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

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  • 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.

Suggested Citation

  • Moghayer, S. & Wagener, F.O.O., 2009. "Genesis of indifference thresholds and infinitely many indifference points in discrete time infinite horizon optimisation problems," CeNDEF Working Papers 09-14, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:09-14
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    References listed on IDEAS

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    1. 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.
    2. Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003. "The Economics of Shallow Lakes," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December.
    3. 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.
    4. Dawid, Herbert & Deissenberg, Christophe, 2005. "On the efficiency-effects of private (dis-)trust in the government," Journal of Economic Behavior & Organization, Elsevier, vol. 57(4), pages 530-550, August.
    5. Olli Tahvonen, 1995. "Dynamics of pollution control when damage is sensitive to the rate of pollution accumulation," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 5(1), pages 9-27, January.
    6. 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.
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    Cited by:

    1. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.

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