	PUNCT
ijassa-1257	37	1	(	(	PUNCT
ijassa-1257	37	2	1.4	1.4	NUM
ijassa-1257	37	3	)	)	PUNCT
ijassa-1257	37	4	formula	formula	NOUN
ijassa-1257	37	5	(	(	PUNCT
ijassa-1257	37	6	1.4	1.4	NUM
ijassa-1257	37	7	)	)	PUNCT
ijassa-1257	37	8	determines	determine	VERB
ijassa-1257	37	9	the	the	DET
ijassa-1257	37	10	dependence	dependence	NOUN
ijassa-1257	37	11	of	of	ADP
ijassa-1257	37	12	the	the	DET
ijassa-1257	37	13	income	income	NOUN
ijassa-1257	37	14	on	on	ADP
ijassa-1257	37	15	the	the	DET
ijassa-1257	37	16	consumption	consumption	NOUN
ijassa-1257	37	17	.	.	PUNCT
ijassa-1257	38	1	1.3	1.3	NUM
ijassa-1257	38	2	.	.	PUNCT
ijassa-1257	39	1	the	the	DET
ijassa-1257	39	2	relative	relative	ADJ
ijassa-1257	39	3	increase	increase	NOUN
ijassa-1257	39	4	of	of	ADP
ijassa-1257	39	5	the	the	DET
ijassa-1257	39	6	income	income	NOUN
ijassa-1257	39	7	for	for	ADP
ijassa-1257	39	8	the	the	DET
ijassa-1257	39	9	cobb	cobb	PROPN
ijassa-1257	39	10	–	–	PUNCT
ijassa-1257	39	11	douglas	douglas	PROPN
ijassa-1257	39	12	production	production	NOUN
ijassa-1257	39	13	function	function	NOUN
ijassa-1257	39	14	consider	consider	VERB
ijassa-1257	39	15	the	the	DET
ijassa-1257	39	16	cobb	cobb	PROPN
ijassa-1257	39	17	–	–	PUNCT
ijassa-1257	39	18	douglas	douglas	PROPN
ijassa-1257	39	19	production	production	NOUN
ijassa-1257	39	20	function	function	NOUN
ijassa-1257	39	21	[	[	X
ijassa-1257	39	22	17	17	NUM
ijassa-1257	39	23	,	,	PUNCT
ijassa-1257	39	24	18	18	NUM
ijassa-1257	39	25	]	]	SYM
ijassa-1257	39	26	:	:	PUNCT
ijassa-1257	39	27	y	y	PROPN
ijassa-1257	39	28	=	=	SYM
ijassa-1257	39	29	f	f	PROPN
ijassa-1257	39	30	(	(	PUNCT
ijassa-1257	39	31	k	k	X
ijassa-1257	39	32	,	,	PUNCT
ijassa-1257	39	33	l	l	NOUN
ijassa-1257	39	34	)	)	PUNCT
ijassa-1257	39	35	=	=	SYM
ijassa-1257	39	36	akαl1−α	akαl1−α	PROPN
ijassa-1257	39	37	,	,	PUNCT
ijassa-1257	39	38	a	a	PRON
ijassa-1257	39	39	=	=	X
ijassa-1257	39	40	const	const	X
ijassa-1257	39	41	>	>	X
ijassa-1257	39	42	0	0	NUM
ijassa-1257	39	43	,	,	PUNCT
ijassa-1257	39	44	0	0	NUM
ijassa-1257	39	45	<	<	X
ijassa-1257	39	46	α	α	X
ijassa-1257	39	47	<	<	X
ijassa-1257	39	48	1	1	NUM
ijassa-1257	39	49	,	,	PUNCT
ijassa-1257	39	50	(	(	PUNCT
ijassa-1257	39	51	1.5	1.5	NUM
ijassa-1257	39	52	)	)	PUNCT
ijassa-1257	39	53	where	where	SCONJ
ijassa-1257	39	54	k	k	PROPN
ijassa-1257	39	55	=	=	SYM
ijassa-1257	39	56	k(t	k(t	PROPN
ijassa-1257	39	57	)	)	PUNCT
ijassa-1257	39	58	is	be	AUX
ijassa-1257	39	59	the	the	DET
ijassa-1257	39	60	capital	capital	NOUN
ijassa-1257	39	61	,	,	PUNCT
ijassa-1257	39	62	l	l	NOUN
ijassa-1257	39	63	=	=	SYM
ijassa-1257	39	64	l(t	l(t	PROPN
ijassa-1257	39	65	)	)	PUNCT
ijassa-1257	39	66	is	be	AUX
ijassa-1257	39	67	the	the	DET
ijassa-1257	39	68	labor	labor	NOUN
ijassa-1257	39	69	,	,	PUNCT
ijassa-1257	39	70	i.e.	i.e.	X
ijassa-1257	39	71	,	,	PUNCT
ijassa-1257	39	72	the	the	DET
ijassa-1257	39	73	number	number	NOUN
ijassa-1257	39	74	of	of	ADP
ijassa-1257	39	75	employees	employee	NOUN
ijassa-1257	39	76	.	.	PUNCT
ijassa-1257	40	1	for	for	ADP
ijassa-1257	40	2	convenience	convenience	NOUN
ijassa-1257	40	3	,	,	PUNCT
ijassa-1257	40	4	let	let	VERB
ijassa-1257	40	5	us	we	PRON
ijassa-1257	40	6	introduce	introduce	VERB
ijassa-1257	40	7	a	a	DET
ijassa-1257	40	8	new	new	ADJ
ijassa-1257	40	9	variable	variable	NOUN
ijassa-1257	41	1	σ	σ	NOUN
ijassa-1257	41	2	=	=	PUNCT
ijassa-1257	41	3	σ(t	σ(t	PROPN
ijassa-1257	41	4	)	)	PUNCT
ijassa-1257	41	5	=	=	SYM
ijassa-1257	41	6	y	y	PROPN
ijassa-1257	41	7	′(t	′(t	PROPN
ijassa-1257	41	8	)	)	PUNCT
ijassa-1257	41	9	y	y	PROPN
ijassa-1257	41	10	(	(	PUNCT
ijassa-1257	41	11	t	t	PROPN
ijassa-1257	41	12	)	)	PUNCT
ijassa-1257	41	13	=	=	PUNCT
ijassa-1257	42	1	α	α	NUM
ijassa-1257	42	2	k	k	PROPN
ijassa-1257	42	3	′(t	′(t	PROPN
ijassa-1257	42	4	)	)	PUNCT
ijassa-1257	42	5	k(t	k(t	NOUN
ijassa-1257	42	6	)	)	PUNCT
ijassa-1257	43	1	+	+	CCONJ
ijassa-1257	43	2	(	(	PUNCT
ijassa-1257	43	3	1−	1−	NUM
ijassa-1257	43	4	α	α	NOUN
ijassa-1257	43	5	)	)	PUNCT
ijassa-1257	43	6	l′(t	l′(t	PROPN
ijassa-1257	43	7	)	)	PUNCT
ijassa-1257	43	8	l(t	l(t	PROPN
ijassa-1257	43	9	)	)	PUNCT
ijassa-1257	43	10	,	,	PUNCT
ijassa-1257	44	1	which	which	PRON
ijassa-1257	44	2	is	be	AUX
ijassa-1257	44	3	called	call	VERB
ijassa-1257	44	4	the	the	DET
ijassa-1257	44	5	relative	relative	ADJ
ijassa-1257	44	6	increase	increase	NOUN
ijassa-1257	44	7	of	of	ADP
ijassa-1257	44	8	the	the	DET
ijassa-1257	44	9	income	income	NOUN
ijassa-1257	44	10	.	.	PUNCT
ijassa-1257	45	1	introduce	introduce	VERB
ijassa-1257	45	2	the	the	DET
ijassa-1257	45	3	standard	standard	ADJ
ijassa-1257	45	4	value	value	NOUN
ijassa-1257	45	5	ν	ν	NOUN
ijassa-1257	45	6	=	=	PUNCT
ijassa-1257	45	7	ν(t	ν(t	PROPN
ijassa-1257	45	8	)	)	PUNCT
ijassa-1257	45	9	=	=	SYM
ijassa-1257	45	10	l′(t	l′(t	PROPN
ijassa-1257	45	11	)	)	PUNCT
ijassa-1257	45	12	l(t	l(t	PROPN
ijassa-1257	45	13	)	)	PUNCT
ijassa-1257	45	14	,	,	PUNCT
ijassa-1257	45	15	(	(	PUNCT
ijassa-1257	45	16	1.6	1.6	NUM
ijassa-1257	45	17	)	)	PUNCT
ijassa-1257	45	18	which	which	PRON
ijassa-1257	45	19	we	we	PRON
ijassa-1257	45	20	call	call	VERB
ijassa-1257	45	21	the	the	DET
ijassa-1257	45	22	rate	rate	NOUN
ijassa-1257	45	23	of	of	ADP
ijassa-1257	45	24	the	the	DET
ijassa-1257	45	25	growth	growth	NOUN
ijassa-1257	45	26	of	of	ADP
ijassa-1257	45	27	labor	labor	NOUN
ijassa-1257	45	28	resources	resource	NOUN
ijassa-1257	45	29	.	.	PUNCT
ijassa-1257	46	1	then	then	ADV
ijassa-1257	46	2	,	,	PUNCT
ijassa-1257	46	3	taking	take	VERB
ijassa-1257	46	4	into	into	ADP
ijassa-1257	46	5	account	account	NOUN
ijassa-1257	46	6	(	(	PUNCT
ijassa-1257	46	7	1.6	1.6	NUM
ijassa-1257	46	8	)	)	PUNCT
ijassa-1257	46	9	,	,	PUNCT
ijassa-1257	46	10	for	for	ADP
ijassa-1257	46	11	the	the	DET
ijassa-1257	46	12	relative	relative	ADJ
ijassa-1257	46	13	increase	increase	NOUN
ijassa-1257	46	14	in	in	ADP
ijassa-1257	46	15	income	income	NOUN
ijassa-1257	46	16	we	we	PRON
ijassa-1257	46	17	have	have	VERB
ijassa-1257	46	18	the	the	DET
ijassa-1257	46	19	expression	expression	NOUN
ijassa-1257	46	20	σ	σ	NOUN
ijassa-1257	46	21	=	=	PUNCT
ijassa-1257	46	22	σ(t	σ(t	PROPN
ijassa-1257	46	23	)	)	PUNCT
ijassa-1257	47	1	=	=	SYM
ijassa-1257	47	2	y	y	PROPN
ijassa-1257	47	3	′(t	′(t	PROPN
ijassa-1257	47	4	)	)	PUNCT
ijassa-1257	47	5	y	y	PROPN
ijassa-1257	47	6	(	(	PUNCT
ijassa-1257	47	7	t	t	PROPN
ijassa-1257	47	8	)	)	PUNCT
ijassa-1257	47	9	=	=	PUNCT
ijassa-1257	48	1	α	α	NUM
ijassa-1257	48	2	k	k	PROPN
ijassa-1257	48	3	′(t	′(t	PROPN
ijassa-1257	48	4	)	)	PUNCT
ijassa-1257	48	5	k(t	k(t	NOUN
ijassa-1257	48	6	)	)	PUNCT
ijassa-1257	49	1	+	+	CCONJ
ijassa-1257	49	2	(	(	PUNCT
ijassa-1257	49	3	1−	1−	NUM
ijassa-1257	49	4	α)ν	α)ν	NOUN
ijassa-1257	49	5	.	.	PUNCT
ijassa-1257	50	1	(	(	PUNCT
ijassa-1257	50	2	1.7	1.7	NUM
ijassa-1257	50	3	)	)	PUNCT
ijassa-1257	50	4	copyright	copyright	NOUN
ijassa-1257	50	5	©	©	PROPN
ijassa-1257	50	6	2022	2022	NUM
ijassa-1257	50	7	assa	assa	NOUN
ijassa-1257	50	8	.	.	PUNCT
ijassa-1257	51	1	adv	adv	PROPN
ijassa-1257	51	2	syst	syst	PROPN
ijassa-1257	51	3	sci	sci	PROPN
ijassa-1257	51	4	appl	appl	PROPN
ijassa-1257	51	5	(	(	PUNCT
ijassa-1257	51	6	2022	2022	NUM
ijassa-1257	51	7	)	)	PUNCT
ijassa-1257	51	8	the	the	DET
ijassa-1257	51	9	optimal	optimal	ADJ
ijassa-1257	51	10	control	control	NOUN
ijassa-1257	51	11	approach	approach	NOUN
ijassa-1257	51	12	in	in	ADP
ijassa-1257	51	13	problems	problem	NOUN
ijassa-1257	51	14	of	of	ADP
ijassa-1257	51	15	the	the	DET
ijassa-1257	51	16	income	income	NOUN
ijassa-1257	51	17	distribution	distribution	NOUN
ijassa-1257	51	18	111	111	NUM
ijassa-1257	51	19	1.4	1.4	NUM
ijassa-1257	51	20	.	.	PUNCT
ijassa-1257	52	1	the	the	DET
ijassa-1257	52	2	balance	balance	NOUN
ijassa-1257	52	3	equation	equation	NOUN
ijassa-1257	52	4	for	for	ADP
ijassa-1257	52	5	capital	capital	NOUN
ijassa-1257	52	6	obviously	obviously	ADV
ijassa-1257	52	7	,	,	PUNCT
ijassa-1257	52	8	the	the	DET
ijassa-1257	52	9	balance	balance	NOUN
ijassa-1257	52	10	equation	equation	NOUN
ijassa-1257	52	11	for	for	ADP
ijassa-1257	52	12	capital	capital	NOUN
ijassa-1257	52	13	has	have	VERB
ijassa-1257	52	14	the	the	DET
ijassa-1257	52	15	form	form	NOUN
ijassa-1257	52	16	k	k	PROPN
ijassa-1257	52	17	′(t	′(t	PROPN
ijassa-1257	52	18	)	)	PUNCT
ijassa-1257	52	19	=	=	SYM
ijassa-1257	52	20	i(t)−	i(t)−	PROPN
ijassa-1257	52	21	µk(t	µk(t	PUNCT
ijassa-1257	52	22	)	)	PUNCT
ijassa-1257	52	23	,	,	PUNCT
ijassa-1257	52	24	(	(	PUNCT
ijassa-1257	52	25	1.8	1.8	NUM
ijassa-1257	52	26	)	)	PUNCT
ijassa-1257	52	27	where	where	SCONJ
ijassa-1257	52	28	µ	µ	NOUN
ijassa-1257	52	29	is	be	AUX
ijassa-1257	52	30	the	the	DET
ijassa-1257	52	31	share	share	NOUN
ijassa-1257	52	32	of	of	ADP
ijassa-1257	52	33	the	the	DET
ijassa-1257	52	34	retired	retire	VERB
ijassa-1257	52	35	capital	capital	NOUN
ijassa-1257	52	36	.	.	PUNCT
ijassa-1257	53	1	the	the	DET
ijassa-1257	53	2	standard	standard	ADJ
ijassa-1257	53	3	assumption	assumption	NOUN
ijassa-1257	53	4	i(t	i(t	PROPN
ijassa-1257	53	5	)	)	PUNCT
ijassa-1257	53	6	=	=	PUNCT
ijassa-1257	53	7	ρy	ρy	X
ijassa-1257	53	8	(	(	PUNCT
ijassa-1257	53	9	t	t	NOUN
ijassa-1257	53	10	)	)	PUNCT
ijassa-1257	53	11	,	,	PUNCT
ijassa-1257	53	12	(	(	PUNCT
ijassa-1257	53	13	1.9	1.9	NUM
ijassa-1257	53	14	)	)	PUNCT
ijassa-1257	53	15	where	where	SCONJ
ijassa-1257	53	16	ρ	ρ	NOUN
ijassa-1257	53	17	=	=	SYM
ijassa-1257	53	18	ρ(t	ρ(t	NUM
ijassa-1257	53	19	)	)	PUNCT
ijassa-1257	53	20	is	be	AUX
ijassa-1257	53	21	the	the	DET
ijassa-1257	53	22	rate	rate	NOUN
ijassa-1257	53	23	of	of	ADP
ijassa-1257	53	24	accumulation	accumulation	NOUN
ijassa-1257	53	25	[	[	X
ijassa-1257	53	26	1	1	NUM
ijassa-1257	53	27	,	,	PUNCT
ijassa-1257	53	28	15	15	NUM
ijassa-1257	53	29	,	,	PUNCT
ijassa-1257	53	30	17	17	NUM
ijassa-1257	53	31	,	,	PUNCT
ijassa-1257	53	32	18	18	NUM
ijassa-1257	53	33	]	]	PUNCT
ijassa-1257	53	34	,	,	PUNCT
ijassa-1257	53	35	leads	lead	VERB
ijassa-1257	53	36	to	to	ADP
ijassa-1257	53	37	the	the	DET
ijassa-1257	53	38	equality	equality	NOUN
ijassa-1257	53	39	k	k	PROPN
ijassa-1257	53	40	′(t	′(t	PROPN
ijassa-1257	53	41	)	)	PUNCT
ijassa-1257	53	42	k(t	k(t	PROPN
ijassa-1257	53	43	)	)	PUNCT
ijassa-1257	54	1	=	=	SYM
ijassa-1257	54	2	ρy	ρy	X
ijassa-1257	54	3	(	(	PUNCT
ijassa-1257	54	4	t	t	NOUN
ijassa-1257	54	5	)	)	PUNCT
ijassa-1257	54	6	k(t	k(t	PROPN
ijassa-1257	54	7	)	)	PUNCT
ijassa-1257	54	8	−	−	PROPN
ijassa-1257	54	9	µ	µ	X
ijassa-1257	54	10	=	=	SYM
ijassa-1257	54	11	ρa	ρa	ADP
ijassa-1257	54	12	(	(	PUNCT
ijassa-1257	54	13	k(t	k(t	NOUN
ijassa-1257	54	14	)	)	PUNCT
ijassa-1257	54	15	l(t	l(t	PROPN
ijassa-1257	54	16	)	)	PUNCT
ijassa-1257	54	17	)	)	PUNCT
ijassa-1257	54	18	α−1	α−1	PROPN
ijassa-1257	54	19	−	−	PROPN
ijassa-1257	54	20	µ.	µ.	NOUN
ijassa-1257	54	21	(	(	PUNCT
ijassa-1257	54	22	1.10	1.10	NUM
ijassa-1257	54	23	)	)	PUNCT
ijassa-1257	54	24	then	then	ADV
ijassa-1257	54	25	,	,	PUNCT
ijassa-1257	54	26	taking	take	VERB
ijassa-1257	54	27	into	into	ADP
ijassa-1257	54	28	account	account	NOUN
ijassa-1257	54	29	(	(	PUNCT
ijassa-1257	54	30	1.7	1.7	NUM
ijassa-1257	54	31	)	)	PUNCT
ijassa-1257	54	32	,	,	PUNCT
ijassa-1257	54	33	we	we	PRON
ijassa-1257	54	34	have	have	VERB
ijassa-1257	54	35	σ(t	σ(t	PROPN
ijassa-1257	54	36	)	)	PUNCT
ijassa-1257	55	1	=	=	PUNCT
ijassa-1257	55	2	αρak(t)α−1	αρak(t)α−1	NUM
ijassa-1257	56	1	+	+	CCONJ
ijassa-1257	56	2	ν	ν	NOUN
ijassa-1257	56	3	−	−	NUM
ijassa-1257	56	4	α(µ+	α(µ+	X
ijassa-1257	56	5	ν	ν	NOUN
ijassa-1257	56	6	)	)	PUNCT
ijassa-1257	56	7	,	,	PUNCT
ijassa-1257	56	8	(	(	PUNCT
ijassa-1257	56	9	1.11	1.11	NUM
ijassa-1257	56	10	)	)	PUNCT
ijassa-1257	56	11	where	where	SCONJ
ijassa-1257	56	12	k(t	k(t	NOUN
ijassa-1257	56	13	)	)	PUNCT
ijassa-1257	56	14	=	=	SYM
ijassa-1257	56	15	k(t)/l(t	k(t)/l(t	NOUN
ijassa-1257	56	16	)	)	PUNCT
ijassa-1257	56	17	is	be	AUX
ijassa-1257	56	18	the	the	DET
ijassa-1257	56	19	capital	capital	NOUN
ijassa-1257	56	20	-	-	PUNCT
ijassa-1257	56	21	labor	labor	NOUN
ijassa-1257	56	22	ratio	ratio	NOUN
ijassa-1257	56	23	.	.	PUNCT
ijassa-1257	57	1	1.5	1.5	NUM
ijassa-1257	57	2	.	.	PUNCT
ijassa-1257	58	1	capital	capital	NOUN
ijassa-1257	58	2	capacity	capacity	NOUN
ijassa-1257	58	3	of	of	ADP
ijassa-1257	58	4	increase	increase	NOUN
ijassa-1257	58	5	in	in	ADP
ijassa-1257	58	6	the	the	DET
ijassa-1257	58	7	solow	solow	PROPN
ijassa-1257	58	8	model	model	PROPN
ijassa-1257	58	9	sine	sine	NOUN
ijassa-1257	58	10	equation	equation	NOUN
ijassa-1257	58	11	(	(	PUNCT
ijassa-1257	58	12	1.11	1.11	NUM
ijassa-1257	58	13	)	)	PUNCT
ijassa-1257	58	14	contains	contain	VERB
ijassa-1257	58	15	the	the	DET
ijassa-1257	58	16	capital	capital	NOUN
ijassa-1257	58	17	-	-	PUNCT
ijassa-1257	58	18	labor	labor	NOUN
ijassa-1257	58	19	ratio	ratio	NOUN
ijassa-1257	58	20	,	,	PUNCT
ijassa-1257	58	21	it	it	PRON
ijassa-1257	58	22	leads	lead	VERB
ijassa-1257	58	23	to	to	ADP
ijassa-1257	58	24	the	the	DET
ijassa-1257	58	25	solow	solow	PROPN
ijassa-1257	58	26	macromodel	macromodel	PROPN
ijassa-1257	59	1	[	[	X
ijassa-1257	59	2	12	12	NUM
ijassa-1257	59	3	]	]	PUNCT
ijassa-1257	59	4	–	–	PUNCT
ijassa-1257	59	5	[	[	X
ijassa-1257	59	6	15	15	NUM
ijassa-1257	59	7	]	]	PUNCT
ijassa-1257	59	8	.	.	PUNCT
ijassa-1257	60	1	using	use	VERB
ijassa-1257	60	2	the	the	DET
ijassa-1257	60	3	equality	equality	NOUN
ijassa-1257	60	4	i(t	i(t	NOUN
ijassa-1257	60	5	)	)	PUNCT
ijassa-1257	60	6	=	=	PUNCT
ijassa-1257	60	7	b(t)y	b(t)y	PROPN
ijassa-1257	60	8	′(t	′(t	PROPN
ijassa-1257	60	9	)	)	PUNCT
ijassa-1257	60	10	for	for	ADP
ijassa-1257	60	11	determination	determination	NOUN
ijassa-1257	60	12	the	the	DET
ijassa-1257	60	13	incremental	incremental	ADJ
ijassa-1257	60	14	capital	capital	NOUN
ijassa-1257	60	15	intensity	intensity	NOUN
ijassa-1257	60	16	and	and	CCONJ
ijassa-1257	60	17	taking	take	VERB
ijassa-1257	60	18	into	into	ADP
ijassa-1257	60	19	account	account	NOUN
ijassa-1257	60	20	(	(	PUNCT
ijassa-1257	60	21	1.9	1.9	NUM
ijassa-1257	60	22	)	)	PUNCT
ijassa-1257	60	23	,	,	PUNCT
ijassa-1257	60	24	we	we	PRON
ijassa-1257	60	25	get	get	VERB
ijassa-1257	60	26	i(t	i(t	NOUN
ijassa-1257	60	27	)	)	PUNCT
ijassa-1257	61	1	=	=	PUNCT
ijassa-1257	61	2	b(t)y	b(t)y	PROPN
ijassa-1257	61	3	′(t	′(t	PROPN
ijassa-1257	61	4	)	)	PUNCT
ijassa-1257	61	5	=	=	PUNCT
ijassa-1257	61	6	ρy	ρy	PROPN
ijassa-1257	61	7	(	(	PUNCT
ijassa-1257	61	8	t	t	NOUN
ijassa-1257	61	9	)	)	PUNCT
ijassa-1257	61	10	,	,	PUNCT
ijassa-1257	61	11	b(t	b(t	NOUN
ijassa-1257	61	12	)	)	PUNCT
ijassa-1257	61	13	=	=	SYM
ijassa-1257	61	14	ρ	ρ	PROPN
ijassa-1257	61	15	σ(t	σ(t	PROPN
ijassa-1257	61	16	)	)	PUNCT
ijassa-1257	61	17	.	.	PUNCT
ijassa-1257	62	1	(	(	PUNCT
ijassa-1257	62	2	1.12	1.12	NUM
ijassa-1257	62	3	)	)	PUNCT
ijassa-1257	62	4	the	the	DET
ijassa-1257	62	5	first	first	ADJ
ijassa-1257	62	6	equality	equality	NOUN
ijassa-1257	62	7	has	have	VERB
ijassa-1257	62	8	a	a	DET
ijassa-1257	62	9	deep	deep	ADJ
ijassa-1257	62	10	economic	economic	ADJ
ijassa-1257	62	11	meaning	meaning	NOUN
ijassa-1257	62	12	.	.	PUNCT
ijassa-1257	63	1	when	when	SCONJ
ijassa-1257	63	2	investing	investing	NOUN
ijassa-1257	63	3	,	,	PUNCT
ijassa-1257	63	4	an	an	DET
ijassa-1257	63	5	investor	investor	NOUN
ijassa-1257	63	6	has	have	VERB
ijassa-1257	63	7	to	to	PART
ijassa-1257	63	8	monitor	monitor	VERB
ijassa-1257	63	9	not	not	PART
ijassa-1257	63	10	only	only	ADV
ijassa-1257	63	11	the	the	DET
ijassa-1257	63	12	high	high	ADJ
ijassa-1257	63	13	capital	capital	NOUN
ijassa-1257	63	14	intensity	intensity	NOUN
ijassa-1257	63	15	of	of	ADP
ijassa-1257	63	16	the	the	DET
ijassa-1257	63	17	income	income	NOUN
ijassa-1257	63	18	growth	growth	NOUN
ijassa-1257	63	19	.	.	PUNCT
ijassa-1257	64	1	one	one	PRON
ijassa-1257	64	2	must	must	AUX
ijassa-1257	64	3	be	be	AUX
ijassa-1257	64	4	sure	sure	ADJ
ijassa-1257	64	5	that	that	SCONJ
ijassa-1257	64	6	this	this	DET
ijassa-1257	64	7	incremental	incremental	ADJ
ijassa-1257	64	8	capital	capital	NOUN
ijassa-1257	64	9	intensity	intensity	NOUN
ijassa-1257	64	10	is	be	AUX
ijassa-1257	64	11	high	high	ADJ
ijassa-1257	64	12	not	not	PART
ijassa-1257	64	13	due	due	ADP
ijassa-1257	64	14	to	to	ADP
ijassa-1257	64	15	the	the	DET
ijassa-1257	64	16	small	small	ADJ
ijassa-1257	64	17	relative	relative	ADJ
ijassa-1257	64	18	increase	increase	NOUN
ijassa-1257	64	19	in	in	ADP
ijassa-1257	64	20	income	income	NOUN
ijassa-1257	64	21	.	.	PUNCT
ijassa-1257	65	1	substituting	substitute	VERB
ijassa-1257	65	2	expression	expression	NOUN
ijassa-1257	65	3	(	(	PUNCT
ijassa-1257	65	4	1.11	1.11	NUM
ijassa-1257	65	5	)	)	PUNCT
ijassa-1257	65	6	into	into	ADP
ijassa-1257	65	7	the	the	DET
ijassa-1257	65	8	right	right	ADJ
ijassa-1257	65	9	-	-	PUNCT
ijassa-1257	65	10	hand	hand	NOUN
ijassa-1257	65	11	formula	formula	NOUN
ijassa-1257	65	12	(	(	PUNCT
ijassa-1257	65	13	1.12	1.12	NUM
ijassa-1257	65	14	)	)	PUNCT
ijassa-1257	65	15	,	,	PUNCT
ijassa-1257	65	16	we	we	PRON
ijassa-1257	65	17	obtain	obtain	VERB
ijassa-1257	65	18	b(t	b(t	NOUN
ijassa-1257	65	19	)	)	PUNCT
ijassa-1257	65	20	=	=	SYM
ijassa-1257	66	1	ρ	ρ	PROPN
ijassa-1257	66	2	αρak(t)α−1	αρak(t)α−1	NUM
ijassa-1257	67	1	+	+	CCONJ
ijassa-1257	67	2	ν	ν	NOUN
ijassa-1257	67	3	−	−	NOUN
ijassa-1257	67	4	αλ	αλ	NUM
ijassa-1257	67	5	,	,	PUNCT
ijassa-1257	67	6	λ	λ	PROPN
ijassa-1257	67	7	=	=	PRON
ijassa-1257	67	8	µ+	µ+	X
ijassa-1257	67	9	ν	ν	PROPN
ijassa-1257	67	10	.	.	PUNCT
ijassa-1257	68	1	(	(	PUNCT
ijassa-1257	68	2	1.13	1.13	NUM
ijassa-1257	68	3	)	)	PUNCT
ijassa-1257	68	4	in	in	ADP
ijassa-1257	68	5	order	order	NOUN
ijassa-1257	68	6	to	to	PART
ijassa-1257	68	7	check	check	VERB
ijassa-1257	68	8	that	that	PRON
ijassa-1257	68	9	(	(	PUNCT
ijassa-1257	68	10	1.13	1.13	NUM
ijassa-1257	68	11	)	)	PUNCT
ijassa-1257	68	12	is	be	AUX
ijassa-1257	68	13	not	not	PART
ijassa-1257	68	14	constant	constant	ADJ
ijassa-1257	68	15	and	and	CCONJ
ijassa-1257	68	16	it	it	PRON
ijassa-1257	68	17	really	really	ADV
ijassa-1257	68	18	depends	depend	VERB
ijassa-1257	68	19	on	on	ADP
ijassa-1257	68	20	time	time	NOUN
ijassa-1257	68	21	,	,	PUNCT
ijassa-1257	68	22	one	one	PRON
ijassa-1257	68	23	can	can	AUX
ijassa-1257	68	24	use	use	VERB
ijassa-1257	68	25	the	the	DET
ijassa-1257	68	26	exact	exact	ADJ
ijassa-1257	68	27	solution	solution	NOUN
ijassa-1257	68	28	of	of	ADP
ijassa-1257	68	29	the	the	DET
ijassa-1257	68	30	solow	solow	PROPN
ijassa-1257	68	31	model	model	NOUN
ijassa-1257	68	32	for	for	ADP
ijassa-1257	68	33	the	the	DET
ijassa-1257	68	34	cobb	cobb	PROPN
ijassa-1257	68	35	–	–	PUNCT
ijassa-1257	68	36	douglas	douglas	PROPN
ijassa-1257	68	37	production	production	NOUN
