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On the existence of a Ramsey equilibrium with endogenous labor supply and borrowing constraints

  • Stefano Bosi

    ()

    (THEMA - Théorie économique, modélisation et applications - CNRS : UMR8184 - Université de Cergy Pontoise)

  • Cuong Le Van

    ()

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, University of Exeter Business School - University of Exeter Business School, VCREME - VanXuan Center of Research in Economics, Management and Environment - VanXuan Center of Research in Economics, Management and Environment)

In this paper, we study the existence of an intertemporal equilibrium in a Ramsey model with heterogenous discounting, elastic labor supply and borrowing constraints. Applying a fixed-point argument by Gale and Mas-Colell (1975), we prove the existence of an equilibrium in a truncated bounded economy. This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. Finally, we prove the existence of an equilibrium in an infinite-horizon economy as a limit of a sequence of truncated economies. On the one hand, our paper generalizes Becker et al. (1991) because of the elastic labor supply and, on the other hand, Bosi and Seegmuller (2010) because of a proof of global existence. Our methodology can be also applied to other Ramsey models with different market imperfections.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00612131.

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Date of creation: Jul 2011
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Handle: RePEc:hal:cesptp:halshs-00612131
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  1. Cuong Le Van & Manh-Hung Nguyen & Yiannis Vailakis, 2005. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197560, HAL.
  2. Robert A. Becker, 2012. "Optimal growth with heterogeneous agents and the twisted turnpike: An example," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 27-47, 03.
  3. Stefano Bosi & Thomas Seegmuller, 2007. "On the Ramsey Equilibrium with heterogeneous consumers and endogenous labor supply," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00143421, HAL.
  4. Gerhard Sorger, 2008. "Strategic saving decisions in the infinite-horizon model," Economic Theory, Springer, vol. 36(3), pages 353-377, September.
  5. Sorger, Gerhard, 2002. "On the Long-Run Distribution of Capital in the Ramsey Model," Journal of Economic Theory, Elsevier, vol. 105(1), pages 226-243, July.
  6. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
  7. 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 133-45, February.
  8. Becker, R.C. & Foias, C., 1992. "The Local Bifurcation of Ramsey Equilibrium," Papers 92-002, Indiana - Center for Econometric Model Research.
  9. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  10. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
  11. 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, vol. 22(4), pages 743-771, November.
  12. Sarte, Pierre-Daniel G., 1997. "Progressive taxation and income inequality in dynamic competitive equilibrium," Journal of Public Economics, Elsevier, vol. 66(1), pages 145-171, October.
  13. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
  14. Becker, Robert A & Boyd, John H, III & Foias, Ciprian, 1991. "The Existence of Ramsey Equilibrium," Econometrica, Econometric Society, vol. 59(2), pages 441-60, March.
  15. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
  16. Becker, Robert A, 1980. "On the Long-Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households," The Quarterly Journal of Economics, MIT Press, vol. 95(2), pages 375-82, September.
  17. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
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