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

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