Estimation of the Demand Function of Water for the Industrial Sector Using Translog Cost Functions (Case Study: Zahedan City)

Document Type : Research Paper


1 MSc in Economic Sciences, University of Sistan and Baluchestan, Zahedan, Iran

2 Associate Professor of Agricultural Economics, University of Sistan and Baluchestan, Zahedan, Iran


The main objective of the current study was to estimate the demand function for
water in the industrial sector of Zahedan city based on the methodology of duality
premise. To this end, the trans-log cost function which is considered as a more
robust framework for the analysis of production relationships was utilized to
estimate the demand function of water in the industrial sector instead of using
conventional production methods. This is an applied survey in which the trans-log
cost function and the cost share equations using Iterative Seemingly Unrelated
Regressions (ISUR) approach. After the estimation of the model, the production
infrastructure technologies, the substitution and price elasticity were calculated
and homothetic, constant return to scale and Cob-Douglas hypotheses for the
production function were tested using Eviews software. The data of the study refer
to 30 active production units located in the industrial clusters of the Zahedan city
during the period from 2011 to 2012. Data were collected through questionnaires.
The determination coefficient of the model was equal to 97 percent which
indicated the goodness of fit. On the other hand, the results of the model
estimation represented water as a non-elastic commodity because the price
elasticity calculated for water was less than 1 (-0.07). Moreover, the calculated
values for Allen-Uzawa and Morishima elasticities indicated a strong substitution
relationship between water as a production input and machinery (6.69) and
building (1.30) inputs. On the other hand, there was a weak substitution effect
between water and land inputs (0.65) and a complementary relationship existed
between water and labor inputs (-0.43). However, it should be mentioned that the
homotheticity, constant returns to scale, and the Cob-Dagoulas form of the cost
function hypotheses were rejected based on the Maximum Likelihood Ratio