ijassa-1257	68	38	function	function	NOUN
ijassa-1257	68	39	.	.	PUNCT
ijassa-1257	69	1	for	for	ADP
ijassa-1257	69	2	the	the	DET
ijassa-1257	69	3	capital	capital	NOUN
ijassa-1257	69	4	-	-	PUNCT
ijassa-1257	69	5	labor	labor	NOUN
ijassa-1257	69	6	ratio	ratio	NOUN
ijassa-1257	69	7	,	,	PUNCT
ijassa-1257	69	8	this	this	PRON
ijassa-1257	69	9	yields	yield	VERB
ijassa-1257	69	10	the	the	DET
ijassa-1257	69	11	equations	equation	NOUN
ijassa-1257	69	12	k′(t	k′(t	X
ijassa-1257	69	13	)	)	PUNCT
ijassa-1257	69	14	=	=	PUNCT
ijassa-1257	70	1	ρf(k(t))−	ρf(k(t))−	NUM
ijassa-1257	70	2	λk(t	λk(t	NOUN
ijassa-1257	70	3	)	)	PUNCT
ijassa-1257	70	4	=	=	PUNCT
ijassa-1257	70	5	ρak(t)α	ρak(t)α	NOUN
ijassa-1257	70	6	−	−	NOUN
ijassa-1257	70	7	λk(t	λk(t	NOUN
ijassa-1257	70	8	)	)	PUNCT
ijassa-1257	70	9	,	,	PUNCT
ijassa-1257	70	10	λ	λ	X
ijassa-1257	70	11	=	=	SYM
ijassa-1257	70	12	const	const	PROPN
ijassa-1257	70	13	.	.	PUNCT
ijassa-1257	71	1	(	(	PUNCT
ijassa-1257	71	2	1.14	1.14	NUM
ijassa-1257	71	3	)	)	PUNCT
ijassa-1257	71	4	setting	set	VERB
ijassa-1257	71	5	the	the	DET
ijassa-1257	71	6	initial	initial	ADJ
ijassa-1257	71	7	condition	condition	NOUN
ijassa-1257	71	8	k(t0	k(t0	NOUN
ijassa-1257	71	9	)	)	PUNCT
ijassa-1257	72	1	=	=	SYM
ijassa-1257	72	2	k0	k0	PROPN
ijassa-1257	72	3	>	>	X
ijassa-1257	72	4	0	0	PROPN
ijassa-1257	72	5	,	,	PUNCT
ijassa-1257	72	6	(	(	PUNCT
ijassa-1257	72	7	1.15	1.15	NUM
ijassa-1257	72	8	)	)	PUNCT
ijassa-1257	72	9	we	we	PRON
ijassa-1257	72	10	get	get	VERB
ijassa-1257	72	11	the	the	DET
ijassa-1257	72	12	cauchy	cauchy	ADJ
ijassa-1257	72	13	problem	problem	NOUN
ijassa-1257	72	14	,	,	PUNCT
ijassa-1257	72	15	whose	whose	DET
ijassa-1257	72	16	exact	exact	ADJ
ijassa-1257	72	17	solution	solution	NOUN
ijassa-1257	72	18	is	be	AUX
ijassa-1257	72	19	given	give	VERB
ijassa-1257	72	20	by	by	ADP
ijassa-1257	72	21	the	the	DET
ijassa-1257	72	22	formula	formula	NOUN
ijassa-1257	72	23	k(t	k(t	NOUN
ijassa-1257	72	24	)	)	PUNCT
ijassa-1257	73	1	=	=	SYM
ijassa-1257	73	2	e−λ(t−t0	e−λ(t−t0	PROPN
ijassa-1257	73	3	)	)	PUNCT
ijassa-1257	73	4	(	(	PUNCT
ijassa-1257	73	5	ρa	ρa	PRON
ijassa-1257	73	6	λ	λ	PROPN
ijassa-1257	73	7	eλ(1−α)(t−t0	eλ(1−α)(t−t0	NOUN
ijassa-1257	73	8	)	)	PUNCT
ijassa-1257	73	9	−	−	PROPN
ijassa-1257	73	10	ρa	ρa	NUM
ijassa-1257	74	1	λ	λ	X
ijassa-1257	74	2	+	+	CCONJ
ijassa-1257	74	3	k1−α	k1−α	PROPN
ijassa-1257	74	4	0	0	NUM
ijassa-1257	74	5	)	)	PUNCT
ijassa-1257	74	6	1	1	NUM
ijassa-1257	74	7	1−α	1−α	NUM
ijassa-1257	74	8	.	.	PUNCT
ijassa-1257	75	1	(	(	PUNCT
ijassa-1257	75	2	1.16	1.16	NUM
ijassa-1257	75	3	)	)	PUNCT
ijassa-1257	75	4	finally	finally	ADV
ijassa-1257	75	5	,	,	PUNCT
ijassa-1257	75	6	from	from	ADP
ijassa-1257	75	7	(	(	PUNCT
ijassa-1257	75	8	1.13	1.13	NUM
ijassa-1257	75	9	)	)	PUNCT
ijassa-1257	75	10	and	and	CCONJ
ijassa-1257	75	11	(	(	PUNCT
ijassa-1257	75	12	1.16	1.16	NUM
ijassa-1257	75	13	)	)	PUNCT
ijassa-1257	75	14	we	we	PRON
ijassa-1257	75	15	have	have	VERB
ijassa-1257	75	16	b(t0	b(t0	NOUN
ijassa-1257	75	17	)	)	PUNCT
ijassa-1257	76	1	=	=	PUNCT
ijassa-1257	76	2	ρ	ρ	NUM
ijassa-1257	76	3	αρakα−1	αρakα−1	NOUN
ijassa-1257	76	4	0	0	PUNCT
ijassa-1257	76	5	+	+	CCONJ
ijassa-1257	76	6	ν	ν	NOUN
ijassa-1257	76	7	−	−	NOUN
ijassa-1257	76	8	αλ	αλ	NUM
ijassa-1257	76	9	,	,	PUNCT
ijassa-1257	76	10	b(+∞	b(+∞	PROPN
ijassa-1257	76	11	)	)	PUNCT
ijassa-1257	76	12	=	=	SYM
ijassa-1257	76	13	ρ	ρ	NUM
ijassa-1257	76	14	ν	ν	NOUN
ijassa-1257	76	15	.	.	PUNCT
ijassa-1257	77	1	(	(	PUNCT
ijassa-1257	77	2	1.17	1.17	NUM
ijassa-1257	77	3	)	)	PUNCT
ijassa-1257	77	4	the	the	DET
ijassa-1257	77	5	obtained	obtain	VERB
ijassa-1257	77	6	formula	formula	NOUN
ijassa-1257	77	7	shows	show	VERB
ijassa-1257	77	8	that	that	SCONJ
ijassa-1257	77	9	the	the	DET
ijassa-1257	77	10	capital	capital	NOUN
ijassa-1257	77	11	intensity	intensity	NOUN
ijassa-1257	77	12	of	of	ADP
ijassa-1257	77	13	the	the	DET
ijassa-1257	77	14	income	income	NOUN
ijassa-1257	77	15	growth	growth	NOUN
ijassa-1257	77	16	depends	depend	VERB
ijassa-1257	77	17	on	on	ADP
ijassa-1257	77	18	time	time	NOUN
ijassa-1257	77	19	and	and	CCONJ
ijassa-1257	77	20	in	in	ADP
ijassa-1257	77	21	the	the	DET
ijassa-1257	77	22	general	general	ADJ
ijassa-1257	77	23	case	case	NOUN
ijassa-1257	77	24	it	it	PRON
ijassa-1257	77	25	is	be	AUX
ijassa-1257	77	26	not	not	PART
ijassa-1257	77	27	constant	constant	ADJ
ijassa-1257	77	28	.	.	PUNCT
ijassa-1257	78	1	copyright	copyright	NOUN
ijassa-1257	78	2	©	©	ADP
ijassa-1257	78	3	2022	2022	NUM
ijassa-1257	78	4	assa	assa	NOUN
ijassa-1257	78	5	.	.	PUNCT
ijassa-1257	79	1	adv	adv	PROPN
ijassa-1257	79	2	syst	syst	PROPN
ijassa-1257	79	3	sci	sci	PROPN
ijassa-1257	79	4	appl	appl	PROPN
ijassa-1257	79	5	(	(	PUNCT
ijassa-1257	79	6	2022	2022	NUM
ijassa-1257	79	7	)	)	PUNCT
ijassa-1257	79	8	112	112	NUM
ijassa-1257	79	9	a.p	a.p	PROPN
ijassa-1257	79	10	.	.	PROPN
ijassa-1257	79	11	chernyaev	chernyaev	PROPN
ijassa-1257	79	12	1.6	1.6	NUM
ijassa-1257	79	13	.	.	PUNCT
ijassa-1257	80	1	the	the	DET
ijassa-1257	80	2	balance	balance	NOUN
ijassa-1257	80	3	equation	equation	NOUN
ijassa-1257	80	4	for	for	ADP
ijassa-1257	80	5	accumulated	accumulate	VERB
ijassa-1257	80	6	household	household	NOUN
ijassa-1257	80	7	savings	saving	NOUN
ijassa-1257	80	8	now	now	ADV
ijassa-1257	80	9	consider	consider	VERB
ijassa-1257	80	10	the	the	DET
ijassa-1257	80	11	household	household	NOUN
ijassa-1257	80	12	micromodel	micromodel	NOUN
ijassa-1257	80	13	as	as	ADP
ijassa-1257	80	14	an	an	DET
ijassa-1257	80	15	economic	economic	ADJ
ijassa-1257	80	16	model	model	NOUN
ijassa-1257	80	17	governed	govern	VERB
ijassa-1257	80	18	by	by	ADP
ijassa-1257	80	19	equation	equation	NOUN
ijassa-1257	80	20	(	(	PUNCT
ijassa-1257	80	21	1.1	1.1	NUM
ijassa-1257	80	22	)	)	PUNCT
ijassa-1257	80	23	;	;	PUNCT
ijassa-1257	80	24	see	see	VERB
ijassa-1257	80	25	[	[	X
ijassa-1257	80	26	?	?	PUNCT
ijassa-1257	80	27	,	,	PUNCT
ijassa-1257	80	28	14	14	NUM
ijassa-1257	80	29	]	]	PUNCT
ijassa-1257	80	30	.	.	PUNCT
ijassa-1257	81	1	then	then	ADV
ijassa-1257	81	2	we	we	PRON
ijassa-1257	81	3	have	have	VERB
ijassa-1257	81	4	the	the	DET
ijassa-1257	81	5	equation	equation	NOUN
ijassa-1257	81	6	x′(t	x′(t	NOUN
ijassa-1257	81	7	)	)	PUNCT
ijassa-1257	81	8	=	=	SYM
ijassa-1257	81	9	p(t)x(t	p(t)x(t	NOUN
ijassa-1257	81	10	)	)	PUNCT
ijassa-1257	82	1	+	+	NOUN
ijassa-1257	83	1	p	p	X
ijassa-1257	83	2	(	(	PUNCT
ijassa-1257	83	3	t)−	t)−	PROPN
ijassa-1257	83	4	c(t	c(t	PROPN
ijassa-1257	83	5	)	)	PUNCT
ijassa-1257	83	6	,	,	PUNCT
ijassa-1257	83	7	(	(	PUNCT
ijassa-1257	83	8	1.18	1.18	NUM
ijassa-1257	83	9	)	)	PUNCT
ijassa-1257	83	10	where	where	SCONJ
ijassa-1257	83	11	x(t	x(t	PROPN
ijassa-1257	83	12	)	)	PUNCT
ijassa-1257	83	13	is	be	AUX
ijassa-1257	83	14	the	the	DET
ijassa-1257	83	15	accumulated	accumulate	VERB
ijassa-1257	83	16	savings	saving	NOUN
ijassa-1257	83	17	,	,	PUNCT
ijassa-1257	83	18	p(t	p(t	NOUN
ijassa-1257	83	19	)	)	PUNCT
ijassa-1257	83	20	is	be	AUX
ijassa-1257	83	21	the	the	DET
ijassa-1257	83	22	bank	bank	NOUN
ijassa-1257	83	23	interest	interest	NOUN
ijassa-1257	83	24	,	,	PUNCT
ijassa-1257	83	25	p	p	X
ijassa-1257	83	26	(	(	PUNCT
ijassa-1257	83	27	t	t	NOUN
ijassa-1257	83	28	)	)	PUNCT
ijassa-1257	83	29	is	be	AUX
ijassa-1257	83	30	determined	determine	VERB
ijassa-1257	83	31	by	by	ADP
ijassa-1257	83	32	salaries	salary	NOUN
ijassa-1257	83	33	,	,	PUNCT
ijassa-1257	83	34	pensions	pension	NOUN
ijassa-1257	83	35	and	and	CCONJ
ijassa-1257	83	36	extra	extra	ADJ
ijassa-1257	83	37	earnings	earning	NOUN
ijassa-1257	83	38	.	.	PUNCT
ijassa-1257	84	1	as	as	ADP
ijassa-1257	84	2	before	before	ADV
ijassa-1257	84	3	,	,	PUNCT
ijassa-1257	84	4	c(t	c(t	PROPN
ijassa-1257	84	5	)	)	PUNCT
ijassa-1257	84	6	means	mean	VERB
ijassa-1257	84	7	the	the	DET
ijassa-1257	84	8	consumption	consumption	NOUN
ijassa-1257	84	9	.	.	PUNCT
ijassa-1257	85	1	if	if	SCONJ
ijassa-1257	85	2	we	we	PRON
ijassa-1257	85	3	assume	assume	VERB
ijassa-1257	85	4	that	that	SCONJ
ijassa-1257	85	5	y	y	PROPN
ijassa-1257	85	6	(	(	PUNCT
ijassa-1257	85	7	t	t	PROPN
ijassa-1257	85	8	)	)	PUNCT
ijassa-1257	85	9	=	=	SYM
ijassa-1257	85	10	p(t)x(t	p(t)x(t	NOUN
ijassa-1257	85	11	)	)	PUNCT
ijassa-1257	85	12	+	+	NOUN
ijassa-1257	85	13	p	p	X
ijassa-1257	85	14	(	(	PUNCT
ijassa-1257	85	15	t	t	PROPN
ijassa-1257	85	16	)	)	PUNCT
ijassa-1257	85	17	is	be	AUX
ijassa-1257	85	18	the	the	DET
ijassa-1257	85	19	income	income	NOUN
ijassa-1257	85	20	and	and	CCONJ
ijassa-1257	85	21	i(t	i(t	NOUN
ijassa-1257	85	22	)	)	PUNCT
ijassa-1257	85	23	=	=	PUNCT
ijassa-1257	86	1	x′(t	x′(t	PROPN
ijassa-1257	86	2	)	)	PUNCT
ijassa-1257	86	3	is	be	AUX
ijassa-1257	86	4	the	the	DET
ijassa-1257	86	5	investments	investment	NOUN
ijassa-1257	86	6	,	,	PUNCT
ijassa-1257	86	7	then	then	ADV
ijassa-1257	86	8	we	we	PRON
ijassa-1257	86	9	come	come	VERB
ijassa-1257	86	10	to	to	ADP
ijassa-1257	86	11	the	the	DET
ijassa-1257	86	12	basic	basic	ADJ
ijassa-1257	86	13	economic	economic	ADJ
ijassa-1257	86	14	identity	identity	NOUN
ijassa-1257	86	15	(	(	PUNCT
ijassa-1257	86	16	1.1	1.1	NUM
ijassa-1257	86	17	)	)	PUNCT
ijassa-1257	86	18	.	.	PUNCT
ijassa-1257	87	1	similarly	similarly	ADV
ijassa-1257	87	2	to	to	ADP
ijassa-1257	87	3	[	[	X
ijassa-1257	87	4	?	?	NOUN
ijassa-1257	87	5	,	,	PUNCT
ijassa-1257	87	6	1	1	NUM
ijassa-1257	87	7	,	,	PUNCT
ijassa-1257	87	8	14	14	NUM
ijassa-1257	87	9	]	]	PUNCT
ijassa-1257	87	10	,	,	PUNCT
ijassa-1257	87	11	we	we	PRON
ijassa-1257	87	12	maximize	maximize	VERB
ijassa-1257	87	13	the	the	DET
ijassa-1257	87	14	integral	integral	ADJ
ijassa-1257	87	15	discounted	discount	VERB
ijassa-1257	87	16	utility	utility	NOUN
ijassa-1257	87	17	of	of	ADP
ijassa-1257	87	18	consumption	consumption	NOUN
ijassa-1257	87	19	j	j	PROPN
ijassa-1257	87	20	=	=	SYM
ijassa-1257	87	21	∫	∫	PROPN
ijassa-1257	87	22	t1	t1	PROPN
ijassa-1257	87	23	t0	t0	PROPN
ijassa-1257	88	1	u(c(t))e−δt	u(c(t))e−δt	PROPN
ijassa-1257	89	1	dt	dt	X
ijassa-1257	89	2	,	,	PUNCT
ijassa-1257	89	3	(	(	PUNCT
ijassa-1257	89	4	1.19	1.19	NUM
ijassa-1257	89	5	)	)	PUNCT
ijassa-1257	89	6	where	where	SCONJ
ijassa-1257	89	7	u	u	NOUN
ijassa-1257	89	8	is	be	AUX
ijassa-1257	89	9	the	the	DET
ijassa-1257	89	10	utility	utility	NOUN
ijassa-1257	89	11	function	function	NOUN
ijassa-1257	89	12	,	,	PUNCT
ijassa-1257	89	13	δ	δ	PROPN
ijassa-1257	89	14	is	be	AUX
ijassa-1257	89	15	the	the	DET
ijassa-1257	89	16	coefficient	coefficient	NOUN
ijassa-1257	89	17	of	of	ADP
ijassa-1257	89	18	discounting	discount	VERB
ijassa-1257	89	19	the	the	DET
ijassa-1257	89	20	future	future	ADJ
ijassa-1257	89	21	utility	utility	NOUN
ijassa-1257	89	22	.	.	PUNCT
ijassa-1257	90	1	1.7	1.7	NUM
ijassa-1257	90	2	.	.	PUNCT
ijassa-1257	91	1	the	the	DET
ijassa-1257	91	2	utility	utility	NOUN
ijassa-1257	91	3	function	function	NOUN
ijassa-1257	91	4	and	and	CCONJ
ijassa-1257	91	5	the	the	DET
ijassa-1257	91	6	risk	risk	NOUN
ijassa-1257	91	7	avoidance	avoidance	NOUN
ijassa-1257	91	8	according	accord	VERB
ijassa-1257	91	9	to	to	ADP
ijassa-1257	91	10	the	the	DET
ijassa-1257	91	11	arrow	arrow	NOUN
ijassa-1257	91	12	–	–	PUNCT
ijassa-1257	91	13	pratt	pratt	PROPN
ijassa-1257	91	14	theory	theory	NOUN
ijassa-1257	91	15	[	[	X
ijassa-1257	91	16	?	?	SYM
ijassa-1257	91	17	,	,	PUNCT
ijassa-1257	91	18	1	1	NUM
ijassa-1257	91	19	,	,	PUNCT
ijassa-1257	91	20	14	14	NUM
ijassa-1257	91	21	]	]	PUNCT
ijassa-1257	91	22	,	,	PUNCT
ijassa-1257	91	23	the	the	DET
ijassa-1257	91	24	utility	utility	NOUN
ijassa-1257	91	25	of	of	ADP
ijassa-1257	91	26	consumption	consumption	NOUN
ijassa-1257	91	27	is	be	AUX
ijassa-1257	91	28	estimated	estimate	VERB
ijassa-1257	91	29	by	by	ADP
ijassa-1257	91	30	the	the	DET
ijassa-1257	91	31	function	function	NOUN
ijassa-1257	91	32	u(c	u(c	PROPN
ijassa-1257	91	33	)	)	PUNCT
ijassa-1257	91	34	,	,	PUNCT
ijassa-1257	91	35	which	which	PRON
ijassa-1257	91	36	describes	describe	VERB
ijassa-1257	91	37	the	the	DET
ijassa-1257	91	38	constant	constant	ADJ
ijassa-1257	91	39	aversion	aversion	NOUN
ijassa-1257	91	40	to	to	PART
ijassa-1257	91	41	risk	risk	VERB
ijassa-1257	91	42	:	:	PUNCT
ijassa-1257	91	43	−	−	PUNCT
ijassa-1257	91	44	u′′(c)c	u′′(c)c	ADP
ijassa-1257	91	45	u′(c	u′(c	ADV
ijassa-1257	91	46	)	)	PUNCT
ijassa-1257	91	47	=	=	SYM
ijassa-1257	91	48	a	a	DET
ijassa-1257	91	49	≥	≥	NOUN
ijassa-1257	91	50	0	0	NUM
ijassa-1257	91	51	.	.	PUNCT
ijassa-1257	92	1	(	(	PUNCT
ijassa-1257	92	2	1.20	1.20	NUM
ijassa-1257	92	3	)	)	PUNCT
ijassa-1257	92	4	the	the	DET
ijassa-1257	92	5	relative	relative	ADJ
ijassa-1257	92	6	measure	measure	NOUN
ijassa-1257	92	7	of	of	ADP
ijassa-1257	92	8	the	the	DET
ijassa-1257	92	9	arrow	arrow	NOUN
ijassa-1257	92	10	–	–	PUNCT
ijassa-1257	92	11	pratt	pratt	NOUN
ijassa-1257	92	12	risk	risk	NOUN
ijassa-1257	92	13	aversion	aversion	NOUN
ijassa-1257	92	14	is	be	AUX
ijassa-1257	92	15	the	the	DET
ijassa-1257	92	16	consumption	consumption	NOUN
ijassa-1257	92	17	elasticity	elasticity	NOUN
ijassa-1257	92	18	of	of	ADP
ijassa-1257	92	19	the	the	DET
ijassa-1257	92	20	marginal	marginal	ADJ
ijassa-1257	92	21	utility	utility	NOUN
ijassa-1257	92	22	taken	take	VERB
ijassa-1257	92	23	with	with	ADP
ijassa-1257	92	24	the	the	DET
ijassa-1257	92	25	opposite	opposite	ADJ
ijassa-1257	92	26	sign	sign	NOUN
ijassa-1257	92	27	.	.	PUNCT
ijassa-1257	93	1	let	let	VERB
ijassa-1257	93	2	us	we	PRON
ijassa-1257	93	3	denote	denote	VERB
ijassa-1257	93	4	by	by	ADP
ijassa-1257	93	5	g(c	g(c	NOUN
ijassa-1257	93	6	)	)	PUNCT
ijassa-1257	93	7	=	=	PUNCT
ijassa-1257	94	1	u′(c	u′(c	NOUN
ijassa-1257	94	2	)	)	PUNCT
ijassa-1257	94	3	the	the	DET
ijassa-1257	94	4	marginal	marginal	ADJ
ijassa-1257	94	5	utility	utility	NOUN
ijassa-1257	94	6	of	of	ADP
ijassa-1257	94	7	consumption	consumption	NOUN
ijassa-1257	94	8	,	,	PUNCT
ijassa-1257	94	9	and	and	CCONJ
ijassa-1257	94	10	by	by	ADP
ijassa-1257	94	11	ec(g	ec(g	NOUN
ijassa-1257	94	12	)	)	PUNCT
ijassa-1257	94	13	=	=	SYM
ijassa-1257	94	14	g′(c	g′(c	NOUN
ijassa-1257	94	15	)	)	PUNCT
ijassa-1257	94	16	g(c)/c	g(c)/c	VERB
ijassa-1257	94	17	the	the	DET
ijassa-1257	94	18	elasticity	elasticity	NOUN
ijassa-1257	94	19	of	of	ADP
ijassa-1257	94	20	variation	variation	NOUN
ijassa-1257	94	21	of	of	ADP
ijassa-1257	94	22	the	the	DET
ijassa-1257	94	23	variable	variable	ADJ
ijassa-1257	94	24	g	g	NOUN
ijassa-1257	94	25	with	with	ADP
ijassa-1257	94	26	respect	respect	NOUN
ijassa-1257	94	27	to	to	ADP
ijassa-1257	94	28	the	the	DET
ijassa-1257	94	29	variable	variable	ADJ
ijassa-1257	94	30	c.	c.	NOUN
ijassa-1257	94	31	then	then	ADV
ijassa-1257	94	32	,	,	PUNCT
ijassa-1257	94	33	similarly	similarly	ADV
ijassa-1257	94	34	to	to	ADP
ijassa-1257	94	35	[	[	X
ijassa-1257	94	36	?	?	NOUN
ijassa-1257	94	37	,	,	PUNCT
ijassa-1257	94	38	1	1	NUM
ijassa-1257	94	39	]	]	PUNCT
ijassa-1257	94	40	,	,	PUNCT
ijassa-1257	94	41	one	one	PRON
ijassa-1257	94	42	can	can	AUX
ijassa-1257	94	43	consider	consider	VERB
ijassa-1257	94	44	(	(	PUNCT
ijassa-1257	94	45	1.20	1.20	NUM
ijassa-1257	94	46	)	)	PUNCT
ijassa-1257	94	47	as	as	ADP
ijassa-1257	94	48	a	a	DET
ijassa-1257	94	49	differential	differential	ADJ
ijassa-1257	94	50	equation	equation	NOUN
ijassa-1257	94	51	for	for	ADP
ijassa-1257	94	52	u(t	u(t	NOUN
ijassa-1257	94	53	)	)	PUNCT
ijassa-1257	94	54	.	.	PUNCT
ijassa-1257	95	1	this	this	DET
ijassa-1257	95	2	yields	yield	NOUN
ijassa-1257	95	3	u′(c	u′(c	ADV
ijassa-1257	95	4	)	)	PUNCT
ijassa-1257	95	5	=	=	SYM
ijassa-1257	95	6	g(c	g(c	NOUN
ijassa-1257	95	7	)	)	PUNCT
ijassa-1257	95	8	=	=	PUNCT
ijassa-1257	96	1	γc−a	γc−a	NOUN
ijassa-1257	96	2	,	,	PUNCT
ijassa-1257	96	3	where	where	SCONJ
ijassa-1257	96	4	γ	γ	X
ijassa-1257	96	5	>	>	X
ijassa-1257	96	6	0	0	NUM
ijassa-1257	96	7	is	be	AUX
ijassa-1257	96	8	the	the	DET
ijassa-1257	96	9	constant	constant	ADJ
ijassa-1257	96	10	of	of	ADP
ijassa-1257	96	11	integration	integration	NOUN
ijassa-1257	96	12	.	.	PUNCT
ijassa-1257	97	1	finally	finally	ADV
ijassa-1257	97	2	,	,	PUNCT
ijassa-1257	97	3	we	we	PRON
ijassa-1257	97	4	have	have	VERB
ijassa-1257	97	5	u(c	u(c	PROPN
ijassa-1257	97	6	)	)	PUNCT
ijassa-1257	97	7	=	=	PUNCT
ijassa-1257	98	1			PUNCT
ijassa-1257	98	2	γc1−a	γc1−a	X
ijassa-1257	98	3	1−	1−	NUM
ijassa-1257	98	4	a	a	DET
ijassa-1257	98	5	+	+	NUM
ijassa-1257	98	6	χ	χ	ADJ
ijassa-1257	98	7	,	,	PUNCT
ijassa-1257	98	8	a	a	DET
ijassa-1257	98	9	6=	6=	NUM
ijassa-1257	98	10	1	1	NUM
ijassa-1257	98	11	,	,	PUNCT
ijassa-1257	98	12	γ	γ	X
ijassa-1257	98	13	lnc	lnc	PROPN
ijassa-1257	98	14	+	+	CCONJ
ijassa-1257	98	15	χ	χ	X
ijassa-1257	98	16	,	,	PUNCT
ijassa-1257	98	17	a	a	DET
ijassa-1257	98	18	=	=	SYM
ijassa-1257	98	19	1	1	NUM
ijassa-1257	98	20	,	,	PUNCT
ijassa-1257	98	21	where	where	SCONJ
ijassa-1257	98	22	χ	χ	NOUN
ijassa-1257	98	23	is	be	AUX
ijassa-1257	98	24	an	an	DET
ijassa-1257	98	25	arbitrary	arbitrary	ADJ
ijassa-1257	98	26	constant	constant	ADJ
ijassa-1257	98	27	.	.	PUNCT
ijassa-1257	99	1	2	2	X
ijassa-1257	99	2	.	.	X
ijassa-1257	99	3	the	the	DET
ijassa-1257	99	4	optimal	optimal	ADJ
ijassa-1257	99	5	control	control	NOUN
ijassa-1257	99	6	approach	approach	NOUN
ijassa-1257	99	7	2.1	2.1	NUM
ijassa-1257	99	8	.	.	PUNCT
ijassa-1257	100	1	optimal	optimal	ADJ
ijassa-1257	100	2	control	control	NOUN
ijassa-1257	100	3	in	in	ADP
ijassa-1257	100	4	the	the	DET
ijassa-1257	100	5	modified	modify	VERB
ijassa-1257	100	6	harrod	harrod	NOUN
ijassa-1257	100	7	–	–	PUNCT
ijassa-1257	100	8	domar	domar	NOUN
ijassa-1257	100	9	model	model	NOUN
ijassa-1257	100	10	according	accord	VERB
ijassa-1257	100	11	to	to	ADP
ijassa-1257	100	12	[	[	X
ijassa-1257	100	13	17	17	NUM
ijassa-1257	100	14	]	]	PUNCT
ijassa-1257	100	15	,	,	PUNCT
ijassa-1257	100	16	households	household	NOUN
ijassa-1257	100	17	are	be	AUX
ijassa-1257	100	18	the	the	DET
ijassa-1257	100	19	best	good	ADJ
ijassa-1257	100	20	savers	saver	NOUN
ijassa-1257	100	21	.	.	PUNCT
ijassa-1257	101	1	this	this	PRON
ijassa-1257	101	2	motivates	motivate	VERB
ijassa-1257	101	3	the	the	DET
ijassa-1257	101	4	maximization	maximization	NOUN
ijassa-1257	101	5	of	of	ADP
ijassa-1257	101	6	the	the	DET
ijassa-1257	101	7	functional	functional	ADJ
ijassa-1257	101	8	(	(	PUNCT
ijassa-1257	101	9	1.19	1.19	NUM
ijassa-1257	101	10	)	)	PUNCT
ijassa-1257	101	11	in	in	ADP
ijassa-1257	101	12	the	the	DET
ijassa-1257	101	13	framework	framework	NOUN
ijassa-1257	101	14	of	of	ADP
ijassa-1257	101	15	the	the	DET
ijassa-1257	101	16	modified	modify	VERB
ijassa-1257	101	17	harrod	harrod	NOUN
ijassa-1257	101	18	–	–	PUNCT
ijassa-1257	101	19	domar	domar	NOUN
ijassa-1257	101	20	model	model	NOUN
