Some considerations on a class of macro-economic production functions

Summary It is demonstrated that dimensional analysis can be a tool in investigating the properties of a production function. First, the economic implications of the CES Function are shown. Secondly, endorsing the statements made by the SMAC Group that the Leontief and the Cobb and Douglas types of the production function arise as limiting cases of the CES production function, detailed proofs of these statements are given that maintain the dimensional homogeneity in proceeding to the limits. It is shown that certain dimensional constants of the CES production function become dimensionless entities in the limit.Finally, an expression for the curvature of the isoquants is derived. A dimensionally homogeneous relation is presented between the elasticity of substitution, the slope, the curvature and the factor endowments. This relation can be used to derive a general Variable Elasticity of Substitution production function.1970-71 Visiting Professor, Department of Economics, F.S.U. (Florida State University, Tallahassee, Florida, U.S.A.).The authors thank Professor Th. van de Klundert, Dr. H. de Haan and Dr. S. K. Kuipers for their useful comments on the first draft of this paper.