A Generalization of the CES Production Function

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T HE CES (constant elasticity of substitution) production function derived by Arrow, Chenery, Minhas, and Solow [2] has become widely known and widely used. Possibly the weakest point of the SMAC (Arrow, Chenery, Minhas and Solow) formulation is the assumption of. . . the existence of a relationship between V/L (value added per unit of labor) and W (the wage rates), independent of the stock of capital [2, p. 231]. If this assumption does not hold, the value of the elasticity of substitution derived from the estimated CES function may be biased. The CES function is also subject to the limitation that the value of the elasticity of substitution is constant, although not necessarily unity. However, when the capital/ labor ratio varies, due to changes in the factor price ratio, it is possible that the elasticity of substitution will vary as the capital/labor ratio varies. The purposes of this paper are (1) to derive a more general form of the CES production function that does not depend on the SMAC assumption of independence and with a property of variable elasticity of substitution, (2) to examine the elasticity of substitution of the new function, and (3) to present some evidence of the desirability of using the new function.