3 - Analytical Results

Summary

This chapter studies the properties of environmental externality from general equilibrium perspective in the four basic models --- SEEE, SEEN, DEEE, and DEEN models. The chapter establishes the key results of environmental externality provision. They are the triangular equivalence relationship among the Lindahl equilibrium without transfer, the Nash bargaining solution with the payoffs of Cournot-Nash equilibrium as the status quo point, and the social optimum under the Lindahl weights. In this framework, the mapping of efficient solutions of the models and the simplex of social welfare weights plays a critical role. To facilitate the application of these results in empirical research, we provide analytical and numerical examples to validate these results as well as the algorithmic approach to solve the solution concepts derived from the key results. In contrast to the Lindahl equilibrium, we also critically assess the popular Benthamite and Negishi solutions of environmental externality provisions as well as transfer issues. In the appendix, we offer the programming codes in GAMS language for the numerical example.