A resource dependent fishery model with optimal harvesting policy

Abstract

A dynamic model for a single-species fishery, which depends partially on a logistically growing resource with functional response, is proposed using taxation as control instrument to protect fish population from overexploitation. The analysis of the model shows that both the equilibrium density of fish population as well as the maximum sustainable yield increase as resource biomass density increases. The optimal harvesting policy is also discussed with the help of Pontryagin's Maximum Principle. It is found that for the optimum equilibrium value of resource biomass density, the total user's cost of harvest per unit effort must be equal to the discounted value of future price at the steady state.