Contestability in a Resource Market with Non-Convex Costs

Abstract

Consider an intertemporal resource market with N identical firms, each managing an exhaustible resource deposit, the extraction from which is governed by a U-shaped average cost curve. Eswaran, Lewis and Heaps (1983) (ELH) show that such a market cannot have a competitive equilibrium. In their comments on ELH, Kimmel (1984) and Mumy (1984) point out, however, that the ELH result is driven by there being a small number of firms which is inconsistent with price-taking behavior. This provides a motivation for analyzing the situation considered by ELH under alternative assumptions of market behavior. In general, perfect contestability applies to circumstances where perfect competition is impossible because economies of scale are present; see Baumol et al. (1982). Since the non-convexities in ELH are not caused by once-and-for-all setup (or shut-down) costs' - rather the flow of costs is assumed to be a non-convex function of the flow of extraction - replacing the assumption of price-taking behavior with an assumption of entry2 provides a potential means of restoring a market equilibrium in the present case. Contestability theory holds that the threat of competition by potential entrants can discipline the pricing behavior of the active firms. However, as pointed out by Cairns (1991, footnote 9), a non-active firm can be the source of this kind of discipline in an exhaustible resource market only if its remaining reserves are positive. Caution should therefore be exercised in applying contestability theory to a resource market. In this note, existence of an equilibrium in such an exhaustible resource market is shown partly by relying on the possibility of ultra-free entry. We