Optimal Extraction of Nonrenewable Resources When Prices are Uncertain and Costs Cumulate

Abstract

Advances in economic theory and optimal control methods have considerably improved the prescriptions for the extraction of renewable and nonrenewable resources. While the classic analyses, going back to Hotelling (1931), proceeded under assumptions of price certainty, recent work addresses the considerable uncertainty in resource prices (which is of the same order as that of stock prices). For tractability, this newer literature assumes a constant marginal cost of extraction which ignores the considerable emphasis in the older literature on increasing marginal costs. We frame and solve the nonrenewable resource extraction problem (in the context of a typical mine) that jointly accounts for the significant price uncertainties as well as the dependence of extraction costs on the extraction rate and on the cumulative amount extracted. We find that ignoring cumulating cost when determining extraction strategy can lead to significant loss of value. Our analysis also establishes the general tools to pursue, for instance, the optimal taxation of natural resource sector that is of significant policy interest to many developing countries.