ijassa-1257	101	21	,	,	PUNCT
ijassa-1257	101	22	which	which	PRON
ijassa-1257	101	23	is	be	AUX
ijassa-1257	101	24	governed	govern	VERB
ijassa-1257	101	25	by	by	ADP
ijassa-1257	101	26	the	the	DET
ijassa-1257	101	27	equation	equation	NOUN
ijassa-1257	101	28	y	y	PROPN
ijassa-1257	101	29	(	(	PUNCT
ijassa-1257	101	30	t	t	PROPN
ijassa-1257	101	31	)	)	PUNCT
ijassa-1257	101	32	=	=	SYM
ijassa-1257	101	33	c(t	c(t	PROPN
ijassa-1257	101	34	)	)	PUNCT
ijassa-1257	102	1	+	+	ADJ
ijassa-1257	102	2	by	by	ADP
ijassa-1257	102	3	′(t	′(t	NOUN
ijassa-1257	102	4	)	)	PUNCT
ijassa-1257	102	5	.	.	PUNCT
ijassa-1257	103	1	consider	consider	VERB
ijassa-1257	103	2	the	the	DET
ijassa-1257	103	3	maximization	maximization	NOUN
ijassa-1257	103	4	of	of	ADP
ijassa-1257	103	5	the	the	DET
ijassa-1257	103	6	functional	functional	ADJ
ijassa-1257	103	7	(	(	PUNCT
ijassa-1257	103	8	1.19	1.19	NUM
ijassa-1257	103	9	)	)	PUNCT
ijassa-1257	103	10	,	,	PUNCT
ijassa-1257	103	11	where	where	SCONJ
ijassa-1257	103	12	the	the	DET
ijassa-1257	103	13	utility	utility	NOUN
ijassa-1257	103	14	function	function	NOUN
ijassa-1257	103	15	satisfies	satisfy	VERB
ijassa-1257	103	16	the	the	DET
ijassa-1257	103	17	following	follow	VERB
ijassa-1257	103	18	conditions	condition	NOUN
ijassa-1257	103	19	:	:	PUNCT
ijassa-1257	103	20	−	−	PUNCT
ijassa-1257	103	21	u′′(c)c	u′′(c)c	ADP
ijassa-1257	103	22	u′(c	u′(c	ADV
ijassa-1257	103	23	)	)	PUNCT
ijassa-1257	103	24	=	=	SYM
ijassa-1257	103	25	a	a	DET
ijassa-1257	103	26	≥	≥	NOUN
ijassa-1257	103	27	0	0	NUM
ijassa-1257	103	28	,	,	PUNCT
ijassa-1257	103	29	g(c	g(c	NOUN
ijassa-1257	103	30	)	)	PUNCT
ijassa-1257	103	31	=	=	PUNCT
ijassa-1257	103	32	u′(c	u′(c	NOUN
ijassa-1257	103	33	)	)	PUNCT
ijassa-1257	103	34	,	,	PUNCT
ijassa-1257	103	35	ec(g	ec(g	NOUN
ijassa-1257	103	36	)	)	PUNCT
ijassa-1257	103	37	=	=	SYM
ijassa-1257	103	38	−a	−a	NOUN
ijassa-1257	103	39	,	,	PUNCT
ijassa-1257	103	40	(	(	PUNCT
ijassa-1257	103	41	2.21	2.21	NUM
ijassa-1257	103	42	)	)	PUNCT
ijassa-1257	103	43	copyright	copyright	NOUN
ijassa-1257	103	44	©	©	PROPN
ijassa-1257	103	45	2022	2022	NUM
ijassa-1257	103	46	assa	assa	NOUN
ijassa-1257	103	47	.	.	PUNCT
ijassa-1257	104	1	adv	adv	PROPN
ijassa-1257	104	2	syst	syst	PROPN
ijassa-1257	104	3	sci	sci	PROPN
ijassa-1257	104	4	appl	appl	PROPN
ijassa-1257	104	5	(	(	PUNCT
ijassa-1257	104	6	2022	2022	NUM
ijassa-1257	104	7	)	)	PUNCT
ijassa-1257	104	8	the	the	DET
ijassa-1257	104	9	optimal	optimal	ADJ
ijassa-1257	104	10	control	control	NOUN
ijassa-1257	104	11	approach	approach	NOUN
ijassa-1257	104	12	in	in	ADP
ijassa-1257	104	13	problems	problem	NOUN
ijassa-1257	104	14	of	of	ADP
ijassa-1257	104	15	the	the	DET
ijassa-1257	104	16	income	income	NOUN
ijassa-1257	104	17	distribution	distribution	NOUN
ijassa-1257	104	18	113	113	NUM
ijassa-1257	104	19	under	under	ADP
ijassa-1257	104	20	the	the	DET
ijassa-1257	104	21	following	follow	VERB
ijassa-1257	104	22	constrains	constrain	NOUN
ijassa-1257	104	23	:	:	PUNCT
ijassa-1257	104	24	y	y	PROPN
ijassa-1257	104	25	(	(	PUNCT
ijassa-1257	104	26	t	t	PROPN
ijassa-1257	104	27	)	)	PUNCT
ijassa-1257	104	28	=	=	SYM
ijassa-1257	104	29	c(t	c(t	PROPN
ijassa-1257	104	30	)	)	PUNCT
ijassa-1257	104	31	+	+	ADJ
ijassa-1257	104	32	by	by	ADP
ijassa-1257	104	33	′(t	′(t	NOUN
ijassa-1257	104	34	)	)	PUNCT
ijassa-1257	104	35	,	,	PUNCT
ijassa-1257	104	36	y	y	PROPN
ijassa-1257	104	37	(	(	PUNCT
ijassa-1257	104	38	t0	t0	PROPN
ijassa-1257	104	39	)	)	PUNCT
ijassa-1257	104	40	=	=	PUNCT
ijassa-1257	105	1	y0	y0	VERB
ijassa-1257	105	2	>	>	X
ijassa-1257	105	3	0	0	NUM
ijassa-1257	105	4	,	,	PUNCT
ijassa-1257	105	5	y	y	PROPN
ijassa-1257	105	6	(	(	PUNCT
ijassa-1257	105	7	t1	t1	NOUN
ijassa-1257	105	8	)	)	PUNCT
ijassa-1257	105	9	=	=	PUNCT
ijassa-1257	106	1	y1	y1	NOUN
ijassa-1257	106	2	>	>	X
ijassa-1257	106	3	0	0	NUM
ijassa-1257	106	4	.	.	PUNCT
ijassa-1257	107	1	(	(	PUNCT
ijassa-1257	107	2	2.22	2.22	NUM
ijassa-1257	107	3	)	)	PUNCT
ijassa-1257	107	4	this	this	DET
ijassa-1257	107	5	maximization	maximization	NOUN
ijassa-1257	107	6	problem	problem	NOUN
ijassa-1257	107	7	can	can	AUX
ijassa-1257	107	8	be	be	AUX
ijassa-1257	107	9	solved	solve	VERB
ijassa-1257	107	10	using	use	VERB
ijassa-1257	107	11	the	the	DET
ijassa-1257	107	12	standard	standard	ADJ
ijassa-1257	107	13	variational	variational	ADJ
ijassa-1257	107	14	method	method	NOUN
ijassa-1257	107	15	[	[	X
ijassa-1257	107	16	?	?	X
ijassa-1257	107	17	,	,	PUNCT
ijassa-1257	107	18	1	1	NUM
ijassa-1257	107	19	]	]	PUNCT
ijassa-1257	107	20	.	.	PUNCT
ijassa-1257	108	1	a	a	DET
ijassa-1257	108	2	necessary	necessary	ADJ
ijassa-1257	108	3	condition	condition	NOUN
ijassa-1257	108	4	of	of	ADP
ijassa-1257	108	5	optimality	optimality	NOUN
ijassa-1257	108	6	is	be	AUX
ijassa-1257	108	7	the	the	DET
ijassa-1257	108	8	euler	euler	PROPN
ijassa-1257	108	9	–	–	PUNCT
ijassa-1257	108	10	lagrange	lagrange	NOUN
ijassa-1257	108	11	equation	equation	NOUN
ijassa-1257	108	12	,	,	PUNCT
ijassa-1257	108	13	which	which	PRON
ijassa-1257	108	14	reads	read	VERB
ijassa-1257	108	15	d	d	X
ijassa-1257	108	16	dt	dt	X
ijassa-1257	108	17	(	(	PUNCT
ijassa-1257	108	18	g(c(t))b(t)e−δt	g(c(t))b(t)e−δt	PROPN
ijassa-1257	108	19	)	)	PUNCT
ijassa-1257	109	1	+	+	CCONJ
ijassa-1257	109	2	g(c(t))e−δt	g(c(t))e−δt	NOUN
ijassa-1257	109	3	=	=	SYM
ijassa-1257	109	4	0	0	PROPN
ijassa-1257	109	5	.	.	PUNCT
ijassa-1257	110	1	(	(	PUNCT
ijassa-1257	110	2	2.23	2.23	NUM
ijassa-1257	110	3	)	)	PUNCT
ijassa-1257	110	4	integrating	integrating	NOUN
ijassa-1257	110	5	(	(	PUNCT
ijassa-1257	110	6	2.23	2.23	NUM
ijassa-1257	110	7	)	)	PUNCT
ijassa-1257	110	8	,	,	PUNCT
ijassa-1257	110	9	we	we	PRON
ijassa-1257	110	10	have	have	VERB
ijassa-1257	110	11	c(t	c(t	NUM
ijassa-1257	110	12	)	)	PUNCT
ijassa-1257	110	13	=	=	SYM
ijassa-1257	111	1	g−1	g−1	PROPN
ijassa-1257	111	2	(	(	PUNCT
ijassa-1257	111	3	d	d	NOUN
ijassa-1257	111	4	b(t	b(t	NOUN
ijassa-1257	111	5	)	)	PUNCT
ijassa-1257	111	6	exp	exp	NOUN
ijassa-1257	111	7	{	{	PUNCT
ijassa-1257	111	8	δt−	δt−	NUM
ijassa-1257	111	9	∫	∫	PROPN
ijassa-1257	111	10	t	t	PROPN
ijassa-1257	111	11	t0	t0	PROPN
ijassa-1257	111	12	dτ	dτ	PROPN
ijassa-1257	111	13	b(τ	b(τ	PROPN
ijassa-1257	111	14	)	)	PUNCT
ijassa-1257	111	15	}	}	PUNCT
ijassa-1257	111	16	)	)	PUNCT
ijassa-1257	111	17	,	,	PUNCT
ijassa-1257	111	18	(	(	PUNCT
ijassa-1257	111	19	2.24	2.24	NUM
ijassa-1257	111	20	)	)	PUNCT
ijassa-1257	111	21	where	where	SCONJ
ijassa-1257	111	22	d	d	NOUN
ijassa-1257	111	23	is	be	AUX
ijassa-1257	111	24	the	the	DET
ijassa-1257	111	25	constant	constant	ADJ
ijassa-1257	111	26	of	of	ADP
ijassa-1257	111	27	integration	integration	NOUN
ijassa-1257	111	28	.	.	PUNCT
ijassa-1257	112	1	finally	finally	ADV
ijassa-1257	112	2	,	,	PUNCT
ijassa-1257	112	3	condition	condition	NOUN
ijassa-1257	112	4	(	(	PUNCT
ijassa-1257	112	5	2.21	2.21	NUM
ijassa-1257	112	6	)	)	PUNCT
ijassa-1257	112	7	gives	give	VERB
ijassa-1257	112	8	a	a	DET
ijassa-1257	112	9	sufficient	sufficient	ADJ
ijassa-1257	112	10	condition	condition	NOUN
ijassa-1257	112	11	of	of	ADP
ijassa-1257	112	12	optimality	optimality	NOUN
ijassa-1257	112	13	.	.	PUNCT
ijassa-1257	113	1	theorem	theorem	VERB
ijassa-1257	113	2	2.1	2.1	NUM
ijassa-1257	113	3	:	:	PUNCT
ijassa-1257	113	4	under	under	ADP
ijassa-1257	113	5	the	the	DET
ijassa-1257	113	6	above	above	ADJ
ijassa-1257	113	7	conditions	condition	NOUN
ijassa-1257	113	8	,	,	PUNCT
ijassa-1257	113	9	the	the	DET
ijassa-1257	113	10	total	total	ADJ
ijassa-1257	113	11	consumption	consumption	NOUN
ijassa-1257	113	12	c(t	c(t	PROPN
ijassa-1257	113	13	)	)	PUNCT
ijassa-1257	113	14	is	be	AUX
ijassa-1257	113	15	given	give	VERB
ijassa-1257	113	16	by	by	ADP
ijassa-1257	113	17	the	the	DET
ijassa-1257	113	18	formula	formula	NOUN
ijassa-1257	113	19	c(t	c(t	PROPN
ijassa-1257	113	20	)	)	PUNCT
ijassa-1257	113	21	=	=	PUNCT
ijassa-1257	113	22	(	(	PUNCT
ijassa-1257	113	23	y0	y0	NOUN
ijassa-1257	113	24	−	−	NOUN
ijassa-1257	113	25	y1	y1	NOUN
ijassa-1257	113	26	exp{−β(t1	exp{−β(t1	NOUN
ijassa-1257	113	27	)	)	PUNCT
ijassa-1257	113	28	}	}	PUNCT
ijassa-1257	113	29	)	)	PUNCT
ijassa-1257	113	30	b(t	b(t	NOUN
ijassa-1257	113	31	)	)	PUNCT
ijassa-1257	113	32	1	1	NUM
ijassa-1257	113	33	a	a	DET
ijassa-1257	113	34	exp	exp	NOUN
ijassa-1257	113	35	{	{	PUNCT
ijassa-1257	113	36	1	1	NUM
ijassa-1257	113	37	a	a	DET
ijassa-1257	113	38	β(t)−	β(t)−	PROPN
ijassa-1257	113	39	δ	δ	PROPN
ijassa-1257	113	40	a	a	DET
ijassa-1257	113	41	t}∫	t}∫	PROPN
ijassa-1257	113	42	t1	t1	NOUN
ijassa-1257	113	43	t0	t0	PROPN
ijassa-1257	113	44	b(τ	b(τ	PROPN
ijassa-1257	113	45	)	)	PUNCT
ijassa-1257	113	46	1	1	NUM
ijassa-1257	113	47	a	a	DET
ijassa-1257	113	48	−1	−1	NOUN
ijassa-1257	113	49	exp	exp	NOUN
ijassa-1257	113	50	{	{	PUNCT
ijassa-1257	113	51	(	(	PUNCT
ijassa-1257	113	52	1	1	NUM
ijassa-1257	113	53	a	a	DET
ijassa-1257	113	54	−	−	PROPN
ijassa-1257	113	55	1)β(τ)−	1)β(τ)−	NUM
ijassa-1257	113	56	δ	δ	PROPN
ijassa-1257	113	57	a	a	DET
ijassa-1257	113	58	τ	τ	PROPN
ijassa-1257	113	59	}	}	PUNCT
ijassa-1257	113	60	dτ	dτ	NOUN
ijassa-1257	113	61	,	,	PUNCT
ijassa-1257	113	62	(	(	PUNCT
ijassa-1257	113	63	2.25	2.25	NUM
ijassa-1257	113	64	)	)	PUNCT
ijassa-1257	113	65	where	where	SCONJ
ijassa-1257	113	66	the	the	DET
ijassa-1257	113	67	auxiliary	auxiliary	ADJ
ijassa-1257	113	68	function	function	NOUN
ijassa-1257	113	69	β	β	X
ijassa-1257	113	70	is	be	AUX
ijassa-1257	113	71	defined	define	VERB
ijassa-1257	113	72	as	as	ADP
ijassa-1257	113	73	β(t	β(t	PROPN
ijassa-1257	113	74	)	)	PUNCT
ijassa-1257	114	1	=	=	PUNCT
ijassa-1257	115	1	∫	∫	PROPN
ijassa-1257	115	2	t	t	PROPN
ijassa-1257	115	3	t0	t0	PROPN
ijassa-1257	115	4	ds	ds	PRON
ijassa-1257	115	5	b(s	b(	NOUN
ijassa-1257	115	6	)	)	PUNCT
ijassa-1257	115	7	.	.	PUNCT
ijassa-1257	116	1	proof	proof	NOUN
ijassa-1257	116	2	from	from	ADP
ijassa-1257	116	3	(	(	PUNCT
ijassa-1257	116	4	2.24	2.24	NUM
ijassa-1257	116	5	)	)	PUNCT
ijassa-1257	116	6	we	we	PRON
ijassa-1257	116	7	have	have	VERB
ijassa-1257	116	8	g(c(t))b(t	g(c(t))b(t	NOUN
ijassa-1257	116	9	)	)	PUNCT
ijassa-1257	116	10	=	=	PUNCT
ijassa-1257	117	1	d	d	X
ijassa-1257	117	2	exp{δt−	exp{δt−	PROPN
ijassa-1257	117	3	β(t	β(t	PROPN
ijassa-1257	117	4	)	)	PUNCT
ijassa-1257	117	5	}	}	PUNCT
ijassa-1257	117	6	,	,	PUNCT
ijassa-1257	118	1	d	d	NOUN
ijassa-1257	118	2	=	=	SYM
ijassa-1257	118	3	const	const	X
ijassa-1257	118	4	>	>	X
ijassa-1257	118	5	0	0	NUM
ijassa-1257	118	6	.	.	PUNCT
ijassa-1257	118	7	(	(	PUNCT
ijassa-1257	118	8	2.26	2.26	NUM
ijassa-1257	118	9	)	)	PUNCT
ijassa-1257	118	10	on	on	ADP
ijassa-1257	118	11	the	the	DET
ijassa-1257	118	12	other	other	ADJ
ijassa-1257	118	13	hand	hand	NOUN
ijassa-1257	118	14	,	,	PUNCT
ijassa-1257	118	15	from	from	ADP
ijassa-1257	118	16	(	(	PUNCT
ijassa-1257	118	17	2.21	2.21	NUM
ijassa-1257	118	18	)	)	PUNCT
ijassa-1257	118	19	we	we	PRON
ijassa-1257	118	20	get	get	VERB
ijassa-1257	118	21	g(c	g(c	NOUN
ijassa-1257	118	22	)	)	PUNCT
ijassa-1257	118	23	=	=	PUNCT
ijassa-1257	119	1	γc−a	γc−a	ADJ
ijassa-1257	119	2	,	,	PUNCT
ijassa-1257	119	3	γ	γ	X
ijassa-1257	119	4	=	=	SYM
ijassa-1257	119	5	const	const	X
ijassa-1257	119	6	>	>	X
ijassa-1257	119	7	0	0	X
ijassa-1257	119	8	.	.	PUNCT
ijassa-1257	120	1	substituting	substitute	VERB
ijassa-1257	120	2	this	this	DET
ijassa-1257	120	3	expression	expression	NOUN
ijassa-1257	120	4	into	into	ADP
ijassa-1257	120	5	(	(	PUNCT
ijassa-1257	120	6	2.21	2.21	NUM
ijassa-1257	120	7	)	)	PUNCT
ijassa-1257	120	8	,	,	PUNCT
ijassa-1257	120	9	we	we	PRON
ijassa-1257	120	10	have	have	VERB
ijassa-1257	120	11	c(t	c(t	PROPN
ijassa-1257	120	12	)	)	PUNCT
ijassa-1257	120	13	=	=	PUNCT
ijassa-1257	120	14	(	(	PUNCT
ijassa-1257	121	1	γb(t	γb(t	NOUN
ijassa-1257	121	2	)	)	PUNCT
ijassa-1257	121	3	d	d	NOUN
ijassa-1257	121	4	)	)	PUNCT
ijassa-1257	121	5	1	1	NUM
ijassa-1257	121	6	a	a	DET
ijassa-1257	121	7	exp{a−1(β(t)−	exp{a−1(β(t)−	PROPN
ijassa-1257	121	8	δt	δt	NOUN
ijassa-1257	121	9	)	)	PUNCT
ijassa-1257	121	10	}	}	PUNCT
ijassa-1257	121	11	.	.	PUNCT
ijassa-1257	122	1	(	(	PUNCT
ijassa-1257	122	2	2.27	2.27	NUM
ijassa-1257	122	3	)	)	PUNCT
ijassa-1257	122	4	now	now	ADV
ijassa-1257	122	5	from	from	ADP
ijassa-1257	122	6	(	(	PUNCT
ijassa-1257	122	7	1.4	1.4	NUM
ijassa-1257	122	8	)	)	PUNCT
ijassa-1257	122	9	and	and	CCONJ
ijassa-1257	122	10	(	(	PUNCT
ijassa-1257	122	11	2.22	2.22	NUM
ijassa-1257	122	12	)	)	PUNCT
ijassa-1257	122	13	we	we	PRON
ijassa-1257	122	14	obtain	obtain	VERB
ijassa-1257	122	15	the	the	DET
ijassa-1257	122	16	equality∫	equality∫	NOUN
ijassa-1257	122	17	t1	t1	PROPN
ijassa-1257	122	18	t0	t0	PROPN
ijassa-1257	122	19	c(τ	c(τ	PROPN
ijassa-1257	122	20	)	)	PUNCT
ijassa-1257	122	21	b(τ	b(τ	PROPN
ijassa-1257	122	22	)	)	PUNCT
ijassa-1257	122	23	e−β(τ)dτ	e−β(τ)dτ	NOUN
ijassa-1257	122	24	=	=	SYM
ijassa-1257	122	25	y0	y0	PROPN
ijassa-1257	122	26	−	−	NOUN
ijassa-1257	122	27	y1e	y1e	PROPN
ijassa-1257	122	28	−β(t1	−β(t1	PROPN
ijassa-1257	122	29	)	)	PUNCT
ijassa-1257	122	30	,	,	PUNCT
ijassa-1257	122	31	(	(	PUNCT
ijassa-1257	122	32	2.28	2.28	NUM
ijassa-1257	122	33	)	)	PUNCT
ijassa-1257	122	34	and	and	CCONJ
ijassa-1257	122	35	from	from	ADP
ijassa-1257	122	36	(	(	PUNCT
ijassa-1257	122	37	2.27	2.27	NUM
ijassa-1257	122	38	)	)	PUNCT
ijassa-1257	122	39	and	and	CCONJ
ijassa-1257	122	40	(	(	PUNCT
ijassa-1257	122	41	2.28	2.28	NUM
ijassa-1257	122	42	)	)	PUNCT
ijassa-1257	122	43	one	one	PRON
ijassa-1257	122	44	can	can	AUX
ijassa-1257	122	45	express	express	VERB
ijassa-1257	122	46	the	the	DET
ijassa-1257	122	47	constant	constant	ADJ
ijassa-1257	122	48	:(	:(	PUNCT
ijassa-1257	122	49	γ	γ	PROPN
ijassa-1257	122	50	d	d	PROPN
ijassa-1257	122	51	)	)	PUNCT
ijassa-1257	122	52	1	1	NUM
ijassa-1257	122	53	a	a	DET
ijassa-1257	122	54	=	=	SYM
ijassa-1257	122	55	y0	y0	NOUN
ijassa-1257	122	56	−	−	NOUN
ijassa-1257	122	57	y1e	y1e	PROPN
ijassa-1257	123	1	−β(t1)∫	−β(t1)∫	PROPN
ijassa-1257	123	2	t1	t1	PROPN
ijassa-1257	123	3	t0	t0	PROPN
ijassa-1257	123	4	b(τ	b(τ	PROPN
ijassa-1257	123	5	)	)	PUNCT
ijassa-1257	123	6	1	1	NUM
ijassa-1257	123	7	a	a	DET
ijassa-1257	123	8	−1	−1	NOUN
ijassa-1257	123	9	exp	exp	NOUN
ijassa-1257	123	10	{	{	PUNCT
ijassa-1257	123	11	(	(	PUNCT
ijassa-1257	123	12	1	1	NUM
ijassa-1257	123	13	a	a	DET
ijassa-1257	123	14	−	−	PROPN
ijassa-1257	123	15	1)β(τ)−	1)β(τ)−	NUM
ijassa-1257	123	16	δ	δ	PROPN
ijassa-1257	123	17	a	a	DET
ijassa-1257	123	18	τ	τ	PROPN
ijassa-1257	123	19	}	}	PUNCT
ijassa-1257	123	20	dτ	dτ	NOUN
ijassa-1257	123	21	,	,	PUNCT
ijassa-1257	123	22	(	(	PUNCT
ijassa-1257	123	23	2.29	2.29	NUM
ijassa-1257	123	24	)	)	PUNCT
ijassa-1257	123	25	finally	finally	ADV
ijassa-1257	123	26	,	,	PUNCT
ijassa-1257	123	27	substituting	substitute	VERB
ijassa-1257	123	28	the	the	DET
ijassa-1257	123	29	expression	expression	NOUN
ijassa-1257	123	30	(	(	PUNCT
ijassa-1257	123	31	2.29	2.29	NUM
ijassa-1257	123	32	)	)	PUNCT
ijassa-1257	123	33	into	into	ADP
ijassa-1257	123	34	(	(	PUNCT
ijassa-1257	123	35	2.27	2.27	NUM
ijassa-1257	123	36	)	)	PUNCT
ijassa-1257	123	37	and	and	CCONJ
ijassa-1257	123	38	taking	take	VERB
ijassa-1257	123	39	into	into	ADP
ijassa-1257	123	40	account	account	NOUN
ijassa-1257	123	41	(	(	PUNCT
ijassa-1257	123	42	2.22	2.22	NUM
ijassa-1257	123	43	)	)	PUNCT
ijassa-1257	123	44	,	,	PUNCT
ijassa-1257	123	45	we	we	PRON
ijassa-1257	123	46	obtain	obtain	VERB
ijassa-1257	123	47	(	(	PUNCT
ijassa-1257	123	48	2.25	2.25	NUM
ijassa-1257	123	49	)	)	PUNCT
ijassa-1257	123	50	.	.	PUNCT
ijassa-1257	124	1	copyright	copyright	NOUN
ijassa-1257	124	2	©	©	PROPN
ijassa-1257	124	3	2022	2022	NUM
ijassa-1257	124	4	assa	assa	NOUN
ijassa-1257	124	5	.	.	PUNCT
ijassa-1257	125	1	adv	adv	PROPN
ijassa-1257	125	2	syst	syst	PROPN
ijassa-1257	125	3	sci	sci	PROPN
ijassa-1257	125	4	appl	appl	PROPN
ijassa-1257	125	5	(	(	PUNCT
ijassa-1257	125	6	2022	2022	NUM
ijassa-1257	125	7	)	)	PUNCT
ijassa-1257	125	8	114	114	NUM
ijassa-1257	125	9	a.p	a.p	PROPN
ijassa-1257	125	10	.	.	PROPN
ijassa-1257	125	11	chernyaev	chernyaev	PROPN
ijassa-1257	125	12	2.2	2.2	NUM
ijassa-1257	125	13	.	.	PUNCT
ijassa-1257	126	1	optimal	optimal	ADJ
ijassa-1257	126	2	control	control	NOUN
ijassa-1257	126	3	in	in	ADP
ijassa-1257	126	4	the	the	DET
ijassa-1257	126	5	modified	modify	VERB
ijassa-1257	126	6	solow	solow	PROPN
ijassa-1257	126	7	model	model	NOUN
ijassa-1257	126	8	similarly	similarly	ADV
ijassa-1257	126	9	to	to	ADP
ijassa-1257	126	10	the	the	DET
ijassa-1257	126	11	above	above	NOUN
ijassa-1257	126	12	,	,	PUNCT
ijassa-1257	126	13	here	here	ADV
ijassa-1257	126	14	we	we	PRON
ijassa-1257	126	15	consider	consider	VERB
ijassa-1257	126	16	the	the	DET
ijassa-1257	126	17	maximization	maximization	NOUN
ijassa-1257	126	18	of	of	ADP
ijassa-1257	126	19	the	the	PRON
ijassa-1257	126	20	functional	functional	ADJ
ijassa-1257	126	21	j	j	PROPN
ijassa-1257	126	22	=	=	SYM
ijassa-1257	126	23	∫	∫	PROPN
ijassa-1257	126	24	t1	t1	PROPN
ijassa-1257	126	25	t0	t0	PROPN
ijassa-1257	126	26	u(c(t))e−δt	u(c(t))e−δt	PROPN
ijassa-1257	127	1	dt	dt	X
ijassa-1257	127	2	,	,	PUNCT
ijassa-1257	127	3	where	where	SCONJ
ijassa-1257	127	4	c(t	c(t	NOUN
ijassa-1257	127	5	)	)	PUNCT
ijassa-1257	127	6	=	=	SYM
ijassa-1257	127	7	c(t	c(t	PROPN
ijassa-1257	127	8	)	)	PUNCT
ijassa-1257	127	9	l(t	l(t	PROPN
ijassa-1257	127	10	)	)	PUNCT
ijassa-1257	127	11	,	,	PUNCT
ijassa-1257	127	12	(	(	PUNCT
ijassa-1257	127	13	2.30	2.30	NUM
ijassa-1257	127	14	)	)	PUNCT
ijassa-1257	127	15	and	and	CCONJ
ijassa-1257	127	16	the	the	DET
ijassa-1257	127	17	utility	utility	NOUN
ijassa-1257	127	18	function	function	NOUN
ijassa-1257	127	19	u	u	NOUN
ijassa-1257	127	20	satisfies	satisfy	VERB
ijassa-1257	127	21	the	the	DET
ijassa-1257	127	22	conditions	condition	NOUN
ijassa-1257	127	23	similar	similar	ADJ
ijassa-1257	127	24	to	to	ADP
ijassa-1257	127	25	(	(	PUNCT
ijassa-1257	127	26	2.21	2.21	NUM
ijassa-1257	127	27	):	):	PUNCT
ijassa-1257	127	28	−	−	NOUN
ijassa-1257	127	29	u′′(c)c	u′′(c)c	ADP
ijassa-1257	127	30	u′(c	u′(c	ADV
ijassa-1257	127	31	)	)	PUNCT
ijassa-1257	127	32	=	=	SYM
ijassa-1257	127	33	a	a	DET
ijassa-1257	127	34	≥	≥	NOUN
ijassa-1257	127	35	0	0	NUM
ijassa-1257	127	36	,	,	PUNCT
ijassa-1257	127	37	g(c	g(c	NOUN
ijassa-1257	127	38	)	)	PUNCT
ijassa-1257	127	39	=	=	PUNCT
ijassa-1257	128	1	u′(c	u′(c	NOUN
ijassa-1257	128	2	)	)	PUNCT
ijassa-1257	128	3	,	,	PUNCT
ijassa-1257	128	4	ec(g	ec(g	NOUN
ijassa-1257	128	5	)	)	PUNCT
ijassa-1257	128	6	=	=	SYM
ijassa-1257	128	7	−a	−a	NOUN
ijassa-1257	128	8	,	,	PUNCT
ijassa-1257	128	9	(	(	PUNCT
ijassa-1257	128	10	2.31	2.31	NUM
