A geometric perspective on the generalized Cobb-Douglas production functions

In this work we obtain an interesting link between some fundamental notions in the theory of production functions and the differential geometry of hypersurfaces in Euclidean spaces. In fact we establish that a generalized Cobb-Douglas production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. Moreover, this production function has constant return to scale if and only if the corresponding hypersurface is developable.