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Equilibrium adjustment of disequilibrium prices

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Author Info

  • Herings, Jean-Jacques
  • van der Laan, Gerard
  • Talman, Dolf
  • Venniker, Richard

Abstract

We consider an exchange economy in which price rigidities are present. In the short run the non-numeraire commodities have a exible price level with respect to the numeraire commodity but their relative prices are mutually fixed. In the long run prices are assumed to be completely exible. For a given price level and fixed relative prices, markets can be equilibrated by means of quantity rationing on demand and supply. Keeping markets in equilibrium through rationing, we provide an adjustment process in prices and quantities converging from a trivial equilibrium with complete demand rationing on all non-numeraire markets to a Walrasian equilibrium. Along the path initially all relative prices are kept fixed and the price level is increased. Rationing schemes are adjusted to keep markets in equilibrium. Doing so the process reaches a short run equilibrium with only demand rationing and no rationing on the numeraire and at least one of the other commodities. The process allows for a downward price adjustment of non-rationed non-numeraire commodities and reaches a Walrasian equilibrium in the long run.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 27 (1997)
Issue (Month): 1 (February)
Pages: 53-77

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Handle: RePEc:eee:mateco:v:27:y:1997:i:1:p:53-77

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Saari, Donald G, 1985. "Iterative Price Mechanisms," Econometrica, Econometric Society, vol. 53(5), pages 1117-31, September.
  2. Weddepohl, Claus, 1987. "Supply-constrained equilibria in economies with indexed prices," Journal of Economic Theory, Elsevier, vol. 43(2), pages 203-222, December.
  3. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November.
  4. 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.
  5. Dehez, Pierre & Dreze, Jacques H., 1984. "On supply-constrained equilibria," Journal of Economic Theory, Elsevier, vol. 33(1), pages 172-182, June.
  6. Herings, J.J., 1993. "On the Connectedness of the Set of Constrained Equilibria," Papers 9363, Tilburg - Center for Economic Research.
  7. Blad, Michael C., 1978. "On the speed of adjustment in the classical tatonnement process: A limit result," Journal of Economic Theory, Elsevier, vol. 19(1), pages 186-191, October.
  8. Laan, Gerard van der, 1982. "Simplicial approximation of unemployment equilibria," Journal of Mathematical Economics, Elsevier, vol. 9(1-2), pages 83-97, January.
  9. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123.
  10. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July.
  11. Polterovich, Victor, 1993. "Rationing, Queues, and Black Markets," Econometrica, Econometric Society, vol. 61(1), pages 1-28, January.
  12. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
  13. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical Dynamics and Economics," Working Paper Series 293, Research Institute of Industrial Economics.
  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. Wu, Ho-Mou, 1988. "Unemployment equilibrium in a random economy," Journal of Mathematical Economics, Elsevier, vol. 17(4), pages 385-400, September.
  16. Herings, P.J.J., 1992. "On the structure of constrained equilibria," Research Memorandum 587, Tilburg University, Faculty of Economics and Business Administration.
  17. Laroque, G, 1981. "A Comment on "Stable Spillovers among Substitutes."," Review of Economic Studies, Wiley Blackwell, vol. 48(2), pages 355-61, April.
  18. Laan, G. van der & Talman, A.J.J., 1985. "Adjustment processes for finding economic equilibria," Research Memorandum 174, Tilburg University, Faculty of Economics and Business Administration.
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Citations

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Cited by:
  1. Laan, G. van der & Talman, A.J.J., 2002. "Dynamic adjustment of supply constrained disequilibria to Walrasian equilibria," Open Access publications from Tilburg University urn:nbn:nl:ui:12-89455, Tilburg University.
  2. Eric Kemp-Benedict, 2012. "Price and Quantity Trajectories: Second-order Dynamics," Papers 1204.3156, arXiv.org.
  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.
  4. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 1998. "Price-Quantity Adjustment in a Keynesian Economy," Discussion Paper 1998-118, Tilburg University, Center for Economic Research.
  5. Elzen, Antoon van den & Kremers, Hans, 1999. "An adjustment process for nonconvex production economies," Serie Research Memoranda 0001, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  6. Herings, P. Jean-Jacques & van der Laan, Gerard & Venniker, Richard, 1996. "The Transition from a Drèze Equilibrium to a Walrasian Equilibrium," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1996013, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  7. Herings,P. Jean-Jacques, 2000. "Universally Stable Adjustment Processes - A Unifying Approach -," Research Memorandum 006, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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