On some geometric properties of the generalized CES production functions

In this paper we prove that the generalized CES production function has constant return to scale if and only if the corresponding hypersurface is developable. Moreover, we establish that this production function has decreasing/increasing return to scale if and only if the corresponding hypersurface has positive/negative Gaussian curvature. These results are a generalization of some recent results concerning the generalized Cobb–Douglas production functions [G.E. Vîlcu, A geometric perspective on the generalized Cobb–Douglas production functions, Appl. Math. Lett. 24 (2011) 777–783].