EFFECT OF SELECTED INSECTICIDE ON WHITEFLY (Bemisia tabaci) INFESTING BRINJAL PLANTS


82 

 

 

Determining the Role of Inefficiency on Elasticity of Output Supply and Input 

Demand: A Case Study of Irrigated Wheat in 27 provinces of Iran 
 

Alireza Garshasbi
 

Institute for Trade Studies and Research, Iran 

 

Hossein Khosropour, Narges Rahimian
 
and Aref Behrooz

 

Allame Tabatabaee University, Iran 

 

Somaye Sedighi
 

Ferdowsi University, Mashhd, Iran 

 

Abstract 

This article appraises the impressions of technical and price or allocative inefficiency on 

elasticity of the supply of wheat and demand of its inputs in 27 provinces of Iran. To this 

purpose, first the technical, price and economic efficiency has been calculated utilizing the 

stochastic frontier functions of production and cost. The influencing factors of efficiency 

including: the degree of scale economies, the share of technology in manufacturing process, the 

share of governmental supports, the cost of production processes and the experience have been 

estimated via a panel data approach. At the end, rejecting the hypothesis of perfect efficiency of 

farmers in production, the functions of output supply and input demand have been assessed in 

two scenarios (concerning efficiency and inefficiency) using a profit function and the impact of 

general (economic) inefficiency on relative and crossover elasticities of output and input are 

evaluated.  The results show that the average of technical, price and economic efficiency of 

irrigated wheat respectively equal to 69, 63 and 45 percent. The estimated parameters have been 

affected, concerning the inefficiency. Although relative elasticities of output and inputs are 

appeared with expected signs, entering the inefficiency, elasticity of irrigated wheat is generally 

increased.  

Keywords: Stochastic frontier function, profit function, output supply and input demand function, 

irrigated wheat 
 
Introduction

1
 

 
Agriculture has been always one of the most 

important economic subsectors in Iran’s 

economy; so that averagely about 15 percent 

of the gross domestic product (GDP) in the 

period 2000-2009 belongs to this sector, 

                                                           
1
Corresponding author’s 

 Name: Somaye Sedighi 
 Email address: somayesedighi@gmail.com 
 

 

based on central statistics (Central Bank of 

the Islamic Republic of Iran). Therefore, the 

growth and development of this sector can 

play a key role in Iran’s economic 

development. The presence of basic 

commodities in cultivation subgroup of 

agriculture, high proportion of cultivation 

vintages in productions of agricultural sector 

and over 30 percent weight of basic 

cultivation commodities in foods and drinks 

index of household basket have turned this 

subgroup into the center of economic 

planners’ attention for quite a while. Wheat is 

 

 

 

Asian Journal of Agriculture and Rural Development 
 

 

 
journal homepage: http://aessweb.com/journal-detail.php?id=5005  

 

mailto:somayesedighi@gmail.com


Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

83 

 

the most strategic product of Iran among 

agricultural products which government is 

ever trying to be independent in its 

production and secure its need inside the 

country. So, the raise of its production has 

been always one of the most influential 

objectives. Change in wheat production can 

be due to more hiring of production inputs or 

increase of its producers’ efficiency. 

Considering the fact that there are limitations 

for the inputs in economy, politicians have to 

plan to increase the efficiency of productions. 

So efficiency calculation has a high level of 

importance as the first step in determining the 

optimal level of inputs usage. 

 

This sector’s producers just like it in other 

economic sectors, are in pursuit of their 

efficiency increase (especially in cases with 

economies of scale). The most efficient level 

of agricultural production output is achieved 

in a point in which producer is able to attain 

the maximum output with specefic amount of 

input. Nevertheless, it should be noticed that 

the type and amount of farmer’s costs have a 

determining role in his efficiency in devotion 

of costs to inputs (allocative efficiency). 

Surely, there is a straight relationship 

between efficiency (whether technical, 

allocative or economic) and the extent of 

firm’s ability to manufacture the product. 

Also the point which is often left disregarded 

in most studies is the effects which changes 

of efficiency have on the price fluctuations - 

as one of the essential parts of agricultural 

sector; the reason is that efficiency is in 

relationship with production and supply and 

they have also relation with price. The 

empirical studies done on agricultural 

production efficiency have been classified in 

two main groups during last four decades. 

First, studies which estimate inefficiency of 

different producer, regardless of the price 

reactions (like Battese and Seiford), while the 

second group have investigated the price 

reactions of agricultural production supplies 

and input demand with obvious efficiency 

(like Ball; Shumway, Saez, and terttoG). In 

the first group on which studies are usually 

done, there isn’t the possibility of scrutinizing 

the impacts of price changes on inefficiency. 

