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Optimal Feeding and Harvest Time for Fish with Weight-Dependent Prices

Like agriculture, decisions regarding aquacultural production are complex. In addition to controlling harvest, feeding schedules, and culling rates, one must consider a number of practical considerations that may supersede other factors in economic importance. Among these pragmatic considerations are unusual aspects of the market price for fish. Fish markets provide premiums for larger-sized fish, and the premiums are often piecewise linear. This paper extends existing research by demonstrating general solutions for optimal feeding schedules and harvesting time under conditions of piecewise-continuous, weight-dependent prices. The solutions are characterized by idiosyncratic responses to marginal changes in exogenous parameters. For instance, a 1% decline in the interest rate can induce a 70% increase in the optimal weight. In general, as the interest rate decreases, optimal harvest weight and harvest time increase in a stepwise, nonlinear fashion.