The Optimal Exploitation of an Unknown Reserve.

This paper, while treating the first issue with some generality, will take a rather limited view of the way in which information about the distribution of total reserves is assimilated. We shall assume that the planner begins with a given probability distribution of possible endowments of the natural resource, and that he updates this distribution over time by conditioning on the knowledge of his cumulative consumption at each instant. Thus we will abstract from the activity of exploration. This is a regrettable omission which we hope to correct in a later paper. The treatment of this initial problem seems essential to further progress in any event. The plan of the paper is as follows. We begin with a review of the problem of optimal depletion without production in a certain environment. Variational techniques are then employed to deduce necessary conditions for a solution to the problem of optimal exploitation under uncertainty. It is seen that the possibility of premature exhaustion considerably alters the requirements of an optimal path. We then determine a more complete characterization of an optimum and prove a number of qualitative and comparative static results, using dynamic programming arguments. An explicit solution for the problem is exhibited in a class of cases, and its properties studied. Finally, we consider the ability of the market mechanism to support the optimal allocation. [ABSTRACT FROM AUTHOR]