The study of inefficiency impact on the price 

functions is neither possible in the second 

group. The simultaneous study of the 

relationship between efficiency and price 

enables the researcher to survey the impacts 

of inefficiency on price without concerning 

the assumption of exogenous efficiency or 

price fluctuations. As, the reaction of the 

prices to which producers are in touch is 

presented in output supply and input demand, 

the study of inefficiency impacts on the price 

of agricultural sector can be realized thanks 

to its impacts on the output supply and input 

demand. Hence, this study aims to scrutinize 

the changes of inputs elasticity as it appraises 

the effective factors on efficiency and effects 

of output supply and input demand to be able 

to offer policy recommendations for 

increasing the efficiency of Iranian wheat 

farmers. 

 

Data and methodology 
 

Types of efficiency   

The issue of efficiency started with the study 

of Farrell  (1957) based on the study of 

Debrev and Coopeman. Farrell suggested that 

the efficiency of an economic unit consists of 

two parts: 1. Technical efficiency and 2. Price 

(allocative) efficiency. The combination of 

these two touchstones together presents the 

general (economic) efficiency. According to 

Farrell’s definition, there are two approaches 

to investigate the precise definition of 

efficiency and its calculating relations. 

 

Measuring the efficiency based on 

minimizing the factors of production 

(input oriented) 

Farrell presented the definition of varieties of 

efficiency, using a simple sample in which a 

firm uses two inputs of x1 and x2 for 

manufacturing one unit product of “q” under 

the fixed economies of scale. The isoquant 

curve of an economic unit that the distance 

function of which stands on the production 

possibilities frontier curve, is illustrated by  

 SS   in diagram(2). 

 

 

 
   

    



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

84 

 

 


 


 

o qx /2
 

qx /1
 

px2
 Qx2

 

Qx1
 

px1
 

P 

Q 

 

Q 

P 
 


 


 S  

o qx /2
 

qx /1
 

S 

R 


 
Q 

TC 

 
(A)             (B)        

Diagram 1: The definition of different types of efficiency based on minimizing the 

production factors 

 

If an assumed firm hires the inputs in a 

level which could be defined by the P 

situation; It is possible to present different 

types of efficiency based on diagram (1) 

from Farrell’s perspective by the use of 

distance functions characteristics: 

 

Technical efficiency: It is predicated as the 

firm’s ability to produce the maximum 

product by the specific collection of input. 

If the production of assumed firm P, using 

inputs x1P, x2P only equals the production 

level which is shown by the SS   isoquant 

curve at the point Q, so this firm will reach 

the same production by decreasing the use 

of input. From diagram perspective, the 

firm P can preserve its production level by 

decreasing the  x1P-x1Q  for the first input 

and  x2P-x2Q for the second input (part B 

diagram 1). This means that by decreasing 

QP/OP  percent of the x1P and x2P, the firm 

can reach the point in which it has used the 

minimum of inputs for the production. 

Based on this explanation, the proportion 

OQ/OP  represents the technical efficiency 

of the firm P which is less than 1 (equation 

1). It is obvious that if the firm was in the 

Q point, this proportion would be equal to 

“1” which meant that the firm was 

technically efficient. 

 

OPOQTE /        (1) 

 

Price efficiency (Allocative): It refers to 

the ability of the firm in choosing a 

collection of optimal inputs with minimal 

cost. Therefore, the price and technical 

efficiency is presented as equation (2) 

about the assumed firm P.  

 

 
OQ

OR

XW

XW
AE 






ˆ

*

      (2) 

 

Where: W is the vector of inputs price, X is 

the vector of inputs observed at point P, 

X̂ is the vector of a technically efficient 

input (point Q) and 
*X is demonstrator of 

input vector with the minimal cost ( Q  
point). If production accomplishes in 

Q (price and technical efficiency) instead 

of Q point (technical efficiency and price 

inefficiency) on an isoquant curve, the 

above equation would be demonstrator of 

decrease of production costs. Refer to 

diagram (2) for further explanation. 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

85 

 

 


 


 

o qx /2
 

qx /1
 

Qx 
2

 Qx2
 

Qx 
1

 

Q 

Q 

Qx1
 

QTC 

QTC 
 

 
Diagram 2: Definition of price efficiency from Farrell’s perspective 

 

The firm’s cost at the point Q is calculated by 

summing up the first  ( QxPx 11 )  and second 

( QxPx 22 ) purchasing cost of input which is 

on the QTC   isocost line. If producing at the 

point Q , the cost would be calculated by 

summing up the first( QxPx ′11 ) and second 

( QxPx ′22 )purchasing cost of input which is 

on the QTC   isocost line. So, the firm can do 

the same production with decreasing the cost 

of ( QxPx


11 - QxPx 11 ) for the first and 

( QxPx ′22 - QxPx 22 ) for the second input.
2
 

This means that the firm can reach the 

primary levels of production by decreasing 

the cost of QxPx 11   two  QxPx 22   with the 

proportion 
OR

RQ  . So, the price efficiency 

equals to the fraction
OQ

OR . 

