—optimal Control Theoretic Approach—

The problem the fisheries economists face is that of determining and recommending the fishing intensity that will maximize the economic value to the consuming societies and also maximize the producers' surplus at a level of production in perpetuity. In this paper the optimal control theoretic approach is employed to theoretically answer this problem within the framework of a one country-one fish species economy. In order to derive quantitative as well as qualitative results, a quadratic objective function linear population dynamics model is solved for the optimally controlled catch over time. A general conclusion is that if the initial fish population is smaller than the desired or target population to be determined in the text, the fishing intensity must be curtailed to such a degree that fish population can grow so that in the long run the target catch can be attained at the level of steady population(which will be sustained in perpetuity) . A governmental regulation over the total catch ts supported in this case since the social value in the market of a unit catch always exceeds the individual marginal cost of catching the same. Mesh size regulations are also supported due mainly to the fact that the information on the optimal mesh size is external to individual fisherman. In Appendix detailed derivation procedures of the optimal control are developed. Also a model with quadratic objective function and quadratic population dynamics is traced out for optimal control paths by using a phase diagram. ** The author is grateful to his colleague Professor Royall Brandis for his continued advice and encouragement in this work. .;..•• -A-rv ;'-i .•