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.
