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Consumption dynamics in general equilibrium: A characterisation when markets are incomplete

  • Beker, Pablo
  • Chattopadhyay, Subir

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide 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--so 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 (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes 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. In sharp contrast to the results in the case studied by Sandroni (2000) [29] and Blume and Easley (2006) [8] where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 145 (2010)
Issue (Month): 6 (November)
Pages: 2133-2185

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Handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2133-2185
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Tarek Coury & Emanuela Sciubba, 2012. "Belief heterogeneity and survival in incomplete markets," Economic Theory, Springer, vol. 49(1), pages 37-58, January.
  2. Levine, David K. & Zame, William R., 1996. "Debt constraints and equilibrium in infinite horizon economies with incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 26(1), pages 103-131.
  3. 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.
  4. 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.
  5. Beker, Pablo F. & Espino, Emilio, 2011. "The dynamics of efficient asset trading with heterogeneous beliefs," Journal of Economic Theory, Elsevier, vol. 146(1), pages 189-229, January.
  6. Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1998. "Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited," Discussion Papers 1228, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-80, July.
  8. Becker, Robert A. & Foias, Ciprian, 1987. "A characterization of Ramsey equilibrium," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February.
  9. Manuel S. Santos & Michael Woodford, 1993. "Rational Asset Pricing Bubbles," Working Papers 9304, Centro de Investigacion Economica, ITAM.
  10. Bewley, Truman, 1982. "An integration of equilibrium theory and turnpike theory," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September.
  11. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  12. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
  13. Armen A. Alchian, 1950. "Uncertainty, Evolution, and Economic Theory," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211.
  14. Larry Blume & David Easley, 2001. "If You're So Smart, Why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Cowles Foundation Discussion Papers 1319, Cowles Foundation for Research in Economics, Yale University.
  15. Gary Chamberlain & Charles A. Wilson, 2000. "Optimal Intertemporal Consumption Under Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 3(3), pages 365-395, July.
  16. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, June.
  17. Becker, Robert & Zilcha, Itzhak, 1997. "Stationary Ramsey Equilibria under Uncertainty," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July.
  18. Rader, Trout, 1981. "Utility over time: The homothetic case," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October.
  19. 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.
  20. Constantinides,George & Duffie,Darrel, 1992. "Asset pricing with heterogeneous consumers," Discussion Paper Serie A 381, University of Bonn, Germany.
  21. Kubler, Felix & Schmedders, Karl, 2002. "Recursive Equilibria In Economies With Incomplete Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April.
  22. David K. Levine & William Zame, 2001. "Does Market Incompleteness Matter," Levine's Working Paper Archive 78, David K. Levine.
  23. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
  24. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
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