Optimal harvesting of a renewable resource in a polluted environment: An allocation problem of the sole owner

Abstract

AbstractThis study presents an allocation problem of the sole owner between a renewable resource harvesting and pollution reduction. Decline in the revenues due to the presence of pollution in the environment drives the harvester to allocate a part of the available effort capacity towards pollution reduction through environmental treatment and pollutant inflow reduction to improve the resource growth as well as quality of the harvest. Hence, the interest is to find an optimal effort allocation to maximize the present value of the total net revenues on infinite horizon. Therefore, an optimal harvest problem on infinite horizon has been formulated, and it is solved using the standard techniques of optimal control. Results of the study highlight that allocating a part of the available effort capacity towards pollution reduction improves not only the revenue from the harvest but also survival rate of the resource. Key results of the study are demonstrated through numerical simulations.Recommendations for Resource Managers Effect of pollution on the live stock is adverse, and it should be considered as one of the important parameters in resource management objectives. The presence of pollution in the environment affects both the resource growth and quality of biomass, resulting in reduced revenue from the harvest. Pollution is inevitable (especially in developing countries), and hence investing a part of the available effort capacity on pollution reduction (instead of harvesting by the entire capacity) can be considered as an alternative to improve the revenue. Environmental treatment and pollutant inflow reduction are some of the activities that can be applied to reduce pollution. Results of this study provide an important information for the sole owner who faces a decline in the revenue from resource harvesting in a polluted environment.