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Optimality of Impulse Harvesting Policies

  • Katrin Erdlenbruch
  • Alain Jean-Marie
  • Michel MOREAUX
  • Mabel Tidball

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. For the cyclical solution, we establish a link with the discrete-time model by Dawid and Kopel (1997). For the steady state solution, we explore the relation to Clark's (1976) continuous control model. Our model can admit convex and concave profit functions and allows the integration of different stock dependent cost functions. We show that the strict convexity 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.

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File URL: http://www2.toulouse.inra.fr/lerna/travaux/cahiers2010/10.09.315.pdf
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Paper provided by LERNA, University of Toulouse in its series LERNA Working Papers with number 10.09.315.

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Date of creation: Apr 2010
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Handle: RePEc:ler:wpaper:10.09.315
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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. Nishimura, Kazuo, 1985. "Competitive equilibrium cycles," Journal of Economic Theory, Elsevier, vol. 35(2), pages 284-306, August.
  3. Kort, P.M. & Liski, M. & Novak, A.J., 2001. "Increasing returns and cycles in fishing," Other publications TiSEM 005cdced-611c-4158-a257-8, Tilburg University, School of Economics and Management.
  4. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer, vol. 5(3), pages 371-82, May.
  5. Rognvaldur Hannesson, 1975. "Fishery Dynamics: A North Atlantic Cod Fishery," Canadian Journal of Economics, Canadian Economics Association, vol. 8(2), pages 151-73, May.
  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. 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.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. Michael Kopel & Gustav Feichtinger & Herbert Dawid, 1997. "Complex solutions of nonconcave dynamic optimization models (*)," Economic Theory, Springer, vol. 9(3), pages 427-439.
  13. 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.
  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. 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.
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