Classification of $h$-homogeneous production functions with constant elasticity of substitution

Main Article Content

Bang-Yen Chen


Almost all economic theories presuppose a production function, either on the firm level or the aggregate level. In this sense the production function is one of the key concepts of mainstream neoclassical theories. There is a very important class of production functions that are often analyzed in both microeconomics and macroeonomics; namely, $h$-homogeneous production functions. This class of production functions includes two important production functions; namely, the generalized Cobb-Douglas production functions and ACMS production functions. It was proved in 2010 by L. Losonczi \cite{L} that twice differentiable two-inputs $h$-homogeneous production functions with constant elasticity of substitution (CES) property are Cobb-Douglas' and ACMS production functions. Lozonczi also pointed out in \cite{L} that his proof does not work for production functions of $n$-inputs with $n>2$

Article Details

How to Cite
Chen, B.-Y. (2012). Classification of $h$-homogeneous production functions with constant elasticity of substitution. Tamkang Journal of Mathematics, 43(2), 321–328.


J. Acz'el and G Maksa, Solution of the rectangular $mtimes n$ generalized bisymmetry equation and of the problem of consistent aggregation, J. Math. Anal. Appl., 203(2) (1996),104--126.

R. G. Allen and J. R. Hicks, A Reconsideration of the Theory of Value, Pt. II, Economica, 1(1934), 196--219.

K. J. Arrow, H. B. Chenery, B. S. Minhas and R. M. Solow, Capital-labor substitution and economic efficiency, Rev. Econom. Stat., 43(1961), 225--250.

B.-Y. Chen, On some geometric properties of $h$-homogeneous production function in microeconomics, Kragujevac J. Math., 35(3) (2011), 343--357.

B.-Y. Chen, On some geometric properties of quasi-sum production models, J. Math. Anal. Appl., 392(2012), 192--199.

B.-Y. Chen and G. E. Vilcu, Geometric classifications of homogeneous production functions, Math. Social Sci., (submitted).

C. W. Cobb and P. H. Douglas, A theory of production, Amer. Econom. Rev., 18 (1928), 139--165.

P. H. Douglas, The Cobb-Douglas production function once again: Its history, its testing, and some new empirical values, J. Polit. Econom., 84(5) (1976), 903--916.

W. Eichorn, Characterization of CES production functions by quasilinearity, in Production Theory (W. Eichorn, R. Henn, O. Opitz and R. W. Shephard eds.), Springer-Verlag, pp. 21--33, 1974.

J. Filipe and G. Adams, The Estimation of the Cobb Douglas function, Eastern Econom. J., 31(3) (2005), 427--445.

J. R. Hicks, Theory of Wages , London, Macmillan, 1932.

L. Losonczi, Production functions having the CES property, Acta Math. Acad. Paedagog. Nyh'ai. (N.S.) 26(1) (2010), 113--125.

D. McFadden, Constant Elasticity of Substitution Production Functions, The Review of Economic Studies, 30(2) (1963), 73--83.

S. K. Mishra, A brief history of production functions, IUP J. Manage. Econom., 8(4) (2010), 6--34.

B. Nyul, Production functions and their characterizations, Alk. Mat. Lapok, 26(2) (2009), 351--363.

F. Stehling, Eine neue Charakterisierung der CD- und ACMS-Produktiosfunktionen, Operations Research-Verfahren, 21(1975), 222--238.

A. D. Vilcu and G. E.Vilcu, On some geometric properties of the generalized CES production functions, Appl. Math. Comput., 218(1) (2011), 124--129.

G. E. Vilcu, A geometric perspective on the generalized Cobb-Douglas production functions, Appl. Math. Lett., 24(5) (2011), 777--783.