A Generalized Production Function and its Special Cases

Abstract

A Generalized Production Function and its Special Cases

Sixteen years ago Arrow, Chenery, Minhas and Solow derived the Constant Elasticity of Substitution (CES) production function. Its derivation proceeded in two steps. The first one was to estimate a stochastic equation in which labor productivity is a function of the wage rate. The second step involved a linkage of this empirically determined equation with the body of establıshed neoclassical theory: the wage rate was assumed to be determined competitively and a function of the capital-labor ration. In this paper above procedure for the derivation of the CES function was modified. First, the empirical proposition is that labor productivity is determined by the wage rate and the capital-labor ratio. Second, the wage rate is assumed to be determined in a non-competitive manner.. With these two changes a much wider class of linear homogeneous production functions is obtained. It includes as special cases the Variable Elasticity of Substitution (VES) production function and the CES function. As is wellknown, the latter in turn includes as special cases (a) the perfect elasticity of substitution production function, (b) the Cobb-Douglas production function and (c) the Leontief fixed proportion production function