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Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor

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Abstract

The paper extends the canonical representative agent Ramsey model to include heterogeneous agents and elastic labor supply. The welfare maximization problem is analyzed and shown to be equivalent to a non-stationary reduced form model. An iterative procedure is exploited to prove the supermodularity of the indirect utility function. Supermodularity is subsequently used to establish the convergence of optimal paths

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  • Cuong Le Van & Manh Hung Nguyen & Yiannis Vailakis, 2005. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Cahiers de la Maison des Sciences Economiques b05096, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b05096
    DOI: 10.1016/j.jmateco.2006.06.003
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    File URL: https://halshs.archives-ouvertes.fr/halshs-00197560
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    14. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Post-Print halshs-00119095, HAL.
    15. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
    16. Robert A. Becker, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(2), pages 375-382.
    17. Mitra, Tapan, 1979. "On Optimal Economic Growth with Variable Discount Rates: Existence and Stability Results," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 133-145, February.
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    Cited by:

    1. Goenka, Aditya & Nguyen, Manh-Hung, 2009. "Existence of Competitive Equilibrium in an Optimal Growth Model with Elastic Labor Supply and Smoothness of the Policy Function," TSE Working Papers 09-064, Toulouse School of Economics (TSE).
    2. Robert Becker & Stefano Bosi & Cuong Van & Thomas Seegmuller, 2015. "On existence and bubbles of Ramsey equilibrium with borrowing constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 329-353, February.
    3. Takashi Kamihigashi, 2015. "Multiple interior steady states in the Ramsey model with elastic labor supply," International Journal of Economic Theory, The International Society for Economic Theory, vol. 11(1), pages 25-37, March.
    4. Stefano Bosi & Eleni Iliopulos & Hubert Jayet, 2011. "Optimal Immigration Policy: When The Public Good Is Rival," The Japanese Economic Review, Japanese Economic Association, vol. 62(4), pages 460-484, December.
    5. Bosi, Stefano & Seegmuller, Thomas, 2010. "On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 475-492, July.
    6. Aditya Goenka & Cuong Le Van & Manh-Hung Nguyen, 2011. "A study of the dynamic of influence through differential equations," Documents de travail du Centre d'Economie de la Sorbonne 11023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Stefano Bosi & Cuong Le Van, 2011. "On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints," Post-Print halshs-00612131, HAL.
    8. repec:ipg:wpaper:201404 is not listed on IDEAS
    9. Goenka, Aditya & Le Van, Cuong & Nguyen, Manh-Hung, 2012. "Existence Of Competitive Equilibrium In An Optimal Growth Model With Heterogeneous Agents And Endogenous Leisure," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 33-51, April.
    10. Nishimura, Kazuo & Nourry, Carine & Seegmuller, Thomas & Venditti, Alain, 2016. "Public Spending As A Source Of Endogenous Business Cycles In A Ramsey Model With Many Agents," Macroeconomic Dynamics, Cambridge University Press, vol. 20(2), pages 504-524, March.
    11. Goenka, Aditya & Nguyen, Manh-Hung, 2011. "Equilibrium in the growth model with an endogenous labor-leisure choice," LERNA Working Papers 11.06.340, LERNA, University of Toulouse.
    12. Robert Becker & Stefano Bosi & Cuong Le Van & Thomas Seegmuller, 2012. "On existence, efficiency and bubbles of Ramsey equilibrium with borrowing constraints," Caepr Working Papers 2012-001, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    13. Borissov, Kirill & Dubey, Ram Sewak, 2015. "A characterization of Ramsey equilibrium in a model with limited borrowing," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 67-78.
    14. Goenka, Aditya & Nguyen, Manh-Hung, 2020. "General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 90-98.
    15. repec:hal:journl:hal-01302535 is not listed on IDEAS
    16. Augeraud-Veron, Emmanuelle & Boucekkine, Raouf & Gozzi, Fausto & Venditti, Alain & Zou, Benteng, 2024. "Fifty years of mathematical growth theory: Classical topics and new trends," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    17. Becker, Robert A. & Borissov, Kirill & Dubey, Ram Sewak, 2015. "Ramsey equilibrium with liberal borrowing," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 296-304.
    18. Robert Becker & Stefano Bosi & Cuong Le Van & Thomas Seegmuller, 2012. "On existence, efficiency and bubbles of Ramsey equilibrium with borrowing constraints," CAEPR Working Papers 2012-001, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.
    19. repec:hal:psewpa:halshs-00793530 is not listed on IDEAS
    20. repec:ipg:wpaper:2013-004 is not listed on IDEAS
    21. 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.
    22. repec:ipg:wpaper:4 is not listed on IDEAS
    23. Becker, Robert A. & Borissov, Kirill & Dubey, Ram Sewak, 2015. "Ramsey equilibrium with liberal borrowing," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 296-304.

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    More about this item

    Keywords

    Single-sector growth model; heterogeneous agents; elastic labor supply;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical

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