Environmental Subsidy Modeling: Asymmetric Firms and Uncertainty

This paper extends the theoretical framework developed by Pal et al. (J Public Econ Theory 25(1):90–122, 2023) on optimal subsidy policies for industries generating positive environmental externalities. We develop three significant extensions: (1) heterogeneity among firms in production efficiency and environmental impact, (2) uncertainty in the magnitude of environmental benefits, and (3) the joint presence of firm heterogeneity and benefit uncertainty. For asymmetric firms, we establish that differentiated subsidy rates based on firm-specific environmental efficiency are welfare-superior to uniform subsidies. Under uncertainty, we prove that regulatory conservatism—lower subsidy rates—is optimal when the social welfare function is concave in environmental benefits. When both heterogeneity and uncertainty coexist, differentiated subsidies must be further adjusted downward, with the magnitude depending on the covariance between firm-specific environmental efficiency and benefit uncertainty. We also compare per-unit and lump-sum subsidy schemes under both extensions, showing that the welfare ranking established by Pal et al. (2023) is generally preserved but may be reversed for sufficiently heterogeneous firms. These extensions provide critical refinements to environmental policy design in more realistic market settings.