Dynamic analysis of degradation thresholds for sustainable environmental management

We examine environmental protection in an oligopolistic setting in which a Pigouvian pollution tax is levied whenever environmental degradation exceeds a certain threshold set by a regulator. This threshold mechanism defines two scenarios, one with low environmental degradation in which firms do not internalize pollution, and one with high degradation in which firms are involved not only in production activities but also in abatement to ease the burden of the environmental tax. The purpose of this paper is to examine how the periodic dynamics of environmental degradation, described by a Lorenz map, are influenced by the main policy parameters. Regarding policy implications, we show how to construct a careful alignment between the border of the no-tax area and the level of taxation, which is crucial for reducing environmental degradation and avoiding fluctuations.