A geometric characterization of homogeneous production models in economics

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, by combining this with Chen and V?lcu?s recent results, we obtain a new geometric characterization of homogeneous production functions having constant return to scale.