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Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure

Author

Listed:
  • Aditya Goenka

    (NUS - National University of Singapore)

  • Cuong Le Van

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, University of Exeter Business School - University of Exeter, Hanoi WRU - Department of Economics, 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, VCREME - Van Xuan Center of Research in Economics, Management and Environment)

  • Manh-Hung Nguyen

    (VCREME - Van Xuan Center of Research in Economics, Management and Environment, 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, 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)

Abstract

This paper proves the existence of competitive equilibrium in a single-sector dynamic economy with heterogeneous agents, elastic labor supply and complete assets markets. The method of proof relies on some recent results concerning the existence of Lagrange multipliers in in nite dimensional spaces and their representation as a summable sequence and a direct application of the inward boundary fixed point theorem.

Suggested Citation

  • Aditya Goenka & Cuong Le Van & Manh-Hung Nguyen, 2011. "Existence of competitive equilibrium in an optimal growth model with heterogeneous agents and endogenous leisure," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00639739, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00639739
    DOI: 10.1017/S1365100511000587
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00639739
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    References listed on IDEAS

    as
    1. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    2. Cuong Le Van & Rose-Anne Dana, 2003. "Dynamic Programming in Economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00119098, HAL.
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    4. Dechert, W. D., 1982. "Lagrange multipliers in infinite horizon discrete time optimal control models," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 285-302, March.
    5. 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.
    6. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-377, October.
    8. Kim, K. H., 1990. "Existence and optimality of competitive equilibria. : C.D. Aliprantis, D.J. Brown, and O. Burkinshaw, Berlin: Springer-Verlag, 1989, 284 pages, 110 DM," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 197-197, October.
    9. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    10. Cuong Le Van & Rose-Anne Dana, 2003. "Dynamic Programming in Economics," Post-Print halshs-00119098, HAL.
    11. 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.
    12. Cuong Le Van & Yiannis Vailakis, 2003. "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 743-771, November.
    13. repec:dau:papers:123456789/13605 is not listed on IDEAS
    14. Cuong Le Van & Yiannis Vailakis, 2004. "Existence of competitive equilibrium in a single-sector growth model with elastic labour," Cahiers de la Maison des Sciences Economiques b04123, Université Panthéon-Sorbonne (Paris 1).
    15. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    16. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
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    Citations

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    Cited by:

    1. 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.
    2. Cai, Yiyong & Kamihigashi, Takashi & Stachurski, John, 2014. "Stochastic optimal growth with risky labor supply," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 167-176.
    3. Sanou Issa, 2021. "Jealousy and Wealth Inequality: The Cases of Heterogeneous Preferences and Elastic Labor Supply," Working Papers hal-03408115, HAL.

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    More about this item

    Keywords

    Elastic labor supply; Optimal growth model; Lagrange multipliers; Competitive equilib- rium; Individually Rational Pareto Optimum; Elastic labor supply.;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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