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Economic Survival when Markets are Incomplete

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  • Pablo F. Beker
  • Subir Chattopadhyay

Abstract

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. Tarek Coury & Emanuela Sciubba, 2012. "Belief heterogeneity and survival in incomplete markets," Economic Theory, Springer, vol. 49(1), pages 37-58, January.
  3. Constantinides, George M & Duffie, Darrell, 1996. "Asset Pricing with Heterogeneous Consumers," Journal of Political Economy, University of Chicago Press, vol. 104(2), pages 219-40, April.
  4. Krebs, Tom, 2004. "Non-existence of recursive equilibria on compact state spaces when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 115(1), pages 134-150, March.
  5. 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.
  6. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  7. 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.
  8. David K. Levine & William Zame, 2001. "Does Market Incompleteness Matter," Levine's Working Paper Archive 78, David K. Levine.
  9. 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.
  10. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  11. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  12. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, 07.
  13. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  14. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
  15. 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.
  16. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  17. 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.
  18. repec:cup:macdyn:v:6:y:2002:i:2:p:284-306 is not listed on IDEAS
  19. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
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Cited by:
  1. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.

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