On quasi-homogeneous production functions with constant elasticity of factors substitution - Khatskevich, Guennadi A.; Pranevich, Andrei F. (Journal of the Belarusian State University. Economics, 2018)
The study of the shape and properties of production functions is a subject of great interest in economic analysis. The class of production functions with constant Hicks elasticity of substitution includes many important production functions in economics; in particular, Cobb – Douglas production function and CES production function. In 2010, L. Losonczi proved that a two-factor homogeneous production function satisfies the constant Hicks elasticity of substitution property if and only if this homogeneous function is either a Cobb – Douglas production function or a CES production function. The similar result for multi-factor homogeneous production functions was proved by B.-Y. Chen in 2012. In this paper we generalize results of L. Losonczi and B.-Y. Chen to the class of quasi-homogeneous two-factor production functions with constant Hicks elasticity of substitution. Namely the notion of quasi-homogeneous two-factor production functions is introduced, relation between the condition of homogeneity and the condition of quasi-homogeneity is established, and the class of quasi-homogeneous two-factor production functions with constant elasticity of factors substitution by Hicks is obtained. Moreover, we pointed out the analytical form for quasi-homogeneous two-factor production functions with unit elasticity of substitution. The obtained results can be applied in modeling of production processes.