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Quantity Constrained Equilibria

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  • 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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 01-116/1.

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Date of creation: 06 Dec 2001
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Handle: RePEc:dgr:uvatin:20010116

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Web page: http://www.tinbergen.nl

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Keywords: exchange economy; price rigidities; equilibrium; rationing.;

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References

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  1. Nguyen, Trien T & Whalley, John, 1990. "General Equilibrium Analysis of Price Controls: A Computational Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 667-84, August.
  2. Herings, P.J.J. & Talman, A.J.J. & Yang, Z.F., 1996. "The computation of a continuum of constrained equilibria," Open Access publications from Tilburg University urn:nbn:nl:ui:12-72887, Tilburg University.
  3. Herings,P. Jean-Jacques & Polemarchakis,H. M., 2000. "Pareto Improving Price Regulation When the Asset Market Is Incomplete," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  4. Tuinstra, Jan, 2000. "The emergence of political business cycles in a two-sector general equilibrium model," European Journal of Political Economy, Elsevier, vol. 16(3), pages 509-534, September.
  5. Weddepohl, Claus, 1987. "Supply-constrained equilibria in economies with indexed prices," Journal of Economic Theory, Elsevier, vol. 43(2), pages 203-222, December.
  6. van der Laan, Gerard, 1984. "Supply-constrained fixed price equilibria in monetary economies," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 171-187, October.
  7. Citanna, Alessandro & Cres, Herve & Dreze, Jacques & Herings, P. Jean-Jacques & Villanacci, Antonio, 2001. "Continua of underemployment equilibria reflecting coordination failures, also at Walrasian prices," Journal of Mathematical Economics, Elsevier, vol. 36(3), pages 169-200, December.
  8. Herings, P.J.J., 1994. "Endogenously determined price rigidities," Discussion Paper 1994-30, Tilburg University, Center for Economic Research.
  9. Herings, P Jean-Jacques, 1996. "Equilibrium Existence Results for Economies with Price Rigidities," Economic Theory, Springer, vol. 7(1), pages 63-80, January.
  10. Jacques H.DREZE, 2001. "On the Macroeconomics of Uncertainty and Incomplete Markets," Discussion Papers (REL - Recherches Economiques de Louvain) 2001011, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  11. van der LAAN, Gerard, . "Simplicial approximation of unemployment equilibria," CORE Discussion Papers RP -467, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  12. Cox, Charles C, 1980. "The Enforcement of Public Price Controls," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 887-916, October.
  13. Benassy, Jean-Pascal, 1975. "Neo-Keynesian Disequilibrium Theory in a Monetary Economy," Review of Economic Studies, Wiley Blackwell, vol. 42(4), pages 503-23, October.
  14. GINSBURGH, Victor A. & VAN DER HEYDEN, Ludo, . "On extending the Negishi approach to computing equilibria: the case of government price support policies," CORE Discussion Papers RP -787, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Nguyen, Trien T. & Whalley, John, 1986. "Equilibrium under price controls with endogenous transactions costs," Journal of Economic Theory, Elsevier, vol. 39(2), pages 290-300, August.
  16. van der Laan, Gerard, 1980. "Equilibrium under Rigid Prices with Compensation for the consumers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 63-73, February.
  17. Benassy, Jean-Pascal, 1993. "Nonclearing Markets: Microeconomic Concepts and Macroeconomic Applications," Journal of Economic Literature, American Economic Association, vol. 31(2), pages 732-61, June.
  18. Herings,P. Jean-Jacques & Polemarchakis,H. M., 2000. "Pareto Improving Price Regulation When the Asset Market Is Incomplete," Research Memorandum 008, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  19. Herings, P. Jean-Jacques, 1998. "On the existence of a continuum of constrained equilibria1," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 257-273, October.
  20. Dehez, Pierre & Dreze, Jacques H., 1984. "On supply-constrained equilibria," Journal of Economic Theory, Elsevier, vol. 33(1), pages 172-182, June.
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Citations

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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," Discussion Paper 2003-73, Tilburg University, Center for Economic Research.
  2. Herings, P.J.J. & Koshevoy, G.A. & Talman, A.J.J. & Yang, Z.F., 2004. "A general existence theorem of zero points," Open Access publications from Tilburg University urn:nbn:nl:ui:12-123911, Tilburg University.
  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.

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