Variational inequalities for marketable pollution permits with technological investment opportunities: The case of oligopolistic markets

In this paper, we develop a variational inequality framework for the modeling, qualitative analysis, and computation of equilibrium patterns in multiproduct, multipollutant oligopolistic markets with marketable pollution permits along with opportunities for investment in production technology and/or emission-abatement technology. The model deals explicitly with spatial differentiation and also guarantees that the imposed environmental standards are met through the initial allocation of licenses. An algorithm is proposed, with convergence results, to compute the profitmaximized quantities of oligopolistic firmsʹ products and the quantities of emissions, along with the equilibrium allocation of licenses and their prices, as well as the optimal investments in the technologies. Numerical examples are presented to illustrate the model and the algorithm.