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Balanced cycles in an OLG model with a continuum of finitely-lived individuals

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  • Hippolyte d’Albis
  • Emmanuelle Augeraud-Véron

Abstract

This paper studies the intertemporal equilibrium of a barter economy populated with a continuum of finitely-lived overlapping generations. Assuming isoelastic preferences and zero endowments at the beginning and the end of the individual's 'life-span, it proves the existence of an Hopf bifurcation and provides sufficient conditions on parameters for its occurrence.
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Suggested Citation

  • Hippolyte d’Albis & Emmanuelle Augeraud-Véron, 2007. "Balanced cycles in an OLG model with a continuum of finitely-lived individuals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 181-186, January.
    • Handle: RePEc:spr:joecth:v:30:y:2007:i:1:p:181-186
    DOI: 10.1007/s00199-005-0043-9
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    1. Céline Rochon & Herakles Polemarchakis, 2006. "Debt, liquidity and dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(1), pages 179-211, January.
    2. Céline Rochon & Herakles Polemarchakis, 2006. "Debt, liquidity and dynamics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(1), pages 179-211, 01.
    3. Benhabib, Jess & Rustichini, Aldo, 1991. "Vintage capital, investment, and growth," Journal of Economic Theory, Elsevier, vol. 55(2), pages 323-339, December.
    4. Philippe Michel & Alain Venditti, 1997. "Optimal growth and cycles in overlapping generations models (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(3), pages 511-528.
    5. S. Rao Aiyagari, 1989. "Can There Be Short-Period Deterministic Cycles When People Are Long Lived?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 163-185.
    6. Akiomi Kitagawa & Akihisa Shibata, 2005. "Endogenous growth cycles in an overlapping generations model with investment gestation lags," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(3), pages 751-762, April.
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    1. Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2013. "Frequency of trade and the determinacy of equilibrium in economies of overlapping generations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 85-100, March.
    2. Mauro Bambi & Cristina Girolami & Salvatore Federico & Fausto Gozzi, 2017. "Generically distributed investments on flexible projects and endogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 521-558, February.
    3. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Stability and determinacy conditions for mixed-type functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 53(C), pages 119-129.
    4. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Schubert, Katheline, 2010. "Demographic-economic equilibria when the age at motherhood is endogenous," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1211-1221, November.
    5. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    6. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2015. "Local determinacy of prices in an overlapping generations model with continuous trading," Journal of Mathematical Economics, Elsevier, vol. 58(C), pages 16-24.
    7. Augeraud Veron, E. & Marhuenda, F. & Picard, P.M., 2021. "Local social interaction and urban equilibria," Mathematical Social Sciences, Elsevier, vol. 112(C), pages 72-83.
    8. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
    9. Augeraud-Véron, Emmanuelle & D'Albis, Hippolyte, 2009. "Continuous-Time Overlapping Generations Models," TSE Working Papers 09-047, Toulouse School of Economics (TSE).
    10. Hippolyte d'Albis & Emmanuelle Augeraud-véron, 2009. "Competitive Growth In A Life-Cycle Model: Existence And Dynamics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 459-484, May.
    11. Jean-François Mertens & Anna Rubinchik, 2013. "Equilibria in an overlapping generations model with transfer policies and exogenous growth," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 537-595, November.
    12. Edmond, Chris, 2008. "An integral equation representation for overlapping generations in continuous time," Journal of Economic Theory, Elsevier, vol. 143(1), pages 596-609, November.

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    More about this item

    Keywords

    Overlapping-generations models; Mixed-type functional differential equations; Endogenous fluctuations; Hopf bifurcation; C6; D9;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D9 - Microeconomics - - Micro-Based Behavioral Economics

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