A variational inequality approach for marketable pollution permits

Abstract

In this paper, we present a variational inequality framework for the modeling, qualitative analysis, and computation of equilibria in markets in pollution permits. The models developed herein allow for different modes of competitive behavior, including oligopolistic behavior, while taking into account the cost of polluting plus the prices of the licenses to pollute at different receptor points. The models deal explicitly with spatial differentiation and also ensure that the imposed environmental quality standards are met through the initial allocation of licenses. An algorithm is proposed, along with convergence results, to compute the profit-maximized quantities of the firms' products and quantities of emissions, as well as the equilibrium allocation of licenses and their prices. Numerical examples are included to illustrate the approach. This is the first time that this methodology is utilized in environmental economics.