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Optimal Exploitation of Renewable Resources under Uncertainty and the Extinction of Species

Author

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  • Mitra, Tapan

    (Cornell U)

  • Roy, Santanu

    (Southern Methodist U)

Abstract

Under a minimal set of assumptions, the paper identifies conditions on the transition function of a Markov process leading to the following three scenarios: extinction, conservation, and the existence of a safe standard of conservation. These conditions are used to obtain restrictions on a framework of optimal exploitation of a renewable resource, under which the above three scenarios would occur. The biological growth function is allowed to be non-concave, and is subject to a random environmental shock, thereby making the results suitable for applications in a wide variety of models in renewable resource management.

Suggested Citation

  • Mitra, Tapan & Roy, Santanu, 2003. "Optimal Exploitation of Renewable Resources under Uncertainty and the Extinction of Species," Working Papers 03-10, Cornell University, Center for Analytic Economics.
  • Handle: RePEc:ecl:corcae:03-10
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    File URL: https://cae.economics.cornell.edu/MRExtinctionAug2003.pdf
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    References listed on IDEAS

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    1. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    2. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
    3. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
    4. Boylan, Edward S., 1979. "On the avoidance of extinction in one-sector growth models," Journal of Economic Theory, Elsevier, vol. 20(2), pages 276-279, April.
    5. Mirman, Leonard J. & Spulber, Daniel F., 1984. "Uncertainty and markets for renewable resources," Journal of Economic Dynamics and Control, Elsevier, vol. 8(3), pages 239-264, December.
    6. Mirman, Leonard J & Zilcha, Itzhak, 1976. "Unbounded Shadow Prices for Optimal Stochastic Growth Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 121-132, February.
    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 950-961, 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. Olson, Lars J. & Roy, Santanu, 2000. "Dynamic Efficiency of Conservation of Renewable Resources under Uncertainty," Journal of Economic Theory, Elsevier, vol. 95(2), pages 186-214, December.
    10. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June.
    11. Mukul Majumdar & Tapan Mitra, 1983. "Dynamic Optimization with a Non-Convex Technology: The Case of a Linear Objective Function," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 143-151.
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    Citations

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    Cited by:

    1. Pierre Dupraz & Karine Latouche & Nadine Turpin, 2007. "Programmes agri-environnementaux en présence d’effets de seuil," Cahiers d'Economie et Sociologie Rurales, INRA Department of Economics, vol. 82, pages 5-32.
    2. Leizarowitz, Arie & Tsur, Yacov, 2012. "Renewable resource management with stochastic recharge and environmental threats," Journal of Economic Dynamics and Control, Elsevier, vol. 36(5), pages 736-753.
    3. Takashi Kamihigashi & John Stachurski, 2011. "Existence, Stability and Computation of Stationary Distributions: An Extension of the Hopenhayn-Prescott Theorem," Discussion Paper Series DP2011-32, Research Institute for Economics & Business Administration, Kobe University.
    4. Leonard J. Mirman & Kevin Reffett & John Stachurski, 2005. "Some stability results for Markovian economic semigroups," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 57-72.
    5. Brozovic, Nicholas & Schlenker, Wolfram, 2011. "Optimal management of an ecosystem with an unknown threshold," Ecological Economics, Elsevier, vol. 70(4), pages 627-640, February.
    6. Diekert, Florian K., 2017. "Threatening thresholds? The effect of disastrous regime shifts on the non-cooperative use of environmental goods and services," Journal of Public Economics, Elsevier, vol. 147(C), pages 30-49.
    7. Kiran Krishnamurthy, Chandra, 2012. "Optimal Management of Groundwater under Uncertainty: A Unified Approach," CERE Working Papers 2012:19, CERE - the Center for Environmental and Resource Economics, revised 30 Jun 2014.
    8. Santanu Roy & Itzhak Zilcha, 2012. "Stochastic growth with short-run prediction of shocks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 539-580, November.
    9. Kamihigashi, Takashi, 2007. "Stochastic optimal growth with bounded or unbounded utility and with bounded or unbounded shocks," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 477-500, April.
    10. Nishimura, Kazuo & Rudnicki, Ryszard & Stachurski, John, 2006. "Stochastic optimal growth with nonconvexities," Journal of Mathematical Economics, Elsevier, vol. 42(1), pages 74-96, February.
    11. Stachurski, John & Kamihigashi, Takashi, 2014. "Stochastic stability in monotone economies," Theoretical Economics, Econometric Society, vol. 9(2), May.
    12. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    13. Tapan Mitra & Gerhard Sorger, 2014. "Extinction in common property resource models: an analytically tractable example," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(1), pages 41-57, September.
    14. Chatterjee, Partha & Shukayev, Malik, 2008. "Note on positive lower bound of capital in the stochastic growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 32(7), pages 2137-2147, July.
    15. Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.
    16. Mitra, Tapan & Roy, Santanu, 2007. "On the possibility of extinction in a class of Markov processes in economics," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 842-854, September.
    17. Fesselmeyer, Eric & Santugini, Marc, 2013. "Strategic exploitation of a common resource under environmental risk," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 125-136.
    18. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers 28601, University of Maryland, Department of Agricultural and Resource Economics.
    19. Lars Olson & Santanu Roy, 2008. "Controlling a biological invasion: a non-classical dynamic economic model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 36(3), pages 453-469, September.
    20. Chen, Yong & Jayaprakash, Ciriyam & Irwin, Elena, 2012. "Threshold management in a coupled economic–ecological system," Journal of Environmental Economics and Management, Elsevier, vol. 64(3), pages 442-455.

    More about this item

    JEL classification:

    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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