# 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 e?ectively 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) and Blume and Easley (2006) 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. JEL Codes: D52 ; D61## Download Info

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## Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 921.

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**Date of creation:**2009

**Date of revision:**

**Handle:**RePEc:wrk:warwec:921

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## Related research

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**Other versions of this item:**

- Beker, Pablo & Chattopadhyay, Subir, 2010.
"
**Consumption dynamics in general equilibrium: A characterisation when markets are incomplete**," Journal of Economic Theory, Elsevier, Elsevier, vol. 145(6), pages 2133-2185, November.

**Find related papers by JEL classification:**

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

**This paper has been announced in the following NEP Reports:**

- NEP-ALL-2009-12-05 (All new papers)
- NEP-BEC-2009-12-05 (Business Economics)
- NEP-CTA-2009-12-05 (Contract Theory & Applications)
- NEP-DGE-2009-12-05 (Dynamic General Equilibrium)

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## Citations

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

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

- Tarek Coury & Emanuela Sciubba, 2006.
"
**Belief Heterogeneity and Survival in Incomplete Markets**," Birkbeck Working Papers in Economics and Finance, Birkbeck, Department of Economics, Mathematics & Statistics 0613, Birkbeck, Department of Economics, Mathematics & Statistics.

- Tarek Coury & Emanuela Sciubba, 2006.
"
- Ani Guerdijkova & Emanuela Sciubba, 2012.
"
**Survival with Ambiguity**," Birkbeck Working Papers in Economics and Finance, Birkbeck, Department of Economics, Mathematics & Statistics 1216, Birkbeck, Department of Economics, Mathematics & Statistics. - Dan Cao, 2011.
"
**Collateral Shortages, Asset Price and Investment Volatility with Heterogeneous Beliefs**," Working Papers, Georgetown University, Department of Economics gueconwpa~11-11-01, Georgetown University, Department of Economics. - Braido, Luis H. B., 2013.
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**Ergodic Markov equilibrium with incomplete markets and short sales**," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(1), January.

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