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Economic Survival when Markets are Incomplete

  • Pablo F. Beker
  • Subir Chattopadhyay

We consider an infinite horizon economy with incomplete markets with two agents and one good. We begin with an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually. This implies that either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that the first possibility is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. Our results mark a sharp contrast with the case studied by Sandroni (2000) and Blume and Easley (2004) where markets are complete.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 784828000000000422.

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Date of creation: 13 Sep 2005
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Handle: RePEc:cla:levarc:784828000000000422
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  1. Magill,Michael & Quinzii,Martine, 1992. "Infinite horizon,Incomplete markets," Discussion Paper Serie A 384, University of Bonn, Germany.
  2. Lawrence Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Working Papers 01-06-031, Santa Fe Institute.
  3. David K. Levine & William Zame, 2001. "Does Market Incompleteness Matter," Levine's Working Paper Archive 78, David K. Levine.
  4. 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.
  5. repec:cup:macdyn:v:6:y:2002:i:2:p:284-306 is not listed on IDEAS
  6. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
  7. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  8. David K. Levine & William Zame, 1996. "Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets," Levine's Working Paper Archive 1954, David K. Levine.
  9. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  10. Tarek Coury & Emanuela Sciubba, 2006. "Belief Heterogeneity and Survival in Incomplete Markets," Birkbeck Working Papers in Economics and Finance 0613, Birkbeck, Department of Economics, Mathematics & Statistics.
  11. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  12. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  13. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  14. Hernandez D., Alejandro & Santos, Manuel S., 1996. "Competitive Equilibria for Infinite-Horizon Economies with Incomplete Markets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 102-130, October.
  15. Tom Krebs, 2002. "Non-Existence of Recursive Equilibria on Compact State Spaces When Markets are Incomplete," Working Papers 2002-17, Brown University, Department of Economics.
  16. Constantinides,George & Duffie,Darrel, 1992. "Asset pricing with heterogeneous consumers," Discussion Paper Serie A 381, University of Bonn, Germany.
  17. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  18. 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.
  19. Krebs, Tom, 2004. "Testable implications of consumption-based asset pricing models with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 191-206, February.
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