Elasticity of Substitution & Returns to Scale in Indian Chemical Industry

This paper examines whether there has been a change in. the elasticity of substitution and returns to scale in the Indian chemical industry due to the reforms introduced in 1991. The results reveal that reforms have helped the chemical industry in India adapt new technology which is more capital intensive. As a result, the elasticity of substitution as well as the returns to scale has changed in the post-reforms period from those in the pre-reforms period. Introduction Numerous papers have looked in to the impact of reforms on the efficiency and productivity of the Indian industry in the pre and post-reforms periods. The increased competition after reforms may have forced firms to improve their efficiency and or productivity, which the literature tried to capture. Productivity or efficiency changes can also happen if firms adopt better technologies of production. Since the elasticity of substitution and the returns to scale depend on the output and input mix, a change in technology should also affect the elasticity of substitution and the returns to scale. This paper intends to take a path, which not many papers have taken in the recent past. It tries to capture the change in technology by looking at elasticity of substitution and returns to scale and if there has been any change in them in the pre-reforms and the post-reforms period in the context of the Indian chemical industry. Literature Review & Methodology Important for any production function is the elasticity of substitution parameter. The popular Cobb-Douglas production assumes this to have a unitary value, while the Constant Elasticity of Substitution (CES) production function assumes the elasticity of substitution to be a constant. In addition, there have been studies that allow for variable elasticity of substitution (Revankar 1971). As in many industries, the optimum size of a firm is small in relation to the total market; economists have often assumed that there are constant returns to scale. However, there are industries where few firms control a large share of the total supply, hence these industries might have increasing returns to scale (Diwan 1966). In addition to the known constant, decreasing, and increasing returns to scale, the literature also has looked at production functions that allow variable returns to scale. For example, Zellner and Revankar (1969) in their paper introduced a generalized production function where the returns to scale function is a variable and satisfies a pre-assigned relationship to the output level. However, given the objective of this study, we compute the average value of the elasticity of substitution and the returns to scale during the pre-reforms period and the post-reforms period. Sankar's (1970) is the only study in literature that estimates the elasticities of substitution and returns to scale in Indian manufacturing. The study uses the CES production function for 15 manufacturing industries in India, modified to allow for possible non-constant returns to scale. The estimate of elasticity of substitution obtained in the study exhibits considerable variation among industries, which suggests that a CES production function would be preferable in such studies. Hence in this study we will use the CES production function. Following Diwan (1966), the CES function for non-constant returns to scale can be written as Q = A [[[delta][K.sup.-[rho]] + (1-[delta]) [L.sub.-[rho]].sup.-v/[rho]] [e.sup.[lambda]t]. (1) Here v is the parameter reflecting returns to scale while [rho] is the parameter of substitution which is related to elasticity of substitution by [sigma] = 1 / (1+[rho]). (2) Estimating a CES production function is essentially a two step process, where one or two parameters are estimated from another function and their values are plugged into the CES function to estimate the other parameters. We follow Knox Lovell (1973) for the estimation of the CES function. …