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Competitive Growth in a Life-cycle Model: Existence and Dynamics

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  • Hippolyte d'Albis

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, LERNA - Economie des Ressources Naturelles - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - CEA - Commissariat à l'énergie atomique et aux énergies alternatives)

  • Emmanuelle Augeraud-Véron

    (MIA - Mathématiques, Image et Applications - EA 3165 - ULR - La Rochelle Université)

Abstract

The dynamic behavior of the capital growth rate is analyzed using an overlapping-generations model with continuous trading. Assuming a technology satisfying constant social returns to capital, the equilibrium growth rate is piecewise-defined by functional differential equations with both delayed and advanced terms. The main result concerns the existence of a solution expressed as a series of exponentials, which is shown to crucially depend on the initial wealth distribution among cohorts. Upon existence, the dynamics of the capital growth rate has a saddle-point trajectory that converges to a unique steady state. Along the transition path, the growth rate exhibits exponentially decreasing oscillations.

Suggested Citation

  • Hippolyte d'Albis & Emmanuelle Augeraud-Véron, 2009. "Competitive Growth in a Life-cycle Model: Existence and Dynamics," Post-Print hal-00630459, HAL.
    • Handle: RePEc:hal:journl:hal-00630459
    DOI: 10.1111/j.1468-2354.2009.00537.x
    Note: View the original document on HAL open archive server: https://hal.science/hal-00630459
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    as
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    1. Visite guidée au coeur des travaux du Meilleur jeune économiste 2012 (2/2)
      by Matthieu Solignac in Regards croisés sur l'économie on 2012-06-11 03:05:40

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    Cited by:

    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. Michael Kuhn & Klaus Prettner, 2015. "Population Structure and Consumption Growth: Evidence from National Transfer Accounts," VID Working Papers 1503, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
    3. Hippolyte D'Albis & Emmanuelle Augeraud-Veron, 2008. "Endogenous Retirement and Monetary Cycles," Mathematical Population Studies, Taylor & Francis Journals, vol. 15(4), pages 214-229.
    4. D'ALBIS Hippolyte & AUGERAUD-VÉRON Emmanuelle, 2009. "Continuous-Time Overlapping Generations Models," LERNA Working Papers 09.15.291, LERNA, University of Toulouse.
    5. 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.
    6. d’Albis, Hippolyte & Augeraud-Veron, Emmanuelle & Venditti, Alain, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Journal of Mathematical Economics, Elsevier, vol. 48(5), pages 295-308.
    7. Jochen Mierau & Stephen Turnovsky, 2014. "Capital accumulation and the sources of demographic change," Journal of Population Economics, Springer;European Society for Population Economics, vol. 27(3), pages 857-894, July.
    8. Brito, Paulo & Dilão, Rui, 2010. "Equilibrium price dynamics in an overlapping-generations exchange economy," Journal of Mathematical Economics, Elsevier, vol. 46(3), pages 343-355, May.
    9. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
    10. Belyakov, A.O. & Kurbatskiy, A.N. & Prettner, K., 2021. "The growth effects of anticipated versus unanticipated population aging," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    11. David Oxborrow & Stephen J. Turnovsky, 2017. "Closing the Small Open Economy Model: A Demographic Approach," Review of International Economics, Wiley Blackwell, vol. 25(1), pages 44-75, February.
    12. Brito, Paulo, 2014. "Interest rates and endogenous population growth: joint age-dependent dynamics," MPRA Paper 58656, University Library of Munich, Germany.
    13. 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.
    14. Michael Kuhn & Klaus Prettner, 2018. "Population age structure and consumption growth: evidence from National Transfer Accounts," Journal of Population Economics, Springer;European Society for Population Economics, vol. 31(1), pages 135-153, January.
    15. Mertens, Jean-François & Rubinchik, Anna, 2019. "Regularity And Stability Of Equilibria In An Overlapping Generations Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 23(2), pages 699-729, March.
    16. Turnovsky, Stephen J., 2019. "Demographic structures, savings, and international capital flows," Journal of International Money and Finance, Elsevier, vol. 98(C), pages 1-1.
    17. Jochen Mierau & Stephen Turnovsky, 2014. "Demography, growth, and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(1), pages 29-68, January.

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    More about this item

    Keywords

    OVERLAPPING GENERATIONS MODELS; ENDOGENOUS GROWTH; FUNCTIONAL DIFFERENTIAL EQUATIONS OF MIXED TYPE;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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