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.
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Xiaoshu Wang (2016) studied this question.