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

  • Robert Becker
  • Stefano Bosi
  • Cuong Le Van
  • Thomas Seegmuller

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 con- straints. 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 equi- librium 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 differ- ent 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 Department of Research, Ipag Business School in its series Working Papers with number 2013-004.

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Length: 37 pages
Date of creation: 04 May 2013
Date of revision:
Handle: RePEc:ipg:wpaper:2013-004
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  1. 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.
  2. Becker, Robert & Mitra, Tapan, 2011. "Efficient Ramsey Equilibria," Working Papers 11-02, Cornell University, Center for Analytic Economics.
  3. Alberto Martin & Jaume Ventura, 2003. "Economic growth with bubbles," Economics Working Papers 848, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2011.
  4. repec:hal:journl:halshs-00101237 is not listed on IDEAS
  5. 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.
  6. 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.
  7. Becker, Robert A & Foias, Ciprian, 1994. "The Local Bifurcation of Ramsey Equilibrium," Economic Theory, Springer, vol. 4(5), pages 719-44, August.
  8. Jean Tirole & Emmanuel Farhi, 2011. "Bubbly Liquidity," 2011 Meeting Papers 1081, Society for Economic Dynamics.
  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. 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.
  11. LE VAN, Cuong & VAILAKIS, Yiannis, . "Existence of a competitive equilibrium in a one sector growth model with heterogeneous agents and irreversible investment," CORE Discussion Papers RP -1762, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Monique Florenzano & Pascal Gourdel, 1996. "Incomplete Markets In Infinite Horizon: Debt Constraints Versus Node Prices," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 167-196.
  13. 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.
  14. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
  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. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  17. 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.
  18. 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.
  19. 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.
  20. Timothy J. Kehoe & David K. Levine & Paul M. Romer, 1989. "Determinacy of equilibria in dynamic models with finitely many consumers," Staff Report 118, Federal Reserve Bank of Minneapolis.
  21. 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.
  22. 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.
  23. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  24. Gerhard Sorger, 2008. "Strategic saving decisions in the infinite-horizon model," Economic Theory, Springer, vol. 36(3), pages 353-377, September.
  25. 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.
  26. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
  27. 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.
  28. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  29. Tirole, Jean, 1982. "On the Possibility of Speculation under Rational Expectations," Econometrica, Econometric Society, vol. 50(5), pages 1163-81, September.
  30. 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.
  31. Tirole, Jean, 1985. "Asset Bubbles and Overlapping Generations," Econometrica, Econometric Society, vol. 53(6), pages 1499-1528, November.
  32. Becker, Robert A. & Foias, Ciprian, 2007. "Strategic Ramsey equilibrium dynamics," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 318-346, April.
  33. 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.
  34. 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.
  35. 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.
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