Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

Abstract

Abstract The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

Keywords

• System of nonlinear PDEs
• Production function
• Elasticity of substitution
• CES property