ijassa-1257	128	11	)	)	PUNCT
ijassa-1257	128	12	under	under	ADP
ijassa-1257	128	13	the	the	DET
ijassa-1257	128	14	following	follow	VERB
ijassa-1257	128	15	constrains	constrain	NOUN
ijassa-1257	128	16	(	(	PUNCT
ijassa-1257	128	17	see	see	VERB
ijassa-1257	128	18	(	(	PUNCT
ijassa-1257	128	19	1.14	1.14	NUM
ijassa-1257	128	20	)	)	PUNCT
ijassa-1257	128	21	):	):	PUNCT
ijassa-1257	128	22	k′(t	k′(t	X
ijassa-1257	128	23	)	)	PUNCT
ijassa-1257	128	24	=	=	SYM
ijassa-1257	129	1	ρ(t)f(k(t))−	ρ(t)f(k(t))−	NUM
ijassa-1257	129	2	λk(t	λk(t	NOUN
ijassa-1257	129	3	)	)	PUNCT
ijassa-1257	129	4	,	,	PUNCT
ijassa-1257	129	5	k(t0	k(t0	NOUN
ijassa-1257	129	6	)	)	PUNCT
ijassa-1257	129	7	=	=	SYM
ijassa-1257	129	8	k0	k0	PROPN
ijassa-1257	129	9	≥	≥	NUM
ijassa-1257	129	10	0	0	NUM
ijassa-1257	129	11	,	,	PUNCT
ijassa-1257	129	12	k(t1	k(t1	X
ijassa-1257	129	13	)	)	PUNCT
ijassa-1257	130	1	=	=	SYM
ijassa-1257	130	2	k1	k1	X
ijassa-1257	130	3	≥	≥	NOUN
ijassa-1257	130	4	0	0	NUM
ijassa-1257	130	5	.	.	PUNCT
ijassa-1257	131	1	(	(	PUNCT
ijassa-1257	131	2	2.32	2.32	NUM
ijassa-1257	131	3	)	)	PUNCT
ijassa-1257	131	4	taking	take	VERB
ijassa-1257	131	5	into	into	ADP
ijassa-1257	131	6	account	account	NOUN
ijassa-1257	131	7	the	the	DET
ijassa-1257	131	8	formulas	formula	NOUN
ijassa-1257	131	9	c(t	c(t	PROPN
ijassa-1257	131	10	)	)	PUNCT
ijassa-1257	131	11	=	=	PUNCT
ijassa-1257	131	12	c	c	NOUN
ijassa-1257	131	13	l	l	NOUN
ijassa-1257	132	1	=	=	PUNCT
ijassa-1257	132	2	y	y	PROPN
ijassa-1257	132	3	−	−	NOUN
ijassa-1257	133	1	i	i	PRON
ijassa-1257	133	2	l	l	NOUN
ijassa-1257	134	1	=	=	PUNCT
ijassa-1257	134	2	y	y	PROPN
ijassa-1257	134	3	−	−	NOUN
ijassa-1257	134	4	ρy	ρy	ADP
ijassa-1257	134	5	l	l	NOUN
ijassa-1257	134	6	=	=	SYM
ijassa-1257	134	7	(	(	PUNCT
ijassa-1257	134	8	1−	1−	NUM
ijassa-1257	134	9	ρ	ρ	NOUN
ijassa-1257	134	10	)	)	PUNCT
ijassa-1257	134	11	y	y	PROPN
ijassa-1257	134	12	l	l	NOUN
ijassa-1257	135	1	=	=	PUNCT
ijassa-1257	135	2	(	(	PUNCT
ijassa-1257	135	3	1−	1−	NUM
ijassa-1257	135	4	ρ)f(k	ρ)f(k	NUM
ijassa-1257	135	5	)	)	PUNCT
ijassa-1257	135	6	,	,	PUNCT
ijassa-1257	135	7	k′(t	k′(t	X
ijassa-1257	135	8	)	)	PUNCT
ijassa-1257	135	9	=	=	SYM
ijassa-1257	135	10	cρ	cρ	PROPN
ijassa-1257	135	11	1−	1−	NUM
ijassa-1257	135	12	ρ	ρ	NOUN
ijassa-1257	135	13	−	−	PROPN
ijassa-1257	135	14	λk	λk	PROPN
ijassa-1257	135	15	,	,	PUNCT
ijassa-1257	135	16	c(t	c(t	PROPN
ijassa-1257	135	17	)	)	PUNCT
ijassa-1257	135	18	=	=	SYM
ijassa-1257	135	19	1−	1−	NUM
ijassa-1257	135	20	ρ	ρ	NUM
ijassa-1257	135	21	ρ	ρ	PROPN
ijassa-1257	135	22	(	(	PUNCT
ijassa-1257	135	23	k′	k′	PROPN
ijassa-1257	135	24	+	+	PROPN
ijassa-1257	135	25	λk	λk	PROPN
ijassa-1257	135	26	)	)	PUNCT
ijassa-1257	135	27	,	,	PUNCT
ijassa-1257	135	28	0	0	NUM
ijassa-1257	135	29	<	<	X
ijassa-1257	135	30	ρ	ρ	X
ijassa-1257	135	31	<	<	X
ijassa-1257	135	32	1	1	NUM
ijassa-1257	135	33	,	,	PUNCT
ijassa-1257	135	34	the	the	DET
ijassa-1257	135	35	euler	euler	PROPN
ijassa-1257	135	36	–	–	PUNCT
ijassa-1257	135	37	lagrange	lagrange	NOUN
ijassa-1257	135	38	equation	equation	NOUN
ijassa-1257	135	39	(	(	PUNCT
ijassa-1257	135	40	a	a	DET
ijassa-1257	135	41	necessary	necessary	ADJ
ijassa-1257	135	42	condition	condition	NOUN
ijassa-1257	135	43	of	of	ADP
ijassa-1257	135	44	optimality	optimality	NOUN
ijassa-1257	135	45	)	)	PUNCT
ijassa-1257	135	46	reads	read	VERB
ijassa-1257	135	47	−	−	PROPN
ijassa-1257	135	48	d	d	X
ijassa-1257	135	49	dt	dt	X
ijassa-1257	135	50	(	(	PUNCT
ijassa-1257	135	51	g(c(t	g(c(t	PROPN
ijassa-1257	135	52	)	)	PUNCT
ijassa-1257	135	53	)	)	PUNCT
ijassa-1257	136	1	1−	1−	NUM
ijassa-1257	136	2	ρ	ρ	PROPN
ijassa-1257	136	3	ρ	ρ	PROPN
ijassa-1257	136	4	e−δt	e−δt	PROPN
ijassa-1257	136	5	)	)	PUNCT
ijassa-1257	137	1	+	+	CCONJ
ijassa-1257	137	2	g(c(t	g(c(t	NOUN
ijassa-1257	137	3	)	)	PUNCT
ijassa-1257	137	4	)	)	PUNCT
ijassa-1257	138	1	1−	1−	NUM
ijassa-1257	138	2	ρ	ρ	NUM
ijassa-1257	138	3	ρ	ρ	PROPN
ijassa-1257	138	4	λe−δt	λe−δt	X
ijassa-1257	138	5	=	=	SYM
ijassa-1257	138	6	0	0	X
ijassa-1257	138	7	.	.	PUNCT
ijassa-1257	139	1	(	(	PUNCT
ijassa-1257	139	2	2.33	2.33	NUM
ijassa-1257	139	3	)	)	PUNCT
ijassa-1257	139	4	integrating	integrating	NOUN
ijassa-1257	139	5	(	(	PUNCT
ijassa-1257	139	6	2.33	2.33	NUM
ijassa-1257	139	7	)	)	PUNCT
ijassa-1257	139	8	(	(	PUNCT
ijassa-1257	139	9	see	see	VERB
ijassa-1257	139	10	[	[	X
ijassa-1257	139	11	1	1	NUM
ijassa-1257	139	12	]	]	NUM
ijassa-1257	139	13	)	)	PUNCT
ijassa-1257	139	14	,	,	PUNCT
ijassa-1257	139	15	we	we	PRON
ijassa-1257	139	16	have	have	VERB
ijassa-1257	139	17	c(t	c(t	NUM
ijassa-1257	139	18	)	)	PUNCT
ijassa-1257	139	19	=	=	SYM
ijassa-1257	140	1	g−1	g−1	PROPN
ijassa-1257	140	2	(	(	PUNCT
ijassa-1257	140	3	dρ	dρ	PROPN
ijassa-1257	140	4	1−	1−	NUM
ijassa-1257	140	5	ρ	ρ	NUM
ijassa-1257	140	6	exp	exp	NOUN
ijassa-1257	140	7	{	{	PUNCT
ijassa-1257	140	8	δt+	δt+	ADJ
ijassa-1257	140	9	∫	∫	PROPN
ijassa-1257	140	10	t	t	PROPN
ijassa-1257	140	11	t0	t0	PROPN
ijassa-1257	140	12	λ(s)ds	λ(s)ds	ADP
ijassa-1257	140	13	}	}	PUNCT
ijassa-1257	140	14	)	)	PUNCT
ijassa-1257	140	15	.	.	PUNCT
ijassa-1257	141	1	(	(	PUNCT
ijassa-1257	141	2	2.34	2.34	NUM
ijassa-1257	141	3	)	)	PUNCT
ijassa-1257	141	4	the	the	DET
ijassa-1257	141	5	condition	condition	NOUN
ijassa-1257	141	6	(	(	PUNCT
ijassa-1257	141	7	2.31	2.31	NUM
ijassa-1257	141	8	)	)	PUNCT
ijassa-1257	141	9	gives	give	VERB
ijassa-1257	141	10	a	a	DET
ijassa-1257	141	11	sufficient	sufficient	ADJ
ijassa-1257	141	12	condition	condition	NOUN
ijassa-1257	141	13	of	of	ADP
ijassa-1257	141	14	optimality	optimality	NOUN
ijassa-1257	141	15	.	.	PUNCT
ijassa-1257	142	1	theorem	theorem	VERB
ijassa-1257	142	2	2.2	2.2	NUM
ijassa-1257	142	3	:	:	PUNCT
ijassa-1257	142	4	under	under	ADP
ijassa-1257	142	5	the	the	DET
ijassa-1257	142	6	above	above	ADJ
ijassa-1257	142	7	conditions	condition	NOUN
ijassa-1257	142	8	,	,	PUNCT
ijassa-1257	142	9	the	the	DET
ijassa-1257	142	10	total	total	ADJ
ijassa-1257	142	11	consumption	consumption	NOUN
ijassa-1257	142	12	c(t	c(t	PROPN
ijassa-1257	142	13	)	)	PUNCT
ijassa-1257	142	14	is	be	AUX
ijassa-1257	142	15	given	give	VERB
ijassa-1257	142	16	by	by	ADP
ijassa-1257	142	17	the	the	DET
ijassa-1257	142	18	formula	formula	NOUN
ijassa-1257	142	19	c(t	c(t	PROPN
ijassa-1257	142	20	)	)	PUNCT
ijassa-1257	142	21	=	=	PUNCT
ijassa-1257	143	1	(	(	PUNCT
ijassa-1257	143	2	k1e	k1e	X
ijassa-1257	143	3	λ(t1	λ(t1	INTJ
ijassa-1257	143	4	)	)	PUNCT
ijassa-1257	143	5	−	−	PROPN
ijassa-1257	143	6	k0	k0	PROPN
ijassa-1257	143	7	)	)	PUNCT
ijassa-1257	143	8	r(t	r(t	NOUN
ijassa-1257	143	9	)	)	PUNCT
ijassa-1257	143	10	1	1	NUM
ijassa-1257	143	11	a	a	DET
ijassa-1257	143	12	exp	exp	NOUN
ijassa-1257	143	13	{	{	PUNCT
ijassa-1257	143	14	−	−	PROPN
ijassa-1257	143	15	1	1	NUM
ijassa-1257	143	16	a	a	PRON
ijassa-1257	143	17	(	(	PUNCT
ijassa-1257	143	18	λ(t	λ(t	NOUN
ijassa-1257	143	19	)	)	PUNCT
ijassa-1257	143	20	+	+	NUM
ijassa-1257	143	21	δt	δt	X
ijassa-1257	143	22	)	)	PUNCT
ijassa-1257	143	23	}	}	PUNCT
ijassa-1257	143	24	∫	∫	PROPN
ijassa-1257	143	25	t1	t1	PROPN
ijassa-1257	143	26	t0	t0	PROPN
ijassa-1257	143	27	r(τ	r(τ	PROPN
ijassa-1257	143	28	)	)	PUNCT
ijassa-1257	143	29	1	1	NUM
ijassa-1257	143	30	a	a	DET
ijassa-1257	143	31	−1	−1	NOUN
ijassa-1257	143	32	exp	exp	NOUN
ijassa-1257	143	33	{	{	PUNCT
ijassa-1257	143	34	(	(	PUNCT
ijassa-1257	143	35	1−	1−	NUM
ijassa-1257	143	36	1	1	NUM
ijassa-1257	143	37	a	a	PRON
ijassa-1257	143	38	)	)	PUNCT
ijassa-1257	143	39	λ(τ)−	λ(τ)−	NOUN
ijassa-1257	143	40	δ	δ	PROPN
ijassa-1257	143	41	a	a	PRON
ijassa-1257	143	42	τ	τ	PROPN
ijassa-1257	143	43	}	}	PUNCT
ijassa-1257	143	44	dτ	dτ	PROPN
ijassa-1257	143	45	(	(	PUNCT
ijassa-1257	143	46	2.35	2.35	NUM
ijassa-1257	143	47	)	)	PUNCT
ijassa-1257	143	48	where	where	SCONJ
ijassa-1257	143	49	the	the	DET
ijassa-1257	143	50	auxiliary	auxiliary	ADJ
ijassa-1257	143	51	functions	function	NOUN
ijassa-1257	143	52	l	l	NOUN
ijassa-1257	143	53	and	and	CCONJ
ijassa-1257	143	54	r	r	NOUN
ijassa-1257	143	55	are	be	AUX
ijassa-1257	143	56	defined	define	VERB
ijassa-1257	143	57	as	as	ADP
ijassa-1257	143	58	λ(t	λ(t	NOUN
ijassa-1257	143	59	)	)	PUNCT
ijassa-1257	143	60	=	=	PUNCT
ijassa-1257	144	1	∫	∫	PROPN
ijassa-1257	144	2	t	t	PROPN
ijassa-1257	144	3	t0	t0	PROPN
ijassa-1257	144	4	λ(s)ds	λ(s)ds	PROPN
ijassa-1257	144	5	,	,	PUNCT
ijassa-1257	144	6	r(t	r(t	NOUN
ijassa-1257	144	7	)	)	PUNCT
ijassa-1257	144	8	=	=	SYM
ijassa-1257	144	9	1−	1−	NUM
ijassa-1257	144	10	ρ(t	ρ(t	NUM
ijassa-1257	144	11	)	)	PUNCT
ijassa-1257	144	12	ρ(t	ρ(t	NUM
ijassa-1257	144	13	)	)	PUNCT
ijassa-1257	144	14	.	.	PUNCT
ijassa-1257	145	1	proof	proof	NOUN
ijassa-1257	145	2	from	from	ADP
ijassa-1257	145	3	(	(	PUNCT
ijassa-1257	145	4	2.34	2.34	NUM
ijassa-1257	145	5	)	)	PUNCT
ijassa-1257	145	6	we	we	PRON
ijassa-1257	145	7	have	have	VERB
ijassa-1257	145	8	g(c(t))r(t)e−δt	g(c(t))r(t)e−δt	NOUN
ijassa-1257	145	9	=	=	SYM
ijassa-1257	145	10	deλ(t	deλ(t	NOUN
ijassa-1257	145	11	)	)	PUNCT
ijassa-1257	145	12	,	,	PUNCT
ijassa-1257	145	13	d	d	NOUN
ijassa-1257	145	14	=	=	SYM
ijassa-1257	145	15	const	const	X
ijassa-1257	145	16	>	>	X
ijassa-1257	145	17	0	0	NUM
ijassa-1257	145	18	.	.	PUNCT
ijassa-1257	146	1	(	(	PUNCT
ijassa-1257	146	2	2.36	2.36	NUM
ijassa-1257	146	3	)	)	PUNCT
ijassa-1257	146	4	copyright	copyright	NOUN
ijassa-1257	146	5	©	©	PROPN
ijassa-1257	146	6	2022	2022	NUM
ijassa-1257	146	7	assa	assa	NOUN
ijassa-1257	146	8	.	.	PUNCT
ijassa-1257	147	1	adv	adv	PROPN
ijassa-1257	147	2	syst	syst	PROPN
ijassa-1257	147	3	sci	sci	PROPN
ijassa-1257	147	4	appl	appl	PROPN
ijassa-1257	147	5	(	(	PUNCT
ijassa-1257	147	6	2022	2022	NUM
ijassa-1257	147	7	)	)	PUNCT
ijassa-1257	147	8	the	the	DET
ijassa-1257	147	9	optimal	optimal	ADJ
ijassa-1257	147	10	control	control	NOUN
ijassa-1257	147	11	approach	approach	NOUN
ijassa-1257	147	12	in	in	ADP
ijassa-1257	147	13	problems	problem	NOUN
ijassa-1257	147	14	of	of	ADP
ijassa-1257	147	15	the	the	DET
ijassa-1257	147	16	income	income	NOUN
ijassa-1257	147	17	distribution	distribution	NOUN
ijassa-1257	147	18	115	115	NUM
ijassa-1257	147	19	on	on	ADP
ijassa-1257	147	20	the	the	DET
ijassa-1257	147	21	other	other	ADJ
ijassa-1257	147	22	hand	hand	NOUN
ijassa-1257	147	23	,	,	PUNCT
ijassa-1257	147	24	from	from	ADP
ijassa-1257	147	25	(	(	PUNCT
ijassa-1257	147	26	2.31	2.31	NUM
ijassa-1257	147	27	)	)	PUNCT
ijassa-1257	147	28	we	we	PRON
ijassa-1257	147	29	get	get	VERB
ijassa-1257	147	30	g(c	g(c	NOUN
ijassa-1257	147	31	)	)	PUNCT
ijassa-1257	147	32	=	=	PUNCT
ijassa-1257	147	33	γc−a	γc−a	ADJ
ijassa-1257	147	34	,	,	PUNCT
ijassa-1257	147	35	γ	γ	X
ijassa-1257	147	36	=	=	SYM
ijassa-1257	147	37	const	const	X
ijassa-1257	147	38	>	>	X
ijassa-1257	147	39	0	0	X
ijassa-1257	147	40	.	.	PUNCT
ijassa-1257	147	41	substituting	substitute	VERB
ijassa-1257	147	42	this	this	DET
ijassa-1257	147	43	expression	expression	NOUN
ijassa-1257	147	44	into	into	ADP
ijassa-1257	147	45	(	(	PUNCT
ijassa-1257	147	46	2.36	2.36	NUM
ijassa-1257	147	47	)	)	PUNCT
ijassa-1257	147	48	,	,	PUNCT
ijassa-1257	147	49	we	we	PRON
ijassa-1257	147	50	have	have	VERB
ijassa-1257	147	51	c(t	c(t	NUM
ijassa-1257	147	52	)	)	PUNCT
ijassa-1257	147	53	=	=	PUNCT
ijassa-1257	147	54	(	(	PUNCT
ijassa-1257	147	55	γ	γ	X
ijassa-1257	147	56	d	d	X
ijassa-1257	147	57	r(t	r(t	NOUN
ijassa-1257	147	58	)	)	PUNCT
ijassa-1257	147	59	)	)	PUNCT
ijassa-1257	148	1	1	1	NUM
ijassa-1257	148	2	a	a	DET
ijassa-1257	148	3	exp{−a−1(λ(t	exp{−a−1(λ(t	NOUN
ijassa-1257	148	4	)	)	PUNCT
ijassa-1257	148	5	+	+	NUM
ijassa-1257	148	6	δt	δt	X
ijassa-1257	148	7	)	)	PUNCT
ijassa-1257	148	8	}	}	PUNCT
ijassa-1257	148	9	.	.	PUNCT
ijassa-1257	149	1	(	(	PUNCT
ijassa-1257	149	2	2.37	2.37	NUM
ijassa-1257	149	3	)	)	PUNCT
ijassa-1257	149	4	substituting	substituting	NOUN
ijassa-1257	149	5	(	(	PUNCT
ijassa-1257	149	6	2.37	2.37	NUM
ijassa-1257	149	7	)	)	PUNCT
ijassa-1257	149	8	into	into	ADP
ijassa-1257	149	9	the	the	DET
ijassa-1257	149	10	equation	equation	NOUN
ijassa-1257	149	11	k′(t	k′(t	X
ijassa-1257	149	12	)	)	PUNCT
ijassa-1257	149	13	=	=	SYM
ijassa-1257	150	1	cρ	cρ	PROPN
ijassa-1257	150	2	1−	1−	NUM
ijassa-1257	150	3	ρ	ρ	NOUN
ijassa-1257	150	4	−	−	PROPN
ijassa-1257	151	1	λk	λk	ADP
ijassa-1257	151	2	,	,	PUNCT
ijassa-1257	151	3	we	we	PRON
ijassa-1257	151	4	get	get	VERB
ijassa-1257	151	5	a	a	DET
ijassa-1257	151	6	linear	linear	ADJ
ijassa-1257	151	7	differential	differential	ADJ
ijassa-1257	151	8	equation	equation	NOUN
ijassa-1257	151	9	for	for	ADP
ijassa-1257	151	10	k(t	k(t	PROPN
ijassa-1257	151	11	)	)	PUNCT
ijassa-1257	151	12	.	.	PUNCT
ijassa-1257	152	1	integrating	integrate	VERB
ijassa-1257	152	2	it	it	PRON
ijassa-1257	152	3	,	,	PUNCT
ijassa-1257	152	4	we	we	PRON
ijassa-1257	152	5	found	find	VERB
ijassa-1257	152	6	k(t	k(t	NOUN
ijassa-1257	152	7	)	)	PUNCT
ijassa-1257	153	1	=	=	SYM
ijassa-1257	153	2	e−λ(t	e−λ(t	NOUN
ijassa-1257	153	3	)	)	PUNCT
ijassa-1257	153	4	∫	∫	PROPN
ijassa-1257	153	5	t	t	PROPN
ijassa-1257	153	6	t0	t0	PROPN
ijassa-1257	153	7	c(τ	c(τ	PROPN
ijassa-1257	153	8	)	)	PUNCT
ijassa-1257	153	9	r(τ	r(τ	PROPN
ijassa-1257	153	10	)	)	PUNCT
ijassa-1257	154	1	eλ(τ)dτ	eλ(τ)dτ	NOUN
ijassa-1257	155	1	+	+	CCONJ
ijassa-1257	155	2	k0e	k0e	ADJ
ijassa-1257	155	3	−λ(t	−λ(t	NOUN
ijassa-1257	155	4	)	)	PUNCT
ijassa-1257	155	5	.	.	PUNCT
ijassa-1257	156	1	(	(	PUNCT
ijassa-1257	156	2	2.38	2.38	NUM
ijassa-1257	156	3	)	)	PUNCT
ijassa-1257	156	4	from	from	ADP
ijassa-1257	156	5	(	(	PUNCT
ijassa-1257	156	6	2.37	2.37	NUM
ijassa-1257	156	7	)	)	PUNCT
ijassa-1257	156	8	and	and	CCONJ
ijassa-1257	156	9	(	(	PUNCT
ijassa-1257	156	10	2.38	2.38	NUM
ijassa-1257	156	11	)	)	PUNCT
ijassa-1257	156	12	it	it	PRON
ijassa-1257	156	13	follows	follow	VERB
ijassa-1257	156	14	k1e	k1e	PROPN
ijassa-1257	156	15	λ(t1	λ(t1	INTJ
ijassa-1257	156	16	)	)	PUNCT
ijassa-1257	156	17	−	−	PROPN
ijassa-1257	156	18	k0	k0	PROPN
ijassa-1257	156	19	=	=	PUNCT
ijassa-1257	156	20	(	(	PUNCT
ijassa-1257	156	21	γ	γ	X
ijassa-1257	156	22	d	d	PROPN
ijassa-1257	156	23	)	)	PUNCT
ijassa-1257	156	24	1	1	NUM
ijassa-1257	156	25	a	a	DET
ijassa-1257	156	26	∫	∫	PROPN
ijassa-1257	156	27	t1	t1	PROPN
ijassa-1257	156	28	t0	t0	PROPN
ijassa-1257	156	29	r(τ	r(τ	PROPN
ijassa-1257	156	30	)	)	PUNCT
ijassa-1257	156	31	1	1	NUM
ijassa-1257	156	32	a	a	DET
ijassa-1257	156	33	−1	−1	NOUN
ijassa-1257	156	34	exp	exp	NOUN
ijassa-1257	156	35	{	{	PUNCT
ijassa-1257	156	36	(	(	PUNCT
ijassa-1257	156	37	1	1	NUM
ijassa-1257	156	38	a	a	DET
ijassa-1257	156	39	−	−	PROPN
ijassa-1257	156	40	1)λ(τ)−	1)λ(τ)−	PROPN
ijassa-1257	156	41	δ	δ	PROPN
ijassa-1257	156	42	a	a	DET
ijassa-1257	156	43	τ}dτ	τ}dτ	PROPN
ijassa-1257	156	44	.	.	PUNCT
ijassa-1257	157	1	(	(	PUNCT
ijassa-1257	157	2	2.39	2.39	NUM
ijassa-1257	157	3	)	)	PUNCT
ijassa-1257	157	4	the	the	DET
ijassa-1257	157	5	obtained	obtain	VERB
ijassa-1257	157	6	equality	equality	NOUN
ijassa-1257	157	7	allows	allow	VERB
ijassa-1257	157	8	us	we	PRON
ijassa-1257	157	9	to	to	PART
ijassa-1257	157	10	express	express	VERB
ijassa-1257	157	11	the	the	DET
ijassa-1257	157	12	constant	constant	ADJ
ijassa-1257	157	13	(	(	PUNCT
ijassa-1257	157	14	γ	γ	X
ijassa-1257	157	15	/	/	SYM
ijassa-1257	157	16	d	d	NOUN
ijassa-1257	157	17	)	)	PUNCT
ijassa-1257	157	18	1	1	NUM
ijassa-1257	157	19	a	a	NOUN
ijassa-1257	157	20	.	.	PUNCT
ijassa-1257	158	1	therefore	therefore	ADV
ijassa-1257	158	2	,	,	PUNCT
ijassa-1257	158	3	from	from	ADP
ijassa-1257	158	4	the	the	DET
ijassa-1257	158	5	equalities	equality	NOUN
ijassa-1257	158	6	(	(	PUNCT
ijassa-1257	158	7	2.37	2.37	NUM
ijassa-1257	158	8	)	)	PUNCT
ijassa-1257	158	9	and	and	CCONJ
ijassa-1257	158	10	(	(	PUNCT
ijassa-1257	158	11	2.39	2.39	NUM
ijassa-1257	158	12	)	)	PUNCT
ijassa-1257	158	13	we	we	PRON
ijassa-1257	158	14	obtain	obtain	VERB
ijassa-1257	158	15	(	(	PUNCT
ijassa-1257	158	16	2.35	2.35	NUM
ijassa-1257	158	17	)	)	PUNCT
ijassa-1257	158	18	.	.	PUNCT
ijassa-1257	159	1	2.3	2.3	NUM
ijassa-1257	159	2	.	.	PUNCT
ijassa-1257	160	1	optimum	optimum	ADJ
ijassa-1257	160	2	consumption	consumption	NOUN
ijassa-1257	160	3	management	management	NOUN
ijassa-1257	160	4	in	in	ADP
ijassa-1257	160	5	household	household	NOUN
ijassa-1257	160	6	model	model	NOUN
ijassa-1257	160	7	in	in	ADP
ijassa-1257	160	8	this	this	DET
ijassa-1257	160	9	section	section	NOUN
ijassa-1257	160	10	,	,	PUNCT
ijassa-1257	160	11	we	we	PRON
ijassa-1257	160	12	study	study	VERB
ijassa-1257	160	13	a	a	DET
ijassa-1257	160	14	household	household	NOUN
ijassa-1257	160	15	model	model	NOUN
ijassa-1257	160	16	in	in	ADP
ijassa-1257	160	17	more	more	ADJ
ijassa-1257	160	18	detail	detail	NOUN
ijassa-1257	160	19	,	,	PUNCT
ijassa-1257	160	20	see	see	VERB
ijassa-1257	160	21	[	[	X
ijassa-1257	160	22	17	17	NUM
ijassa-1257	160	23	,	,	PUNCT
ijassa-1257	160	24	21	21	NUM
ijassa-1257	160	25	]	]	PUNCT
ijassa-1257	160	26	.	.	PUNCT
ijassa-1257	161	1	as	as	ADP
ijassa-1257	161	2	in	in	ADP
ijassa-1257	161	3	the	the	DET
ijassa-1257	161	4	solow	solow	PROPN
ijassa-1257	161	5	model	model	NOUN
ijassa-1257	161	6	,	,	PUNCT
ijassa-1257	161	7	the	the	DET
ijassa-1257	161	8	study	study	NOUN
ijassa-1257	161	9	is	be	AUX
ijassa-1257	161	10	based	base	VERB
ijassa-1257	161	11	on	on	ADP
ijassa-1257	161	12	the	the	DET
ijassa-1257	161	13	maximization	maximization	NOUN
ijassa-1257	161	14	of	of	ADP
ijassa-1257	161	15	the	the	DET
ijassa-1257	161	16	functional	functional	ADJ
ijassa-1257	161	17	(	(	PUNCT
ijassa-1257	161	18	2.30	2.30	NUM
ijassa-1257	161	19	)	)	PUNCT
ijassa-1257	161	20	,	,	PUNCT
ijassa-1257	161	21	and	and	CCONJ
ijassa-1257	161	22	the	the	DET
ijassa-1257	161	23	utility	utility	NOUN
ijassa-1257	161	24	function	function	NOUN
ijassa-1257	161	25	u(c	u(c	PROPN
ijassa-1257	161	26	)	)	PUNCT
ijassa-1257	161	27	satisfies	satisfy	VERB
ijassa-1257	161	28	the	the	DET
ijassa-1257	161	29	conditions	condition	NOUN
ijassa-1257	161	30	(	(	PUNCT
ijassa-1257	161	31	2.31	2.31	NUM
ijassa-1257	161	32	)	)	PUNCT
ijassa-1257	161	33	.	.	PUNCT
ijassa-1257	162	1	however	however	ADV
ijassa-1257	162	2	,	,	PUNCT
ijassa-1257	162	3	the	the	DET
ijassa-1257	162	4	constrains	constrain	NOUN
ijassa-1257	162	5	now	now	ADV
ijassa-1257	162	6	have	have	VERB
ijassa-1257	162	7	the	the	DET
ijassa-1257	162	8	form	form	NOUN
ijassa-1257	162	9	of	of	ADP
ijassa-1257	162	10	the	the	DET
ijassa-1257	162	11	balance	balance	NOUN
ijassa-1257	162	12	equation	equation	NOUN
ijassa-1257	162	13	for	for	ADP
ijassa-1257	162	14	accumulated	accumulate	VERB
ijassa-1257	162	15	household	household	NOUN
ijassa-1257	162	16	savings	saving	NOUN
