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

DOI: 10.5556/j.tkjm.43.2012.321-328

Keywords: Homogeneous production function , constant elasticity of substitution , Cobb-Douglas production function , ACMS production function

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Abstract:

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 $n>2$

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