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Quantity Constrained Equilibria

Author

Listed:
  • P. Jean-Jacques Herings

    (Universiteit Maastricht)

  • Gerard van der Laan

    (Vrije Universiteit Amsterdam)

  • Dolf Talman

    (Universiteit Tilburg)

Abstract

In a standard general equilibrium model it is assumed that there are no price restictionsand that prices adjust infinitely fast to their equilibrium values. In this paper the set ofadmissible prices is allowed to be an arbitrary convex set. For such an arbitrary set it cannotbe guaranteed that there exists a constrained equilibrium satisfying the usual condition that aprice will be on its upper or lower bound in case of rationing. Therefore we introduce a moregeneral equilibrium concept, called Quantity Constrained Equilibrium (QCE). At such an equilibriumthe levels of supply and demand rationing are completely determined by the components of adirection in which the price system cannot be moved further without leaving the set of admissibleprices. When the set is compact, we show the existence of a connected set of QCEs, containing twotrivial no-trade equilibria. Moreover, the set contains for every commodity a generalized Drèzeequilibrium, being a QCE at which this commodity is not being rationed, and also a generalizedsupply-constrained equilibrium without demand rationing. We apply this main result to severalspecial cases, including the case of an unbounded set of admissible prices.

Suggested Citation

  • P. Jean-Jacques Herings & Gerard van der Laan & Dolf Talman, 2001. "Quantity Constrained Equilibria," Tinbergen Institute Discussion Papers 01-116/1, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20010116
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    Cited by:

    1. Talman, A.J.J. & Yang, Z.F., 2003. "On the Connectedness of Coincidences and Zero Points of Mappings," Other publications TiSEM b061dd09-2b7f-4fe3-af6e-d, Tilburg University, School of Economics and Management.
    2. P. J. J. Herings & G. A. Koshevoy & A. J. J. Talman & Z. Yang, 2004. "General Existence Theorem of Zero Points," Journal of Optimization Theory and Applications, Springer, vol. 120(2), pages 375-394, February.
    3. Sander van der Hoog, 2004. "Credit and Cash-in-Advance in Disequilibrium Models," Computing in Economics and Finance 2004 294, Society for Computational Economics.

    More about this item

    Keywords

    exchange economy; price rigidities; equilibrium; rationing.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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