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

Autori
Kojić, Vedran ; Lukač, Zrinka ; Puljić, Krunoslav

Izvornik
Croatian Operational Research Review (1848-0225) 12 (2021), 1; 37-48

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
generalized Sato production function ; cost minimization problem ; unique solution

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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Ekonomija

POVEZANOST RADA