Noncompliant oligopolistic firms and marketable pollution permits: Staticsand dynamics

In this paper, we consider the modeling, analysis, and computation of solut ions to both static and dynamic models of multiproduct, multipollutant nonc ompliant oligopolistic firms who engage in a market for pollution permits. In the case of the static model, we utilize variational inequality theory f or the formulation of the governing equilibrium conditions as well as the q ualitative analysis of the equilibrium pattern, including sensitivity analy sis. We then propose a dynamic model, using the theory of projected dynamic al systems, whose set of stationary points coincides with the set of soluti ons to the variational inequality problem. We propose an algorithm, which i s a discretization in time of the dynamic adjustment process, and provide c onvergence results using the stability analysis results that are also provi ded herein. Finally, we apply the algorithm to several numerical examples t o compute the profit-maximized quantities of the oligopolistic firms' produ cts and the quantities of emissions, along with the equilibrium allocation of licenses and their prices, as well as the possible noncompliant overflow s and underflows. This is the first time that these methodologies have been utilized in conjunction to study a problem drawn from environmental policy modeling and analysis.