Optimal pollution standards and non-compliance in a dynamic framework

Abstract

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, and balances current costs of investments in a capital stock which allows for future emission reductions. We show that the optimal effective pollution limit path, which is the pollution level above which the fine is truly imposed, decreases overtime, inducing a rise in capital stock and a decrease in both emissions and the level of non-compliance. If the effective pollution limit coincides with the pollution limit set by the regulator, we generally find a bounded value of the severity of the fine that maximizes social welfare. If the effective pollution limit is larger than the pollution limit set by the regulator due to fine discounts in exchange for firm’s investment in capital, the effect of a more severe fine depends on the magnitude of this discount. In the limiting scenario with a sufficiently large severity of the fine, emissions coincide with the effective pollution limit and no penalties are levied, since the firm shows adequate adaptation progress through capital investment.