THE OPTIMAL DEPLETION OF EXHAUSTIBLE RESOURCES

Abstract

0.1. In any given economy there must be a number of commodities that enter into production and which are used up, and whose available stock cannot be increased. Examples like fossil fuels come readily to mind. It would seem reasonable to argue that in the long run the limited availability of these commodities, together with their technological importance, would begin to act as a constraint on the economy's growth potential. In fact several recent studies have laid great emphasis on this possibility.3 Although the point is an obvious one, most economic studies of the properties of long-run plans neglect it.4 In this paper, therefore, we explore in a rather preliminary way the problems that appear to arise naturally when the existence of exhaustible resources is incorporated into the study of intertemporal plans. It appears that questions in this area are hard to answer. For even in the simplest of environments where it is supposed that there is perfect foresight, one is concerned not merely with the optimal depletion of exhaustible resources but with the optimal rate of investment as well. The two must plainly be interrelated. The latter problem on its own is hard, and the combined problem is very complex. In fact it will appear in the course of the arguments that follow that intuition is not a very good guide for this joint problem. In any case, the assumption of perfect foresight is particularly dubious here since it would appear almost immediate that an investigation of intertemporal plans in the presence of exhaustible resources readily invites consideration of the possibilities of large-scale alterations in technology at dates in the future that are inherently uncertain. Moreover, it is clear that such extensive technological changes would not be achievable costlessly. In this paper, therefore, we attempt to demonstrate how one might, in a relatively simple manner, bring such considerations as these to bear on a set of questions that have generated a considerable amount of interest in recent years. 0.2. It is plain of course that the mere existence of a resource that is exhaustible is not a