ijassa-1257	162	17	(	(	PUNCT
ijassa-1257	162	18	see	see	VERB
ijassa-1257	162	19	(	(	PUNCT
ijassa-1257	162	20	1.19	1.19	NUM
ijassa-1257	162	21	)	)	PUNCT
ijassa-1257	162	22	)	)	PUNCT
ijassa-1257	162	23	,	,	PUNCT
ijassa-1257	162	24	that	that	ADV
ijassa-1257	162	25	is	be	AUX
ijassa-1257	162	26	,	,	PUNCT
ijassa-1257	162	27	x′(t	x′(t	PROPN
ijassa-1257	162	28	)	)	PUNCT
ijassa-1257	162	29	=	=	SYM
ijassa-1257	162	30	p(t)x(t	p(t)x(t	NOUN
ijassa-1257	162	31	)	)	PUNCT
ijassa-1257	163	1	+	+	NOUN
ijassa-1257	164	1	p	p	X
ijassa-1257	164	2	(	(	PUNCT
ijassa-1257	164	3	t)−	t)−	PROPN
ijassa-1257	164	4	c(t	c(t	PROPN
ijassa-1257	164	5	)	)	PUNCT
ijassa-1257	164	6	,	,	PUNCT
ijassa-1257	164	7	x(t0	x(t0	PROPN
ijassa-1257	164	8	)	)	PUNCT
ijassa-1257	165	1	=	=	PUNCT
ijassa-1257	166	1	x0	x0	PROPN
ijassa-1257	166	2	≥	≥	NOUN
ijassa-1257	166	3	0	0	NUM
ijassa-1257	166	4	,	,	PUNCT
ijassa-1257	166	5	x(t1	x(t1	PUNCT
ijassa-1257	166	6	)	)	PUNCT
ijassa-1257	167	1	=	=	PUNCT
ijassa-1257	167	2	x1	x1	NUM
ijassa-1257	167	3	≥	≥	NOUN
ijassa-1257	167	4	0	0	NUM
ijassa-1257	167	5	.	.	PUNCT
ijassa-1257	168	1	(	(	PUNCT
ijassa-1257	168	2	2.40	2.40	NUM
ijassa-1257	168	3	)	)	PUNCT
ijassa-1257	168	4	then	then	ADV
ijassa-1257	168	5	the	the	DET
ijassa-1257	168	6	euler	euler	PROPN
ijassa-1257	168	7	–	–	PUNCT
ijassa-1257	168	8	lagrange	lagrange	NOUN
ijassa-1257	168	9	equation	equation	NOUN
ijassa-1257	168	10	(	(	PUNCT
ijassa-1257	168	11	a	a	DET
ijassa-1257	168	12	necessary	necessary	ADJ
ijassa-1257	168	13	condition	condition	NOUN
ijassa-1257	168	14	of	of	ADP
ijassa-1257	168	15	optimality	optimality	NOUN
ijassa-1257	168	16	)	)	PUNCT
ijassa-1257	168	17	reads	read	VERB
ijassa-1257	168	18	d	d	X
ijassa-1257	168	19	dt	dt	X
ijassa-1257	168	20	(	(	PUNCT
ijassa-1257	168	21	g(c(t))e−δt	g(c(t))e−δt	PROPN
ijassa-1257	168	22	)	)	PUNCT
ijassa-1257	169	1	+	+	CCONJ
ijassa-1257	169	2	g(c(t))p(t)e−δt	g(c(t))p(t)e−δt	PROPN
ijassa-1257	169	3	=	=	SYM
ijassa-1257	169	4	0	0	X
ijassa-1257	169	5	.	.	PUNCT
ijassa-1257	170	1	(	(	PUNCT
ijassa-1257	170	2	2.41	2.41	NUM
ijassa-1257	170	3	)	)	PUNCT
ijassa-1257	170	4	integrating	integrating	NOUN
ijassa-1257	170	5	(	(	PUNCT
ijassa-1257	170	6	2.41	2.41	NUM
ijassa-1257	170	7	)	)	PUNCT
ijassa-1257	170	8	,	,	PUNCT
ijassa-1257	170	9	we	we	PRON
ijassa-1257	170	10	have	have	VERB
ijassa-1257	170	11	c(t	c(t	NUM
ijassa-1257	170	12	)	)	PUNCT
ijassa-1257	170	13	=	=	SYM
ijassa-1257	171	1	g−1	g−1	PROPN
ijassa-1257	171	2	(	(	PUNCT
ijassa-1257	171	3	d	d	NOUN
ijassa-1257	171	4	exp	exp	X
ijassa-1257	171	5	{	{	PUNCT
ijassa-1257	171	6	δt−	δt−	NUM
ijassa-1257	171	7	∫	∫	PROPN
ijassa-1257	171	8	t	t	PROPN
ijassa-1257	171	9	t0	t0	PROPN
ijassa-1257	171	10	p(s)ds	p(s)ds	PROPN
ijassa-1257	171	11	}	}	PUNCT
ijassa-1257	171	12	)	)	PUNCT
ijassa-1257	171	13	.	.	PUNCT
ijassa-1257	172	1	(	(	PUNCT
ijassa-1257	172	2	2.42	2.42	NUM
ijassa-1257	172	3	)	)	PUNCT
ijassa-1257	172	4	as	as	ADP
ijassa-1257	172	5	before	before	ADV
ijassa-1257	172	6	,	,	PUNCT
ijassa-1257	172	7	the	the	DET
ijassa-1257	172	8	condition	condition	NOUN
ijassa-1257	172	9	(	(	PUNCT
ijassa-1257	172	10	2.31	2.31	NUM
ijassa-1257	172	11	)	)	PUNCT
ijassa-1257	172	12	gives	give	VERB
ijassa-1257	172	13	a	a	DET
ijassa-1257	172	14	sufficient	sufficient	ADJ
ijassa-1257	172	15	condition	condition	NOUN
ijassa-1257	172	16	of	of	ADP
ijassa-1257	172	17	optimality	optimality	NOUN
ijassa-1257	172	18	.	.	PUNCT
ijassa-1257	173	1	moreover	moreover	ADV
ijassa-1257	173	2	,	,	PUNCT
ijassa-1257	173	3	for	for	ADP
ijassa-1257	173	4	the	the	DET
ijassa-1257	173	5	cauchy	cauchy	ADJ
ijassa-1257	173	6	problem	problem	NOUN
ijassa-1257	173	7	obtained	obtain	VERB
ijassa-1257	173	8	from	from	ADP
ijassa-1257	173	9	the	the	DET
ijassa-1257	173	10	condition	condition	NOUN
ijassa-1257	173	11	(	(	PUNCT
ijassa-1257	173	12	2.40	2.40	NUM
ijassa-1257	173	13	)	)	PUNCT
ijassa-1257	173	14	by	by	ADP
ijassa-1257	173	15	elimination	elimination	NOUN
ijassa-1257	173	16	the	the	DET
ijassa-1257	173	17	last	last	ADJ
ijassa-1257	173	18	equality	equality	NOUN
ijassa-1257	173	19	(	(	PUNCT
ijassa-1257	173	20	for	for	ADP
ijassa-1257	173	21	x(t1	x(t1	NOUN
ijassa-1257	173	22	)	)	PUNCT
ijassa-1257	173	23	)	)	PUNCT
ijassa-1257	174	1	one	one	PRON
ijassa-1257	174	2	can	can	AUX
ijassa-1257	174	3	write	write	VERB
ijassa-1257	174	4	the	the	DET
ijassa-1257	174	5	solution	solution	NOUN
ijassa-1257	174	6	:	:	PUNCT
ijassa-1257	174	7	x(t	x(t	PROPN
ijassa-1257	174	8	)	)	PUNCT
ijassa-1257	175	1	=	=	SYM
ijassa-1257	175	2	ew	ew	INTJ
ijassa-1257	175	3	(	(	PUNCT
ijassa-1257	175	4	t	t	PROPN
ijassa-1257	175	5	)	)	PUNCT
ijassa-1257	175	6	(	(	PUNCT
ijassa-1257	175	7	x0	x0	PROPN
ijassa-1257	175	8	+	+	CCONJ
ijassa-1257	175	9	∫	∫	PROPN
ijassa-1257	175	10	t	t	PROPN
ijassa-1257	175	11	t0	t0	PROPN
ijassa-1257	175	12	(	(	PUNCT
ijassa-1257	175	13	p	p	X
ijassa-1257	175	14	(	(	PUNCT
ijassa-1257	175	15	τ)−	τ)−	PROPN
ijassa-1257	175	16	c(τ))e−w	c(τ))e−w	PROPN
ijassa-1257	175	17	(	(	PUNCT
ijassa-1257	175	18	τ)dτ	τ)dτ	PROPN
ijassa-1257	175	19	)	)	PUNCT
ijassa-1257	175	20	,	,	PUNCT
ijassa-1257	175	21	w	w	PROPN
ijassa-1257	175	22	(	(	PUNCT
ijassa-1257	175	23	t	t	PROPN
ijassa-1257	175	24	)	)	PUNCT
ijassa-1257	175	25	=	=	SYM
ijassa-1257	176	1	∫	∫	PROPN
ijassa-1257	176	2	t	t	PROPN
ijassa-1257	176	3	t0	t0	PROPN
ijassa-1257	176	4	p(s)ds	p(s)ds	ADV
ijassa-1257	176	5	.	.	PUNCT
ijassa-1257	177	1	(	(	PUNCT
ijassa-1257	177	2	2.43	2.43	NUM
ijassa-1257	177	3	)	)	PUNCT
ijassa-1257	177	4	theorem	theorem	VERB
ijassa-1257	177	5	2.3	2.3	NUM
ijassa-1257	177	6	:	:	PUNCT
ijassa-1257	177	7	under	under	ADP
ijassa-1257	177	8	the	the	DET
ijassa-1257	177	9	above	above	ADJ
ijassa-1257	177	10	conditions	condition	NOUN
ijassa-1257	177	11	,	,	PUNCT
ijassa-1257	177	12	the	the	DET
ijassa-1257	177	13	total	total	ADJ
ijassa-1257	177	14	consumption	consumption	NOUN
ijassa-1257	177	15	c(t	c(t	PROPN
ijassa-1257	177	16	)	)	PUNCT
ijassa-1257	177	17	is	be	AUX
ijassa-1257	177	18	given	give	VERB
ijassa-1257	177	19	by	by	ADP
ijassa-1257	177	20	the	the	DET
ijassa-1257	177	21	formula	formula	NOUN
ijassa-1257	177	22	c(t	c(t	PROPN
ijassa-1257	177	23	)	)	PUNCT
ijassa-1257	177	24	=	=	SYM
ijassa-1257	178	1	∫	∫	PROPN
ijassa-1257	178	2	t1	t1	PROPN
ijassa-1257	178	3	t0	t0	PROPN
ijassa-1257	178	4	p	p	X
ijassa-1257	178	5	(	(	PUNCT
ijassa-1257	178	6	τ)e−w	τ)e−w	PUNCT
ijassa-1257	178	7	(	(	PUNCT
ijassa-1257	178	8	τ)dτ	τ)dτ	ADJ
ijassa-1257	178	9	+	+	NUM
ijassa-1257	178	10	x0	x0	PROPN
ijassa-1257	178	11	−	−	PROPN
ijassa-1257	178	12	x1e	x1e	PROPN
ijassa-1257	178	13	−w	−w	ADV
ijassa-1257	178	14	(	(	PUNCT
ijassa-1257	178	15	t1)∫	t1)∫	PROPN
ijassa-1257	178	16	t1	t1	PROPN
ijassa-1257	178	17	t0	t0	PROPN
ijassa-1257	178	18	exp	exp	NOUN
ijassa-1257	178	19	{	{	PUNCT
ijassa-1257	178	20	(	(	PUNCT
ijassa-1257	178	21	1	1	NUM
ijassa-1257	178	22	a	a	DET
ijassa-1257	178	23	−	−	PROPN
ijassa-1257	178	24	1)w	1)w	NUM
ijassa-1257	178	25	(	(	PUNCT
ijassa-1257	178	26	τ)−	τ)−	PROPN
ijassa-1257	178	27	δ	δ	PROPN
ijassa-1257	178	28	a	a	PRON
ijassa-1257	178	29	τ	τ	PROPN
ijassa-1257	178	30	}	}	PUNCT
ijassa-1257	178	31	dτ	dτ	NOUN
ijassa-1257	178	32	exp	exp	NOUN
ijassa-1257	178	33	{	{	PUNCT
ijassa-1257	178	34	1	1	NUM
ijassa-1257	178	35	a	a	PRON
ijassa-1257	178	36	(	(	PUNCT
ijassa-1257	178	37	w	w	NOUN
ijassa-1257	178	38	(	(	PUNCT
ijassa-1257	178	39	t)−	t)−	PROPN
ijassa-1257	178	40	δt	δt	NOUN
ijassa-1257	178	41	)	)	PUNCT
ijassa-1257	178	42	}	}	PUNCT
ijassa-1257	178	43	.	.	PUNCT
ijassa-1257	179	1	(	(	PUNCT
ijassa-1257	179	2	2.44	2.44	NUM
ijassa-1257	179	3	)	)	PUNCT
ijassa-1257	179	4	copyright	copyright	NOUN
ijassa-1257	179	5	©	©	PROPN
ijassa-1257	179	6	2022	2022	NUM
ijassa-1257	179	7	assa	assa	NOUN
ijassa-1257	179	8	.	.	PUNCT
ijassa-1257	180	1	adv	adv	PROPN
ijassa-1257	180	2	syst	syst	PROPN
ijassa-1257	180	3	sci	sci	PROPN
ijassa-1257	180	4	appl	appl	PROPN
ijassa-1257	180	5	(	(	PUNCT
ijassa-1257	180	6	2022	2022	NUM
ijassa-1257	180	7	)	)	PUNCT
ijassa-1257	180	8	116	116	NUM
ijassa-1257	180	9	a.p	a.p	PROPN
ijassa-1257	180	10	.	.	PROPN
ijassa-1257	180	11	chernyaev	chernyaev	PROPN
ijassa-1257	180	12	proof	proof	NOUN
ijassa-1257	180	13	from	from	ADP
ijassa-1257	180	14	(	(	PUNCT
ijassa-1257	180	15	2.34	2.34	NUM
ijassa-1257	180	16	)	)	PUNCT
ijassa-1257	180	17	we	we	PRON
ijassa-1257	180	18	have	have	VERB
ijassa-1257	180	19	g(c(t	g(c(t	NOUN
ijassa-1257	180	20	)	)	PUNCT
ijassa-1257	180	21	)	)	PUNCT
ijassa-1257	181	1	=	=	PUNCT
ijassa-1257	182	1	d	d	NOUN
ijassa-1257	182	2	exp{δt−w	exp{δt−w	X
ijassa-1257	182	3	(	(	PUNCT
ijassa-1257	182	4	t	t	PROPN
ijassa-1257	182	5	)	)	PUNCT
ijassa-1257	182	6	}	}	PUNCT
ijassa-1257	182	7	,	,	PUNCT
ijassa-1257	182	8	d	d	NOUN
ijassa-1257	182	9	=	=	SYM
ijassa-1257	182	10	const	const	X
ijassa-1257	182	11	>	>	X
ijassa-1257	182	12	0	0	NUM
ijassa-1257	182	13	.	.	PUNCT
ijassa-1257	182	14	(	(	PUNCT
ijassa-1257	182	15	2.45	2.45	NUM
ijassa-1257	182	16	)	)	PUNCT
ijassa-1257	182	17	from	from	ADP
ijassa-1257	182	18	(	(	PUNCT
ijassa-1257	182	19	2.31	2.31	NUM
ijassa-1257	182	20	)	)	PUNCT
ijassa-1257	182	21	we	we	PRON
ijassa-1257	182	22	get	get	VERB
ijassa-1257	182	23	g(c	g(c	NOUN
ijassa-1257	182	24	)	)	PUNCT
ijassa-1257	182	25	=	=	PUNCT
ijassa-1257	183	1	γc−a	γc−a	ADJ
ijassa-1257	183	2	,	,	PUNCT
ijassa-1257	183	3	γ	γ	X
ijassa-1257	183	4	=	=	SYM
ijassa-1257	183	5	const	const	X
ijassa-1257	183	6	>	>	X
ijassa-1257	183	7	0	0	X
ijassa-1257	183	8	.	.	PUNCT
ijassa-1257	184	1	substituting	substitute	VERB
ijassa-1257	184	2	this	this	DET
ijassa-1257	184	3	expression	expression	NOUN
ijassa-1257	184	4	into	into	ADP
ijassa-1257	184	5	(	(	PUNCT
ijassa-1257	184	6	2.45	2.45	NUM
ijassa-1257	184	7	)	)	PUNCT
ijassa-1257	184	8	,	,	PUNCT
ijassa-1257	184	9	we	we	PRON
ijassa-1257	184	10	obtain	obtain	VERB
ijassa-1257	184	11	the	the	DET
ijassa-1257	184	12	equation	equation	NOUN
ijassa-1257	184	13	c(t	c(t	PROPN
ijassa-1257	184	14	)	)	PUNCT
ijassa-1257	184	15	=	=	SYM
ijassa-1257	184	16	c0	c0	PROPN
ijassa-1257	184	17	exp	exp	PROPN
ijassa-1257	184	18	{	{	PUNCT
ijassa-1257	184	19	1	1	NUM
ijassa-1257	184	20	a	a	PRON
ijassa-1257	184	21	(	(	PUNCT
ijassa-1257	184	22	w	w	NOUN
ijassa-1257	184	23	(	(	PUNCT
ijassa-1257	184	24	t)−	t)−	PROPN
ijassa-1257	184	25	δt	δt	NOUN
ijassa-1257	184	26	)	)	PUNCT
ijassa-1257	184	27	}	}	PUNCT
ijassa-1257	184	28	,	,	PUNCT
ijassa-1257	184	29	c0	c0	NOUN
ijassa-1257	184	30	=	=	PUNCT
ijassa-1257	184	31	(	(	PUNCT
ijassa-1257	184	32	γ	γ	X
ijassa-1257	184	33	d	d	PROPN
ijassa-1257	184	34	)	)	PUNCT
ijassa-1257	184	35	1	1	NUM
ijassa-1257	184	36	a	a	PRON
ijassa-1257	184	37	.	.	PUNCT
ijassa-1257	185	1	(	(	PUNCT
ijassa-1257	185	2	2.46	2.46	NUM
ijassa-1257	185	3	)	)	PUNCT
ijassa-1257	185	4	after	after	ADP
ijassa-1257	185	5	that	that	PRON
ijassa-1257	185	6	,	,	PUNCT
ijassa-1257	185	7	from	from	ADP
ijassa-1257	185	8	(	(	PUNCT
ijassa-1257	185	9	2.40	2.40	NUM
ijassa-1257	185	10	)	)	PUNCT
ijassa-1257	185	11	,	,	PUNCT
ijassa-1257	185	12	(	(	PUNCT
ijassa-1257	185	13	2.43	2.43	NUM
ijassa-1257	185	14	)	)	PUNCT
ijassa-1257	185	15	,	,	PUNCT
ijassa-1257	185	16	(	(	PUNCT
ijassa-1257	185	17	2.46	2.46	NUM
ijassa-1257	185	18	)	)	PUNCT
ijassa-1257	185	19	we	we	PRON
ijassa-1257	185	20	have	have	VERB
ijassa-1257	185	21	the	the	DET
ijassa-1257	185	22	equality	equality	NOUN
ijassa-1257	185	23	x1e	x1e	PROPN
ijassa-1257	185	24	−w	−w	ADV
ijassa-1257	185	25	(	(	PUNCT
ijassa-1257	185	26	t1	t1	NOUN
ijassa-1257	185	27	)	)	PUNCT
ijassa-1257	186	1	−	−	NOUN
ijassa-1257	187	1	x0	x0	PROPN
ijassa-1257	188	1	=	=	SYM
ijassa-1257	189	1	∫	∫	PROPN
ijassa-1257	189	2	t1	t1	PROPN
ijassa-1257	189	3	t0	t0	PROPN
ijassa-1257	189	4	(	(	PUNCT
ijassa-1257	189	5	p	p	X
ijassa-1257	189	6	(	(	PUNCT
ijassa-1257	189	7	τ)−	τ)−	PROPN
ijassa-1257	189	8	c0	c0	PROPN
ijassa-1257	189	9	exp	exp	PROPN
ijassa-1257	189	10	{	{	PUNCT
ijassa-1257	189	11	1	1	NUM
ijassa-1257	189	12	a	a	DET
ijassa-1257	189	13	(	(	PUNCT
ijassa-1257	189	14	w	w	PROPN
ijassa-1257	189	15	(	(	PUNCT
ijassa-1257	189	16	τ)−	τ)−	PROPN
ijassa-1257	189	17	δτ	δτ	VERB
ijassa-1257	189	18	)	)	PUNCT
ijassa-1257	189	19	}	}	PUNCT
ijassa-1257	189	20	)	)	PUNCT
ijassa-1257	189	21	e−w	e−w	NOUN
ijassa-1257	189	22	(	(	PUNCT
ijassa-1257	189	23	τ)dτ	τ)dτ	PROPN
ijassa-1257	189	24	,	,	PUNCT
ijassa-1257	189	25	(	(	PUNCT
ijassa-1257	189	26	2.47	2.47	NUM
ijassa-1257	189	27	)	)	PUNCT
ijassa-1257	189	28	which	which	PRON
ijassa-1257	189	29	yields	yield	VERB
ijassa-1257	189	30	c0	c0	PROPN
ijassa-1257	189	31	=	=	SYM
ijassa-1257	189	32	∫	∫	PROPN
ijassa-1257	189	33	t1	t1	PROPN
ijassa-1257	189	34	t0	t0	PROPN
ijassa-1257	189	35	p	p	X
ijassa-1257	189	36	(	(	PUNCT
ijassa-1257	189	37	τ)e−w	τ)e−w	PUNCT
ijassa-1257	189	38	(	(	PUNCT
ijassa-1257	189	39	τ)dτ	τ)dτ	ADJ
ijassa-1257	189	40	+	+	NUM
ijassa-1257	189	41	x0	x0	PROPN
ijassa-1257	189	42	−	−	PROPN
ijassa-1257	189	43	x1e	x1e	PROPN
ijassa-1257	189	44	−w	−w	ADV
ijassa-1257	189	45	(	(	PUNCT
ijassa-1257	189	46	t1)∫	t1)∫	PROPN
ijassa-1257	189	47	t1	t1	PROPN
ijassa-1257	189	48	t0	t0	PROPN
ijassa-1257	189	49	exp	exp	NOUN
ijassa-1257	189	50	{	{	PUNCT
ijassa-1257	189	51	1	1	NUM
ijassa-1257	189	52	a	a	DET
ijassa-1257	189	53	(	(	PUNCT
ijassa-1257	189	54	w	w	PROPN
ijassa-1257	189	55	(	(	PUNCT
ijassa-1257	189	56	τ)−	τ)−	PROPN
ijassa-1257	189	57	δτ)−w	δτ)−w	PROPN
ijassa-1257	189	58	(	(	PUNCT
ijassa-1257	189	59	τ)}dτ	τ)}dτ	PROPN
ijassa-1257	189	60	.	.	PUNCT
ijassa-1257	190	1	(	(	PUNCT
ijassa-1257	190	2	2.48	2.48	NUM
ijassa-1257	190	3	)	)	PUNCT
ijassa-1257	190	4	finally	finally	ADV
ijassa-1257	190	5	,	,	PUNCT
ijassa-1257	190	6	from	from	ADP
ijassa-1257	190	7	(	(	PUNCT
ijassa-1257	190	8	2.46	2.46	NUM
ijassa-1257	190	9	)	)	PUNCT
ijassa-1257	190	10	and	and	CCONJ
ijassa-1257	190	11	(	(	PUNCT
ijassa-1257	190	12	2.48	2.48	NUM
ijassa-1257	190	13	)	)	PUNCT
ijassa-1257	190	14	we	we	PRON
ijassa-1257	190	15	obtain	obtain	VERB
ijassa-1257	190	16	(	(	PUNCT
ijassa-1257	190	17	2.44	2.44	NUM
ijassa-1257	190	18	)	)	PUNCT
ijassa-1257	190	19	.	.	PUNCT
ijassa-1257	191	1	2.4	2.4	NUM
ijassa-1257	191	2	.	.	PUNCT
ijassa-1257	191	3	restrictions	restriction	NOUN
ijassa-1257	191	4	on	on	ADP
ijassa-1257	191	5	the	the	DET
ijassa-1257	191	6	accumulated	accumulate	VERB
ijassa-1257	191	7	savings	saving	NOUN
ijassa-1257	191	8	in	in	ADP
ijassa-1257	191	9	household	household	NOUN
ijassa-1257	191	10	model	model	NOUN
ijassa-1257	191	11	in	in	ADP
ijassa-1257	191	12	this	this	DET
ijassa-1257	191	13	section	section	NOUN
ijassa-1257	191	14	,	,	PUNCT
ijassa-1257	191	15	we	we	PRON
ijassa-1257	191	16	obtain	obtain	VERB
ijassa-1257	191	17	conditions	condition	NOUN
ijassa-1257	191	18	for	for	ADP
ijassa-1257	191	19	no	no	DET
ijassa-1257	191	20	debt	debt	NOUN
ijassa-1257	191	21	in	in	ADP
ijassa-1257	191	22	the	the	PRON
ijassa-1257	191	23	in	in	ADP
ijassa-1257	191	24	the	the	DET
ijassa-1257	191	25	household	household	NOUN
ijassa-1257	191	26	model	model	NOUN
ijassa-1257	191	27	considered	consider	VERB
ijassa-1257	191	28	above	above	ADV
ijassa-1257	191	29	.	.	PUNCT
ijassa-1257	192	1	in	in	ADP
ijassa-1257	192	2	our	our	PRON
ijassa-1257	192	3	notations	notation	NOUN
ijassa-1257	192	4	,	,	PUNCT
ijassa-1257	192	5	no	no	DET
ijassa-1257	192	6	debt	debt	NOUN
ijassa-1257	192	7	is	be	AUX
ijassa-1257	192	8	the	the	DET
ijassa-1257	192	9	inequality	inequality	NOUN
ijassa-1257	192	10	x(t	x(t	PROPN
ijassa-1257	192	11	)	)	PUNCT
ijassa-1257	192	12	≥	≥	NOUN
ijassa-1257	192	13	0	0	NUM
ijassa-1257	192	14	,	,	PUNCT
ijassa-1257	192	15	t0	t0	PROPN
ijassa-1257	192	16	≤	≤	PROPN
ijassa-1257	192	17	t	t	PROPN
ijassa-1257	192	18	≤	≤	NUM
ijassa-1257	192	19	t1	t1	PROPN
ijassa-1257	192	20	.	.	PUNCT
ijassa-1257	193	1	(	(	PUNCT
ijassa-1257	193	2	2.49	2.49	NUM
ijassa-1257	193	3	)	)	PUNCT
ijassa-1257	193	4	theorem	theorem	VERB
ijassa-1257	193	5	2.4	2.4	NUM
ijassa-1257	193	6	:	:	PUNCT
ijassa-1257	193	7	a	a	DET
ijassa-1257	193	8	sufficient	sufficient	ADJ
ijassa-1257	193	9	condition	condition	NOUN
ijassa-1257	193	10	for	for	ADP
ijassa-1257	193	11	(	(	PUNCT
ijassa-1257	193	12	2.49	2.49	NUM
ijassa-1257	193	13	)	)	PUNCT
ijassa-1257	193	14	is	be	AUX
ijassa-1257	193	15	given	give	VERB
ijassa-1257	193	16	by	by	ADP
ijassa-1257	193	17	the	the	DET
ijassa-1257	193	18	inequality	inequality	NOUN
ijassa-1257	193	19	φ(t)−	φ(t)−	PROPN
ijassa-1257	193	20	φ(t1	φ(t1	PROPN
ijassa-1257	193	21	)	)	PUNCT
ijassa-1257	193	22	≥	≥	NOUN
ijassa-1257	193	23	0	0	NUM
ijassa-1257	193	24	,	,	PUNCT
ijassa-1257	193	25	t0	t0	PROPN
ijassa-1257	193	26	≤	≤	PROPN
ijassa-1257	193	27	t	t	PROPN
ijassa-1257	193	28	≤	≤	NUM
ijassa-1257	193	29	t1	t1	PROPN
ijassa-1257	193	30	.	.	PUNCT
ijassa-1257	194	1	(	(	PUNCT
ijassa-1257	194	2	2.50	2.50	NUM
ijassa-1257	194	3	)	)	PUNCT
ijassa-1257	194	4	proof	proof	NOUN
ijassa-1257	194	5	first	first	ADV
ijassa-1257	194	6	,	,	PUNCT
ijassa-1257	194	7	let	let	VERB
ijassa-1257	194	8	us	we	PRON
ijassa-1257	194	9	prove	prove	VERB
ijassa-1257	194	10	that	that	SCONJ
ijassa-1257	194	11	the	the	DET
ijassa-1257	194	12	inequality	inequality	NOUN
ijassa-1257	194	13	x(t	x(t	PROPN
ijassa-1257	194	14	)	)	PUNCT
ijassa-1257	194	15	≥	≥	NOUN
ijassa-1257	194	16	x0	x0	PROPN
ijassa-1257	195	1	+	+	CCONJ
ijassa-1257	195	2	∫	∫	PROPN
ijassa-1257	195	3	t	t	PROPN
ijassa-1257	195	4	t0	t0	PROPN
ijassa-1257	195	5	p(τ)x(τ)dτ	p(τ)x(τ)dτ	PROPN
ijassa-1257	195	6	,	,	PUNCT
ijassa-1257	195	7	t0	t0	PROPN
ijassa-1257	195	8	≤	≤	PROPN
ijassa-1257	195	9	t	t	PROPN
ijassa-1257	195	10	≤	≤	NUM
ijassa-1257	195	11	t1	t1	PROPN
ijassa-1257	195	12	,	,	PUNCT
ijassa-1257	195	13	(	(	PUNCT
ijassa-1257	195	14	2.51	2.51	NUM
ijassa-1257	195	15	)	)	PUNCT
ijassa-1257	195	16	is	be	AUX
ijassa-1257	195	17	equivalent	equivalent	ADJ
ijassa-1257	195	18	to	to	ADP
ijassa-1257	195	19	∫	∫	PROPN
ijassa-1257	195	20	t	t	PROPN
ijassa-1257	195	21	t0	t0	PROPN
ijassa-1257	195	22	(	(	PUNCT
ijassa-1257	195	23	p	p	X
ijassa-1257	195	24	(	(	PUNCT
ijassa-1257	195	25	τ)−	τ)−	PROPN
ijassa-1257	195	26	c(τ))dτ	c(τ))dτ	PROPN
ijassa-1257	195	27	,	,	PUNCT
ijassa-1257	195	28	t0	t0	PROPN
ijassa-1257	195	29	≤	≤	PROPN
ijassa-1257	195	30	t	t	PROPN
ijassa-1257	195	31	≤	≤	NUM
ijassa-1257	195	32	t1	t1	PROPN
ijassa-1257	195	33	.	.	PUNCT
ijassa-1257	196	1	(	(	PUNCT
ijassa-1257	196	2	2.52	2.52	NUM
ijassa-1257	196	3	)	)	PUNCT
ijassa-1257	196	4	indeed	indeed	ADV
ijassa-1257	196	5	,	,	PUNCT
ijassa-1257	196	6	integrating	integrate	VERB
ijassa-1257	196	7	the	the	DET
ijassa-1257	196	8	both	both	DET
