In this paper we present a Stackelberg differential game to study the dynamic
interaction between a polluting firm and a regulator who sets pollution limits overtime. At
each time, the firm settles emissions taking into account the fine for non-compliance with
the pollution limit, and balances current costs of investments in a capital stock which allows
for future emission reductions. We derive two main results. First, we show that the optimal
pollution limit decreases as the capital stock increases, while both emissions and the level
of non-compliance decrease. Second, we find that offering fine discounts in exchange for
firm’s capital investment is socially desirable. We numerically obtain the optimal value of
such discount, which crucially depends on the severity of the fine. In the limiting scenario
with a very large severity of the fine, the optimal discount implies that no penalties are levied,
since the firm shows adequate adaptation progress through capital investment.
