Optimal Tax Policy of a Stage Structured Prey Predator Fishery: A Dynamic Reaction Model

In a fully dynamic model of an open-access fishery, the level of fishing effort expands or contracts according as the perceived rent (i.e., the net economic revenue to the fishermen) is positive or negative. A model reflecting this dynamic interaction between the perceived rent and the effort in a fishery is called a dynamic reaction model. In this paper, we study a dynamic reaction model, in which the prey species is subjected to harvesting in the presence of predator and it is assumed that an external agency regulates the fishery by imposing a suitable tax per unit biomass of landed fish. The fishing effort is taken as a dynamic variable depending on the capital invested in the fishery. The steady states and their stability are studied. The problem of the optimal tax policy is solved by Pontryagin’s maximum principle keeping the ecological balance.