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Optimal timing of regime switching in optimal growth models: A Sobolev space approach

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  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, University of Exeter Business School - University of Exeter, VCREME - Van Xuan Center of Research in Economics, Management and Environment)

  • Erol Dogan

    (Bilkent University [Ankara])

  • Cagri Saglam

    (Bilkent University [Ankara])

Abstract

This paper analyses the optimal timing of switching between alternative and consecutive regimes in optimal growth models. We derive the appropriate necessary conditions for such problems by means of the standard techniques from calculus of variations and some basic properties of Sobolev spaces.

Suggested Citation

  • Cuong Le Van & Erol Dogan & Cagri Saglam, 2011. "Optimal timing of regime switching in optimal growth models: A Sobolev space approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639729, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00639729
    DOI: 10.1016/j.mathsocsci.2010.11.005
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00639729
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Saglam, Cagri & Valléee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 250-271, April.
    2. Raouf Boucekkine & Fernando Del Río & Omar Licandro, 2003. "Embodied Technological Change, Learning‐by‐doing and the Productivity Slowdown," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(1), pages 87-98, March.
    3. Askenazy, Philippe & Le Van, Cuong, 1999. "A Model of Optimal Growth Strategy," Journal of Economic Theory, Elsevier, vol. 85(1), pages 24-51, March.
    4. Cuong Van & Raouf Boucekkine & Cagri Saglam, 2007. "Optimal Control in Infinite Horizon Problems: A Sobolev Space Approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 497-509, September.
    5. Jeremy Greenwood & Boyan Jovanovic, 2001. "Accounting for Growth," NBER Chapters, in: New Developments in Productivity Analysis, pages 179-224, National Bureau of Economic Research, Inc.
    6. Raouf Boucekkine & Jacek Krawczyk & Thomas Vallée, 2011. "Environmental quality versus economic performance: A dynamic game approach," Post-Print hal-03193660, HAL.
    7. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
    8. Tomiyama, Ken & Rossana, Robert J., 1989. "Two-stage optimal control problems with an explicit switch point dependence : Optimality criteria and an example of delivery lags and investment," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 319-337, July.
    9. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355, Elsevier.
    10. repec:cor:louvrp:-2335 is not listed on IDEAS
    11. Tomiyama, Ken, 1985. "Two-stage optimal control problems and optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 9(3), pages 317-337, November.
    12. Makris, Miltiadis, 2001. "Necessary conditions for infinite-horizon discounted two-stage optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1935-1950, December.
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    Cited by:

    1. Erin Cottle Hunt & Frank N. Caliendo, 2022. "Social security and longevity risk: An analysis of couples," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(3), pages 547-579, June.
    2. Dieter Grass & Richard F. Hartl & Peter M. Kort, 2012. "Capital Accumulation and Embodied Technological Progress," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 588-614, August.
    3. Jean-Michel Grandmont, 2013. "Tribute to Cuong Le Van," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 5-10, March.
    4. Caliendo, Frank N. & Gorry, Aspen & Slavov, Sita, 2019. "The cost of uncertainty about the timing of Social Security reform," European Economic Review, Elsevier, vol. 118(C), pages 101-125.

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    Keywords

    Multi-stage optimal control; Sobolev spaces; Optimal growth models;
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