IDEAS home Printed from https://ideas.repec.org/p/ams/ndfwpp/09-14.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://cendef.uva.nl/binaries/content/assets/subsites/amsterdam-school-of-economics/amsterdam-school-of-economics-research-institute/cendef/working-papers-2009/genesis---discrete.pdf?1363343328214
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. W. Davis Dechert & Kazuo Nishimura, 2012. "A Complete Characterization of Optimal Growth Paths in an Aggregated Model with a Non-Concave Production Function," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 237-257, Springer.
    4. W.A. Brock & W.D. Dechert, 2008. "The polluted ecosystem game," Indian Growth and Development Review, Emerald Group Publishing Limited, vol. 1(1), pages 7-31, April.
    5. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, December.
    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.
    7. Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
    8. J. P. Caulkins & G. Feichtinger & D. Grass & G. Tragler, 2007. "Bifurcating DNS Thresholds in a Model of Organizational Bridge Building," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 19-35, April.
    9. 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.
    10. 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.
    11. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    12. W.A. Brock & W.D. Dechert, 2008. "The polluted ecosystem game," Indian Growth and Development Review, Emerald Group Publishing Limited, vol. 1(1), pages 7-31, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


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

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 60-73.
    2. Tatiana Kiseleva & Florian Wagener, 2015. "Bifurcations of Optimal Vector Fields," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 24-55, February.
    3. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    4. Heijnen, P. & Wagener, F.O.O., 2013. "Avoiding an ecological regime shift is sound economic policy," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1322-1341.
    5. Yuri Yegorov & Dieter Grass & Magda Mirescu & Gustav Feichtinger & Franz Wirl, 2020. "Growth and Collapse of Empires: A Dynamic Optimization Model," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 620-643, August.
    6. I. Zeiler & J.P. Caulkins & G. Tragler, 2011. "Optimal Control of Interacting Systems with DNSS Property: The Case of Illicit Drug Use," Post-Print hal-00978258, HAL.
    7. Yegorov, Yury & Wirl, Franz & Grass, Dieter & Eigruber, Markus & Feichtinger, Gustav, 2022. "On the matthew effect on individual investments in skills in arts, sports and science," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 178-199.
    8. Zeiler, I. & Caulkins, J.P. & Tragler, G., 2011. "Optimal control of interacting systems with DNSS property: The case of illicit drug use," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 60-73, April.
    9. Francesco Bartaloni, 2021. "Existence of the Optimum in Shallow Lake Type Models with Hysteresis Effect," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 358-392, August.
    10. Wagener, F.O.O., 2013. "Economics of environmental regime shifts," CeNDEF Working Papers 13-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    11. Florian Wagener, 2013. "Shallow lake economics run deep: nonlinear aspects of an economic-ecological interest conflict," Computational Management Science, Springer, vol. 10(4), pages 423-450, December.
    12. Dmitry Gromov & Thorsten Upmann, 2021. "Dynamics and Economics of Shallow Lakes: A Survey," Sustainability, MDPI, vol. 13(24), pages 1-16, December.
    13. F. O. O. Wagener, 2006. "Skiba Points for Small Discount Rates," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 261-277, February.
    14. Rosser Jr., J. Barkley, 2007. "The rise and fall of catastrophe theory applications in economics: Was the baby thrown out with the bathwater?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3255-3280, October.
    15. Kiseleva, Tatiana & Wagener, F.O.O., 2010. "Bifurcations of optimal vector fields in the shallow lake model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(5), pages 825-843, May.
    16. Grass, D., 2012. "Numerical computation of the optimal vector field: Exemplified by a fishery model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(10), pages 1626-1658.
    17. Dieter Grass, 2015. "From 0D to 1D spatial models using OCMat," Papers 1505.03956, arXiv.org.
    18. Kossioris, G. & Plexousakis, M. & Xepapadeas, A. & de Zeeuw, A., 2011. "On the optimal taxation of common-pool resources," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1868-1879.
    19. G. Feichtinger & A. Steindl, 2006. "DNS Curves in a Production/Inventory Model," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 295-308, February.
    20. Feichtinger, Gustav & Grass, Dieter & Kort, Peter M. & Seidl, Andrea, 2021. "On the Matthew effect in research careers," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ams:ndfwpp:09-14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Cees C.G. Diks (email available below). General contact details of provider: https://edirc.repec.org/data/cnuvanl.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.