The impact of pollution reduction on the optimal harvesting strategy in a seasonally changing and polluted environment

Abstract

This paper deals with the optimal harvesting of single-species populations in a polluted and seasonally varying environment. The presence of pollution negatively impacts resource growth, and as a consequence, the economic rent from harvest suffers. Assuming that pollution is inevitable, the harvester, who has a fixed flow of funds for harvesting activity, intends to invest the unused funds left over after harvesting in pollution control, expecting some increment in the economic rent. Thus, optimal harvesting problems in two different scenarios have been studied, and the solutions are compared to evaluate the impact of investing in pollution reduction on revenues. Pontryagin's maximum principle and the concept of blocked intervals are used to solve the aforesaid problems.  Findings of the study indicate that funding pollution control programs should be considered as an alternative to promote  conservation of resources and enhance net economic rent for harvesting systems impacted by pollution and seasonal fluctuations.