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Optimal pricing, use and exploration of uncertain natural resources

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  • Patrick Hagan
  • Diana Woodward
  • Russel Caflisch
  • Joseph Keller

Abstract

We consider Arrow's model for an economy engaged in consuming a randomly distributed natural resource, and in exploring previously unexplored land to find more of the resource. After modifying the model so that each discovery reveals a random amount of the resource, we use dynamic programming techniques to derive the equations governing optimal rates of exploration, consumption, and pricing of the resource. We analyse these equations asymptotically when the typical amount discovered is small compared with the total amount of the resource, and approximately when the amount is medium or large. In both cases we obtain formulas for the optimal exploration, consumption, and pricing policies. We demonstrate the accuracy of these analytical results by comparing them with numerically-determined exact solutions, and discuss economic implications of these results.

Suggested Citation

  • Patrick Hagan & Diana Woodward & Russel Caflisch & Joseph Keller, 1994. "Optimal pricing, use and exploration of uncertain natural resources," Applied Mathematical Finance, Taylor & Francis Journals, vol. 1(1), pages 87-108.
    • Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:87-108
    DOI: 10.1080/13504869400000005
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    References listed on IDEAS

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    1. Harold Hotelling, 1931. "The Economics of Exhaustible Resources," Journal of Political Economy, University of Chicago Press, vol. 39(2), pages 137-137.
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    Cited by:

    1. Michael Ludkovski & Xuwei Yang, 2017. "Mean Field Game Approach to Production and Exploration of Exhaustible Commodities," Papers 1710.05131, arXiv.org.
    2. 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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