A dynamic reaction model of a two-species fishery with taxation as a control instrument: a capital theoretic analysis

In a fully dynamic model of an open-access fishery, the level of fishing ef fort expands or contracts according as the perceived rent (i.e., the net ec onomic revenue to the fishermen) is positive or negative. A model reflectin g this dynamic interaction between the perceived rent and the effort in a f ishery, is called a dynamic reaction model. The present paper deals with a dynamic reaction model of a fishery consisting of two competing species, ea ch of which obeys the logistic law of growth. A regulatory agency controls exploitation of the fishery by imposing a tax per unit biomass of the lande d fish. It is also assumed that the gross rate of investment of capital in the fishery is proportional to the perceived rent. With this capital theore tic approach, the dynamical system consisting of the growth equations of th e two-species and also of the fishing effort is formulated. The existence o f its steady states and their stability are then studied using eigen value analysis. The optimal harvest policy is discussed next with the help of Pon tryagin's maximum principle. The results are then illustrated using numeric al examples. (C) 1999 Elsevier Science B.V. All rights reserved.