                  
The economic (general) efficiency: It 

indicates the firm’s ability in the maximal 

production of output, selecting the optimal 

collection of inputs (the highest output with 

the lowest cost in the technical frontier) 

(equation 3). When the input price is 

determined, this kind of efficiency can be 

calculated. If W is the inputs price vector and 

X is the observed vector of inputs at the point 

                                                           
2
 It is assumed that the cost of factors hasn’t 

changed.  

P, X̂ is also the demonstrator of the 

technically efficient input frontier (Q point) 

and 
*X is demonstrator of input vector with 

minimal cost (
Q′ point). Thus, the general 

efficiency of the firm is equal to the 

proportion of input costs related to the input 

vectors in X and   
*X  which are related to P 

and
Q

. 

OP

OR

XW

XW
EE 






*

  

 (3)  

 

The distance is RQ. This can be shown 

drawing two isocost lines from the points Q 

and Q . Also, economic efficiency is 

calculated by multiplying technical and 

allocative efficiency. (Equation 4) 

 

EE
OP

OR

OQ

OR

OP

OQ
AETE





 

 (4) 

 
Technical, price and general efficiency will 

fluctuate between zero and one that reveals 

that the general efficiency is always less than 

or equal to the technical efficiency. 

 

The practical action mentioned above to 

measure different types of efficiency, began 

by publishing Farrell’s article in scrutinizing 

the efficiency of agricultural sector in the 

economy of United States. Farrell’s method is 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

86 

 

based on the comparison of the actual 

performance of production in the firm and the 

best performance on the frontier production. 

As a whole, measuring the efficiency is 

possible by two methods of 1. Non-arametric 

and 2. Parametric. The nonparametric method 

in measuring efficiency is highly affected by 

quantitative and qualitative variables’ 

categorization in the form of Data  

Envelopment Analysis. In this analysis, 

measuring different types of efficiency is 

only possible by integrating the amounts of 

inputs and outputs and by the linear planning 

method. In parametric method, the 

econometric calculation methods are used for 

estimation of different types of efficiency 

which are typically done in the form of 

stochastic frontier analysis (Parmeter and et 

al., 2013). Both methods are used in various 

papers and they have their own particular 

advantages and disadvantages.  

  

Table (3) presents the concise comparison of 

the weak and strength points of both methods. 

 

“The Stochastic Frontier Analysis method has 

more popularity through the research 

methodology and innumerable empirical 

studies during recent decades.” (Kuosmanen 

& Kortelainen, 2012) Econometric methods 

in efficiency estimation by frontier analysis 

method (in parametric method) can be 

categorized in two branches of primary and 

dual. The primary method (or straight based 

on production function) is the most popular 

method for the estimation of efficient frontier 

which the invalidity of model parameters 

through being biased and inconsistent, are the 

most vital problems of this method 

(Henderson & Parmeter, 2013). Noting the 

existence of uncontrollable factors like 

climatic changes, a "stochastic frontier 

analysis" is preferred over a "data covering 

analysis" for estimation. Furthermore, as dual 

method has the possibility of presenting the 

replacement behavioral objectives (minimal 

cost or maximal profit) and gives the 

researcher the possibility of estimation of 

multiple products, it is a more valid method 

for estimation (Greene2003). So, the frontier 

production function is used for technical 

efficiency estimation and the frontier cost is 

used for allocative efficiency estimation 

(Battese and Coelli 1992). 

 

niUV

xfY

itit

ijijtit

,...,2,1)(

exp),(



 

 (5) 

kjTtNi

UVXYfTC ititijijtitit

,...,1;,...,1;,...,1

)(),,(



 

  (6) 

In model (5), Y is the produced wheat of each 

province, X is the vector of inputs including 

the under cultivation level, sowing, labor 

force (number of labor force used in plowing, 

flattening, fertilizing, sowing, irrigation, and 

other operations), poisons (including the used 

amount of poisons for feeds, insects, molds 

and other kinds of poison), animal an 

chemical fertilizers (including phosphate, 

nitrogen, potassium and other kinds of 

fertilizers and their prices that achieved from 

Ministry of Jihad Agriculture in 2000-2009 

period),   is the vector of these inputs 

parameters, V is the stochastic disturb term 

(related to the uncontrollable economic 

variables of each economic unit), U is the 

effects of inefficiency (Aigner  and Lovell 

1977).  

