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Optimality of impulse harvesting policies

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  • Katrin Erdlenbruch

    ()

  • Alain Jean-Marie

    ()

  • Michel Moreaux

    ()

  • Mabel Tidball

    ()

Abstract

We explore the link between cyclical and smooth resource exploitation. We define an impulse control framework which can generate both cyclical solutions and steady-state solutions. Our model can admit convex and concave profit functions and allows the integration of different stock-dependent profit functions. We show that the strict concavity of the profit function is only a special case of a more general condition, related to submodularity, that ensures the existence of optimal cyclical policies. We then establish a link with the discrete-time models with cyclical solutions by Benhabib and Nishimura (J Econ Theory 35:284–306, 1985 ) and Dawid and Kopel (J Econ Theory 76:272–297, 1997 ). For the steady-state solution, we explore the relation to Clark’s ( 1976 ) continuous control model. Copyright Springer-Verlag 2013

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 52 (2013)
Issue (Month): 2 (March)
Pages: 429-459

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Handle: RePEc:spr:joecth:v:52:y:2013:i:2:p:429-459

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Related research

Keywords: Optimal control; Impulse control; Renewable resource economics; Submodularity; C61; Q2;

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References

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  1. Nishimura, Kazuo & Sorger, Gerhard & Yano, Makoto, 1994. "Ergodic Chaos in Optimal Growth Models with Low Discount Rates," Economic Theory, Springer, vol. 4(5), pages 705-17, August.
  2. Dawid, Herbert & Kopel, Michael, 1997. "On the Economically Optimal Exploitation of a Renewable Resource: The Case of a Convex Environment and a Convex Return Function," Journal of Economic Theory, Elsevier, vol. 76(2), pages 272-297, October.
  3. Hartman, Richard, 1976. "The Harvesting Decision When a Standing Forest Has Value," Economic Inquiry, Western Economic Association International, vol. 14(1), pages 52-58, March.
  4. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
  5. Kort, P.M. & Liski, M. & Novak, A.J., 2001. "Increasing returns and cycles in fishing," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86776, Tilburg University.
  6. Michael Kopel & Herbert Dawid, 1999. "On optimal cycles in dynamic programming models with convex return function," Economic Theory, Springer, vol. 13(2), pages 309-327.
  7. Majumdar, Mukul & Mitra, Tapan, 1994. "Periodic and Chaotic Programs of Optimal Intertemporal Allocation in an Aggregative Model with Wealth Effects," Economic Theory, Springer, vol. 4(5), pages 649-76, August.
  8. Wirl Franz, 1995. "The Cyclical Exploitation of Renewable Resource Stocks May Be Optimal," Journal of Environmental Economics and Management, Elsevier, vol. 29(2), pages 252-261, September.
  9. Michael Kopel & Gustav Feichtinger & Herbert Dawid, 1997. "Complex solutions of nonconcave dynamic optimization models (*)," Economic Theory, Springer, vol. 9(3), pages 427-439.
  10. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer, vol. 5(3), pages 371-82, May.
  11. Tracy R. Lewis & Richard Schmalensee, 1979. "Non-convexity and Optimal Harvesting Strategies for Renewable Resources," Canadian Journal of Economics, Canadian Economics Association, vol. 12(4), pages 677-91, November.
  12. Spence, A Michael & Starrett, David, 1975. "Most Rapid Approach Paths in Accumulation Problems," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 16(2), pages 388-403, June.
  13. Rognvaldur Hannesson, 1975. "Fishery Dynamics: A North Atlantic Cod Fishery," Canadian Journal of Economics, Canadian Economics Association, vol. 8(2), pages 151-73, May.
  14. Berck, Peter, 1981. "Optimal management of renewable resources with growing demand and stock externalities," Journal of Environmental Economics and Management, Elsevier, vol. 8(2), pages 105-117, June.
  15. Akiomi Kitagawa & Akihisa Shibata, 2005. "Endogenous growth cycles in an overlapping generations model with investment gestation lags," Economic Theory, Springer, vol. 25(3), pages 751-762, 04.
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Citations

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Cited by:
  1. Grass, D. & Chahim, M., 2012. "Numerical Algorithms for Deterministic Impulse Control Models with Applications," Discussion Paper 2012-081, Tilburg University, Center for Economic Research.
  2. Reddy, P.V. & Schumacher, J.M. & Engwerda, J.C., 2012. "Optimal Management and Differential Games in the Presence of Threshold Effects - The Shallow Lake Model," Discussion Paper 2012-001, Tilburg University, Center for Economic Research.
  3. Chahim, Mohammed & Hartl, Richard F. & Kort, Peter M., 2012. "A tutorial on the deterministic Impulse Control Maximum Principle: Necessary and sufficient optimality conditions," European Journal of Operational Research, Elsevier, vol. 219(1), pages 18-26.

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