The Interplay Between Subsidy and Regulation under Competition

This study extends the work of Anand and Giraud-Carrier (2020) [Pollution regulation of competitive markets. Management Science. 66(9), 4193–4206] to an even more general case in which the government offers a subsidy to firms. For the purpose of investigating the interplay between subsidies (rewarding positive externalities) and regulation (punishing negative externalities) under competition, we propose a game-theoretic model to formulate the problem. By Karush–Kuhn–Tucker (KKT) conditions and backward induction, we obtain the following results. They are unique in our new scenario compared to Anand and Giraud-Carrier (2020). First, in terms of abatement, the effects of regulation and subsidy offset when the abatement efficiency is relatively high, and reinforce when abatement is inefficient. From the perspective of social welfare (SW), the effects of regulation are often offset by the effects of subsidy, and vice versa. Second, the relationship between the optimal subsidy rate and regulation depends heavily on the degree of competition and marginal cost of public funds. Third, in product and abatement subsidy schemes, cap-and-trade and taxes remain equivalent under competition. Finally, under certain conditions, a higher product subsidy rate will not necessarily give rise to higher SW at certain regulatory levels. Our research can provide a rationale for social planners who aim to achieve peak of CO2 emissions and carbon neutrality.