Nonconvexity,efficiency and equilibrium in exhaustible resource depletion

We consider the problem of efficiency and existence of a competitive equilibrium in exhaustible resource markets where extraction costs are nonconvex. Nonconvexity is shown to imply that (1) (efficient) extraction ceases to the left of the minimum efficient scale, i.e., where average costs exceed marginal costs; and (2) a competitive equilibrium does not exist. Introduction of a backstop technology (which induces a flat portion of the industry demand curve) restores both existence and efficiency, provided that the backstop price is sufficiently low. If firms face even a small amount of uncertainty regarding their rivals' stocks, a backstop technology is sufficient to restore existence of competitive equilibrium, even if the backstop price is very high. In this case, however, the competitive equilibrium is not efficient.