 

It is necessary to mention that the difference 

of two terms )( itit UV   is asymmetric and 

abnormal and the degree of asymmetry 

depends on the fraction of
u v  . If 02 u  

, the mentioned function would change to a 

normal regression with a disturb term with 

the normal distribution.
3
 In mode (6) TC is 

the wheat production cost in each province, X 

is the price vector of mentioned inputs in 

model (5) and other variables are the same 

variables of first model. )(0f  Is an 

appropriate functional shape for estimating 

                                                           
3 See Kim (2006), Kim and Nelson (2006), 

and Kutlu and Sickles (2010) 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

87 

 

the model. As what Coelli, Rao, Donnell and 

Battese emphasize in the book "efficiency 

and productivity analysis", the feature of an 

appropriate mathematic function is to have 

capablities such as the flexibility, linearity, 

order and similarity of the parameters. In 

order to estimate the model of "symmetry 

imposition" on inputs own cross, the price of 

inputs and outputs is necessary (Coelli, 1996) 

The study information has been extracted for 

different years from statistical yearbook of 

Ministry of Agriculture Jihad, provincial 

information and Iran’s Center of Statistic for 

the period 2000-2009.  

 

To eliminate  the impact of inflation on the 

estimated pattern (equations 5 and 6), all of 

variables have been changed to actual value 

based on price index of 2004 (as the basic) 

and this data have been used for the 

estimation. The calculations have been done 

by the use of Frontier 4,1  and Stata11 

software. Before estimation, it is needed to 

test the stationarity of variables and according 

to the data structure the method of Im, 

Pesaran and Shin is used for this mean. The 

results show stationarity of the variables.  

 

Therefore, by insuring the stationarity of 

variables, there is no need to do the variables 

convergence and  nonliarity tests. In next 

stage, in order to estimate (5) and (6) 

equations , it is necessary to perform the data 

poolability test in the form of a panel data 

pattern against pooled data pattern or F 

Leymer test that this test’s amount is equal to 

13,45 percent for the production level and 

22.08 per cent for the cost model which 

confirms the panel model. In this state, the 

inefficiency is estimated based on Coelli’s 

assumptions without any change during time 

(pattern1) or with change during time (pattern 

2). The results of calculated efficiency for 

irrigated wheat are presented in tables (1). 

 

Table 1: The average of irrigated wheat different kinds of efficiency in the period 2000-

2009 divided to country’s states 

Row State Name Technical Allocative Economical 

1 Kermanshah 0.9 0.88 0.79 

2 Mazandaran 0.89 0.85 0.75 

3 Fars 0.89 0.88 0.79 

4 Tehran 0.89 0.87 0.78 

5 Zanjan 0.87 0.77 0.67 

6 Kohgiluye 0.86 0.73 0.64 

7 Koerdestan 0.86 0.75 0.65 

8 Ardebil 0.85 0.81 0.69 

9 Esfehan 0.84 0.88 0.74 

10 Bushehr 0.84 0.52 0.44 

11 Ghazvin 0.83 0.87 0.72 

12 Semnan 0.83 0.86 0.71 

13 Markazi 0.82 0.84 0.68 

14 Charmahal 0.82 0.75 0.61 

15 Ilam 0.8 0.71 0.58 

16 Yazd 0.8 0.8 0.63 

17 Hamedan 0.8 0.88 0.71 

18 Hormozgan 0.8 0.88 0.7 

19 Qom 0.79 0.91 0.71 

20 Western Azarbayjan 0.78 0.69 0.54 

21 Sistan 0.76 0.49 0.38 

22 Eastern Azarbayjan 0.76 0.73 0.55 

23 Kerman 0.75 0.75 0.57 

24 Lorestan 0.75 0.71 0.54 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

88 

 

25 Golestan 0.72 0.75 0.55 

26 Khorasan 0.53 0.69 0.37 

27 Khoozestan 0.51 0.79 0.42 
Source: Research calculations 
 

According to table (1), technical, price 

(allocative) and economic efficiency of 

irrigated wheat in the discussed provinces 

respectively equal to 69, 63 and 45 per cent 

for the studying period. This amount of 

efficiency proves the existence of 

widespread inefficiency in the wheat 

production. The primary investigation 

shows that every kinds of efficiency react 

to the under cultivating level of wheat. All 

kinds of efficiencies have been confronted 

a decrease in 2008; is directly related to the 

decrease of under cultivating level of 

wheat
4
. Surveying the under cultivating 

level shows that in the studying period , 77 

per cent of whole used lands in the wheat 

production relates to dry lands and only 23 

per cent of them relates to the irrigated 

wheat. As, any decrease or increase in 

under cultivating level in, the supply of 

wheat will increase or decrease. In 2008, 

we witness a harsh decrease on the 

technical efficiency because of straight 

effect on output wheat supply and also on 

the allocative efficiency because of inputs 

purchase and no utilization of index 

advantages in smaller lands. As technical 

and allocative efficiency change, economic 

efficiency would also change. 

