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Existence of equilibria in exhaustible resource markets with economies of scale and inventories

Author

Listed:
  • Antoine Bommier

    (EM - EMLyon Business School)

  • Lucas Bretschger
  • François Le Grand

Abstract

The paper proves the existence of equilibrium in non-renewable resource markets when extraction costs are non-convex and resource storage is possible. Inventories flatten the consumption path and eliminate price jumps at the end of the extraction period, so that market equilibrium becomes possible. We distinguish between two types of solutions, one with immediate and one with delayed buildup of inventories. For both cases, we do not only characterize potential optimal paths but also show that equilibria actually exist under fairly general conditions. It is found that optimum resource extraction involves increasing quantities over a period of time. What is generally interpreted as an indicator of increasing resource abundance is thus perfectly compatible with constant resource stocks.

Suggested Citation

  • Antoine Bommier & Lucas Bretschger & François Le Grand, 2017. "Existence of equilibria in exhaustible resource markets with economies of scale and inventories," Post-Print hal-02313368, HAL.
    • Handle: RePEc:hal:journl:hal-02313368
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    1. 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.
    2. Le Van, Cuong & Schubert, Katheline & Nguyen, Tu Anh, 2010. "With exhaustible resources, can a developing country escape from the poverty trap?," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2435-2447, November.
    3. van der Meijden, Gerard & Smulders, Sjak, 2018. "Technological Change During The Energy Transition," Macroeconomic Dynamics, Cambridge University Press, vol. 22(4), pages 805-836, June.
    4. 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.
    5. 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.
    6. Le Van, Cuong & Schubert, Katheline & Nguyen, Tu Anh, 2010. "With exhaustible resources, can a developing country escape from the poverty trap?," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2435-2447, November.
    7. Asheim, G.B., 1989. "Contestability In A Resource Market With Non-Convex Costs," Papers 02-89, Norwegian School of Economics and Business Administration-.
    8. Cairns, Robert D, 1991. " On Non-convex Costs and Dynamic Consistency in an Exhaustible-Resource Market," Scandinavian Journal of Economics, Wiley Blackwell, vol. 93(1), pages 89-100.
    9. Lewis, Tracy R & Matthews, Steven A & Burness, H Stuart, 1979. "Monopoly and the Rate of Extraction of Exhaustible Resources: Note," American Economic Review, American Economic Association, vol. 69(1), pages 227-230, March.
    10. 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.
    11. Asheim, Geir B, 1992. " Contestability in a Resource Market with Non-convex Costs," Scandinavian Journal of Economics, Wiley Blackwell, vol. 94(4), pages 609-618.
    12. Ujjayant Chakravorty & Michel Moreaux & Mabel Tidball, 2008. "Ordering the Extraction of Polluting Nonrenewable Resources," American Economic Review, American Economic Association, vol. 98(3), pages 1128-1144, June.
    13. 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.
    14. 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.
    15. Lozada, Gabriel A., 1996. "Existence of equilibria in exhaustible resource industries Nonconvexities and discrete vs. continuous time," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 433-444.
    16. Bård Harstad, 2012. "Buy Coal! A Case for Supply-Side Environmental Policy," Journal of Political Economy, University of Chicago Press, vol. 120(1), pages 77-115.
    17. Gerard Gaudet & Michel Moreaux & Stephen W. Salant, 2001. "Intertemporal Depletion of Resource Sites by Spatially Distributed Users," American Economic Review, American Economic Association, vol. 91(4), pages 1149-1159, September.
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    Cited by:

    1. 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.
    2. Wang, Xiaolin & Qiu, Yangyang & Chen, Jun & Hu, Xiangping, 2022. "Evaluating natural gas supply security in China: An exhaustible resource market equilibrium model," Resources Policy, Elsevier, vol. 76(C).

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    More about this item

    Keywords

    Exhaustible resources; Non-convex extraction cost; Equilibrium existence; Resource storage;
    All these keywords.

    JEL classification:

    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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