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This paper, describes a prey-predator fishery model incorporating prey refuge. The proposed model reflecting the dynamic interaction between the net economic revenue and the fishing effort used to harvest the prey species in the presence of predation and a suitable tax. The steady states of the system are determined and the dynamic behavior of the model system is discussed. The occurrence of Hopf bifurcation of the proposed model system is examined through considering density-dependent mortality for the predator as bifurcation parameter. The optimal taxation policy is formulated and solved with the help of Pontryagin's maximal principle. The objective of the paper is to maximize the monetary social benefit as well as prevent the predator species from extinction, keeping the ecological balance. Results are illustrated with the help of numerical examples.

This paper deals with the surplus production models of Verhulst-Schaefer and Gompertz-Fox that are applied to the European Hake fishery to develop static as well as dynamic frameworks to investigate the sustainability properties of the stock, optimal utilization of the resource and the management of the fishery. To illustrate the approach through which long-run sustainability can achieve an optimum exploitation of the fishery, a conventional economic model is combined with a biological population growth model to develop a deterministic bioeconomic model. The parameters of the bioeconomic model are estimated using empirical data of catch and effort of the European Hake fishery. Standard reference points are analyzed and tax policies are introduced to attain the standard reference points. In order to achieve maximum profit from the fishery, optimal steady state solutions are determined for separate discount rates.