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

  • Robert Becker

    ()

    (Indiana University)

  • Stefano Bosi

    ()

    (EPEE, University of Evry)

  • Cuong Le Van

    ()

    (CES, CNRS, VCREME and Hanoi WRU)

  • Thomas Seegmuller

    ()

    (GREQAM, Aix-Marseille University)

We address the fundamental issues of existence and efficiency of a Ramsey equilibrium with heterogenous discounting, elastic labor supply and borrowing constraints. 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 infinite-horizon 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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File URL: http://www.iub.edu/~caepr/RePEc/PDF/2012/CAEPR2012-001.pdf
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Paper provided by Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington in its series Caepr Working Papers with number 2012-001.

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Length: 42 pages
Date of creation: Feb 2012
Date of revision:
Handle: RePEc:inu:caeprp:2012-001
Contact details of provider: Postal: 812-855-1021
Phone: 812-855-1021
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Web page: http://www.iub.edu/~caepr
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  1. Emmanuel Farhi & Jean Tirole, 2012. "Bubbly Liquidity," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 678-706.
  2. Timothy J. Kehoe & David K. Levine & Paul Romer, 1990. "Determinacy of Equilibrium in Dynamic Models with Finitely Many Consumers," Levine's Working Paper Archive 165, David K. Levine.
  3. Robert Becker, 2011. "Optimal Growth with Heterogeneous Agents and the Twisted Turnpike: An Example," Caepr Working Papers 2011-008, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  4. Timothy J Kehoe & David K Levine, 1985. "Comparative Statics and Perfect Foresight in Infinite Horizon Economies," Levine's Working Paper Archive 1873, David K. Levine.
  5. 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.
  6. Martin, Alberto & Ventura, Jaume, 2010. "Economic Growth with Bubbles," CEPR Discussion Papers 7770, C.E.P.R. Discussion Papers.
  7. 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.
  8. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
  9. 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).
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. Florenzano, Monique & Gourdel, Pascal, 1993. "Incomplete markets in infinite horizon : debt constraints versus node prices," CEPREMAP Working Papers (Couverture Orange) 9329, CEPREMAP.
  16. Stefano Bosi & Thomas Seegmuller, 2007. "On the Ramsey equilibrium with heterogeneous consumers and endogenous labor supply," Documents de travail du Centre d'Economie de la Sorbonne v07003a, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2007.
  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. 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.
  19. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  20. Robert A. Becker & Tapan Mitra, 2011. "Efficient Ramsey Equilbria," Caepr Working Papers 2011-009, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  21. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  22. Paul A. Samuelson, 1958. "An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money," Journal of Political Economy, University of Chicago Press, vol. 66, pages 467.
  23. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
  24. Gerhard Sorger, 2008. "Strategic saving decisions in the infinite-horizon model," Economic Theory, Springer, vol. 36(3), pages 353-377, September.
  25. Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer, vol. 4(5), pages 719-44, August.
  26. 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.
  27. Sorger, Gerhard, 1994. "On the Structure of Ramsey Equilibrium: Cycles, Indeterminacy, and Sunspots," Economic Theory, Springer, vol. 4(5), pages 745-64, August.
  28. Manuel S. Santos & Michael Woodford, 1997. "Rational Asset Pricing Bubbles," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.
  29. Bergstrom, Theodore C., 1976. "How to discard `free disposability' - at no cost," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 131-134, July.
  30. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  31. 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.
  32. repec:hal:journl:halshs-00101237 is not listed on IDEAS
  33. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
  34. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
  35. 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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