Three essays on sustainable growth and environmental control

This thesis studies the issues on sustainability with nonrenewable resources and on practical problem with environment: regulation to control pollution. The first essay proves the converse of Hartwick's rule with general production function. Hartwick's rule shows that if one reinvests all the rents from nonrenewable resource, then constant sustainable consumption can be maintained. This ensures intergenerational equity. The converse of Hartwick's rule is proved by directly solving ordinary differential equations. It means the constant consumption must imply the total reinvesting of the rents from the exhaustible resource, and so the Hartwick's rule prescribes the unique sustainable policy.In the second essay, Rawls' "just saving principle" is fonnulated with a model for constant utility in an intergenerational allocation framework. A term comparing consumption of adjacent generations is added to the utility function. The model is analyzed in the context of optimal control theory. In a two-sector economy, consumption growth is incorporated with equity. This property removes the disadvantage that a society starting out poor will be in such poverty forever, which is inherent in the model of constant consumption with nonrenewable resources. Different forms of generalized Hartwick's Rule are obtained. Optimal consumption path is characterized to achieve the highest utility.The third essay investigates the optimal emission tax schemes for oligopolistic firms with differentiated goods. In the model, pollution stock creates disutility on social welfare. Firms play dynamic games against themselves, trying to maximize the long-run profit given the tax rules and their opponents' behavior. Open-loop and Markov Nash Equilibria are studied. The model is analyzed with optimal control theory and differential game theory. Time-independent tax rules are shown to exist that guide polluting oligopolists to produce along socially optimum path. For linear market demand and quadratic damage function, the tax rules are shown to be linear in the pollution stock. Numerical examples show that even the polluting firm can receive subsidy at the periods when initial pollution stock is low. The optimal tax in general is dependent on the current pollutant stock. The results shed a light on policy making of the related market structure