Pollution Control Policies and Natural Resource Dynamics: A Theoretical Analysis

Policies for the management of natural resources and the resources themselves interact to form complex systems. In this paper, we present a highly simplified model that can be used to study the general features of those systems. The model has three state variables, the abundance of the resource, environmental pollution, and the capital devoted to pollution control. We analyze it graphically using the singular perturbation approach. Two modes of behavior are possible, stationary and cyclic. When the abundance of the resources varies cyclically, the length of the period of resource scarcity depends on population size, economic activity, pollution per unit of output and on policy constraints. We distinguish between two classes of policies, one in which decision-makers base their investments in pollution control capital on the abundance of the resource, and another in which those decisions depend on the amount of pollution. We show that policies based on the observation of pollution are safer than those based on resource abundance, because in the latter case, small changes in policy variables can much more easily lead to a collapse of the resource. Increases in population size, even when accompanied by an equiproportional increase in the pollution control budget can lead to a change from stationary to cyclic behavior, especially where policies are based on resource abundance.