# 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

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## 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

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

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