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Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems

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Author Info

  • Moghayer, S.

    ()
    (University of Amsterdam)

  • Wagener, F.O.O.

    ()
    (University of Amsterdam)

Abstract

This article investigates the discrete time indifference-attractor bifurcation of infinite horizon continous-time optimal control problems with a single state variable. We show that these bifurcations are linked to a heteroclinic bifurcation scenario of the state-costate equations, and we analyse the consequences for the optimal solutions. In particular, we can characterise the bifurcation value at which indifference thresholds appear by a geometric condition, and we find that for certain parameter values, there are countably infinitely many indifference points. We apply our results to a modified version of the shallow lake pollution management problem.

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File URL: http://www1.fee.uva.nl/cendef/publications/papers/discrete.pdf
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Bibliographic Info

Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Working Papers with number 09-14.

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Date of creation: 2009
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Handle: RePEc:ams:ndfwpp:09-14

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Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands
Phone: + 31 20 525 52 58
Fax: + 31 20 525 52 83
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Web page: http://www.fee.uva.nl/cendef/
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  1. Olli Tahvonen, 1995. "Dynamics of pollution control when damage is sensitive to the rate of pollution accumulation," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 5(1), pages 9-27, January.
  2. Herbert Dawid & Christophe Deissenberg, . "On the Efficiency-Effects of Private (Dis-)Trust in the Government," Modeling, Computing, and Mastering Complexity 2003 25, Society for Computational Economics.
  3. Mäler, K-G. & Xepapadeas, A. & Zeeuw, A.J. de, 2003. "The economics of shallow lakes," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123314, Tilburg University.
  4. 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.
  5. Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July.
  6. Grune, Lars & Semmler, Willi, 2004. "Using dynamic programming with adaptive grid scheme for optimal control problems in economics," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2427-2456, December.
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Cited by:
  1. Kiseleva, T. & Wagener, F.O.O., 2011. "Bifurcations of Optimal Vector Fields," CeNDEF Working Papers 11-05, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

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