Elasticity of Substitution—A Summary

Abstract

This paper has a very specific purpose of explaining the differences among Allen elasticity of substitution, Morishima elasticity of substitution and McFadden elasticity of substitution. It is roughly divided into three sections. The first section traces the evolutionary trajectory and provides a summarized description(including formula) of these three measurements. The next section discusses a hypothetical scenario to bring out the intuition behind elasticity of substitution more vividly. In the last section the ASI all India-industry wise (unbalanced) panel data for 29 two digit industry for 2002 to 2013 is taken for a case study to empirically compare the three measures of elasticity of substitution. The square root production function under random effect model is used as it was the only functional form that satisfies the properties of production function which are-monotonicity, quasi-concavity, twice continuous-differentiability, positive marginal physical product and diminishing marginal productivity of factors of production. Each measure of elasticity of substitution has its own merits and demerits.The direct elasticity of substitution between two input factors doesn't account for the other input factors, hence it is the least advisable measure of elasticity of substitution. Allen elasticity of substitution is a ratio of cross price elasticity and share of the input. So basically it just scaling up or down the cross price elasticity. The measure of elasticity of substitution that does overcome the shortcomings of above two is Morishima Elasticity of Substitution. Itmeasures the change in any two input demands (say capital and labor) in a move to new cost minimisation where the cost minimising land derived demand also changes. The decision of which measure to use is the discretion of the researcher who should take the objective of the study as the primary criterion of judgement.

Keywords: Elasticity substitution (ES), Allen elasticity, labor ratio