Competitive Equilibria in Exhaustible Resource Markets with Decreasing Costs: A Comment on Eswaran, Lewis, and Heaps's Demonstration of Nonexistence

Abstract

In a recent article, Eswaran, Lewis, and Heaps (1983) (ELH) correctly pointed out that many analyses of exhaustible resource markets assume the existence of a competitive equilibrium for the industry without checking to see if such an equilibrium is consistent with the behavior of the industry's constituent mining firms. ELH have attempted to rectify this situation by analyzing the behavior of an industry's firms and seeing if that behavior is consistent with the existence of a competitive equilibrium. ELH reach the startling conclusion that it takes nothing more than firms with U-shaped average cost curves, implying an initial range of increasing returns to scale, to eliminate the existence of a competitive equilibrium. On its own terms, ELHI's analysis is sound and provides a needed corrective to a major oversight in the literature. However, given the dramatic nature of their conclusion, the assumptions on which ELH's analysis is based require careful scrutiny. On this score, it seems to me that ELH's assumptions are implicitly at odds with the conditions that economists usually think of as characterizing competitive price-taking behavior. To show this, ELH's analysis is summarized, in Section I, so as to emphasize that their results depend crucially on the assumption that the number of producing firms cannot be treated as a continuously changing variable over time. In Section II, intertemporal equilibrium is characterized for the case where the number of producing firms is treated as a continuous variable, and it is argued that this assumed continuity is not only convenient but actually required for consistency with the assumption of competitive price-taking behavior. Then, to further demonstrate the dependence of the nonexistence result on continuity assumptions, an equilibrium solution is computed for a specific case set in discrete time. Section III contains conclusions.