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Optimal Supply of a Depletable Resource with a Backstop Technology: Heal's Theorem Revisited

Author

Listed:
  • Shmuel S. Oren

    (University of California, Berkeley, California)

  • Stephen G. Powell

    (Wang Laboratories, Inc., Lowell, Massachusetts)

Abstract

Heal's theorem states that if the extraction cost of a depletable resource increases with cumulative extraction, and if a backstop technology exists, the user cost of the depletable resource declines to zero at the date of exhaustion. In this paper, we first present a simple method for proving this proposition, using a social planning model that determines the optimal rates both of extraction of the depletable resource and of production of the backstop technology. We then present two examples that show how this method can be used to solve more difficult problems in the theory of resource economics. The first example involves learning-by-doing in the backstop sector; that is, backstop costs decline with cumulative production. The second example involves uncertainty of backstop costs.

Suggested Citation

  • Shmuel S. Oren & Stephen G. Powell, 1985. "Optimal Supply of a Depletable Resource with a Backstop Technology: Heal's Theorem Revisited," Operations Research, INFORMS, vol. 33(2), pages 277-292, April.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:2:p:277-292
    DOI: 10.1287/opre.33.2.277
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    Citations

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    Cited by:

    1. CHAKRAVORTY Ujjayant & LEACH Andrew & MOREAUX Michel, 2008. ""Twin Peaks" in Energy Prices: A Polluting Fossil Fuel with Learning in the Clean Substitute," LERNA Working Papers 08.15.259, LERNA, University of Toulouse.
    2. Peter Hartley & Kenneth B. Medlock III & Ted Temzelides & Xinya Zhang, 2016. "Energy Sector Innovation and Growth: An Optimal Energy Crisis," The Energy Journal, , vol. 37(1), pages 233-258, January.
    3. Fabre, Adrien & Fodha, Mouez & Ricci, Francesco, 2020. "Mineral resources for renewable energy: Optimal timing of energy production," Resource and Energy Economics, Elsevier, vol. 59(C).
    4. Carolyn Fischer & Cees Withagen & Michael Toman, 2004. "Optimal Investment in Clean Production Capacity," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 28(3), pages 325-345, July.
    5. Peter R. Hartley & Kenneth B. Medlock III, 2017. "The Valley of Death for New Energy Technologies," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    6. Lancker, Kira & Quaas, Martin F., 2019. "Increasing marginal costs and the efficiency of differentiated feed-in tariffs," Energy Economics, Elsevier, vol. 83(C), pages 104-118.
    7. Chakravorty, Ujjayant & Leach, Andrew & Moreaux, Michel, 2012. "Cycles in nonrenewable resource prices with pollution and learning-by-doing," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1448-1461.
    8. Martin Machay, 2012. "The Principle of Population for the 21st Century: The Never Coming Stationary State," MENDELU Working Papers in Business and Economics 2012-18, Mendel University in Brno, Faculty of Business and Economics.
    9. Hartley, Peter & Medlock III, Kenneth B., 2008. "A model of the operation and development of a National Oil Company," Energy Economics, Elsevier, vol. 30(5), pages 2459-2485, September.
    10. Bahel, Eric, 2011. "Optimal management of strategic reserves of nonrenewable natural resources," Journal of Environmental Economics and Management, Elsevier, vol. 61(3), pages 267-280, May.
    11. Peter R. Hartley & Kenneth B. Medlock III, 2017. "The Valley of Death for New Energy Technologies," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3).
    12. Bahel, Eric, 2011. "Optimal management of strategic reserves of nonrenewable natural resources," Journal of Environmental Economics and Management, Elsevier, vol. 61(3), pages 267-280, May.

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