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

## Abstract

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.## Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are**not**on the IDEAS site. Please be patient as the files may be large.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

## Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.
**Volume (Year):** 145 (2010)

**Issue (Month):** 6 (November)

**Pages:** 2133-2185

**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

## Related research

**Keywords:**General equilibrium Dynamically incomplete markets Consumption Survival Market selection hypothesis Asset prices;

**Other versions of this item:**

- Beker, Pablo & Subir Chattopadhyay, 2009.
"
**Consumption Dynamics in General Equilibrium : A Characterisation when Markets are Incomplete**," The Warwick Economics Research Paper Series (TWERPS) 921, University of Warwick, Department of Economics.

**Find related papers by JEL classification:**

**D52**- Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets**D61**- Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

## References

**References listed on IDEAS**

Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

- Sandroni, Alvaro, 2005.
"
**Market selection when markets are incomplete**," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February. - 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.

- 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.

- Tom Krebs, 2002.
"
- 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.

- Tarek Coury & Emanuela Sciubba, 2012.
"
**Belief heterogeneity and survival in incomplete markets**," Economic Theory, Springer, vol. 49(1), pages 37-58, January.

- Tarek Coury & Emanuela Sciubba, 2012.
"
- Duffie, Darrell, et al, 1994.
"
**Stationary Markov Equilibria**," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July. - Pablo F Beker & Emilio Espino, 2007.
"
**The Dynamics of Efficient Asset Trading with Heterogeneous Beliefs**," Levine's Bibliography 122247000000001715, UCLA Department of Economics.

- 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.

- Beker, Pablo F. & Espino, Emilio, 2011.
"
- David K. Levine & William Zame, 2001.
"
**Does Market Incompleteness Matter**," Levine's Working Paper Archive 78, David K. Levine.

- David K. Levine & William R. Zame, 2002.
"
**Does Market Incompleteness Matter?**," Econometrica, Econometric Society, vol. 70(5), pages 1805-1839, September.

- David K. Levine & William R. Zame, 2002.
"
- 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.

- 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. - 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.

- Lawrence Blume & David Easley, 2001.
"
- David K. Levine & William R. Zame, 1992.
"
**Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets**," UCLA Economics Working Papers 666, UCLA Department of Economics.

- 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.

- David K. Levine & William R. Zame, 1993.
"
**Debt Constraints and Equilibrium in Infinite Horizon Economies with Incomplete Markets**," UCLA Economics Working Papers 703, UCLA Department of Economics. - 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.

- Levine, David K. & Zame, William R., 1996.
"
- Magill,Michael & Quinzii,Martine, 1992.
"
**Infinite horizon,Incomplete markets**," Discussion Paper Serie A 384, University of Bonn, Germany.

- Magill, Michael & Quinzii, Martine, 1994.
"
**Infinite Horizon Incomplete Markets**," Econometrica, Econometric Society, vol. 62(4), pages 853-80, July.

- Magill, M. & Quinzii, M., 1993.
"
**Infinite Horizon Incomplete Markets**," Papers 9320, Southern California - Department of Economics. - Magill, M. & Quinzii, M., 1992.
"
**Infinite Horizon Incomplete Markets**," DELTA Working Papers 92-26, DELTA (Ecole normale supĂ©rieure). - Magill, M. & Quinzii, M., 1992.
"
**Infinite Horizon Incomplete Markets**," Papers 413a, California Davis - Institute of Governmental Affairs.

- Magill, Michael & Quinzii, Martine, 1994.
"
- Bewley, Truman, 1982.
"
**An integration of equilibrium theory and turnpike theory**," Journal of Mathematical Economics, Elsevier, vol. 10(2-3), pages 233-267, September. - 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.

- Constantinides,George & Duffie,Darrel, 1992.
"
**Asset pricing with heterogeneous consumers**," Discussion Paper Serie A 381, University of Bonn, Germany.

- Constantinides,George & Duffie,Darrel, 1992.
"
- Becker, Robert A. & Foias, Ciprian, 1987.
"
**A characterization of Ramsey equilibrium**," Journal of Economic Theory, Elsevier, vol. 41(1), pages 173-184, February. - Lars Ljungqvist & Thomas J. Sargent, 2004.
"
**Recursive Macroeconomic Theory, 2nd Edition**," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December. - Rader, Trout, 1981.
"
**Utility over time: The homothetic case**," Journal of Economic Theory, Elsevier, vol. 25(2), pages 219-236, October. - 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. - repec:fth:starer:8415 is not listed on IDEAS
- Manuel S. Santos & Michael Woodford, 1993.
"
**Rational Asset Pricing Bubbles**," Working Papers 9304, Centro de Investigacion Economica, ITAM.

- Manuel S. Santos & Michael Woodford, 1997.
"
**Rational Asset Pricing Bubbles**," Econometrica, Econometric Society, vol. 65(1), pages 19-58, January.

- Manuel S. Santos & Michael Woodford, 1997.
"
- 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.

- Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999.
"
**Bayesian Representation of Stochastic Processes under Learning: de Finetti Revisited**," Econometrica, Econometric Society, vol. 67(4), pages 875-894, July.

- Matthew O. Jackson & Ehud Kalai & Rann Smorodinsky, 1999.
"
- 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. - Kubler, Felix & Schmedders, Karl, 2002.
"
**Recursive Equilibria In Economies With Incomplete Markets**," Macroeconomic Dynamics, Cambridge University Press, vol. 6(02), pages 284-306, April. - Armen A. Alchian, 1950.
"
**Uncertainty, Evolution, and Economic Theory**," Journal of Political Economy, University of Chicago Press, vol. 58, pages 211. - Becker, Robert & Zilcha, Itzhak, 1997.
"
**Stationary Ramsey Equilibria under Uncertainty**," Journal of Economic Theory, Elsevier, vol. 75(1), pages 122-140, July. - 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. - Truman Bewley, 2010.
"
**An Integration of Equilibrium Theory and Turnpike Theory**," Levine's Working Paper Archive 1381, David K. Levine. - 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.

**Full references**(including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.**Cited by:**

- Ani Guerdijkova & Emanuela Sciubba, 2012.
"
**Survival with Ambiguity**," Birkbeck Working Papers in Economics and Finance 1216, Birkbeck, Department of Economics, Mathematics & Statistics. - 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.

- Tarek Coury & Emanuela Sciubba, 2012.
"
**Belief heterogeneity and survival in incomplete markets**," Economic Theory, Springer, vol. 49(1), pages 37-58, January.

- Tarek Coury & Emanuela Sciubba, 2012.
"
- Dan Cao, 2011.
"
**Collateral Shortages, Asset Price and Investment Volatility with Heterogeneous Beliefs**," Working Papers gueconwpa~11-11-01, Georgetown University, Department of Economics. - Braido, Luis H. B., 2013.
"
**Ergodic Markov equilibrium with incomplete markets and short sales**," Theoretical Economics, Econometric Society, vol. 8(1), January.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.## Statistics

Access and download statistics## Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:145:y:2010:i:6:p:2133-2185. See general information about how to correct material in RePEc.For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.