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Global asymptotic stability of a competitive equilibrium with recursive preferences

Author

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  • Hyun Park

    (Department of Economics, University of Essex, Colchester, CO4 3SQ, UK)

Abstract

This paper demonstrates global stability of a competitive equilibrium in a multi-sector model of many firms, each of which exhibits constant returns to scale technology, and of infinitely lived consumers, whose preferences are recursive but not necessarily additively separable. In the topology induced by a sup-norm, the dominant diagonal blocks condition (Araujo and Scheinkman (Econometrica 45, 1977)) allows us to apply the implicit function theorem to obtain continuity of the equilibrium path. If a stationary equilibrium is locally asymptotically stable, then the continuity of the equilibrium path and smoothness of a weight function on heterogeneous consumers imply that all equilibrium paths converge to the steady state. The dominant diagonal blocks condition is also shown to be sufficient for the local asymptotic turnpike property.

Suggested Citation

  • Hyun Park, 2000. "Global asymptotic stability of a competitive equilibrium with recursive preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 565-584.
    • Handle: RePEc:spr:joecth:v:15:y:2000:i:3:p:565-584
    Note: Received: December 13, 1996; revised version: June 2, 1999
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    Citations

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    Cited by:

    1. Hyun Park, 2008. "Endogenous Equilibrium Growth With Recursive Preferences And Increasing Returns," Journal of Economic Development, Chung-Ang Unviersity, Department of Economics, vol. 33(2), pages 167-188, December.
    2. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    3. W D A Bryant, 2009. "General Equilibrium:Theory and Evidence," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6875, August.
    4. Paul Oslington, 2012. "General Equilibrium: Theory and Evidence," The Economic Record, The Economic Society of Australia, vol. 88(282), pages 446-448, September.

    More about this item

    Keywords

    Turnpike property; Recursive preferences; Heterogeneous agents.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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