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

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Beker, Pablo and Chattopadhyay, Subir (2010) Consumption dynamics in general equilibrium : a characterisation when markets are incomplete. Journal of Economic Theory, Volume 145 (Number 6). pp. 2133-2185. doi:10.1016/j.jet.2010.03.007 ISSN 0022-0531.

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Official URL: http://dx.doi.org/10.1016/j.jet.2010.03.007

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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. (C) 2010 Elsevier Inc. All

Item Type:

Journal Article

Subjects:

H Social Sciences > HB Economic Theory

Divisions:

Faculty of Social Sciences > Economics

Library of Congress Subject Headings (LCSH):

Consumption (Economics), Equilibrium (Economics)

Series Name:

The Warwick Economics Research Paper Series (TWERPS)

Journal or Publication Title:

Journal of Economic Theory

Publisher:

Academic Press

Place of Publication:

Department of Economics, University of Warwick

ISSN:

0022-0531

Official Date:

November 2010

Dates:

Date	Event
November 2010	Published

Volume:

Volume 145

Number:

Number 6

Page Range:

pp. 2133-2185

DOI:

10.1016/j.jet.2010.03.007

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Restricted or Subscription Access

Version or Related Resource:

Beker, P. and Chattopadhyay, S. (2009). Consumption dynamics in general equilibrium: a characterisation when markets are incomplete. Coventry: Department of Economics, University of Warwick. (The Warwick Economics Research Paper Series no. 921). http://wrap.warwick.ac.uk/id/eprint/3540

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