Control on Nonpoint Source Pollution under Uncertain Welfare

Abstract

This study develops a Cournot duopoly model in which production generates nonpoint-source pollution and firms producing differentiated goods jointly determine output and abatement technology under an ambient charge. Unlike point-source pollution, nonpoint-source pollution cannot be directly monitored; the regulator observes only ambient pollution concentrations. By explicitly incorporating this informational constraint, the model provides a tractable analytical framework for examining strategic interactions between firms and the regulator. The analysis proceeds in two stages. In the second stage, closed-form expressions for equilibrium output and abatement are derived as functions of the ambient charge, and feasibility conditions are established. It is shown that total emissions decrease monotonically with the charge rate, regardless of whether firms are homogeneous or heterogeneous, ensuring policy effectiveness even when individual firms exhibit perverse responses. In the first stage, random fluctuations in ambient pollution are introduced to characterize the optimal charge rate that maximizes expected social welfare under uncertainty. Overall, the results confirm that ambient-based regulatory instruments constitute a robust and analytically transparent approach to controlling nonpoint-source pollution, even in the presence of firm heterogeneity and uncertainty.