Economics, Mathematical Models and Environmental Policy

This paper briefly reviews several models of externality which provide the theoretical basis of environmental economics. An externality may be defined as a situation where the output or action of a firm or individual affects the production possibilities or welfare of another firm or individual who has no direct control over the initial level of the output or activity. Pollution, resulting from the disposal of residual wastes, is a classic example of externality.Three static models examine the optimality conditions for (1) a two-person externality, (2) a many-person externality (where the externality takes the form of a “pure public bad”), and (3) a two-plant polluter. In the case of a two-person externality negotiation between the affected parties may lead to the optimal level for the externality regardless of the initial assignment of property rights. In the many- person case, environmental policies, such as direct controls or economic incentives, may be required to achieve an optimal allocation of resources. Economic incentives may take the form of per unit taxes on emissions or transferable discharge rights. In the third model it is shown how a tax can induce optimal (least cost) treatment from a two-plant polluter.Two dynamic models examine the cases where (1) a pollution stock may accumulate or degrade according to rates of discharge and biodegradation and (2) a toxic residual must be transported from sites where it is generated to sites where it may be safely stored. The latter problem poses environmental risks from spills in transit or leakage at storage sites.While radioactive and toxic wastes are likely to continue to be regulated by direct controls some of the more “benign” residuals are suitable for regulation by economics incentives. Effluent taxes in France and the Netherlands, transferable discharge permits on the Fox River in Wisconsin, transferable stove permits in Telluride, Colorado and the EPA’s emission-offset policy are indications that economic incentives will play a greater role in the future management of environmental quality.