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Consumption Dynamics in General Equilibrium : A Characterisation when Markets are Incomplete

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  • Beker, Pablo

    (University of Warwick)

  • Subir Chattopadhyay

    (University of York)

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

Suggested Citation

  • 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.
  • Handle: RePEc:wrk:warwec:921
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Timothy Cogley & Thomas J. Sargent & Viktor Tsyrennikov, 2014. "Wealth Dynamics in a Bond Economy with Heterogeneous Beliefs," Economic Journal, Royal Economic Society, vol. 124(575), pages 1-30, March.
    2. Tarek Coury & Emanuela Sciubba, 2012. "Belief heterogeneity and survival in incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 37-58, January.
    3. Pietro Dindo & Filippo Massari, 2017. "The Wisdom of the Crowd in Dynamic Economies," Working Papers 2017:17, Department of Economics, University of Venice "Ca' Foscari".
    4. Hervé Crès & Tobias Markeprand & Mich Tvede, 2016. "Incomplete financial markets and jumps in asset prices," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 201-219, June.
    5. Kogan, Leonid & Ross, Stephen A. & Wang, Jiang & Westerfield, Mark M., 2017. "Market selection," Journal of Economic Theory, Elsevier, vol. 168(C), pages 209-236.
    6. Guerdjikova, Ani & Sciubba, Emanuela, 2015. "Survival with ambiguity," Journal of Economic Theory, Elsevier, vol. 155(C), pages 50-94.
    7. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Momentum and Reversal in Financial Markets with Persistent Heterogeneity," LEM Papers Series 2018/04, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    8. Pietro Dindo, 2015. "Survival in Speculative Markets," LEM Papers Series 2015/32, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    9. Braido, Luis H. B., 2013. "Ergodic Markov equilibrium with incomplete markets and short sales," Theoretical Economics, Econometric Society, vol. 8(1), January.
    10. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2015. "Long-run Heterogeneity in an Exchange Economy with Fixed-Mix Traders," LEM Papers Series 2015/29, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    11. Blume, Lawrence & Easley, David, 2009. "The market organism: Long-run survival in markets with heterogeneous traders," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1023-1035, May.
    12. Dan Vu Cao, 2010. "Collateral Shortages, Asset Price And Investment Volatility With Heterogeneous Beliefs," 2010 Meeting Papers 1233, Society for Economic Dynamics.
    13. Matthew Hoelle & M. Udara Peiris, 2013. "On the Efficiency of Nominal GDP Targeting in a Large Open Economy," Purdue University Economics Working Papers 1273, Purdue University, Department of Economics.

    More about this item

    JEL classification:

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

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