 

The investigated statistics show that the 

most shares of cost relate to the cost of 

agricultural land renting which straightly 

influence the technical and price efficiency. 

Despite the 8 per cent increase in irrigated 

wheat production, we see the salient 

increase in usage of inputs; so that, by 3 per 

cent increase of under cultivating level, the 

amount of variable inputs like labor force, 

                                                           
4 In order to discuss the state of under cultivated 

level on wheat supply refer to article of 

Garshasbi et al. (2012)  agriculture economics 

journal as Survey of Affected Price and Non 

price Factors on Wheat Supply in Country’s 

States by the Use of Panel Data. 

seed, chemical fertilizer, poisons in every 

irrigated wheat hectare have increased 

respectively up to 25, 5, 18 and 45 per cent. 

The increase of governmental subsidies to 

chemical fertilizers and poisons in 2002, on 

the one hand and the on time distribution of 

agricultural fertilizer and poisons in the 

planting and harvesting period on the other 

hand have had important role in increasing 

the amount of inputs use. Other kinds of 

agricultural poisons have had an important 

role in increase of inputs usage in planting 

and harvesting period on the other hand. 

Other important cases can be presented as 

below: 

 

At the end of 2002 and after three years of 

relative drought which ended in lowering 

the level of water sources used for planting 

the irrigated wheat, the atmospheric status 

kind of improved; so that , the atmospheric 

downfalls increased up to 40 percent. This 

issue led to improving the level of function 

in level unit and increasing the technical 

efficiency during 1382 and 1383. The 

economic efficiency increased too 

following the increase of technical 

efficiency.  

 

In 2002 and after three respective 

continuous droughts, the financial need of 

farmers made them to desire to increase the 

amount of production by any probable 

method and after significant increase in 

guaranteed price, in order to acquire more 

financial resources by selling the product 

out to the government. It has been also 

effective in the amount of inputs usage like 

chemical fertilizer and poisons. 

 

The fluctuations of under cultivating level 

of irrigated wheat in country are not so 

high. Meanwhile, what matters most is the 

usage of other inputs used for cultivation 

that highly depends on the governmental 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

89 

 

policies. According to the article number 

(103) and fourth law of development plan 

about reforming the targeted subsidies act 

of agricultural inputs in 2005 and its 

significant decrease, a tangible decrease in 

price efficiency (allocative) and 

conclusively decrease of general 

(economic) efficiency is seen. This point 

should be noted that wheat production has 

experienced a developing process for years 

except in 2008 which confronted a 

significant decrease.  Indeed, the amount of 

increase has been salient from 2002. A 

main share of wheat production is bought 

by government guaranteed. Wheat is 

consumed in three ways of human, bestial 

and medical in Iran. Human consumptions 

specify 80 per cent which are mainly 

consumed as bakery flour.5 Bakery flour 

suppliants are the bakers. 

 

Technical and price efficiency effect on 

output supply and input demand 

The condition of optimization is reached by 

solving the problem of maximization of 

profit along with the price and technical 

(allocative) inefficiency in profit function 

as in equation (7). 

 

  

   wyCyp

wp
y

,

max,

1







 (7) 

 

Where: II is profit function,  is the 

technical inefficiency,  is price or 

allocative inefficiency, y is output vector 

and C(y,x) is the production cost. 

Derivation from profit function to output 

price, results in equations (8) and (9). 

 

                                                           
5 Ministry of trade (2010)  

    

 
 

i

iii

iii

i

i

i

i

p

p

p

y

y

wyC
y

p

wp


















 






 ,, 1

 (8) 

 

  
 

 

 
 iii

i
iiii

i

iii

i

iii

i

p

y
py

p

y

py
p

wp

























0

,

 (9) 

Similarly, Derivations to input prices is 

presented by equation (10). 

 

  

   

j

i

ij

j

w

y

y

wyC

w

wyC

o
w

wp
























,,

,

1

1






(10) 

Using equation (11) we have: 

 

  

 

 
j

i
ii

i

j

i
ii

i

j

w

y
p

x

w

y
p

x
w

wp























 







 11,

 (11) 

 

The relations of output supply and input 

demands can be easily estimated in 

equations (10) and (11). According to 

theoric discussions and in order to survey 

the inefficiency effects on output supply 

and input demands, a normal profit 

function in tanslog form is used in equation 

(12). 

