Regulation of Combined Harvesting of an Inshore-Offshore Fishery by Taxation

This paper deals with the combined harvesting of an inshore-offshore fishery with taxation as a control instrument. Here fishing is permitted in both the inshore and offshore areas though the inshore area is the breeding place for the species. But in order to control the overexploitation of the species the regulatory agencies impose a higher tax for fishing in the inshore area compared to the tax for fishing in the offshore area. The fish sub population in inshore area obeys the logistic law of growth [1]. Only the non-trivial steady state is determined. The local and global stability of the non-trivial steady state are discussed. Taking the taxes as control variables, the optimal harvest policy is formulated and solved as a control problem. The results are illustrated with the help of a numerical example.