INFLUENCE OF INVESTING IN TREATING A POLLUTED ENVIRONMENT ON THE HARVEST: A PROBLEM OF OPTIMAL ALLOCATION

Abstract

This study is concerned with harvesting a renewable resource that is surviving in a polluted environment. Fall in the revenue from the resource due to presence of pollution in the environment drives the sole owner to allocate a part of the available effort towards treating the environment and the interest is to find the optimal allocation of the available effort towards harvesting the resource and treating the environment so that the revenue is maximized. Resource-pollution dynamics are studied, maximum sustainable yield and maximum sustainable revenue have been evaluated. Further, an optimal allocation problem has been formulated on infinite horizon and optimal solutions are obtained. Key results of the study are demonstrated through numerical illustrations.