 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

90 

 

   

   

7,...,2,1,,...,2,1

)(2/1

ln

6

1

6

1

**

2*

1

*

1

*
















 








 





jkni

UwLnwLn

wLnw

Ln
P

Ln

it

j k

ktjtjkt

it

n

i

itit

n

i

ito

it

it
it







 (12) 

 

Where: 

*

it
 is normal profit function 

which is attained from division of profit 

( it
 ) by the product price ( itp

 ). 

jtw*

and ktw*

 are the price of production 

inputs including renting price of the land, 

seed, labor force, poisons, animal and 

chemical fertilizers which have become 

normalized with the product’s price. In 

order to examine th effects of technical and 

price inefficiency (allocative) on output 

supply and input demand, it is necessary to 

consider the profit function regarding 

inefficiency. 

 

 

   

 
 

7,...,2,1,,...,2,1

)(
2/1

1

6

1

6

1
*

*

2*

1

*

1

*



















 





jkni

U
wLn

wLn

wLnw

LnLn

it

j k ktkt

jtjtitjkt

itit

n

i

itititit

n

i

ititititoit









 (13) 

We can reach to the functions of input and 

product share from profit by profit function 

derivation of outputs prices and product 

price and by utilizing Hotelling’s Lemma 

(Arnade and Trueblood 2002). Equation 

(14) shows the share function of input 

profit and equation (15) shows the share 

function of product’s profit. 

 

 
 

 
   

6,...2,1,,...,2,1

2/1

2

*

*

*

*

*

*


















jkni

wLn

wLn

wLn

LnXw
S

jtitijt

ktktitiktitit

itit

ititit
it

w j









(14) 

 

*

*









y

LnP

Ln
S

y

it

it
y

(15) 

 

According to equation (15), it
w jS  is the 

share of jth input profit, 
 ititw *

is the 

price of ith input considering the price 

inefficiency which have been normalized 

by the price of product. it
 is technical 

inefficiency, it
 , ikt

, and ijt
 are the 

passive parameters. As before, inputs 

includes under cultivating level of wheat 

(X1), seed ( X2), labor force (X3), poisons 

(X4), animal fertilizer (X5), chemical 

fertilizer (X6) and inputs price also 

includes renting price of land (W1), seed 

price (W2), labor force wage (W3), poisons 

price (W4), animal fertilizer price (W5) and 

chemical fertilizer price (W6). 

In equation (16), it
yS is the share of the 

profit, 

y

itP
is the guaranteed price of wheat 

and y represents the product supply which 

is resulted from its multiplying by the 

product price and total income and profit 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

91 

 

(II) is attained after subtraction of costs and 

the normal profit
*  is attained after 

division of profit by
y

itP
. 

  

Considering the existence of common 

parameters in equations (15) and (16), the 

estimation should be done simultaneously. 

As coefficients are equal in input demand 

and output supply, symmetry and similar 

coefficients restrictions have been applied 

in ultimate level too. These restrictions  are 

presented as equation (16). 

 

   

 
6,...2,1,

*

**

*










jk

wLn

S

wLnwLn

Ln

jt

w

it

jjtitit

i





 (16) 

In order to investigate the effectiveness of 

inefficiency on the share of demand 

supplies, equations (17) and (18) are 

respectively the demonstrators of the 

mentioed functions for the states of 

considering and not considering 

inefficiency. 

 
 

 

6,...2,1,

5.0

*

*











jk

wLnb

wLnbb
wLn

Ln
S

ktjkt

jtjjtjt

jt

it
x j

 (17)  

 

 

 

 

Without inefficiency 

 

 
 

6,...2,1,

5.0

*

*

*

*















jk

w

Lnbw

Lnbb

wLn

Ln
S

ktkt

jktjtjt

jjtjtjt

jtjt

it
x j









 (18) 

 

With inefficiency 

According to equations (17) and (18), 

considering the inefficiency, intercept 

would decrease, but a precise opinion 

cannot be given about price variables 

coefficients. For the same reason, it is not 

possible to give a precise opinion about the 

share function of supply profit. In other 

words, these coefficients can be increased 

or decreased. These conditions are 

indefeasible for both irrigated and dry land 

wheat. 

 

The changes of elasticity of irrigated and 

dry land wheat 

One of the most important usages of the 

attained functions in previous part, is the 

changes of relative and cross elasticities of 

inputs and supply.6 In order to obtain the 

relative price elasticity of input X demand, 

we should act like equation (19). 

 

                                                           
6 Hojabr Kiani and Haji Ahmad (2002) 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

92 

 

i

ii
i

ii

ii

i
ii

S

b
S

LnP

Ln

LnP

Ln

LnP

Ln

LnP

LnX






























1

1




 (19) 

 

In order to obtain the cross price elasticity 

of input X demand, we should proceed as 

equation (20). 

