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Nonconvexity, efficiency and equilibrium in exhaustible resource depletion

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  • Anthony Fisher
  • Larry Karp

Abstract

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. Copyright Kluwer Academic Publishers 1993

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  • Anthony Fisher & Larry Karp, 1993. "Nonconvexity, efficiency and equilibrium in exhaustible resource depletion," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 3(1), pages 97-106, February.
    • Handle: RePEc:kap:enreec:v:3:y:1993:i:1:p:97-106
    DOI: 10.1007/BF00338322
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    1. Hartwick, John M. & Kemp, Murray C. & Van Long, Ngo, 1986. "Set-up costs and theory of exhaustible resources," Journal of Environmental Economics and Management, Elsevier, vol. 13(3), pages 212-224, September.
    2. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
    3. Richard J. Gilbert, 1979. "Optimal Depletion of an Uncertain Stock," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(1), pages 47-57.
    4. Mumy, Gene E, 1984. "Competitive Equilibria in Exhaustible Resource Markets with Decreasing Costs: A Comment on Eswaran, Lewis, and Heaps's Demonstration of Nonexistence," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1168-1174, December.
    5. Eswaran, Mukesh & Lewis, Tracy R & Heaps, Terry, 1983. "On the Nonexistence of Market Equilibria in Exhaustible Resource Markets with Decreasing Costs," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 154-167, February.
    6. Schulze, William D., 1974. "The optimal use of non-renewable resources: The theory of extraction," Journal of Environmental Economics and Management, Elsevier, vol. 1(1), pages 53-73, May.
    7. Farrow, Scott, 1985. "Testing the Efficiency of Extraction from a Stock Resource," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 452-487, June.
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    Cited by:

    1. Chermak, Janie M. & Patrick, Robert H., 2001. "A Microeconometric Test of the Theory of Exhaustible Resources," Journal of Environmental Economics and Management, Elsevier, vol. 42(1), pages 82-103, July.
    2. Carolyn Fischer, 2005. "Competition in Markets for Depletable Resources with Setup Costs," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 30(3), pages 243-257, March.
    3. Antoine Bommier & Lucas Bretschger & François Grand, 2017. "Existence of equilibria in exhaustible resource markets with economies of scale and inventories," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 687-721, March.
    4. Holland, Stephen P., 2003. "Set-up costs and the existence of competitive equilibrium when extraction capacity is limited," Journal of Environmental Economics and Management, Elsevier, vol. 46(3), pages 539-556, November.
    5. Chermak, Janie M. & Crafton, James & Norquist, Suzanne M. & Patrick, Robert H., 1999. "A hybrid economic-engineering model for natural gas production," Energy Economics, Elsevier, vol. 21(1), pages 67-94, February.
    6. Robert Cairns, 2008. "Exhaustible Resources, Non-Convexity and Competitive Equilibrium," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 40(2), pages 177-193, June.
    7. Fischer, Carolyn, 1998. "Once-and-for-All Costs and Exhaustible Resource Markets," Discussion Papers 10623, Resources for the Future.
    8. Mason, Charles F., 2012. "On equilibrium in resource markets with scale economies and stochastic prices," Journal of Environmental Economics and Management, Elsevier, vol. 64(3), pages 288-300.

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