Second-best taxation for a polluting monopoly with abatement investment

Highlights: • The optimal tax depends on the difference between social and private shadow prices of pollution stock. • The optimal tax is time-consistent in the short run and in the long run. • With constant marginal damages, the optimal tax is constant. • With increasing marginal damages, the optimal tax depends on the pollution stock and abatement capacity. • The steady state in both cases is globally stable. - Abstract: This paper characterizes the optimal tax rule to regulate a polluting monopoly when the firm has the possibility of investing in an abatement technology and the environmental damages are caused by a stock pollutant. The optimal policy is given by the stagewise feedback Stackelberg equilibrium of a dynamic policy game between a regulator and a monopolist. The regulator playing as the leader chooses an emission tax to maximize net social welfare, and the monopolist acting as the follower selects the output and the investment in abatement technology to maximize profits. We find that the optimal tax has two components. The first component is negative and equal to the gap between the marginal revenue and the price caused by the firm market power; the second component is given by the difference between the social and private shadow prices of the pollution stock. Considering a linear-quadratic model we show that if marginal environmental damages are constant, the difference between social and private shadow prices is positive and the optimal policy consists of taxing emissions at a constant rate if the marginal damages are large enough. However, if the marginal environmental damages are increasing the numerical exercises carried out show that this difference is negative at the steady state and the optimal policy gives the firm a subsidy when approaching the steady state regardless of the importance of the environmental damages. This result is explained by the negative effect that abatement technology accumulation has on the tax. Finally, it can be pointed out that although both models yield different predictions about the sign of the optimal policy the dynamics is globally stable for both cases.