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On some geometric properties of the generalized CES production functions. (English) Zbl 1231.91278

Summary: 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, 777–783, (2011)].

MSC:

91B38 Production theory, theory of the firm
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