Cost minimization and input substitution in the production of gilthead seabream

Abstract

This paper studies cost minimization decisions by utilizing a simple bioeconomic model for gilthead seabream (Sparus aurata). This model is based on a biological growth model which accounts for the effects of temperature and ration size. Although the implicit production function derived from the growth model is shown to be quasiconcave, it is not homothetic nor quasilinear. Further, technology shows increasing returns with respect to ration size and harvesting time. Optimization decisions are analyzed in two different contexts, a restricted biological setting and an expanded economic problem. It is shown that the optimal ration size increases for the latter context, reaching values commonly accepted in current industrial practice. Even though the elasticity of substitution to the shadow input prices is positive at the optimal ration size, the latter is rather robust to changes in input prices. However, optimal costs show larger sensitivity to the labor price than to the feeding and managerial costs.