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Optimal Consumption of a Nonrenewable Resource with Stochastic Discoveries and a Random Environment

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  • Sudhakar D. Deshmukh
  • Stanley R. Pliska

Abstract

We present a general model for the optimal consumption of a nonrenewable resource under two kinds of uncertainties. One source of uncertainty is in the resource discovery process and the other is in the economic environment that affects resource supply and demand conditions, such as exhaustion and development of a substitute. The problem is formulated as one of optimally controlling a storage process with Markov additive discoveries. The optimal value of the resource stock is characterized as the solution of a functional equation and the existence of an optimal consumption policy is established. It is shown that, in a given environment, the optimal consumption rate is increasing and the resource price is decreasing in the level of proven reserves. A counterexample is provided to show that better environments may in fact mean higher prices and lower consumption rates. Finally, a variety of examples is given to illustrate the scope and applicability of the general model.

Suggested Citation

  • Sudhakar D. Deshmukh & Stanley R. Pliska, 1983. "Optimal Consumption of a Nonrenewable Resource with Stochastic Discoveries and a Random Environment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 543-554.
    • Handle: RePEc:oup:restud:v:50:y:1983:i:3:p:543-554.
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    File URL: http://hdl.handle.net/10.2307/2297680
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    Cited by:

    1. Junhe Chen & Matt Davison, 2021. "Deterministic Asymmetric-cost Differential Games for Energy Production with Production Bounds," SN Operations Research Forum, Springer, vol. 2(4), pages 1-38, December.
    2. Sudhakar D. Deshmukh & Stanley R. Pliskaf, 1983. "A Martingale Characterization of the Price of a Nonrenewable Resource with Decisions Involving Uncertainty," Discussion Papers 565, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Güntner, Jochen H.F., 2019. "How do oil producers respond to giant oil field discoveries?," Energy Economics, Elsevier, vol. 80(C), pages 59-74.
    4. Ivar Ekeland & Wolfram Schlenker & Peter Tankov & Brian Wright, 2022. "Optimal Exploration of an Exhaustible Resource with Stochastic Discoveries," Papers 2203.01614, arXiv.org.

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