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Equilibria with coordination failures

Author Info

  • Herings, P. Jean-Jacques
  • van der Laan, Gerard
  • Talman, Dolf

Abstract

This paper extends the literature on equilibria with coordination failures to arbitrary convex sets of admissible prices. This makes it possible to address coordination failures for cases with price indexation or more general price linkages between commodities. We introduce a new equilibrium concept, called quantity constrained equilibrium (QCE), giving a unified treatment to all cases considered in the literature so far. At a QCE the expected trade opportunities on supply and demand are completely determined by a rationing vector satisfying that the prevailing price system maximizes the value of the rationing vector within the set of admissible prices. When the set of admissible prices is compact, we show the existence of a connected set of QCEs. This set connects two trivial no-trade equilibria, one with completely pessimistic expectations concerning supply opportunities and one with completely pessimistic expectations concerning demand opportunities. Moreover, the set contains for every commodity a generalized Drèze equilibrium, being a QCE at which for that commodity no binding trade opportunities on both supply and demand are expected, and also a generalized supply-constrained equilibrium at which no binding constraints on demand opportunities are expected and for at least one commodity also not on supply. We apply this main result to several special cases, and also discuss the case of an unbounded set of admissible prices.

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

Volume (Year): 45 (2009)
Issue (Month): 1-2 (January)
Pages: 23-37

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Handle: RePEc:eee:mateco:v:45:y:2009:i:1-2:p:23-37
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

Keywords: Exchange economy Rationing Coordination failures Price rigidities;

Other versions of this item:

Find related papers by 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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  1. P. J. J. Herings & H. M. Polemarchakis, 2003. "Pareto Improving Price Regulation When the Asset Market is Incomplete," Discussion Papers 03-20, University of Copenhagen. Department of Economics.
  2. Gérard Debreu (ed.), 1996. "General Equilibrium Theory," Books, Edward Elgar Publishing, volume 0, number 548.
  3. Kurz, Mordecai, 1982. "Unemployment equilibrium in an economy with linked prices," Journal of Economic Theory, Elsevier, vol. 26(1), pages 100-123, February.
  4. Alessandro Citanna & Hervé Crès & Jacques H. Drèze & Jean-Jacques Herings & Antonio Villanacci, 2001. "Continua of Underemployment Equilibria Reflecting Coordination Failures, Also at Walrasian Prices," Working Papers hal-00597197, HAL.
  5. DREZE, Jacques & GOLLIER, Christian, . "Risk sharing on the labour market and second-best wage rigidities," CORE Discussion Papers RP 1073, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. 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.
  7. Dehez, Pierre & Dreze, Jacques H., 1984. "On supply-constrained equilibria," Journal of Economic Theory, Elsevier, vol. 33(1), pages 172-182, June.
  8. 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.
  9. P. Jean-Jacques Herings, 1995. "Equilibrium existence results for economies with price rigidities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 63-80.
  10. Weddepohl, Claus, 1987. "Supply-constrained equilibria in economies with indexed prices," Journal of Economic Theory, Elsevier, vol. 43(2), pages 203-222, December.
  11. Herings, P.J.J. & Talman, A.J.J. & Zang, Z., 1994. "The computation of a continuum of constrained equilibria," Discussion Paper 1994-38, Tilburg University, Center for Economic Research.
  12. 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.
  13. 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).
  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. 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. Roberts, John, 1987. "An Equilibrium Model with Involuntary Unemployment at Flexible, Competitive Prices and Wages," American Economic Review, American Economic Association, vol. 77(5), pages 856-74, December.
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