ijassa-1257	196	9	sides	side	NOUN
ijassa-1257	196	10	of	of	ADP
ijassa-1257	196	11	the	the	DET
ijassa-1257	196	12	equation	equation	NOUN
ijassa-1257	196	13	(	(	PUNCT
ijassa-1257	196	14	2.40	2.40	NUM
ijassa-1257	196	15	)	)	PUNCT
ijassa-1257	196	16	,	,	PUNCT
ijassa-1257	196	17	we	we	PRON
ijassa-1257	196	18	have	have	VERB
ijassa-1257	196	19	the	the	DET
ijassa-1257	196	20	equality	equality	NOUN
ijassa-1257	196	21	x(t)−	x(t)−	PROPN
ijassa-1257	196	22	x0	x0	PROPN
ijassa-1257	197	1	=	=	PUNCT
ijassa-1257	197	2	∫	∫	PROPN
ijassa-1257	197	3	t	t	PROPN
ijassa-1257	197	4	t0	t0	PROPN
ijassa-1257	197	5	p(τ)x(τ)dτ	p(τ)x(τ)dτ	PROPN
ijassa-1257	198	1	+	+	CCONJ
ijassa-1257	198	2	∫	∫	PROPN
ijassa-1257	198	3	t	t	PROPN
ijassa-1257	198	4	t0	t0	PROPN
ijassa-1257	198	5	(	(	PUNCT
ijassa-1257	198	6	p	p	X
ijassa-1257	198	7	(	(	PUNCT
ijassa-1257	198	8	τ)−	τ)−	PROPN
ijassa-1257	198	9	c(τ))dτ	c(τ))dτ	PROPN
ijassa-1257	198	10	,	,	PUNCT
ijassa-1257	198	11	which	which	PRON
ijassa-1257	198	12	shows	show	VERB
ijassa-1257	198	13	the	the	DET
ijassa-1257	198	14	equivalence	equivalence	NOUN
ijassa-1257	198	15	of	of	ADP
ijassa-1257	198	16	(	(	PUNCT
ijassa-1257	198	17	2.51	2.51	NUM
ijassa-1257	198	18	)	)	PUNCT
ijassa-1257	198	19	and	and	CCONJ
ijassa-1257	198	20	(	(	PUNCT
ijassa-1257	198	21	2.52	2.52	NUM
ijassa-1257	198	22	)	)	PUNCT
ijassa-1257	198	23	.	.	PUNCT
ijassa-1257	199	1	it	it	PRON
ijassa-1257	199	2	should	should	AUX
ijassa-1257	199	3	be	be	AUX
ijassa-1257	199	4	noted	note	VERB
ijassa-1257	199	5	that	that	SCONJ
ijassa-1257	199	6	the	the	DET
ijassa-1257	199	7	inequality	inequality	NOUN
ijassa-1257	199	8	(	(	PUNCT
ijassa-1257	199	9	2.51	2.51	NUM
ijassa-1257	199	10	)	)	PUNCT
ijassa-1257	199	11	has	have	VERB
ijassa-1257	199	12	an	an	DET
ijassa-1257	199	13	obvious	obvious	ADJ
ijassa-1257	199	14	economic	economic	ADJ
ijassa-1257	199	15	meaning	meaning	NOUN
ijassa-1257	199	16	:	:	PUNCT
ijassa-1257	199	17	the	the	DET
ijassa-1257	199	18	righthand	righthand	NOUN
ijassa-1257	199	19	side	side	NOUN
ijassa-1257	199	20	of	of	ADP
ijassa-1257	199	21	(	(	PUNCT
ijassa-1257	199	22	2.51	2.51	NUM
ijassa-1257	199	23	)	)	PUNCT
ijassa-1257	199	24	is	be	AUX
ijassa-1257	199	25	the	the	DET
ijassa-1257	199	26	amount	amount	NOUN
ijassa-1257	199	27	of	of	ADP
ijassa-1257	199	28	money	money	NOUN
ijassa-1257	199	29	that	that	PRON
ijassa-1257	199	30	would	would	AUX
ijassa-1257	199	31	be	be	AUX
ijassa-1257	199	32	on	on	ADP
ijassa-1257	199	33	the	the	DET
ijassa-1257	199	34	deposit	deposit	NOUN
ijassa-1257	199	35	account	account	NOUN
ijassa-1257	199	36	at	at	ADP
ijassa-1257	199	37	the	the	DET
ijassa-1257	199	38	moment	moment	NOUN
ijassa-1257	199	39	t	t	NOUN
ijassa-1257	199	40	if	if	SCONJ
ijassa-1257	199	41	the	the	DET
ijassa-1257	199	42	amount	amount	NOUN
ijassa-1257	199	43	x0	x0	PROPN
ijassa-1257	199	44	was	be	AUX
ijassa-1257	199	45	deposited	deposit	VERB
ijassa-1257	199	46	on	on	ADP
ijassa-1257	199	47	the	the	DET
ijassa-1257	199	48	account	account	NOUN
ijassa-1257	199	49	at	at	ADP
ijassa-1257	199	50	the	the	DET
ijassa-1257	199	51	moment	moment	NOUN
ijassa-1257	199	52	t0	t0	PROPN
ijassa-1257	199	53	.	.	PUNCT
ijassa-1257	200	1	copyright	copyright	NOUN
ijassa-1257	200	2	©	©	PROPN
ijassa-1257	200	3	2022	2022	NUM
ijassa-1257	200	4	assa	assa	NOUN
ijassa-1257	200	5	.	.	PUNCT
ijassa-1257	201	1	adv	adv	PROPN
ijassa-1257	201	2	syst	syst	PROPN
ijassa-1257	201	3	sci	sci	PROPN
ijassa-1257	201	4	appl	appl	PROPN
ijassa-1257	201	5	(	(	PUNCT
ijassa-1257	201	6	2022	2022	NUM
ijassa-1257	201	7	)	)	PUNCT
ijassa-1257	201	8	the	the	DET
ijassa-1257	201	9	optimal	optimal	ADJ
ijassa-1257	201	10	control	control	NOUN
ijassa-1257	201	11	approach	approach	NOUN
ijassa-1257	201	12	in	in	ADP
ijassa-1257	201	13	problems	problem	NOUN
ijassa-1257	201	14	of	of	ADP
ijassa-1257	201	15	the	the	DET
ijassa-1257	201	16	income	income	NOUN
ijassa-1257	201	17	distribution	distribution	NOUN
ijassa-1257	201	18	117	117	NUM
ijassa-1257	201	19	second	second	ADJ
ijassa-1257	201	20	,	,	PUNCT
ijassa-1257	201	21	let	let	VERB
ijassa-1257	201	22	us	we	PRON
ijassa-1257	201	23	present	present	VERB
ijassa-1257	201	24	(	(	PUNCT
ijassa-1257	201	25	2.52	2.52	NUM
ijassa-1257	201	26	)	)	PUNCT
ijassa-1257	201	27	in	in	ADP
ijassa-1257	201	28	the	the	DET
ijassa-1257	201	29	form	form	NOUN
ijassa-1257	201	30	x(t	x(t	PROPN
ijassa-1257	201	31	)	)	PUNCT
ijassa-1257	202	1	=	=	SYM
ijassa-1257	202	2	ψ(t)ew	ψ(t)ew	NOUN
ijassa-1257	202	3	(	(	PUNCT
ijassa-1257	202	4	t)(φ(t)−	t)(φ(t)−	NOUN
ijassa-1257	202	5	φ(t1	φ(t1	NUM
ijassa-1257	202	6	)	)	PUNCT
ijassa-1257	202	7	)	)	PUNCT
ijassa-1257	203	1	+	+	CCONJ
ijassa-1257	203	2	x1	x1	PROPN
ijassa-1257	203	3	φ(t	φ(t	PROPN
ijassa-1257	203	4	)	)	PUNCT
ijassa-1257	203	5	φ(t1	φ(t1	NOUN
ijassa-1257	203	6	)	)	PUNCT
ijassa-1257	204	1	ew	ew	INTJ
ijassa-1257	204	2	(	(	PUNCT
ijassa-1257	204	3	t)−w	t)−w	PROPN
ijassa-1257	204	4	(	(	PUNCT
ijassa-1257	204	5	t1	t1	PROPN
ijassa-1257	204	6	)	)	PUNCT
ijassa-1257	204	7	,	,	PUNCT
ijassa-1257	204	8	(	(	PUNCT
ijassa-1257	204	9	2.53	2.53	NUM
ijassa-1257	204	10	)	)	PUNCT
ijassa-1257	204	11	with	with	ADP
ijassa-1257	204	12	the	the	DET
ijassa-1257	204	13	functions	function	NOUN
ijassa-1257	204	14	ψ(t	ψ(t	PROPN
ijassa-1257	204	15	)	)	PUNCT
ijassa-1257	204	16	=	=	SYM
ijassa-1257	204	17	∫	∫	PROPN
ijassa-1257	204	18	t	t	PROPN
ijassa-1257	204	19	t0	t0	PROPN
ijassa-1257	204	20	exp	exp	X
ijassa-1257	204	21	{	{	PUNCT
ijassa-1257	204	22	(	(	PUNCT
ijassa-1257	204	23	1	1	NUM
ijassa-1257	204	24	a	a	DET
ijassa-1257	204	25	−	−	PROPN
ijassa-1257	204	26	1)w	1)w	NUM
ijassa-1257	204	27	(	(	PUNCT
ijassa-1257	204	28	τ)−	τ)−	PROPN
ijassa-1257	204	29	δ	δ	PROPN
ijassa-1257	204	30	a	a	PRON
ijassa-1257	204	31	τ	τ	PROPN
ijassa-1257	204	32	}	}	PUNCT
ijassa-1257	204	33	dτ	dτ	PROPN
ijassa-1257	204	34	,	,	PUNCT
ijassa-1257	204	35	φ(t	φ(t	PROPN
ijassa-1257	204	36	)	)	PUNCT
ijassa-1257	204	37	=	=	PUNCT
ijassa-1257	205	1	(	(	PUNCT
ijassa-1257	205	2	x0	x0	PROPN
ijassa-1257	205	3	+	+	CCONJ
ijassa-1257	205	4	∫	∫	PROPN
ijassa-1257	205	5	t	t	PROPN
ijassa-1257	205	6	t0	t0	PROPN
ijassa-1257	205	7	p	p	X
ijassa-1257	205	8	(	(	PUNCT
ijassa-1257	205	9	τ)e−w	τ)e−w	ADJ
ijassa-1257	205	10	(	(	PUNCT
ijassa-1257	205	11	τ)dτ	τ)dτ	PROPN
ijassa-1257	205	12	)	)	PUNCT
ijassa-1257	205	13	ψ−1(t	ψ−1(t	PROPN
ijassa-1257	205	14	)	)	PUNCT
ijassa-1257	205	15	.	.	PUNCT
ijassa-1257	206	1	(	(	PUNCT
ijassa-1257	206	2	2.54	2.54	NUM
ijassa-1257	206	3	)	)	PUNCT
ijassa-1257	206	4	since	since	SCONJ
ijassa-1257	206	5	the	the	DET
ijassa-1257	206	6	function	function	NOUN
ijassa-1257	206	7	ψ	ψ	NOUN
ijassa-1257	206	8	is	be	AUX
ijassa-1257	206	9	strictly	strictly	ADV
ijassa-1257	206	10	positive	positive	ADJ
ijassa-1257	206	11	and	and	CCONJ
ijassa-1257	206	12	x1	x1	PRON
ijassa-1257	206	13	≥	≥	NOUN
ijassa-1257	206	14	0	0	NUM
ijassa-1257	206	15	,	,	PUNCT
ijassa-1257	206	16	the	the	DET
ijassa-1257	206	17	equality	equality	NOUN
ijassa-1257	206	18	(	(	PUNCT
ijassa-1257	206	19	2.53	2.53	NUM
ijassa-1257	206	20	)	)	PUNCT
ijassa-1257	206	21	obviously	obviously	ADV
ijassa-1257	206	22	shows	show	VERB
ijassa-1257	206	23	that	that	SCONJ
ijassa-1257	206	24	(	(	PUNCT
ijassa-1257	206	25	2.50	2.50	NUM
ijassa-1257	206	26	)	)	PUNCT
ijassa-1257	206	27	implies	imply	VERB
ijassa-1257	206	28	(	(	PUNCT
ijassa-1257	206	29	2.49	2.49	NUM
ijassa-1257	206	30	)	)	PUNCT
ijassa-1257	206	31	.	.	PUNCT
ijassa-1257	207	1	the	the	DET
ijassa-1257	207	2	function	function	NOUN
ijassa-1257	207	3	φ	φ	PROPN
ijassa-1257	207	4	defined	define	VERB
ijassa-1257	207	5	above	above	ADV
ijassa-1257	207	6	is	be	AUX
ijassa-1257	207	7	called	call	VERB
ijassa-1257	207	8	the	the	DET
ijassa-1257	207	9	indicator	indicator	NOUN
ijassa-1257	207	10	function	function	NOUN
ijassa-1257	207	11	of	of	ADP
ijassa-1257	207	12	the	the	DET
ijassa-1257	207	13	model	model	NOUN
ijassa-1257	207	14	.	.	PUNCT
ijassa-1257	208	1	theorem	theorem	VERB
ijassa-1257	208	2	2.4	2.4	NUM
ijassa-1257	208	3	states	state	NOUN
ijassa-1257	208	4	that	that	SCONJ
ijassa-1257	208	5	if	if	SCONJ
ijassa-1257	208	6	the	the	DET
ijassa-1257	208	7	indicator	indicator	NOUN
ijassa-1257	208	8	function	function	NOUN
ijassa-1257	208	9	decreases	decrease	VERB
ijassa-1257	208	10	,	,	PUNCT
ijassa-1257	208	11	then	then	ADV
ijassa-1257	208	12	the	the	DET
ijassa-1257	208	13	condition	condition	NOUN
ijassa-1257	208	14	(	(	PUNCT
ijassa-1257	208	15	2.49	2.49	NUM
ijassa-1257	208	16	)	)	PUNCT
ijassa-1257	208	17	holds	hold	VERB
ijassa-1257	208	18	true	true	ADJ
ijassa-1257	208	19	.	.	PUNCT
ijassa-1257	209	1	3	3	X
ijassa-1257	209	2	.	.	X
ijassa-1257	209	3	examples	example	NOUN
ijassa-1257	209	4	of	of	ADP
ijassa-1257	209	5	indicator	indicator	NOUN
ijassa-1257	209	6	functions	function	NOUN
ijassa-1257	209	7	here	here	ADV
ijassa-1257	209	8	we	we	PRON
ijassa-1257	209	9	discuss	discuss	VERB
ijassa-1257	209	10	several	several	ADJ
ijassa-1257	209	11	examples	example	NOUN
ijassa-1257	209	12	of	of	ADP
ijassa-1257	209	13	monotonically	monotonically	ADV
ijassa-1257	209	14	decreasing	decrease	VERB
ijassa-1257	209	15	indicator	indicator	NOUN
ijassa-1257	209	16	functions	function	NOUN
ijassa-1257	209	17	in	in	ADP
ijassa-1257	209	18	the	the	DET
ijassa-1257	209	19	household	household	NOUN
ijassa-1257	209	20	model	model	NOUN
ijassa-1257	209	21	.	.	PUNCT
ijassa-1257	210	1	let	let	VERB
ijassa-1257	210	2	p	p	NOUN
ijassa-1257	210	3	(	(	PUNCT
ijassa-1257	210	4	t	t	NOUN
ijassa-1257	210	5	)	)	PUNCT
ijassa-1257	210	6	=	=	NOUN
ijassa-1257	210	7	p0e	p0e	NOUN
ijassa-1257	210	8	r(t−t0	r(t−t0	PROPN
ijassa-1257	210	9	)	)	PUNCT
ijassa-1257	210	10	,	,	PUNCT
ijassa-1257	210	11	p0	p0	NOUN
ijassa-1257	210	12	=	=	SYM
ijassa-1257	210	13	const	const	X
ijassa-1257	210	14	>	>	X
ijassa-1257	210	15	0	0	NUM
ijassa-1257	210	16	,	,	PUNCT
ijassa-1257	210	17	p(t	p(t	NOUN
ijassa-1257	210	18	)	)	PUNCT
ijassa-1257	211	1	=	=	PUNCT
ijassa-1257	212	1	p	p	NOUN
ijassa-1257	212	2	=	=	PUNCT
ijassa-1257	212	3	const	const	X
ijassa-1257	212	4	>	>	X
ijassa-1257	212	5	0	0	NUM
ijassa-1257	212	6	.	.	PUNCT
ijassa-1257	213	1	(	(	PUNCT
ijassa-1257	213	2	3.55	3.55	NUM
ijassa-1257	213	3	)	)	PUNCT
ijassa-1257	213	4	then	then	ADV
ijassa-1257	213	5	from	from	ADP
ijassa-1257	213	6	(	(	PUNCT
ijassa-1257	213	7	2.54	2.54	NUM
ijassa-1257	213	8	)	)	PUNCT
ijassa-1257	213	9	we	we	PRON
ijassa-1257	213	10	have	have	VERB
ijassa-1257	213	11	φ(t	φ(t	PROPN
ijassa-1257	213	12	)	)	PUNCT
ijassa-1257	214	1	=	=	SYM
ijassa-1257	214	2	x0e	x0e	PUNCT
ijassa-1257	214	3	p(t−t0	p(t−t0	PROPN
ijassa-1257	214	4	)	)	PUNCT
ijassa-1257	215	1	+	+	CCONJ
ijassa-1257	215	2	p0e	p0e	NOUN
ijassa-1257	215	3	pt−rt0	pt−rt0	VERB
ijassa-1257	215	4	∫	∫	PROPN
ijassa-1257	215	5	t	t	PROPN
ijassa-1257	215	6	t0	t0	PROPN
ijassa-1257	215	7	e(r−p)τdτ	e(r−p)τdτ	PROPN
ijassa-1257	215	8	ep(t−t0	ep(t−t0	PROPN
ijassa-1257	215	9	/	/	SYM
ijassa-1257	215	10	a	a	NOUN
ijassa-1257	215	11	)	)	PUNCT
ijassa-1257	215	12	∫	∫	PROPN
ijassa-1257	215	13	t	t	PROPN
ijassa-1257	215	14	t0	t0	PROPN
ijassa-1257	215	15	exp	exp	PROPN
ijassa-1257	215	16	{	{	PUNCT
ijassa-1257	215	17	(	(	PUNCT
ijassa-1257	215	18	(	(	PUNCT
ijassa-1257	215	19	1	1	NUM
ijassa-1257	215	20	a	a	DET
ijassa-1257	215	21	−	−	PROPN
ijassa-1257	215	22	1)p−	1)p−	NUM
ijassa-1257	215	23	δ	δ	PROPN
ijassa-1257	215	24	a	a	PRON
ijassa-1257	215	25	)	)	PUNCT
ijassa-1257	215	26	τ}dτ	τ}dτ	PROPN
ijassa-1257	215	27	.	.	PUNCT
ijassa-1257	216	1	(	(	PUNCT
ijassa-1257	216	2	3.56	3.56	NUM
ijassa-1257	216	3	)	)	PUNCT
ijassa-1257	216	4	to	to	PART
ijassa-1257	216	5	simplify	simplify	VERB
ijassa-1257	216	6	further	further	ADJ
ijassa-1257	216	7	calculations	calculation	NOUN
ijassa-1257	216	8	,	,	PUNCT
ijassa-1257	216	9	we	we	PRON
ijassa-1257	216	10	introduce	introduce	VERB
ijassa-1257	216	11	new	new	ADJ
ijassa-1257	216	12	notations	notation	NOUN
ijassa-1257	216	13	:	:	PUNCT
ijassa-1257	216	14	θ	θ	X
ijassa-1257	216	15	=	=	PUNCT
ijassa-1257	216	16	(	(	PUNCT
ijassa-1257	216	17	1	1	NUM
ijassa-1257	216	18	a	a	DET
ijassa-1257	216	19	−	−	PROPN
ijassa-1257	216	20	1)p−	1)p−	NUM
ijassa-1257	216	21	δ	δ	PROPN
ijassa-1257	216	22	a	a	X
ijassa-1257	216	23	,	,	PUNCT
ijassa-1257	217	1	θ	θ	X
ijassa-1257	217	2	=	=	PUNCT
ijassa-1257	217	3	r	r	NOUN
ijassa-1257	218	1	−	−	PROPN
ijassa-1257	218	2	p.	p.	NOUN
ijassa-1257	218	3	first	first	ADV
ijassa-1257	218	4	,	,	PUNCT
ijassa-1257	218	5	consider	consider	VERB
ijassa-1257	218	6	the	the	DET
ijassa-1257	218	7	generic	generic	ADJ
ijassa-1257	218	8	case	case	NOUN
ijassa-1257	218	9	:	:	PUNCT
ijassa-1257	218	10	θ	θ	PROPN
ijassa-1257	218	11	6=	6=	ADP
ijassa-1257	218	12	0	0	NUM
ijassa-1257	218	13	and	and	CCONJ
ijassa-1257	218	14	θ	θ	PROPN
ijassa-1257	218	15	6=	6=	ADP
ijassa-1257	218	16	0	0	NUM
ijassa-1257	218	17	.	.	PUNCT
ijassa-1257	219	1	then	then	ADV
ijassa-1257	219	2	formula	formula	NOUN
ijassa-1257	219	3	(	(	PUNCT
ijassa-1257	219	4	3.56	3.56	NUM
ijassa-1257	219	5	)	)	PUNCT
ijassa-1257	219	6	yields	yield	VERB
ijassa-1257	219	7	the	the	DET
ijassa-1257	219	8	indicator	indicator	NOUN
ijassa-1257	219	9	function	function	PROPN
ijassa-1257	219	10	φ(t	φ(t	PROPN
ijassa-1257	219	11	)	)	PUNCT
ijassa-1257	219	12	=	=	PUNCT
ijassa-1257	220	1	e	e	PART
ijassa-1257	220	2	δ	δ	PROPN
ijassa-1257	220	3	a	a	DET
ijassa-1257	220	4	t0	t0	PROPN
ijassa-1257	220	5	(	(	PUNCT
ijassa-1257	220	6	x0	x0	PROPN
ijassa-1257	220	7	θ	θ	PROPN
ijassa-1257	220	8	eθ(t−t0	eθ(t−t0	NOUN
ijassa-1257	220	9	)	)	PUNCT
ijassa-1257	220	10	−	−	NOUN
ijassa-1257	220	11	1	1	NUM
ijassa-1257	221	1	+	+	NUM
ijassa-1257	221	2	p0	p0	NOUN
ijassa-1257	221	3	θ(eθ(t−t0	θ(eθ(t−t0	NUM
ijassa-1257	221	4	)	)	PUNCT
ijassa-1257	221	5	−	−	ADP
ijassa-1257	221	6	1	1	NUM
ijassa-1257	221	7	)	)	PUNCT
ijassa-1257	221	8	θ(eθ(t−t0	θ(eθ(t−t0	PROPN
ijassa-1257	221	9	)	)	PUNCT
ijassa-1257	221	10	−	−	ADP
ijassa-1257	221	11	1	1	NUM
ijassa-1257	221	12	)	)	PUNCT
ijassa-1257	221	13	)	)	PUNCT
ijassa-1257	221	14	.	.	PUNCT
ijassa-1257	222	1	(	(	PUNCT
ijassa-1257	222	2	3.57	3.57	NUM
ijassa-1257	222	3	)	)	PUNCT
ijassa-1257	222	4	now	now	ADV
ijassa-1257	222	5	consider	consider	VERB
ijassa-1257	222	6	the	the	DET
ijassa-1257	222	7	partial	partial	ADJ
ijassa-1257	222	8	cases	case	NOUN
ijassa-1257	222	9	:	:	PUNCT
ijassa-1257	222	10	1	1	X
ijassa-1257	222	11	.	.	X
ijassa-1257	222	12	assume	assume	VERB
ijassa-1257	222	13	that	that	SCONJ
ijassa-1257	222	14	θ	θ	PROPN
ijassa-1257	222	15	=	=	SYM
ijassa-1257	222	16	θ	θ	PROPN
ijassa-1257	222	17	and	and	CCONJ
ijassa-1257	222	18	θ	θ	PROPN
ijassa-1257	222	19	6=	6=	ADP
ijassa-1257	222	20	0	0	NUM
ijassa-1257	222	21	.	.	PUNCT
ijassa-1257	223	1	then	then	ADV
ijassa-1257	223	2	we	we	PRON
ijassa-1257	223	3	have	have	VERB
ijassa-1257	223	4	the	the	DET
ijassa-1257	223	5	function	function	NOUN
ijassa-1257	223	6	φ(t	φ(t	PROPN
ijassa-1257	223	7	)	)	PUNCT
ijassa-1257	223	8	=	=	PUNCT
ijassa-1257	223	9	e	e	PART
ijassa-1257	223	10	δ	δ	PROPN
ijassa-1257	223	11	a	a	DET
ijassa-1257	223	12	t0	t0	PROPN
ijassa-1257	223	13	(	(	PUNCT
ijassa-1257	223	14	x0	x0	PROPN
ijassa-1257	223	15	θ	θ	PROPN
ijassa-1257	223	16	eθ(t−t0	eθ(t−t0	NOUN
ijassa-1257	223	17	)	)	PUNCT
ijassa-1257	223	18	−	−	NOUN
ijassa-1257	223	19	1	1	NUM
ijassa-1257	223	20	+	+	NUM
ijassa-1257	223	21	p0	p0	NOUN
ijassa-1257	223	22	)	)	PUNCT
ijassa-1257	223	23	,	,	PUNCT
ijassa-1257	223	24	which	which	PRON
ijassa-1257	223	25	is	be	AUX
ijassa-1257	223	26	monotonically	monotonically	ADV
ijassa-1257	223	27	decreasing	decrease	VERB
ijassa-1257	223	28	.	.	PUNCT
ijassa-1257	224	1	2	2	X
ijassa-1257	224	2	.	.	X
ijassa-1257	224	3	assume	assume	VERB
ijassa-1257	224	4	that	that	SCONJ
ijassa-1257	224	5	θ	θ	PROPN
ijassa-1257	224	6	>	>	X
ijassa-1257	224	7	0	0	PUNCT
ijassa-1257	224	8	and	and	CCONJ
ijassa-1257	224	9	θ	θ	PROPN
ijassa-1257	224	10	=	=	SYM
ijassa-1257	225	1	0	0	X
ijassa-1257	225	2	.	.	PUNCT
ijassa-1257	225	3	then	then	ADV
ijassa-1257	225	4	taking	take	VERB
ijassa-1257	225	5	to	to	ADP
ijassa-1257	225	6	the	the	DET
ijassa-1257	225	7	limit	limit	NOUN
ijassa-1257	225	8	θ	θ	X
ijassa-1257	225	9	→	→	SYM
ijassa-1257	225	10	0	0	NUM
ijassa-1257	225	11	in	in	ADP
ijassa-1257	225	12	(	(	PUNCT
ijassa-1257	225	13	3.57	3.57	NUM
ijassa-1257	225	14	)	)	PUNCT
ijassa-1257	225	15	,	,	PUNCT
ijassa-1257	225	16	we	we	PRON
ijassa-1257	225	17	get	get	VERB
ijassa-1257	225	18	φ(t	φ(t	PROPN
ijassa-1257	225	19	)	)	PUNCT
ijassa-1257	225	20	=	=	PUNCT
ijassa-1257	226	1	e	e	PART
ijassa-1257	226	2	δ	δ	PROPN
ijassa-1257	226	3	a	a	DET
ijassa-1257	226	4	t0	t0	PROPN
ijassa-1257	226	5	(	(	PUNCT
ijassa-1257	226	6	x0	x0	PROPN
ijassa-1257	226	7	θ	θ	PROPN
ijassa-1257	226	8	eθ(t−t0	eθ(t−t0	NOUN
ijassa-1257	226	9	)	)	PUNCT
ijassa-1257	226	10	−	−	NOUN
ijassa-1257	226	11	1	1	NUM
ijassa-1257	226	12	+	+	NUM
ijassa-1257	226	13	p0	p0	NOUN
ijassa-1257	226	14	θ(t−	θ(t−	PROPN
ijassa-1257	226	15	t0	t0	PROPN
ijassa-1257	226	16	)	)	PUNCT
ijassa-1257	226	17	eθ(t−t0	eθ(t−t0	NOUN
ijassa-1257	226	18	)	)	PUNCT
ijassa-1257	226	19	−	−	PROPN
ijassa-1257	226	20	1	1	NUM
ijassa-1257	226	21	)	)	PUNCT
ijassa-1257	226	22	,	,	PUNCT
ijassa-1257	226	23	copyright	copyright	NOUN
ijassa-1257	226	24	©	©	PROPN
ijassa-1257	226	25	2022	2022	NUM
ijassa-1257	226	26	assa	assa	NOUN
ijassa-1257	226	27	.	.	PUNCT
ijassa-1257	227	1	adv	adv	PROPN
ijassa-1257	227	2	syst	syst	PROPN
ijassa-1257	227	3	sci	sci	PROPN
ijassa-1257	227	4	appl	appl	PROPN
ijassa-1257	227	5	(	(	PUNCT
ijassa-1257	227	6	2022	2022	NUM
ijassa-1257	227	7	)	)	PUNCT
ijassa-1257	227	8	118	118	NUM
ijassa-1257	227	9	a.p	a.p	PROPN
ijassa-1257	227	10	.	.	PROPN
ijassa-1257	227	11	chernyaev	chernyaev	PROPN
ijassa-1257	227	12	which	which	PRON
ijassa-1257	227	13	is	be	AUX
ijassa-1257	227	14	also	also	ADV
ijassa-1257	227	15	a	a	DET
ijassa-1257	227	16	monotonically	monotonically	ADV
ijassa-1257	227	17	decreasing	decrease	VERB
ijassa-1257	227	18	function	function	NOUN
ijassa-1257	227	19	.	.	PUNCT
ijassa-1257	228	1	3	3	X
ijassa-1257	228	2	.	.	X
ijassa-1257	228	3	assume	assume	VERB
ijassa-1257	228	4	that	that	SCONJ
ijassa-1257	228	5	θ	θ	PROPN
ijassa-1257	228	6	=	=	SYM
ijassa-1257	228	7	θ	θ	X
ijassa-1257	228	8	=	=	SYM
ijassa-1257	229	1	0	0	X
ijassa-1257	229	2	.	.	PUNCT
ijassa-1257	229	3	then	then	ADV
ijassa-1257	229	4	taking	take	VERB
ijassa-1257	229	5	to	to	ADP
ijassa-1257	229	6	the	the	DET
ijassa-1257	229	7	limit	limit	NOUN
ijassa-1257	229	8	θ	θ	PROPN
ijassa-1257	229	9	,	,	PUNCT
ijassa-1257	229	10	θ	θ	PROPN
ijassa-1257	229	11	→	→	SYM
