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Quantity Constrained Equilibria

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  • Herings, P.J.J.
  • Laan, G. van der
  • Talman, A.J.J.

    (Tilburg University, Center for Economic Research)

Abstract

In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values. Price rigidities may cause that a competitive equilibrium cannot be attained, and rationing on net demands or supplies is needed to clear the markets. Bénassy, Drèze and Younès proved in the mid 1970s that there exist equilibria with rationing. Moreover, rationing is such that not both demand and supply of a good are rationed simultaneously, at least one commodity is not rationed at all, and there is rationing on the net supply or net demand of a good only if the price of that good is on its low or upper bound, respectively. In the 1980s disequilibrium models with only rationing on net supplies were introduced. In all these models prices are restricted by positive lower and upper bounds. In this paper the set of admissible prices is allowed to be an arbitrary convex set. For such an arbitrary set it cannot be guaranteed that there exists a constrained equilibrium satisfying that a price will be on its upper or lower bound in case of rationing. We introduce a more general equilibrium concept, called Quantity Constrained Equilibrium (QCE). At such an equilibrium the levels of supply and demand rationing are completely determined by the components of a direction in which the price system cannot be moved further without leaving the set of admissible prices. When the set is compact, we show the existence of a connected set of QCEs, containing two trivial no-trade equilibria. Moreover, the set contains for every commodity a generalized Drèze equilibrium, begin a QCE at which this commodity is not being rationed, and also a generalized supply-constrained equilibrium without demand rationing. We apply this main result to several special cases, including the case of an unbounded set of admissible prices.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2001-93.

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Date of creation: 2001
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Handle: RePEc:dgr:kubcen:200193

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Keywords: equilibrium theory; market economy; prices;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. 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).
  5. 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).
  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. 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.
  8. 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.
  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. Herings, P.J.J., 1994. "Endogenously determined price rigidities," Discussion Paper 1994-30, Tilburg University, Center for Economic Research.
  11. 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.
  12. Ginsburgh, Victor A. & Van der Heyden, Ludo, 1988. "On extending the negishi approach to computing equilibria: The case of government price support policies," Journal of Economic Theory, Elsevier, vol. 44(1), pages 168-178, February.
  13. Dehez, Pierre & Dreze, Jacques H., 1984. "On supply-constrained equilibria," Journal of Economic Theory, Elsevier, vol. 33(1), pages 172-182, June.
  14. 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.
  15. 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.
  16. 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.
  17. 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).
  18. 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.
  19. Weddepohl, Claus, 1987. "Supply-constrained equilibria in economies with indexed prices," Journal of Economic Theory, Elsevier, vol. 43(2), pages 203-222, December.
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Citations

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Cited by:
  1. Herings, P.J.J. & Koshevoy, G.A. & Talman, A.J.J. & Yang, Z.F., 2002. "A General Existence Thorem of Zero Points," Discussion Paper 2002-107, Tilburg University, Center for Economic Research.
  2. Sander van der Hoog, 2004. "Credit and Cash-in-Advance in Disequilibrium Models," Computing in Economics and Finance 2004 294, Society for Computational Economics.
  3. Dolf Talman & Zaifu Yang, 2003. "On the Connectedness of Coincidences and Zero Points of Mappings," Working Papers 353, Bielefeld University, Center for Mathematical Economics.

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