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On optimal cycles in dynamic programming models with convex return function


Author Info

  • 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)


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.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 13 (1999)
Issue (Month): 2 ()
Pages: 309-327

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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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Keywords: Dynamic programming · Optimal cycles · Bifurcations.;

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Cited by:
  1. 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.
  2. 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.
  3. Lars Olson & Santanu Roy, 2008. "Controlling a biological invasion: a non-classical dynamic economic model," Economic Theory, Springer, vol. 36(3), pages 453-469, September.
  4. Da Rocha, José María & Antelo, Luis T. & Gutiérrez Huerta, María José, 2012. "Selectivity, pulse fishing and endogenous lifespan in Beverton-Holt models," DFAEII Working Papers 2012-11, University of the Basque Country - Department of Foundations of Economic Analysis II.
  5. Katrin Erdlenbruch & Alain Jean-Marie & Michel Moreaux & Mabel Tidball, 2010. "Optimality of Impulse Harvesting Policies," Working Papers hal-00864187, HAL.
  6. 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.


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