Water dynamics and environmental social practice in a differential game

Abstract

This paper investigates how socially and environmentally responsible practice influences the dynamics of a common aquifer and its impact on social welfare. We analyze a differential game between two firms, profit seeking (PS) and environmental corporate social responsibility (ECSR), that pump water to sell it to farmers. The profit of the PS firm is composed of revenues, extraction and taxation cost. Conversely, the ECSR maximizes an objective function composed of profit, consumer surplus, and environmental damage. From the analysis of the model, it emerges that only a balance of the social and the environmental concern can preserve the water table and improve the social welfare.