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On optimal cycles in dynamic programming models with convex return function

Author

Listed:
  • Michael Kopel

    (Department of Managerial Economics and Industrial Organization, Vienna University of Technology, Theresianumgasse 27, A-1040 Vienna, AUSTRIA)

  • Herbert Dawid

    (Institute of Management Science, University of Vienna, AUSTRIA)

Abstract

In this paper we study the behavior of optimal paths in dynamic programming models with a strictly convex return function. Such a model has been investigated in Dawid and Kopel (1997) who assume that the growth of a renewable resource is governed by a piecewise linear function. We prove that in their model the optimal cycles undergo the following qualitative changes or bifurcations: a cycle of period n "bifurcates" into a cycle of period n+1 for increasing elasticity of the return function. We also show that under the assumption of a concave differentiable growth function the qualitative properties of the optimal policy remain valid: oscillating behavior is optimal. Furthermore, we demonstrate numerically that the period of a cyclic optimal path increases if the convexity of the return function (measured by the elasticity) increases.

Suggested Citation

  • Michael Kopel & Herbert Dawid, 1999. "On optimal cycles in dynamic programming models with convex return function," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 309-327.
    • Handle: RePEc:spr:joecth:v:13:y:1999:i:2:p:309-327
    Note: Received: January 22, 1997; revised version: October 13, 1997
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    Citations

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    Cited by:

    1. Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2013. "Optimality of impulse harvesting policies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 429-459, March.
    2. Maroto, Jose M. & Moran, Manuel, 2008. "Increasing marginal returns and the danger of collapse of commercially valuable fish stocks," Ecological Economics, Elsevier, vol. 68(1-2), pages 422-428, December.
    3. 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.
    4. José-María Da-Rocha & Linda Nøstbakken & Marcos Pérez, 2014. "Pulse Fishing and Stock Uncertainty," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 59(2), pages 257-274, October.
    5. Da Rocha, José María & García-Cutrín, Javier & Gutiérrez Huerta, María José & Touza, Julia, 2015. "Reconciling yield stability with international fisheries agencies precautionary preferences: the role of non constant discount factors in age structured models," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    6. Alain Jean-Marie & Mabel Tidball & Michel Moreaux & Katrin Erdlenbruch, 2009. "The Renewable Resource Management Nexus: Impulse versus Continuous Harvesting Policies," Working Papers 09-03, LAMETA, Universtiy of Montpellier, revised Mar 2009.
    7. 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.
    8. Johnson Kakeu, 2023. "Concerns for Long-Run Risks and Natural Resource Policy," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 84(4), pages 1051-1093, April.
    9. José-María Da Rocha & María-Jose Gutiérrez & Luis Antelo, 2013. "Selectivity, Pulse Fishing and Endogenous Lifespan in Beverton-Holt Models," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 54(1), pages 139-154, January.

    More about this item

    Keywords

    Dynamic programming · Optimal cycles · Bifurcations.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

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