Production Functions and Elasticity of Substitution

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Empirical research in economics has tremendously increased both in quality and quantity ever since Cobb and Douglas proposed Cobb-Douglas production function for finding relationships among economic variables. Two important reasons for this are simplicity of Cobb-Douglas production function from an estimation point of view and that it is consistent with most economic data. Even though CobbDouglas production function describes most economic data quite well, it has some serious drawbacks: (1) it requires all inputs to be positively employed and (2) it has a unitary elasticity of substitution for all levels of factors. The generalized constant elasticity of substitution (CES) production function introduced by Arrow, Chenery, Minhas and Solow (ACMS) [2] removes first of these criticisms. On other hand, if elasticity of substitution were to be an index for judging a production function as a means of explaining relationships among economic variables, CES production function has same drawback as Cobb-Douglas production function. Intuitively speaking, one would expect that as one moves along a given isoquant elasticity of substitution increases (decreases) as relevant input ratio goes to infinity as well as to zero. It was this fact that Allen [1, 342] was alluding to when he stated the larger is value of a,1 flatter is constant product curve and more slowly does marginal rate of substitution increase as B is substituted for A.