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On existence, effciency and bubbles of Ramsey equilibrium with borrowing constraints

  • Robert Becker

    (Department of Economics, Indiana University)

  • Stefano Bosi

    (EPEE, University of Evry)

  • Cuong Le Van

    (CES, CNRS, VCREME and Hanoi WRU)

  • Thomas Seegmuller

    (Aix-Marseille University (Aix-Marseille School of Economics), CNRS and EHESS)

We address the fundamental issues of existence and efficiency of an equilibrium in a Ramsey model with many agents, where agents have heterogenous discounting, elastic labor supply and face borrowing constraints. The existence of rational bubbles is also tackled. In the first part, we prove the equilibrium existence in a truncated bounded economy through a fixed-point argument by Gale and Mas-Colell (1975). This equilibrium is also an equilibrium of any unbounded economy with the same fundamentals. The proof of existence is eventually given for an infinitehorizon economy as a limit of a sequence of truncated economies. Our general approach is suitable for applications to other models with different market imperfections. In the second part, we show the impossibility of bubbles in a productive economy and we give sufficient conditions for equilibrium efficiency.

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Paper provided by Development and Policies Research Center (DEPOCEN), Vietnam in its series Working Papers with number 15.

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Length: 36 pages
Date of creation: 2013
Date of revision:
Handle: RePEc:dpc:wpaper:1513
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  1. 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.
  2. Emmanuel Farhi & Jean Tirole, 2012. "Bubbly Liquidity," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 678-706.
  3. Florenzano, M. & Gourdel, P., 1994. "Incomplete Markets in Infinite Horizon: Debt Constraints Versus Node Prices," Papiers d'Economie Mathématique et Applications 94.76, Université Panthéon-Sorbonne (Paris 1).
  4. Martin, Alberto & Ventura, Jaume, 2010. "Economic Growth with Bubbles," CEPR Discussion Papers 7770, C.E.P.R. Discussion Papers.
  5. 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.
  6. 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.
  7. Becker, R.C. & Foias, C., 1992. "The Local Bifurcation of Ramsey Equilibrium," Papers 92-002, Indiana - Center for Econometric Model Research.
  8. 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.
  9. Coles, Jeffrey Link, 1985. "Equilibrium Turnpike Theory with Constant Returns to Scale and Possible Heterogeneous Discount Factors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(3), pages 671-79, October.
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  12. 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.
  13. Robert Becker & Ram Sewak Dubey & Tapan Mitra, 2012. "On Ramsey Equilibrium: Capital Ownership Pattern and Inefficiency," Caepr Working Papers 2012-007, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  14. 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.
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  17. 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.
  18. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
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  27. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  28. 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.
  29. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  30. Coles, Jeffrey L., 1986. "Equilibrium turnpike theory with time-separable utility," Journal of Economic Dynamics and Control, Elsevier, vol. 10(3), pages 367-394, September.
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  32. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
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