A Theory for Building NEO-Classical Production Functions

Abstract

In this study, we propose a mathematical theory for building neoclassical production functions with homogeneous inputs in both aggregate and per capita terms. This theory is based on two concepts: Euler‟s equation and Cauchy‟s condition for first-order partial differential equations. The analysis is restricted to functions that exhibit constant returns to scale (CRS). For the function to meet the law of diminishing marginal returns, we present the necessary and sufficient conditions to be satisfied by the curve that defines Cauchy‟s condition. In this context, we also discuss the Inada conditions. We first present functions that depend on two inputs and then extend and discuss the results for functions that depend on several inputs. The main result of our research is the provision of a clean and clear theory for constructing neo-classical production functions. We believe that this result may contribute to closing the huge methodological gaps that separate schools of economic thought that defend or reject the use of production functions