 

i

ik
k

ik

kk

i
ik

S

b
S

LnP

Ln

LnP

Ln

LnP

Ln

LnP

LnX

































 (20) 

 

In order to obtain input X supply elasticity 

to the product price, we should proceed as 

equation (21). 

 

 





























































n

i i

ik
n

i

iiy

n

k i

ik

y

i
n

i i

iy

iy

y

i

yy

i
iy

S

b
S

S

b

LnP

LnP

LnP

Ln

LnP

Ln

LnP

Ln

LnP

LnP

LnP

Ln

LnP

LnX

11

1

1

1

1









 (21)  

In order to obtain supply elasticity to 

input iX
 price, we should proceed as 

equation (22). 

 













































n

k
n

k

k

ki
iyi

n

k ki

ii

yi

S

b
S

LnP

Ln

LnP

Ln

LnP

Ln

LnP

Lny

1

1

1

1

1








  (22) 

In order to obtain relative elasticity of 

supply, we should proceed as equation 

(23). 

 













 





 





















































n

i

n

k
n

k

k

ki

n

i

iyy

n

i

n

k
n

k

k

ki

y

i
n

i i

yy

n

k iy

yy

yy

S

b
S

S

b

LnP

LnP

LnP

Ln

LnP

Ln

LnP

Ln

LnP

Ln

LnP

Lny

1 1

1

1

1 1

1

1

1

1

1

1











 (23) 

The changes of irrigated wheat elasticity 

are shown in table (2) 

Table 2: Elasticity of irrigated wheat inputs and output 

 
Input. output Price 

  
Land Seed Labor Poisons 

Animal 

fertilizer 

Chemical 

fertilizer 
Wheat 

Without 

considering 

inefficiency 

land -0.34 -1.43 -0.22 -0.19 -0.11 -0.11 0.23 

seed -0.59 -0.86 -0.36 -0.11 -0.01 -0.09 1.78 

Labor force 0.21 -0.16 -0.13 0.07 -0.09 -0.30 2.03 

poisons 0.11 0.59 0.09 -0.26 -0.10 0.24 0.32 

Animal 

fertilizer 
0.11 -0.16 0.06 -0.13 -0.54 0.21 0.03 

Chemical 0.32 -0.19 -0.18 -0.16 0.16 -0.12 0.45 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

93 

 

fertilizer 

Irrigated wheat -1.34 -0.15 -0.21 -0.08 -0.11 -0.14 1.23 

 
Input. output Land Seed Labor Poisons 

Animal 

fertilizer 

Chemical 

fertilizer 
Wheat 

with 

considering 

Technical 

and price 

inefficiency 

land -0.27 -1.13 -0.16 0.09 0.09 -0.39 0.71 

seed -0.31 -0.71 -0.31 -0.07 -0.11 0.51 2.54 

Labor force 0.27 0.10 -0.12 0.04 -0.07 -0.07 2.89 

poisons 0.17 0.51 0.04 -0.23 0.15 0.11 0.56 

Animal 

fertilizer 
0.19 -0.12 0.13 0.11 -0.65 0.17 0.16 

Chemical 

fertilizer 
0.12 0.23 -0.07 -0.23 0.26 -0.38 1.13 

Irrigated wheat -0.77 0.24 -0.36 0.32 0.06 0.53 1.88 

Source: Research calculations 

 

According to results of table, it is denoted 

that all of the relative elasticities have 

been appeared with expected signs. The 

investigation of calculated elasticities 

proves that: 

 

All inputs of irrigated wheat are a little 

elastic. The irrigated wheat product input 

with the lowest elasticity is chemical 

fertilizer which shows that the demand of 

this input does not conspicuously  react to 

the price. Considering the negative 

effects of the share of chemical 

fertilizer’s cost on the economic 

efficiency of irrigated wheat, the low 

elasticity of chemical fertilizer demand 

can be contriving of decrease of the 

efficiency along with increase in the price 

of this input in production. 

 

The relative price elasticity of seed has 

the highest level and therefore, it is the 

most sensitive input that this issue is 

because of the variety of used seeds and 

the possibility to substitute them with 

each other (more than 79 kinds of seed 

are used in provinces of Iran). 

 

The price elasticity of wheat supply is 

more than one which expresses that the 

wheat supply is highly elastic. Hence, the 

change of guaranteed price of wheat can 

have significant effects on the raise of its 

supply. Therefore, announcing the 

guaranteed purchasing prices by 

government will directly impacts on the 

increase of wheat output.7 

The cross elasticity also indicates the 

following items: The cross elasticity of 

land and all other inputs is negative 

which shows that land is a complement 

for other inputs. 

