Solution of the system of nonlinear PDEs characterizing CES property under quasi-homogeneity conditions

Advances in Difference Equations

Haila Alodan¹  Sharief Deshmukh¹  Bang-Yen Chen²  Gabriel-Eduard Vîlcu³ 

[1] Department of Mathematics, King Saud University, 11495, Riyadh, Saudi Arabia;Department of Mathematics, Michigan State University, 48824–1027, East Lansing, Michigan, USA;Research Center in Geometry, Topology and Algebra, University of Bucharest, Str. Academiei 14, 70109, Bucharest, Romania;Department of Cybernetics, Economic Informatics, Finance and Accountancy, Petroleum-Gas University of Ploieşti, Bd. Bucureşti 39, 100680, Ploieşti, Romania;

关键词: System of nonlinear PDEs;    Production function;    Elasticity of substitution;    CES property;    35G50;    91B38;    91B02;    91B15;   

DOI  :  10.1186/s13662-021-03417-6

来源: Springer

【 摘 要 】

The constant elasticity of substitution (CES for short) is a basic property widely used in some areas of economics that involves a system of second-order nonlinear partial differential equations. One of the most remarkable results in mathematical economics states that under homogeneity condition i.e. the production function is a homogeneous function of a certain degree, there are no other production models with the CES property apart from the famous Cobb–Douglas and Arrow–Chenery–Minhas–Solow production functions. In this paper we generalize this classification result to a much wider framework of production functions under quasi-homogeneity conditions, showing in particular the existence of three new classes of production models with the CES property.

【 授权许可】

CC BY