A Geometric Characterization of Homogeneous Production Models in Economics

Abstract

In this paper, we give a simple geometric characterization of homogeneous production functions, by studying geometric properties of their associated graph hypersurfaces. For a homogeneous production function, we prove that its corresponding hypersurface with constant sectional curvature must be flat. Therefore, combining this with Chen and Vilcu's recent results, we obtain a new geometric characterization of homogeneous production functions having constant return to scale.