 

                                                           
7 Considering the importance of the function 

of wheat supply output, this issue has been 

attentively discussed in the appendix of 

article. 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

94 

 

The cross elasticity of seed and all other 

inputs is also negative which shows that 

seed is a complement for other inputs. 

 

The cross elasticity of labor force and 

seed is positive (complement), animal 

and chemical fertilizer and negative 

(substitute) with poisons. 

The cross elasticity of poisons and animal 

fertilizer is negative and positive with 

seed, labor force and chemical fertilizer. 

 

The cross elasticity of chemical fertilizer 

and other inputs but animal fertilizer is 

negative. 

 

The elasticity of all inputs to the wheat 

price is positive. By the increase of the 

wheat price, the most sensitivity belongs 

to input demand of poisons and animal 

fertilizer. Considering the inefficiency, 

the relative elasticities of inputs price has 

remained negative. However, elasticity of 

all inputs except animal and chemical 

fertilizer increases. 

 

Considering the inefficiency, inputs 

elasticity except labor force has increased 

to wheat price, Considering the 

inefficiency, the relative elasticity of 

wheat supply price has increased. In other 

words, the reaction of supply increases. 

 

The elasticity of irrigated wheat supply to 

the price of all irrigated wheat 

production’s inputs except land is low. 

Therefore, the price of land has the 

highest effect on the irrigated wheat 

supply. Whereas, the inputs with the 

lowest elasticity in the irrigated wheat 

supply are animal fertilizer and poisons 

which reveals the absence of reaction by 

wheat supply to animal fertilizer and 

poisons. 

 

Policy recommendations 

 

As inefficiency is not considered in 

estimation of supply and demand 

functions of inputs and outputs of 

agricultural sector inputs and regarding 

the effectiveness of inefficiency on the 

output supply and input demand, it is 

recommended that all studies of this 

district lay away the assumption of 

perfect efficiency of producers in 

estimation of the mentioned functions. 

 

Considering the congeniality between 

efficiency trend and under cultivating 

level of wheat on one hand and positive 

effectiveness of guaranteed rate of wheat 

and negative effectiveness of guaranteed 

rate of barley, the government should act 

in annual rates in a way that the planting 

pattern would not change harmfully to 

the wheat. (The current under cultivating 



Asian Journal of Agriculture and Rural Development, 4(1)2014: 82-95 
 

95 

 

level suffices internal production and 

more production can be achieved by 

developing the efficiency). 

 

Considering the inefficiency of the 

irrigated and dry wheat in country, 

planning for improving the technical 

efficiency of irrigated land wheat, can 

improve the country’s wheat production 

21 per cent. Therefore, the self 

sufficiency (independency) pattern of 

wheat should be codified and executed 

based on the technical efficiency in Iran. 

 

References 

 

Aigner, D., Lovell, K., & Schmidt, P. 

(1977). Formulation and 

Estimation of Frontier Production 

Function Models. Jouranl of 

econometrics, 6, 21-37. 

Battese, G. E., & Coelli, T. J. (1992). 

Frontier Prodution Functions, 

Technical Efficiency and Panel 

Data: With Application to Paddy 

Farmers in India. Journal of 

productivity analysis, 3, 153-169. 

Farrell, M. (1957). The Measurement of 

Productive Efficiency. Journal of 

the royal statistics society, 120, 

253-281. 

Greene, W. (2003). Maximum likelihood 

Estimation of Econometric 

Frontier Functions. Journal of 

economietric, 31, 22 – 36. 

Henderson, D. J., & C. F. Parmeter 

(2013). Nonparametric Methods 

for Practitioners, Chapter 2 and 5. 

Hojabr K., Kambiz, H. A., Narges 

(2002). Estimation of irrigated and 

dry land production and supply 

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Kuosmanen, T., & M. Kortelainen 

(2012). Stochastic non-smooth 

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Journal of Productivity Analysis, 

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General Office of Statistics. 

Parmeter, C. F., S. C. Kumbhakar., & H.-

J. Wang. (2013). Semiparametric 

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financing constraints. manuscript. 

Garshasbi, A, Y., Kazem, N. R., &  

Homayunifar, M. (2012). Affected 

Price and Non-price Factors on 

Wheat Supply in Country’s States 

by the Use of Panel Data. 

Agriculture economics journal, 

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Coelli, J. (1996). Measurement of Total 

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http://ideas.repec.org/a/jae/japmet/v11y1996i1p77-91.html
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http://ideas.repec.org/a/jae/japmet/v11y1996i1p77-91.html
http://ideas.repec.org/a/jae/japmet/v11y1996i1p77-91.html
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