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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 761832, 6 pages
Research Article

Some Characterizations of the Cobb-Douglas and CES Production Functions in Microeconomics

1School of Investment and Construction Management, Dongbei University of Finance and Economics, Dalian 116025, China
2School of Mathematics and Quantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, China

Received 5 November 2013; Accepted 10 December 2013

Academic Editor: Grzegorz Lukaszewicz

Copyright © 2013 Xiaoshu Wang and Yu Fu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that the study of the shape and the properties of the production possibility frontier is a subject of great interest in economic analysis. Vîlcu (Vîlcu, 2011) proved that the generalized Cobb-Douglas production function has constant return to scale if and only if the corresponding hypersurface is developable. Later on, the authors A. D. Vîlcu and G. E. Vîlcu, 2011 extended this result to the case of CES production function. Both results establish an interesting link between some fundamental notions in the theory of production functions and the differential geometry of hypersurfaces in Euclidean spaces. In this paper, we give some characterizations of minimal generalized Cobb-Douglas and CES production hypersurfaces in Euclidean spaces.