Environmental policy modeling and computation: A variational inequality approach

Protection of the environment is among the most pressing public policy challenges and will continue to be so long into the future. Pollution, specifically, has played a pivotal and substantial role in the degradation of the environment. Although numerous analytical techniques and computational solutions have been proposed by theoreticians from disciplines as varied as economics to environmental engineering and decision sciences, significant methodologies that provide a rigorous analysis for the modeling, qualitative analysis, and computation to solutions to environmental problems which are typically complex and large-scale remain yet to be harnessed. The goal of this dissertation is to present a series of models in marketable pollution permits that yield the profit-maximized quantities of the firms\u27 products and the equilibrium quantities of the firms\u27 emissions. In addition, the equilibrium allocation of pollution licenses and their prices are obtained. Furthermore, different modes of market structure, including oligopolistic behavior and non-compliant behavior, and market imperfections such as transactions costs are incorporated into the modeling framework. Investment in technology, specifically production technology and emission-abatement technology, are explicitly considered in the models. Lastly, the dissertation concludes with a shift from the static setting to a dynamic setting and the marketable pollution permit model is analyzed within a dynamic framework that allows firms to be noncompliant. The dissertation begins with a brief historical overview of the evolution of environmental economics followed by the theoretical foundations of the mathematical framework employed. The principal methodology that is utilized for the models in the dissertation is that of variational inequalities. We will also make use of the projected dynamical systems to analyze the models within a dynamic setting. We conclude this dissertation with possible extensions of the models developed and provide suggestions for future research. The dissertation is a major step in the advancement of mathematical methodologies coupled with environmental policy analysis to contribute fundamentally to the formulation and evaluation of environment policy. This research is highly interdisciplinary as it encompasses the fields of management science and operations research, environmental economics, and applied mathematics