Izvorni znanstveni članak

https://doi.org/10.17535/crorr.2021.0004

On the uniqueness of the solution of the cost minimization problem with generalized Sato production function

Vedran Kojić orcid.org/0000-0002-6802-1719 ; Faculty of Economics and Business, University of Zagreb
Zrinka Lukač ; Faculty of Economics and Business, University of Zagreb
Krunoslav Puljić ; Faculty of Economics and Business, University of Zagreb

Sažetak

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.

Ključne riječi

generalized Sato production function; cost minimization problem; unique solution

Hrčak ID:

259472

URI

https://hrcak.srce.hr/259472

Datum izdavanja:

29.6.2021.

Posjeta: 819 *