A Cobb‐Douglas Production Function with Variable Returns to Scale

Abstract

T HE OBJECTIVE of this paper is to present a production function with variable returns to scale over the range of the function. A modified form of the Cobb-Douglas function is developed for this purpose. Data from a sample of farms are used to estimate the parameters of the modified function utilizing single-stage least-squares estimation. The empirical results are presented and some implications of the estimated elasticities of production are discussed. Many attempts have been made in the past to find algebraic forms that are theoretically appropriate and empirically useful for describing and estimating the functional relationships between inputs and outputs [7]. Each alternative functional form has advantages, but each usually imposes certain limitations on the input-output relationship. The conventional Cobb-Douglas function, for example, assumes unitary elasticity of factor substitution and partial and total production elasticities that do not vary over ,the range of the function. Recent efforts to develop more general forms of production functions have focused almost exclusively on the elasticity of factor substitution. Examples of such efforts include the constant elasticity of substitution function [1], the class of homothetic isoquant production functions [2], transcendental production functions [5], and the variable elasticity of substitution production function [6]. These new functional forms elevate the elas-