Open AccessOn the uniqueness of the solution of the cost minimization problem with generalized Sato production function
Author(s) -
Vedran Kojić,
Zrinka Lukač,
Krunoslav Puljić
Publication year - 2021
Publication title -
croatian operational research review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 5
eISSN - 1848-9931
pISSN - 1848-0225
DOI - 10.17535/crorr.2021.0004
Subject(s) - uniqueness , mathematical optimization , minification , quasiconvex function , production (economics) , function (biology) , mathematics , monotone polygon , mathematical economics , elasticity of substitution , profit (economics) , economics , subderivative , convex optimization , regular polygon , microeconomics , mathematical analysis , geometry , evolutionary biology , biology
Whenever a firm is maximizing its profit, it necessarily has to minimize its cost. Thus, the cost minimization problem is one of the central problems in the theory of the firm. When presenting this problem, the majority of microeconomic textbooks use very well-known production functions, such as Leontief, Cobb-Douglas, or other CES production functions. The goal of this paper is to analyze the cost minimization problem with the generalized Sato production function. The generalized Sato production function is one of the non-standard production functions with variable elasticity of substitution. First, we show that the generalized Sato production function is continuous, strictly monotone, strictly quasiconcave and that a positive amount of output requires positive amounts of some of the inputs. Next, by using mathematical programming we show that the cost minimization problem with generalized Sato production function has a unique solution. This result is very important since it implies the existence of the corresponding cost function and conditional input demands.