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On the Existence of a Ramsey Equilibrium with Endogenous Labor Supply and Borrowing Constraints

  • Stefano Bosi

    ()

    (THEMA)

  • Cuong Le Van

    ()

    (CNRS, CES, Exeter University, Paris School of Economics, VCREME.)

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 of 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 applied to other Ramsey models with different market imperfections.

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Paper provided by Development and Policies Research Center (DEPOCEN), Vietnam in its series Working Papers with number 24.

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Length: 28 pages
Date of creation: 2011
Date of revision:
Handle: RePEc:dpc:wpaper:2411
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  1. 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.
  2. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
  3. 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.
  4. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
  5. Becker, Robert & Mitra, Tapan, 2011. "Efficient Ramsey Equilibria," Working Papers 11-02, Cornell University, Center for Analytic Economics.
  6. 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.
  7. 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.
  8. Cuong LE VAN & Yiannis VALAKIS, 2001. "Existence of a competitive equilibrium in one sector growth model with heterogeneous agents and irreversible investment," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001018, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  9. 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.
  10. Gerhard Sorger, 2008. "Strategic saving decisions in the infinite-horizon model," Economic Theory, Springer, vol. 36(3), pages 353-377, September.
  11. 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.
  12. Becker, R.C. & Foias, C., 1992. "The Local Bifurcation of Ramsey Equilibrium," Papers 92-002, Indiana - Center for Econometric Model Research.
  13. Becker, Robert A. & Tsyganov, Eugene N., 2002. "Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households," Journal of Economic Theory, Elsevier, vol. 105(1), pages 188-225, July.
  14. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  15. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
  16. Monique Florenzano, 2008. "General equilibrium," Documents de travail du Centre d'Economie de la Sorbonne b08005, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  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 133-45, February.
  18. 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.
  19. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
  20. 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.
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