Dynamic Theory of Renewable Resource Economics with Economy Population of Size; Optimal Control Theoretic Approach

#465 Summary: The problem the economists in the field of renewable resources face is that of determining and recommending the harvest intensity that will maximize the economic value to the consuming society and also maximize the producers' surplus at a level of production in perpetuity. The optimal control theoretic approach was employed in this paper to theoretically answer this problem within the framework of a one country-one renewable resource with economy of size of resource population. In order to derive quantitative as well as qualitative results, a quadratic objective function-linear population-harvest dynamics model and a quadratic objective function -quadratic population-harvest dynamic model are solved for the optimal harvest paths over time. A general conclusion is that if the initial resource population is smaller than the target population to be determined in the text, the present harvest intensity must be curtailed to an extent that the resource population can grow to a level that can sustain the optimal or target harvest. This establishes a principle of conservation of renewable resources. In this case, a government regulation over the total harvest is supported. In case the initial population is already greater than the target population, the competitive harvest is proved to be the optimal harvest. Detailed analyses of the economy of size effects and the future discount rate effects are presented.