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Uncertainty And Irreversibility In Groundwater Resource Management

  • Tsur, Yacov
  • Zemel, Amos
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    Optimal exploitation of renewable groundwater resources when extraction affects the probability of occurrence of an irreversible event is studied. The term irreversible signifies that the event occurrence renders the resource obsolete. It is found that uncertainty concerning the event occurrence has a profound effect. Under certainty - when the stock level below which the event occurs is known in advance - the optimal state process converges to a unique equilibrium state. Under uncertainty, when the event occurrence level is unknown, we identify equilibrium intervals and show that optimal processes initiated elsewhere converge to a boundary of one of these intervals. Inside an equilibrium interval, the expected loss due to the event occurrence is so high that it does not pay to extract in excess of recharge, even though under certainty doing so would be beneficial. These properties are illuminated by means of an example for which analytic solutions are derived.

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    File URL: http://purl.umn.edu/13590
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    Paper provided by University of Minnesota, Department of Applied Economics in its series Staff Papers with number 13590.

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    Date of creation: 1994
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    Handle: RePEc:ags:umaesp:13590
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    1. Tsur, Yacov & Graham-Tomasi, Theodore, 1991. "The buffer value of groundwater with stochastic surface water supplies," Journal of Environmental Economics and Management, Elsevier, vol. 21(3), pages 201-224, November.
    2. Feinerman, Eli, 1988. "Groundwater Management: Efficiency and Equity Considerations," Agricultural Economics of Agricultural Economists, International Association of Agricultural Economists, vol. 2(1), June.
    3. Loury, Glenn C, 1978. "The Optimal Exploitation of an Unknown Reserve," Review of Economic Studies, Wiley Blackwell, vol. 45(3), pages 621-36, October.
    4. Long, Ngo Van, 1975. "Resource extraction under the uncertainty about possible nationalization," Journal of Economic Theory, Elsevier, vol. 10(1), pages 42-53, February.
    5. Deshmukh, Sudhakar D & Pliska, Stanley R, 1980. "Optimal Consumption and Exploration of Nonrenewable Resources under Uncertainty," Econometrica, Econometric Society, vol. 48(1), pages 177-200, January.
    6. Lewis, Tracy R & Schmalensee, Richard, 1977. "Nonconvexity and Optimal Exhaustion of Renewable Resources," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 535-52, October.
    7. Clark, Colin W, 1973. "Profit Maximization and the Extinction of Animal Species," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 950-61, July-Aug..
    8. Cropper, M. L., 1988. "A note on the extinction of renewable resources," Journal of Environmental Economics and Management, Elsevier, vol. 15(1), pages 64-70, March.
    9. Deshmukh, Sudhakar D. & Pliska, Stanley R., 1985. "A martingale characterization of the price of a nonrenewable resource with decisions involving uncertainty," Journal of Economic Theory, Elsevier, vol. 35(2), pages 322-342, August.
    10. Feinerman, Eli, 1988. "Groundwater management: Efficiency and equity considerations," Agricultural Economics, Blackwell, vol. 2(1), pages 1-18, June.
    11. Gilbert, Richard J, 1979. "Optimal Depletion of an Uncertain Stock," Review of Economic Studies, Wiley Blackwell, vol. 46(1), pages 47-57, January.
    12. Oscar R. Burt, 1964. "Optimal Resource Use Over Time with an Application to Ground Water," Management Science, INFORMS, vol. 11(1), pages 80-93, September.
    13. Cropper, M. L., 1976. "Regulating activities with catastrophic environmental effects," Journal of Environmental Economics and Management, Elsevier, vol. 3(1), pages 1-15, June.
    14. Kamien, Morton I & Schwartz, Nancy L, 1978. "Optimal Exhaustible Resource Depletion with Endogenous Technical Change," Review of Economic Studies, Wiley Blackwell, vol. 45(1), pages 179-96, February.
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