ijassa-1257	229	12	0	0	NUM
ijassa-1257	229	13	in	in	ADP
ijassa-1257	229	14	(	(	PUNCT
ijassa-1257	229	15	3.57	3.57	NUM
ijassa-1257	229	16	)	)	PUNCT
ijassa-1257	229	17	,	,	PUNCT
ijassa-1257	229	18	we	we	PRON
ijassa-1257	229	19	obtain	obtain	VERB
ijassa-1257	229	20	the	the	DET
ijassa-1257	229	21	function	function	NOUN
ijassa-1257	229	22	φ(t	φ(t	PROPN
ijassa-1257	229	23	)	)	PUNCT
ijassa-1257	229	24	=	=	PUNCT
ijassa-1257	229	25	e	e	PART
ijassa-1257	229	26	δ	δ	PROPN
ijassa-1257	229	27	a	a	DET
ijassa-1257	229	28	t0	t0	PROPN
ijassa-1257	229	29	(	(	PUNCT
ijassa-1257	229	30	x0	x0	PROPN
ijassa-1257	229	31	t−	t−	PROPN
ijassa-1257	229	32	t0	t0	PROPN
ijassa-1257	229	33	+	+	CCONJ
ijassa-1257	229	34	p0	p0	NOUN
ijassa-1257	229	35	)	)	PUNCT
ijassa-1257	229	36	.	.	PUNCT
ijassa-1257	230	1	this	this	PRON
ijassa-1257	230	2	is	be	AUX
ijassa-1257	230	3	a	a	DET
ijassa-1257	230	4	monotonically	monotonically	ADV
ijassa-1257	230	5	decreasing	decrease	VERB
ijassa-1257	230	6	function	function	NOUN
ijassa-1257	230	7	as	as	ADV
ijassa-1257	230	8	well	well	ADV
ijassa-1257	230	9	.	.	PUNCT
ijassa-1257	231	1	4	4	X
ijassa-1257	231	2	.	.	X
ijassa-1257	231	3	conclusion	conclusion	VERB
ijassa-1257	231	4	the	the	DET
ijassa-1257	231	5	validity	validity	NOUN
ijassa-1257	231	6	of	of	ADP
ijassa-1257	231	7	the	the	DET
ijassa-1257	231	8	basic	basic	ADJ
ijassa-1257	231	9	economic	economic	ADJ
ijassa-1257	231	10	identity	identity	NOUN
ijassa-1257	231	11	in	in	ADP
ijassa-1257	231	12	all	all	DET
ijassa-1257	231	13	the	the	DET
ijassa-1257	231	14	models	model	NOUN
ijassa-1257	231	15	considered	consider	VERB
ijassa-1257	231	16	in	in	ADP
ijassa-1257	231	17	the	the	DET
ijassa-1257	231	18	paper	paper	NOUN
ijassa-1257	231	19	allows	allow	VERB
ijassa-1257	231	20	to	to	PART
ijassa-1257	231	21	determine	determine	VERB
ijassa-1257	231	22	general	general	ADJ
ijassa-1257	231	23	laws	law	NOUN
ijassa-1257	231	24	.	.	PUNCT
ijassa-1257	232	1	the	the	DET
ijassa-1257	232	2	introduced	introduce	VERB
ijassa-1257	232	3	new	new	ADJ
ijassa-1257	232	4	variable	variable	NOUN
ijassa-1257	232	5	–	–	PUNCT
ijassa-1257	232	6	the	the	DET
ijassa-1257	232	7	relative	relative	ADJ
ijassa-1257	232	8	increase	increase	NOUN
ijassa-1257	232	9	of	of	ADP
ijassa-1257	232	10	the	the	DET
ijassa-1257	232	11	income	income	NOUN
ijassa-1257	232	12	–	–	PUNCT
ijassa-1257	232	13	makes	make	VERB
ijassa-1257	232	14	it	it	PRON
ijassa-1257	232	15	possible	possible	ADJ
ijassa-1257	232	16	to	to	PART
ijassa-1257	232	17	establish	establish	VERB
ijassa-1257	232	18	a	a	DET
ijassa-1257	232	19	correspondence	correspondence	NOUN
ijassa-1257	232	20	between	between	ADP
ijassa-1257	232	21	the	the	DET
ijassa-1257	232	22	harrod	harrod	NOUN
ijassa-1257	232	23	–	–	PUNCT
ijassa-1257	232	24	domar	domar	NOUN
ijassa-1257	232	25	models	model	NOUN
ijassa-1257	232	26	with	with	ADP
ijassa-1257	232	27	variable	variable	ADJ
ijassa-1257	232	28	incremental	incremental	ADJ
ijassa-1257	232	29	capital	capital	NOUN
ijassa-1257	232	30	intensity	intensity	NOUN
ijassa-1257	232	31	and	and	CCONJ
ijassa-1257	232	32	the	the	DET
ijassa-1257	232	33	solow	solow	PROPN
ijassa-1257	232	34	model	model	NOUN
ijassa-1257	232	35	with	with	ADP
ijassa-1257	232	36	variable	variable	ADJ
ijassa-1257	232	37	rate	rate	NOUN
ijassa-1257	232	38	of	of	ADP
ijassa-1257	232	39	accumulation	accumulation	NOUN
ijassa-1257	232	40	.	.	PUNCT
ijassa-1257	233	1	since	since	SCONJ
ijassa-1257	233	2	households	household	NOUN
ijassa-1257	233	3	are	be	AUX
ijassa-1257	233	4	the	the	DET
ijassa-1257	233	5	best	good	ADJ
ijassa-1257	233	6	savers	saver	NOUN
ijassa-1257	233	7	and	and	CCONJ
ijassa-1257	233	8	they	they	PRON
ijassa-1257	233	9	have	have	VERB
ijassa-1257	233	10	the	the	DET
ijassa-1257	233	11	best	good	ADJ
ijassa-1257	233	12	survival	survival	NOUN
ijassa-1257	233	13	rates	rate	NOUN
ijassa-1257	233	14	,	,	PUNCT
ijassa-1257	233	15	the	the	DET
ijassa-1257	233	16	savings	saving	NOUN
ijassa-1257	233	17	regimes	regime	NOUN
ijassa-1257	233	18	in	in	ADP
ijassa-1257	233	19	the	the	DET
ijassa-1257	233	20	harrod	harrod	NOUN
ijassa-1257	233	21	–	–	PUNCT
ijassa-1257	233	22	domar	domar	NOUN
ijassa-1257	233	23	model	model	NOUN
ijassa-1257	233	24	and	and	CCONJ
ijassa-1257	233	25	the	the	DET
ijassa-1257	233	26	solow	solow	PROPN
ijassa-1257	233	27	model	model	NOUN
ijassa-1257	233	28	are	be	AUX
ijassa-1257	233	29	examined	examine	VERB
ijassa-1257	233	30	.	.	PUNCT
ijassa-1257	234	1	finally	finally	ADV
ijassa-1257	234	2	,	,	PUNCT
ijassa-1257	234	3	we	we	PRON
ijassa-1257	234	4	analyze	analyze	VERB
ijassa-1257	234	5	a	a	DET
ijassa-1257	234	6	modification	modification	NOUN
ijassa-1257	234	7	of	of	ADP
ijassa-1257	234	8	the	the	DET
ijassa-1257	234	9	above	above	ADJ
ijassa-1257	234	10	macromodels	macromodel	NOUN
ijassa-1257	234	11	replacing	replace	VERB
ijassa-1257	234	12	the	the	DET
ijassa-1257	234	13	given	give	VERB
ijassa-1257	234	14	production	production	NOUN
ijassa-1257	234	15	functions	function	NOUN
ijassa-1257	234	16	by	by	ADP
ijassa-1257	234	17	setting	set	VERB
ijassa-1257	234	18	the	the	DET
ijassa-1257	234	19	problem	problem	NOUN
ijassa-1257	234	20	of	of	ADP
ijassa-1257	234	21	maximizing	maximize	VERB
ijassa-1257	234	22	the	the	DET
ijassa-1257	234	23	integral	integral	ADJ
ijassa-1257	234	24	discounted	discount	VERB
ijassa-1257	234	25	utility	utility	NOUN
ijassa-1257	234	26	of	of	ADP
ijassa-1257	234	27	the	the	DET
ijassa-1257	234	28	consumption	consumption	NOUN
ijassa-1257	234	29	.	.	PUNCT
ijassa-1257	235	1	in	in	ADP
ijassa-1257	235	2	this	this	DET
ijassa-1257	235	3	case	case	NOUN
ijassa-1257	235	4	,	,	PUNCT
ijassa-1257	235	5	the	the	DET
ijassa-1257	235	6	utility	utility	NOUN
ijassa-1257	235	7	function	function	NOUN
ijassa-1257	235	8	satisfies	satisfy	VERB
ijassa-1257	235	9	the	the	DET
ijassa-1257	235	10	arrow	arrow	NOUN
ijassa-1257	235	11	–	–	PUNCT
ijassa-1257	235	12	pratt	pratt	NOUN
ijassa-1257	235	13	condition	condition	NOUN
ijassa-1257	235	14	of	of	ADP
ijassa-1257	235	15	the	the	DET
ijassa-1257	235	16	relative	relative	ADJ
ijassa-1257	235	17	risk	risk	NOUN
ijassa-1257	235	18	aversion	aversion	NOUN
ijassa-1257	235	19	.	.	PUNCT
ijassa-1257	236	1	references	reference	NOUN
ijassa-1257	236	2	1	1	NUM
ijassa-1257	236	3	.	.	PUNCT
ijassa-1257	236	4	chernyaev	chernyaev	PROPN
ijassa-1257	236	5	a.p	a.p	PROPN
ijassa-1257	236	6	.	.	PROPN
ijassa-1257	236	7	(	(	PUNCT
ijassa-1257	236	8	2020	2020	NUM
ijassa-1257	236	9	)	)	PUNCT
ijassa-1257	236	10	comparison	comparison	NOUN
ijassa-1257	236	11	of	of	ADP
ijassa-1257	236	12	two	two	NUM
ijassa-1257	236	13	dynamic	dynamic	ADJ
ijassa-1257	236	14	models	model	NOUN
ijassa-1257	236	15	of	of	ADP
ijassa-1257	236	16	economic	economic	ADJ
ijassa-1257	236	17	growth	growth	NOUN
ijassa-1257	236	18	,	,	PUNCT
ijassa-1257	236	19	adv	adv	PROPN
ijassa-1257	236	20	.	.	PUNCT
ijassa-1257	236	21	syst	syst	PROPN
ijassa-1257	236	22	.	.	PUNCT
ijassa-1257	237	1	sci	sci	PROPN
ijassa-1257	237	2	.	.	PUNCT
ijassa-1257	237	3	appl	appl	PROPN
ijassa-1257	237	4	.	.	PROPN
ijassa-1257	237	5	,	,	PUNCT
ijassa-1257	237	6	20	20	NUM
ijassa-1257	237	7	2	2	NUM
ijassa-1257	237	8	,	,	PUNCT
ijassa-1257	237	9	71–81	71–81	NUM
ijassa-1257	237	10	.	.	NOUN
ijassa-1257	238	1	2	2	NUM
ijassa-1257	238	2	.	.	X
ijassa-1257	238	3	chernyaev	chernyaev	PROPN
ijassa-1257	238	4	a.p	a.p	PROPN
ijassa-1257	238	5	.	.	PROPN
ijassa-1257	238	6	,	,	PUNCT
ijassa-1257	238	7	meerson	meerson	PROPN
ijassa-1257	238	8	a.yu	a.yu	PROPN
ijassa-1257	238	9	.	.	PROPN
ijassa-1257	238	10	,	,	PUNCT
ijassa-1257	238	11	sukhorukova	sukhorukova	PROPN
ijassa-1257	238	12	i.v	i.v	PROPN
ijassa-1257	238	13	.	.	PROPN
ijassa-1257	238	14	,	,	PUNCT
ijassa-1257	238	15	&	&	CCONJ
ijassa-1257	238	16	fomin	fomin	PROPN
ijassa-1257	238	17	g.p	g.p	PROPN
ijassa-1257	238	18	.	.	PROPN
ijassa-1257	238	19	(	(	PUNCT
ijassa-1257	238	20	2020	2020	NUM
ijassa-1257	238	21	)	)	PUNCT
ijassa-1257	238	22	features	feature	NOUN
ijassa-1257	238	23	of	of	ADP
ijassa-1257	238	24	mathematical	mathematical	ADJ
ijassa-1257	238	25	formulation	formulation	NOUN
ijassa-1257	238	26	and	and	CCONJ
ijassa-1257	238	27	solution	solution	NOUN
ijassa-1257	238	28	of	of	ADP
ijassa-1257	238	29	the	the	DET
ijassa-1257	238	30	problem	problem	NOUN
ijassa-1257	238	31	of	of	ADP
ijassa-1257	238	32	optimal	optimal	ADJ
ijassa-1257	238	33	division	division	NOUN
ijassa-1257	238	34	of	of	ADP
ijassa-1257	238	35	funds	fund	NOUN
ijassa-1257	238	36	in	in	ADP
ijassa-1257	238	37	the	the	DET
ijassa-1257	238	38	construction	construction	NOUN
ijassa-1257	238	39	business	business	NOUN
ijassa-1257	238	40	,	,	PUNCT
ijassa-1257	238	41	iop	iop	PROPN
ijassa-1257	238	42	conf	conf	NOUN
ijassa-1257	238	43	.	.	PUNCT
ijassa-1257	239	1	ser	ser	PROPN
ijassa-1257	239	2	.	.	PUNCT
ijassa-1257	239	3	:	:	PUNCT
ijassa-1257	240	1	materials	material	NOUN
ijassa-1257	240	2	science	science	NOUN
ijassa-1257	240	3	&	&	CCONJ
ijassa-1257	240	4	engineering	engineering	PROPN
ijassa-1257	240	5	,	,	PUNCT
ijassa-1257	240	6	012002	012002	NUM
ijassa-1257	240	7	.	.	PUNCT
ijassa-1257	241	1	3	3	X
ijassa-1257	241	2	.	.	X
ijassa-1257	241	3	harrod	harrod	PROPN
ijassa-1257	241	4	,	,	PUNCT
ijassa-1257	241	5	r.f	r.f	PROPN
ijassa-1257	241	6	.	.	PROPN
ijassa-1257	241	7	(	(	PUNCT
ijassa-1257	241	8	1939	1939	NUM
ijassa-1257	241	9	)	)	PUNCT
ijassa-1257	241	10	an	an	DET
ijassa-1257	241	11	essay	essay	NOUN
ijassa-1257	241	12	in	in	ADP
ijassa-1257	241	13	dynamic	dynamic	ADJ
ijassa-1257	241	14	theory	theory	NOUN
ijassa-1257	241	15	,	,	PUNCT
ijassa-1257	241	16	economic	economic	ADJ
ijassa-1257	241	17	jornal	jornal	NOUN
ijassa-1257	241	18	,	,	PUNCT
ijassa-1257	241	19	49	49	NUM
ijassa-1257	241	20	,	,	PUNCT
ijassa-1257	241	21	14–33	14–33	NUM
ijassa-1257	241	22	.	.	NOUN
ijassa-1257	242	1	4	4	NUM
ijassa-1257	242	2	.	.	X
ijassa-1257	242	3	domar	domar	PROPN
ijassa-1257	242	4	,	,	PUNCT
ijassa-1257	242	5	e.	e.	PROPN
ijassa-1257	242	6	(	(	PUNCT
ijassa-1257	242	7	1946	1946	NUM
ijassa-1257	242	8	)	)	PUNCT
ijassa-1257	242	9	capital	capital	NOUN
ijassa-1257	242	10	expansion	expansion	NOUN
ijassa-1257	242	11	,	,	PUNCT
ijassa-1257	242	12	rate	rate	NOUN
ijassa-1257	242	13	of	of	ADP
ijassa-1257	242	14	growth	growth	NOUN
ijassa-1257	242	15	and	and	CCONJ
ijassa-1257	242	16	employment	employment	NOUN
ijassa-1257	242	17	,	,	PUNCT
ijassa-1257	242	18	econometrica	econometrica	PROPN
ijassa-1257	242	19	,	,	PUNCT
ijassa-1257	242	20	14	14	NUM
ijassa-1257	242	21	(	(	PUNCT
ijassa-1257	242	22	2	2	NUM
ijassa-1257	242	23	)	)	PUNCT
ijassa-1257	242	24	,	,	PUNCT
ijassa-1257	242	25	137–147	137–147	NUM
ijassa-1257	242	26	.	.	NOUN
ijassa-1257	243	1	5	5	NUM
ijassa-1257	243	2	.	.	X
ijassa-1257	244	1	hamburg	hamburg	PROPN
ijassa-1257	244	2	,	,	PUNCT
ijassa-1257	244	3	d.	d.	PROPN
ijassa-1257	244	4	(	(	PUNCT
ijassa-1257	244	5	1981	1981	NUM
ijassa-1257	244	6	)	)	PUNCT
ijassa-1257	244	7	early	early	ADJ
ijassa-1257	244	8	growth	growth	NOUN
ijassa-1257	244	9	theory	theory	NOUN
ijassa-1257	244	10	of	of	ADP
ijassa-1257	244	11	the	the	DET
ijassa-1257	244	12	domar	domar	NOUN
ijassa-1257	244	13	and	and	CCONJ
ijassa-1257	244	14	harrod	harrod	NOUN
ijassa-1257	244	15	.	.	PUNCT
ijassa-1257	245	1	moscow	moscow	PROPN
ijassa-1257	245	2	:	:	PUNCT
ijassa-1257	245	3	progress	progress	NOUN
ijassa-1257	245	4	.	.	PUNCT
ijassa-1257	246	1	6	6	X
ijassa-1257	246	2	.	.	X
ijassa-1257	246	3	meerson	meerson	PROPN
ijassa-1257	246	4	,	,	PUNCT
ijassa-1257	246	5	a.y	a.y	PROPN
ijassa-1257	246	6	.	.	PROPN
ijassa-1257	246	7	&	&	CCONJ
ijassa-1257	246	8	chernyaev	chernyaev	PROPN
ijassa-1257	246	9	,	,	PUNCT
ijassa-1257	246	10	a.p	a.p	PROPN
ijassa-1257	246	11	.	.	PROPN
ijassa-1257	246	12	(	(	PUNCT
ijassa-1257	246	13	2011	2011	NUM
ijassa-1257	246	14	)	)	PUNCT
ijassa-1257	246	15	exact	exact	ADJ
ijassa-1257	246	16	solution	solution	NOUN
ijassa-1257	246	17	of	of	ADP
ijassa-1257	246	18	the	the	DET
ijassa-1257	246	19	macroeconomic	macroeconomic	ADJ
ijassa-1257	246	20	harrod	harrod	NOUN
ijassa-1257	246	21	–	–	PUNCT
ijassa-1257	246	22	domar	domar	NOUN
ijassa-1257	246	23	model	model	NOUN
ijassa-1257	246	24	with	with	ADP
ijassa-1257	246	25	exogenous	exogenous	ADJ
ijassa-1257	246	26	dynamics	dynamic	NOUN
ijassa-1257	246	27	of	of	ADP
ijassa-1257	246	28	the	the	DET
ijassa-1257	246	29	volume	volume	NOUN
ijassa-1257	246	30	of	of	ADP
ijassa-1257	246	31	consumption	consumption	NOUN
ijassa-1257	246	32	of	of	ADP
ijassa-1257	246	33	arbitrary	arbitrary	ADJ
ijassa-1257	246	34	character	character	NOUN
ijassa-1257	246	35	,	,	PUNCT
ijassa-1257	246	36	russian	russian	ADJ
ijassa-1257	246	37	economic	economic	PROPN
ijassa-1257	246	38	university	university	PROPN
ijassa-1257	246	39	bulletin	bulletin	NOUN
ijassa-1257	246	40	,	,	PUNCT
ijassa-1257	246	41	1	1	NUM
ijassa-1257	246	42	,	,	PUNCT
ijassa-1257	246	43	142–147	142–147	NUM
ijassa-1257	246	44	.	.	PUNCT
ijassa-1257	247	1	7	7	X
ijassa-1257	247	2	.	.	X
ijassa-1257	247	3	meerson	meerson	PROPN
ijassa-1257	247	4	,	,	PUNCT
ijassa-1257	247	5	a.y	a.y	PROPN
ijassa-1257	247	6	.	.	PROPN
ijassa-1257	247	7	&	&	CCONJ
ijassa-1257	247	8	chernyaev	chernyaev	PROPN
ijassa-1257	247	9	,	,	PUNCT
ijassa-1257	247	10	a.p	a.p	PROPN
ijassa-1257	247	11	.	.	PROPN
ijassa-1257	247	12	(	(	PUNCT
ijassa-1257	247	13	2013	2013	NUM
ijassa-1257	247	14	)	)	PUNCT
ijassa-1257	247	15	the	the	DET
ijassa-1257	247	16	exact	exact	ADJ
ijassa-1257	247	17	solution	solution	NOUN
ijassa-1257	247	18	of	of	ADP
ijassa-1257	247	19	the	the	DET
ijassa-1257	247	20	cauchy	cauchy	ADJ
ijassa-1257	247	21	problem	problem	NOUN
ijassa-1257	247	22	for	for	ADP
ijassa-1257	247	23	the	the	DET
ijassa-1257	247	24	differential	differential	ADJ
ijassa-1257	247	25	equation	equation	NOUN
ijassa-1257	247	26	of	of	ADP
ijassa-1257	247	27	the	the	DET
ijassa-1257	247	28	harrod	harrod	NOUN
ijassa-1257	247	29	–	–	PUNCT
ijassa-1257	247	30	domar	domar	ADJ
ijassa-1257	247	31	macroeconomic	macroeconomic	ADJ
ijassa-1257	247	32	model	model	NOUN
ijassa-1257	247	33	with	with	ADP
ijassa-1257	247	34	variable	variable	ADJ
ijassa-1257	247	35	coefficient	coefficient	NOUN
ijassa-1257	247	36	of	of	ADP
ijassa-1257	247	37	capital	capital	NOUN
ijassa-1257	247	38	intensity	intensity	NOUN
ijassa-1257	247	39	of	of	ADP
ijassa-1257	247	40	the	the	DET
ijassa-1257	247	41	income	income	NOUN
ijassa-1257	247	42	growth	growth	NOUN
ijassa-1257	247	43	,	,	PUNCT
ijassa-1257	247	44	the	the	DET
ijassa-1257	247	45	journal	journal	NOUN
ijassa-1257	247	46	of	of	ADP
ijassa-1257	247	47	mgup	mgup	PROPN
ijassa-1257	247	48	,	,	PUNCT
ijassa-1257	247	49	3	3	NUM
ijassa-1257	247	50	,	,	PUNCT
ijassa-1257	247	51	252–255	252–255	NUM
ijassa-1257	247	52	.	.	NOUN
ijassa-1257	247	53	8	8	NUM
ijassa-1257	247	54	.	.	X
ijassa-1257	247	55	meerson	meerson	PROPN
ijassa-1257	247	56	,	,	PUNCT
ijassa-1257	247	57	a.y	a.y	PROPN
ijassa-1257	247	58	.	.	PROPN
ijassa-1257	247	59	&	&	CCONJ
ijassa-1257	247	60	chernyaev	chernyaev	PROPN
ijassa-1257	247	61	,	,	PUNCT
ijassa-1257	247	62	a.p	a.p	PROPN
ijassa-1257	247	63	.	.	PROPN
ijassa-1257	247	64	(	(	PUNCT
ijassa-1257	247	65	2014	2014	NUM
ijassa-1257	247	66	)	)	PUNCT
ijassa-1257	247	67	the	the	DET
ijassa-1257	247	68	variational	variational	ADJ
ijassa-1257	247	69	problem	problem	NOUN
ijassa-1257	247	70	of	of	ADP
ijassa-1257	247	71	optimization	optimization	NOUN
ijassa-1257	247	72	of	of	ADP
ijassa-1257	247	73	consumption	consumption	NOUN
ijassa-1257	247	74	of	of	ADP
ijassa-1257	247	75	the	the	DET
ijassa-1257	247	76	harrod	harrod	NOUN
ijassa-1257	247	77	–	–	PUNCT
ijassa-1257	247	78	domar	domar	NOUN
ijassa-1257	247	79	model	model	NOUN
ijassa-1257	247	80	of	of	ADP
ijassa-1257	247	81	economic	economic	ADJ
ijassa-1257	247	82	dynamics	dynamic	NOUN
ijassa-1257	247	83	with	with	ADP
ijassa-1257	247	84	variable	variable	ADJ
ijassa-1257	247	85	coefficient	coefficient	NOUN
ijassa-1257	247	86	of	of	ADP
ijassa-1257	247	87	capital	capital	NOUN
ijassa-1257	247	88	intensity	intensity	NOUN
ijassa-1257	247	89	of	of	ADP
ijassa-1257	247	90	the	the	DET
ijassa-1257	247	91	income	income	NOUN
ijassa-1257	247	92	growth	growth	NOUN
ijassa-1257	247	93	,	,	PUNCT
ijassa-1257	247	94	proc	proc	NOUN
ijassa-1257	247	95	.	.	PUNCT
ijassa-1257	248	1	free	free	ADJ
ijassa-1257	248	2	economic	economic	ADJ
ijassa-1257	248	3	society	society	NOUN
ijassa-1257	248	4	of	of	ADP
ijassa-1257	248	5	russia	russia	PROPN
ijassa-1257	248	6	,	,	PUNCT
ijassa-1257	248	7	186	186	NUM
ijassa-1257	248	8	,	,	PUNCT
ijassa-1257	248	9	502–506	502–506	NUM
ijassa-1257	248	10	.	.	NOUN
ijassa-1257	249	1	9	9	NUM
ijassa-1257	249	2	.	.	X
ijassa-1257	249	3	arutyunov	arutyunov	PROPN
ijassa-1257	249	4	,	,	PUNCT
ijassa-1257	249	5	a.	a.	PROPN
ijassa-1257	249	6	,	,	PUNCT
ijassa-1257	249	7	kotyukov	kotyukov	PROPN
ijassa-1257	249	8	,	,	PUNCT
ijassa-1257	249	9	a.	a.	PROPN
ijassa-1257	249	10	,	,	PUNCT
ijassa-1257	249	11	pavlova	pavlova	PROPN
ijassa-1257	249	12	,	,	PUNCT
ijassa-1257	249	13	n.	n.	PROPN
ijassa-1257	249	14	(	(	PUNCT
ijassa-1257	249	15	2021	2021	NUM
ijassa-1257	249	16	)	)	PUNCT
ijassa-1257	249	17	equilibrium	equilibrium	NOUN
ijassa-1257	249	18	in	in	ADP
ijassa-1257	249	19	market	market	NOUN
ijassa-1257	249	20	models	model	NOUN
ijassa-1257	249	21	with	with	ADP
ijassa-1257	249	22	known	know	VERB
ijassa-1257	249	23	elasticities	elasticity	NOUN
ijassa-1257	249	24	.	.	PUNCT
ijassa-1257	250	1	advances	advance	NOUN
ijassa-1257	250	2	in	in	ADP
ijassa-1257	250	3	systems	system	NOUN
ijassa-1257	250	4	science	science	NOUN
ijassa-1257	250	5	and	and	CCONJ
ijassa-1257	250	6	applications	application	NOUN
ijassa-1257	250	7	,	,	PUNCT
ijassa-1257	250	8	21(4	21(4	NUM
ijassa-1257	250	9	)	)	PUNCT
ijassa-1257	250	10	,	,	PUNCT
ijassa-1257	250	11	130–144	130–144	NUM
ijassa-1257	250	12	.	.	PUNCT
ijassa-1257	251	1	10	10	NUM
ijassa-1257	251	2	.	.	PUNCT
ijassa-1257	252	1	pavlova	pavlova	PROPN
ijassa-1257	252	2	,	,	PUNCT
ijassa-1257	252	3	n.	n.	PROPN
ijassa-1257	252	4	,	,	PUNCT
ijassa-1257	252	5	zhukovskaya	zhukovskaya	PROPN
ijassa-1257	252	6	,	,	PUNCT
ijassa-1257	252	7	z.	z.	PROPN
ijassa-1257	252	8	,	,	PUNCT
ijassa-1257	252	9	zhukovskiy	zhukovskiy	PROPN
ijassa-1257	252	10	,	,	PUNCT
ijassa-1257	252	11	s.	s.	PROPN
ijassa-1257	252	12	(	(	PUNCT
ijassa-1257	252	13	2020	2020	NUM
ijassa-1257	252	14	)	)	PUNCT
ijassa-1257	252	15	equilibrium	equilibrium	NOUN
ijassa-1257	252	16	in	in	ADP
ijassa-1257	252	17	continuous	continuous	ADJ
ijassa-1257	252	18	dynamic	dynamic	ADJ
ijassa-1257	252	19	market	market	NOUN
ijassa-1257	252	20	models	model	NOUN
ijassa-1257	252	21	.	.	PUNCT
ijassa-1257	253	1	proceedings	proceeding	NOUN
ijassa-1257	253	2	of	of	ADP
ijassa-1257	253	3	2020	2020	NUM
ijassa-1257	253	4	15th	15th	ADJ
ijassa-1257	253	5	international	international	ADJ
ijassa-1257	253	6	conference	conference	NOUN
ijassa-1257	253	7	on	on	ADP
ijassa-1257	253	8	stability	stability	NOUN
ijassa-1257	253	9	and	and	CCONJ
ijassa-1257	253	10	oscillations	oscillation	NOUN
ijassa-1257	253	11	of	of	ADP
ijassa-1257	253	12	nonlinear	nonlinear	ADJ
ijassa-1257	253	13	control	control	NOUN
ijassa-1257	253	14	systems	system	NOUN
ijassa-1257	253	15	(	(	PUNCT
ijassa-1257	253	16	pyatnitskiy	pyatnitskiy	NOUN
ijassa-1257	253	17	’s	’s	PART
ijassa-1257	253	18	conference	conference	NOUN
ijassa-1257	253	19	)	)	PUNCT
ijassa-1257	253	20	,	,	PUNCT
ijassa-1257	253	21	stab	stab	NOUN
ijassa-1257	253	22	2020	2020	NUM
ijassa-1257	253	23	,	,	PUNCT
ijassa-1257	253	24	9140586	9140586	NUM
ijassa-1257	253	25	.	.	PUNCT
ijassa-1257	254	1	11	11	NUM
ijassa-1257	254	2	.	.	PUNCT
ijassa-1257	255	1	pavlova	pavlova	PROPN
ijassa-1257	255	2	,	,	PUNCT
ijassa-1257	255	3	n.g	n.g	PROPN
ijassa-1257	255	4	.	.	PROPN
ijassa-1257	255	5	(	(	PUNCT
ijassa-1257	255	6	2020	2020	NUM
ijassa-1257	255	7	)	)	PUNCT
ijassa-1257	255	8	applications	application	NOUN
ijassa-1257	255	9	of	of	ADP
ijassa-1257	255	10	the	the	DET
ijassa-1257	255	11	theory	theory	NOUN
ijassa-1257	255	12	of	of	ADP
ijassa-1257	255	13	covering	cover	VERB
ijassa-1257	255	14	maps	map	NOUN
ijassa-1257	255	15	to	to	ADP
ijassa-1257	255	16	the	the	DET
ijassa-1257	255	17	study	study	NOUN
ijassa-1257	255	18	of	of	ADP
ijassa-1257	255	19	dynamic	dynamic	ADJ
ijassa-1257	255	20	models	model	NOUN
ijassa-1257	255	21	of	of	ADP
ijassa-1257	255	22	economic	economic	ADJ
ijassa-1257	255	23	processes	process	NOUN
ijassa-1257	255	24	with	with	ADP
ijassa-1257	255	25	continuous	continuous	ADJ
ijassa-1257	255	26	time	time	NOUN
ijassa-1257	255	27	.	.	PUNCT
ijassa-1257	256	1	springer	springer	NOUN
ijassa-1257	256	2	proceedings	proceeding	NOUN
ijassa-1257	256	3	in	in	ADP
ijassa-1257	256	4	mathematics	mathematic	NOUN
ijassa-1257	256	5	and	and	CCONJ
ijassa-1257	256	6	statistics	statistic	NOUN
ijassa-1257	256	7	,	,	PUNCT
ijassa-1257	256	8	318	318	NUM
ijassa-1257	256	9	,	,	PUNCT
ijassa-1257	256	10	123–129	123–129	NUM
ijassa-1257	256	11	.	.	PUNCT
ijassa-1257	257	1	copyright	copyright	NOUN
ijassa-1257	257	2	©	©	PROPN
ijassa-1257	257	3	2022	2022	NUM
ijassa-1257	257	4	assa	assa	NOUN
ijassa-1257	257	5	.	.	PUNCT
ijassa-1257	258	1	adv	adv	PROPN
ijassa-1257	258	2	syst	syst	PROPN
ijassa-1257	258	3	sci	sci	PROPN
ijassa-1257	258	4	appl	appl	PROPN
ijassa-1257	258	5	(	(	PUNCT
ijassa-1257	258	6	2022	2022	NUM
ijassa-1257	258	7	)	)	PUNCT
ijassa-1257	258	8	the	the	DET
ijassa-1257	258	9	optimal	optimal	ADJ
ijassa-1257	258	10	control	control	NOUN
ijassa-1257	258	11	approach	approach	NOUN
ijassa-1257	258	12	in	in	ADP
ijassa-1257	258	13	problems	problem	NOUN
ijassa-1257	258	14	of	of	ADP
ijassa-1257	258	15	the	the	DET
ijassa-1257	258	16	income	income	NOUN
ijassa-1257	258	17	distribution	distribution	NOUN
ijassa-1257	258	18	119	119	NUM
ijassa-1257	258	19	12	12	NUM
ijassa-1257	258	20	.	.	PUNCT
ijassa-1257	259	1	solow	solow	PROPN
ijassa-1257	259	2	,	,	PUNCT
ijassa-1257	259	3	r.m	r.m	PROPN
ijassa-1257	259	4	.	.	PROPN
ijassa-1257	259	5	(	(	PUNCT
ijassa-1257	259	6	1956	1956	NUM
ijassa-1257	259	7	)	)	PUNCT
ijassa-1257	259	8	contribution	contribution	NOUN
ijassa-1257	259	9	to	to	ADP
ijassa-1257	259	10	the	the	DET
ijassa-1257	259	11	theory	theory	NOUN
ijassa-1257	259	12	of	of	ADP
ijassa-1257	259	13	economic	economic	ADJ
ijassa-1257	259	14	growth	growth	NOUN
ijassa-1257	259	15	,	,	PUNCT
ijassa-1257	259	16	the	the	DET
ijassa-1257	259	17	quarterly	quarterly	ADJ
ijassa-1257	259	18	journal	journal	NOUN
ijassa-1257	259	19	of	of	ADP
ijassa-1257	259	20	economics	economic	NOUN
ijassa-1257	259	21	,	,	PUNCT
ijassa-1257	259	22	70	70	NUM
ijassa-1257	259	23	(	(	PUNCT
ijassa-1257	259	24	1	1	NUM
ijassa-1257	259	25	)	)	PUNCT
ijassa-1257	259	26	,	,	PUNCT
ijassa-1257	259	27	65–94	65–94	NUM
ijassa-1257	259	28	.	.	PUNCT
ijassa-1257	260	1	13	13	NUM
ijassa-1257	260	2	.	.	X
ijassa-1257	261	1	solow	solow	PROPN
ijassa-1257	261	2	,	,	PUNCT
ijassa-1257	261	3	r.m	r.m	PROPN
ijassa-1257	261	4	.	.	PROPN
ijassa-1257	261	5	(	(	PUNCT
ijassa-1257	261	6	1957	1957	NUM
ijassa-1257	261	7	)	)	PUNCT
ijassa-1257	261	8	technical	technical	ADJ
ijassa-1257	261	9	change	change	NOUN
ijassa-1257	261	10	and	and	CCONJ
ijassa-1257	261	11	the	the	DET
ijassa-1257	261	12	aggregate	aggregate	ADJ
ijassa-1257	261	13	production	production	NOUN
ijassa-1257	261	14	function	function	NOUN
ijassa-1257	261	15	,	,	PUNCT
ijassa-1257	261	16	the	the	DET
ijassa-1257	261	17	review	review	NOUN
ijassa-1257	261	18	of	of	ADP
ijassa-1257	261	19	economics	economic	NOUN
ijassa-1257	261	20	and	and	CCONJ
ijassa-1257	261	21	statistics	statistic	NOUN
ijassa-1257	261	22	,	,	PUNCT
ijassa-1257	261	23	39	39	NUM
ijassa-1257	261	24	(	(	PUNCT
ijassa-1257	261	25	3	3	NUM
ijassa-1257	261	26	)	)	PUNCT
ijassa-1257	261	27	,	,	PUNCT
ijassa-1257	261	28	312–320	312–320	NUM
ijassa-1257	261	29	.	.	PUNCT
ijassa-1257	262	1	14	14	NUM
ijassa-1257	262	2	.	.	PUNCT
ijassa-1257	262	3	romer	romer	PROPN
ijassa-1257	262	4	,	,	PUNCT
ijassa-1257	262	5	d.	d.	PROPN
ijassa-1257	262	6	(	(	PUNCT
ijassa-1257	262	7	2014	2014	NUM
ijassa-1257	262	8	)	)	PUNCT
ijassa-1257	262	9	the	the	DET
ijassa-1257	262	10	higher	high	ADJ
ijassa-1257	262	11	macroeconomics	macroeconomic	NOUN
ijassa-1257	262	12	.	.	PUNCT
ijassa-1257	263	1	higher	high	ADJ
ijassa-1257	263	2	school	school	NOUN
ijassa-1257	263	3	of	of	ADP
ijassa-1257	263	4	economics	economic	NOUN
ijassa-1257	263	5	,	,	PUNCT
ijassa-1257	263	6	2014	2014	NUM
ijassa-1257	263	7	.	.	PUNCT
ijassa-1257	264	1	15	15	NUM
ijassa-1257	264	2	.	.	PUNCT
ijassa-1257	265	1	samarov	samarov	PROPN
ijassa-1257	265	2	,	,	PUNCT
ijassa-1257	265	3	k.l	k.l	PROPN
ijassa-1257	265	4	.	.	PROPN
ijassa-1257	265	5	&	&	CCONJ
ijassa-1257	265	6	samarova	samarova	PROPN
ijassa-1257	265	7	,	,	PUNCT
ijassa-1257	265	8	s.s	s.s	PROPN
ijassa-1257	265	9	.	.	PROPN
ijassa-1257	265	10	(	(	PUNCT
ijassa-1257	265	11	2014	2014	NUM
ijassa-1257	265	12	)	)	PUNCT
ijassa-1257	265	13	robert	robert	PROPN
ijassa-1257	265	14	solow	solow	PROPN
ijassa-1257	265	15	’	'	PUNCT
ijassa-1257	265	16	s	s	PROPN
ijassa-1257	265	17	model	model	NOUN
ijassa-1257	265	18	of	of	ADP
ijassa-1257	265	19	economic	economic	ADJ
ijassa-1257	265	20	growth	growth	NOUN
ijassa-1257	265	21	in	in	ADP
ijassa-1257	265	22	the	the	DET
ijassa-1257	265	23	course	course	NOUN
ijassa-1257	265	24	of	of	ADP
ijassa-1257	265	25	differential	differential	ADJ
ijassa-1257	265	26	equations	equation	NOUN
ijassa-1257	265	27	,	,	PUNCT
ijassa-1257	265	28	information	information	NOUN
ijassa-1257	265	29	technology	technology	NOUN
ijassa-1257	265	30	bulletin	bulletin	NOUN
ijassa-1257	265	31	,	,	PUNCT
ijassa-1257	265	32	2	2	NUM
ijassa-1257	265	33	,	,	PUNCT
ijassa-1257	265	34	81–84	81–84	NOUN
ijassa-1257	265	35	.	.	PUNCT
ijassa-1257	266	1	16	16	NUM
ijassa-1257	266	2	.	.	PUNCT
ijassa-1257	267	1	chernyaev	chernyaev	PROPN
ijassa-1257	267	2	a.p	a.p	PROPN
ijassa-1257	267	3	.	.	PROPN
ijassa-1257	267	4	,	,	PUNCT
ijassa-1257	267	5	meerson	meerson	PROPN
ijassa-1257	267	6	a.yu	a.yu	PROPN
ijassa-1257	267	7	.	.	PROPN
ijassa-1257	267	8	,	,	PUNCT
ijassa-1257	267	9	masenko	masenko	PROPN
ijassa-1257	267	10	a.	a.	NOUN
ijassa-1257	267	11	,	,	PUNCT
ijassa-1257	267	12	&	&	CCONJ
ijassa-1257	267	13	kucherenko	kucherenko	PROPN
ijassa-1257	267	14	d.	d.	PROPN
ijassa-1257	267	15	(	(	PUNCT
ijassa-1257	267	16	2020	2020	NUM
ijassa-1257	267	17	)	)	PUNCT
ijassa-1257	267	18	setting	setting	NOUN
ijassa-1257	267	19	and	and	CCONJ
ijassa-1257	267	20	solution	solution	NOUN
ijassa-1257	267	21	of	of	ADP
ijassa-1257	267	22	the	the	DET
ijassa-1257	267	23	problem	problem	NOUN
ijassa-1257	267	24	of	of	ADP
ijassa-1257	267	25	optimum	optimum	ADJ
ijassa-1257	267	26	separation	separation	NOUN
ijassa-1257	267	27	of	of	ADP
ijassa-1257	267	28	material	material	ADJ
ijassa-1257	267	29	resources	resource	NOUN
ijassa-1257	267	30	for	for	ADP
ijassa-1257	267	31	the	the	DET
ijassa-1257	267	32	consumed	consume	VERB
ijassa-1257	267	33	and	and	CCONJ
ijassa-1257	267	34	accumulated	accumulate	VERB
ijassa-1257	267	35	parts	part	NOUN
ijassa-1257	267	36	in	in	ADP
ijassa-1257	267	37	microeconomics	microeconomics	PROPN
ijassa-1257	267	38	,	,	PUNCT
ijassa-1257	267	39	j.	j.	PROPN
ijassa-1257	267	40	physics	physics	PROPN
ijassa-1257	267	41	:	:	PUNCT
ijassa-1257	267	42	conference	conference	NOUN
ijassa-1257	267	43	series	series	NOUN
ijassa-1257	267	44	,	,	PUNCT
ijassa-1257	267	45	32076	32076	NUM
ijassa-1257	267	46	.	.	PUNCT
ijassa-1257	268	1	17	17	NUM
ijassa-1257	268	2	.	.	PUNCT
ijassa-1257	269	1	guriev	guriev	PROPN
ijassa-1257	269	2	,	,	PUNCT
ijassa-1257	269	3	s.m	s.m	PROPN
ijassa-1257	269	4	.	.	PROPN
ijassa-1257	269	5	,	,	PUNCT
ijassa-1257	269	6	&	&	CCONJ
ijassa-1257	269	7	pospelov	pospelov	PROPN
ijassa-1257	269	8	,	,	PUNCT
ijassa-1257	269	9	i.g	i.g	PROPN
ijassa-1257	269	10	.	.	PROPN
ijassa-1257	269	11	(	(	PUNCT
ijassa-1257	269	12	1994	1994	NUM
ijassa-1257	269	13	)	)	PUNCT
ijassa-1257	269	14	model	model	NOUN
ijassa-1257	269	15	of	of	ADP
ijassa-1257	269	16	general	general	ADJ
ijassa-1257	269	17	equilibrium	equilibrium	NOUN
ijassa-1257	269	18	of	of	ADP
ijassa-1257	269	19	economy	economy	NOUN
ijassa-1257	269	20	of	of	ADP
ijassa-1257	269	21	transition	transition	NOUN
ijassa-1257	269	22	period	period	NOUN
ijassa-1257	269	23	,	,	PUNCT
ijassa-1257	269	24	mathematical	mathematical	ADJ
ijassa-1257	269	25	modeling	modeling	NOUN
ijassa-1257	269	26	.	.	PUNCT
ijassa-1257	270	1	,	,	PUNCT
ijassa-1257	270	2	6	6	NUM
ijassa-1257	270	3	(	(	PUNCT
ijassa-1257	270	4	2	2	NUM
ijassa-1257	270	5	)	)	PUNCT
ijassa-1257	270	6	,	,	PUNCT
ijassa-1257	270	7	3–21	3–21	PROPN
ijassa-1257	270	8	.	.	PUNCT
ijassa-1257	271	1	18	18	NUM
ijassa-1257	271	2	.	.	X
ijassa-1257	271	3	zamkov	zamkov	PROPN
ijassa-1257	271	4	,	,	PUNCT
ijassa-1257	271	5	o.o	o.o	PROPN
ijassa-1257	271	6	.	.	PROPN
ijassa-1257	271	7	,	,	PUNCT
ijassa-1257	271	8	tolstopyatenko	tolstopyatenko	PROPN
ijassa-1257	271	9	,	,	PUNCT
ijassa-1257	271	10	a.v	a.v	PROPN
ijassa-1257	271	11	.	.	PROPN
ijassa-1257	271	12	,	,	PUNCT
ijassa-1257	271	13	&	&	CCONJ
ijassa-1257	271	14	cheremnykh	cheremnykh	PROPN
ijassa-1257	271	15	,	,	PUNCT
ijassa-1257	271	16	yu.n	yu.n	PROPN
ijassa-1257	271	17	.	.	PUNCT
ijassa-1257	271	18	(	(	PUNCT
ijassa-1257	271	19	1998	1998	NUM
ijassa-1257	271	20	)	)	PUNCT
ijassa-1257	271	21	mathematical	mathematical	ADJ
ijassa-1257	271	22	methods	method	NOUN
ijassa-1257	271	23	in	in	ADP
ijassa-1257	271	24	economy	economy	NOUN
ijassa-1257	271	25	.	.	PUNCT
ijassa-1257	272	1	moscow	moscow	PROPN
ijassa-1257	272	2	:	:	PUNCT
ijassa-1257	272	3	msu	msu	PROPN
ijassa-1257	272	4	,	,	PUNCT
ijassa-1257	272	5	dis	dis	PROPN
ijassa-1257	272	6	publishing	publish	VERB
ijassa-1257	272	7	house	house	NOUN
ijassa-1257	272	8	.	.	PUNCT
ijassa-1257	273	1	19	19	NUM
ijassa-1257	273	2	.	.	X
ijassa-1257	273	3	malychin	malychin	PROPN
ijassa-1257	273	4	,	,	PUNCT
ijassa-1257	273	5	v.	v.	PROPN
ijassa-1257	273	6	(	(	PUNCT
ijassa-1257	273	7	2001	2001	NUM
ijassa-1257	273	8	)	)	PUNCT
ijassa-1257	273	9	mathematics	mathematic	NOUN
ijassa-1257	273	10	in	in	ADP
ijassa-1257	273	11	economics	economic	NOUN
ijassa-1257	273	12	:	:	PUNCT
ijassa-1257	273	13	tutorial	tutorial	NOUN
ijassa-1257	273	14	.	.	PUNCT
ijassa-1257	274	1	moscow	moscow	NOUN
ijassa-1257	274	2	:	:	PUNCT
ijassa-1257	274	3	infra	infra	NOUN
ijassa-1257	274	4	-	-	PUNCT
ijassa-1257	274	5	m.	m.	NOUN
ijassa-1257	274	6	20	20	NUM
ijassa-1257	274	7	.	.	PUNCT
ijassa-1257	275	1	kolemayev	kolemayev	PROPN
ijassa-1257	275	2	,	,	PUNCT
ijassa-1257	275	3	v.a	v.a	PROPN
ijassa-1257	275	4	.	.	PROPN
ijassa-1257	275	5	(	(	PUNCT
ijassa-1257	275	6	2002	2002	NUM
ijassa-1257	275	7	)	)	PUNCT
ijassa-1257	275	8	mathematical	mathematical	ADJ
ijassa-1257	275	9	economics	economic	NOUN
ijassa-1257	275	10	:	:	PUNCT
ijassa-1257	275	11	textbook	textbook	NOUN
ijassa-1257	275	12	for	for	ADP
ijassa-1257	275	13	higher	high	ADJ
ijassa-1257	275	14	education	education	NOUN
ijassa-1257	275	15	institutions	institution	NOUN
ijassa-1257	275	16	.	.	PUNCT
ijassa-1257	276	1	moscow	moscow	PROPN
ijassa-1257	276	2	:	:	PUNCT
ijassa-1257	276	3	unity	unity	NOUN
ijassa-1257	276	4	-	-	PUNCT
ijassa-1257	276	5	dana	dana	PROPN
ijassa-1257	276	6	.	.	PUNCT
ijassa-1257	277	1	21	21	NUM
ijassa-1257	277	2	.	.	X
ijassa-1257	277	3	dikusar	dikusar	PROPN
ijassa-1257	277	4	,	,	PUNCT
ijassa-1257	277	5	v.v	v.v	PROPN
ijassa-1257	277	6	.	.	PROPN
ijassa-1257	277	7	,	,	PUNCT
ijassa-1257	277	8	meerson	meerson	PROPN
ijassa-1257	277	9	,	,	PUNCT
ijassa-1257	277	10	a.y	a.y	PROPN
ijassa-1257	277	11	.	.	PROPN
ijassa-1257	277	12	,	,	PUNCT
ijassa-1257	277	13	&	&	CCONJ
ijassa-1257	277	14	chernyaev	chernyaev	PROPN
ijassa-1257	277	15	,	,	PUNCT
ijassa-1257	277	16	a.p	a.p	PROPN
ijassa-1257	277	17	.	.	PROPN
ijassa-1257	277	18	(	(	PUNCT
ijassa-1257	277	19	2004	2004	NUM
ijassa-1257	277	20	)	)	PUNCT
ijassa-1257	277	21	optimal	optimal	ADJ
ijassa-1257	277	22	resource	resource	NOUN
ijassa-1257	277	23	allocation	allocation	NOUN
ijassa-1257	277	24	problems	problem	NOUN
ijassa-1257	277	25	using	use	VERB
ijassa-1257	277	26	households	household	NOUN
ijassa-1257	277	27	as	as	ADP
ijassa-1257	277	28	an	an	DET
ijassa-1257	277	29	example	example	NOUN
ijassa-1257	277	30	.	.	PUNCT
ijassa-1257	278	1	moscow	moscow	PROPN
ijassa-1257	278	2	:	:	PUNCT
ijassa-1257	278	3	dorodnitsyn	dorodnitsyn	ADJ
ijassa-1257	278	4	comp	comp	PROPN
ijassa-1257	278	5	.	.	PUNCT
ijassa-1257	279	1	cent	cent	NOUN
ijassa-1257	279	2	.	.	PUNCT
ijassa-1257	280	1	ras	ras	PROPN
ijassa-1257	280	2	.	.	PUNCT
ijassa-1257	280	3	copyright	copyright	NOUN
ijassa-1257	280	4	©	©	PROPN
ijassa-1257	280	5	2022	2022	NUM
ijassa-1257	280	6	assa	assa	NOUN
ijassa-1257	280	7	.	.	PUNCT
ijassa-1257	281	1	adv	adv	PROPN
ijassa-1257	281	2	syst	syst	PROPN
ijassa-1257	281	3	sci	sci	PROPN
ijassa-1257	281	4	appl	appl	PROPN
ijassa-1257	281	5	(	(	PUNCT
ijassa-1257	281	6	2022	2022	NUM
ijassa-1257	281	7	)	)	PUNCT
ijassa-1257	281	8	the	the	DET
ijassa-1257	281	9	preliminary	preliminary	ADJ
ijassa-1257	281	10	results	result	NOUN
ijassa-1257	281	11	the	the	DET
ijassa-1257	281	12	main	main	ADJ
ijassa-1257	281	13	economic	economic	ADJ
ijassa-1257	281	14	identity	identity	NOUN
ijassa-1257	281	15	the	the	DET
ijassa-1257	281	16	dependence	dependence	NOUN
ijassa-1257	281	17	of	of	ADP
ijassa-1257	281	18	the	the	DET
ijassa-1257	281	19	income	income	NOUN
ijassa-1257	281	20	on	on	ADP
ijassa-1257	281	21	the	the	DET
ijassa-1257	281	22	consumption	consumption	NOUN
ijassa-1257	281	23	in	in	ADP
ijassa-1257	281	24	the	the	DET
ijassa-1257	281	25	harrod	harrod	NOUN
ijassa-1257	281	26	–	–	PUNCT
ijassa-1257	281	27	domar	domar	NOUN
ijassa-1257	281	28	model	model	NOUN
ijassa-1257	281	29	with	with	ADP
ijassa-1257	281	30	varying	vary	VERB
ijassa-1257	281	31	capital	capital	NOUN
ijassa-1257	281	32	intensity	intensity	NOUN
ijassa-1257	281	33	of	of	ADP
ijassa-1257	281	34	the	the	DET
ijassa-1257	281	35	income	income	NOUN
ijassa-1257	281	36	growth	growth	NOUN
ijassa-1257	281	37	the	the	DET
ijassa-1257	281	38	relative	relative	ADJ
ijassa-1257	281	39	increase	increase	NOUN
ijassa-1257	281	40	of	of	ADP
ijassa-1257	281	41	the	the	DET
ijassa-1257	281	42	income	income	NOUN
ijassa-1257	281	43	for	for	ADP
ijassa-1257	281	44	the	the	DET
ijassa-1257	281	45	cobb	cobb	PROPN
ijassa-1257	281	46	–	–	PUNCT
ijassa-1257	281	47	douglas	douglas	PROPN
ijassa-1257	281	48	production	production	NOUN
ijassa-1257	281	49	function	function	VERB
ijassa-1257	281	50	the	the	DET
ijassa-1257	281	51	balance	balance	NOUN
ijassa-1257	281	52	equation	equation	NOUN
ijassa-1257	281	53	for	for	ADP
ijassa-1257	281	54	capital	capital	NOUN
ijassa-1257	281	55	capital	capital	NOUN
ijassa-1257	281	56	capacity	capacity	NOUN
ijassa-1257	281	57	of	of	ADP
ijassa-1257	281	58	increase	increase	NOUN
ijassa-1257	281	59	in	in	ADP
ijassa-1257	281	60	the	the	DET
ijassa-1257	281	61	solow	solow	PROPN
ijassa-1257	281	62	model	model	NOUN
ijassa-1257	281	63	the	the	DET
ijassa-1257	281	64	balance	balance	NOUN
ijassa-1257	281	65	equation	equation	NOUN
ijassa-1257	281	66	for	for	ADP
ijassa-1257	281	67	accumulated	accumulate	VERB
ijassa-1257	281	68	household	household	NOUN
ijassa-1257	281	69	savings	saving	NOUN
ijassa-1257	281	70	the	the	DET
ijassa-1257	281	71	utility	utility	NOUN
ijassa-1257	281	72	function	function	NOUN
ijassa-1257	281	73	and	and	CCONJ
ijassa-1257	281	74	the	the	DET
ijassa-1257	281	75	risk	risk	NOUN
ijassa-1257	281	76	avoidance	avoidance	NOUN
ijassa-1257	281	77	the	the	DET
ijassa-1257	281	78	optimal	optimal	ADJ
ijassa-1257	281	79	control	control	NOUN
ijassa-1257	281	80	approach	approach	VERB
ijassa-1257	281	81	optimal	optimal	ADJ
ijassa-1257	281	82	control	control	NOUN
ijassa-1257	281	83	in	in	ADP
ijassa-1257	281	84	the	the	DET
ijassa-1257	281	85	modified	modify	VERB
ijassa-1257	281	86	harrod	harrod	NOUN
ijassa-1257	281	87	–	–	PUNCT
ijassa-1257	281	88	domar	domar	NOUN
ijassa-1257	281	89	model	model	NOUN
ijassa-1257	281	90	optimal	optimal	ADJ
ijassa-1257	281	91	control	control	NOUN
ijassa-1257	281	92	in	in	ADP
ijassa-1257	281	93	the	the	DET
ijassa-1257	281	94	modified	modify	VERB
ijassa-1257	281	95	solow	solow	PROPN
ijassa-1257	281	96	model	model	NOUN
ijassa-1257	281	97	optimum	optimum	ADJ
ijassa-1257	281	98	consumption	consumption	NOUN
ijassa-1257	281	99	management	management	NOUN
ijassa-1257	281	100	in	in	ADP
ijassa-1257	281	101	household	household	NOUN
ijassa-1257	281	102	model	model	NOUN
ijassa-1257	281	103	restrictions	restriction	NOUN
ijassa-1257	281	104	on	on	ADP
ijassa-1257	281	105	the	the	DET
ijassa-1257	281	106	accumulated	accumulate	VERB
ijassa-1257	281	107	savings	saving	NOUN
ijassa-1257	281	108	in	in	ADP
ijassa-1257	281	109	household	household	NOUN
ijassa-1257	281	110	model	model	NOUN
ijassa-1257	281	111	examples	example	NOUN
ijassa-1257	281	112	of	of	ADP
ijassa-1257	281	113	indicator	indicator	NOUN
ijassa-1257	281	114	functions	function	NOUN
ijassa-1257	281	115	conclusion	conclusion	NOUN