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The Transition from a Drèze Equilibrium to a Walrasian Equilibrium

  • Herings, P. Jean-Jacques

    (UNIVERSITE CATHOLIQUE DE LOUVAIN, Institut de Recherches Economiques et Sociales (IRES))

  • van der Laan, Gerard

    (Free University, Department of Economics and Tinbergen Institute, Amsterdam)

  • Venniker, Richard

    (Free University, Department of Economics and Tinbergen Institute, Amsterdam)

In this paper a continuous time price and quantity adjustment process is considered for an economy facing price rigidities. In the short run prices are assumed to be completely fixed and the markets are cleared by quantity adjustments until a fixed price equilibrium is reached where every market is typically characterized by either supply rationing or demand rationing. Next prices are assumed to move upwards in case of demand rationing on a market and downwards when supply rationing occurs. Markets are kept in equilibrium by infinitesimal quantity adjustments such that at every moment in time a fixed price equilibrium results. Using only standard assumptions on the primitive concepts of the economy it is shown that the price and quantity adjustment process indeed converges to a fixed price equilibrium for the initially given prices. Moreover, in the long run, when prices are allowed to change, the process is shown to reach a Walrasian equilibrium. A simplicial algorithm is developed to approximate the price and quantity adjustment process arbitrarily close. It is shown that the path of price systems and rationing schemes generated by the algorithm converges to the path of the adjustment process.

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Paper provided by Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES) in its series Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) with number 1996013.

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Length: 32
Date of creation: 01 Apr 1996
Date of revision:
Handle: RePEc:ctl:louvir:1996013
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  1. Herings, Jean-Jacques & van der Laan, Gerard & Talman, Dolf & Venniker, Richard, 1997. "Equilibrium adjustment of disequilibrium prices," Journal of Mathematical Economics, Elsevier, vol. 27(1), pages 53-77, February.
  2. van der Laan, G. & Talman, A.J.J., 1987. "A convergent price adjustment process," Other publications TiSEM 0271830c-c03d-46a1-ae6f-f, Tilburg University, School of Economics and Management.
  3. repec:dgr:kubcen:1994111 is not listed on IDEAS
  4. Veendorp, E C H, 1975. "Stable Spillovers among Substitutes," Review of Economic Studies, Wiley Blackwell, vol. 42(3), pages 445-56, July.
  5. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical Dynamics and Economics," Working Paper Series 293, Research Institute of Industrial Economics.
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  7. Herings, P.J.J., 1994. "A globally and universally stable quantity adjustment process for an exchange economy with price rigidities," Discussion Paper 1994-111, Tilburg University, Center for Economic Research.
  8. repec:dgr:kubcen:199452 is not listed on IDEAS
  9. Jean-Jacques Herings, P., 1997. "A globally and universally stable price adjustment process," Journal of Mathematical Economics, Elsevier, vol. 27(2), pages 163-193, March.
  10. Keisler, H Jerome, 1995. "Approximate Tatonnement Processes," Economic Theory, Springer, vol. 5(1), pages 127-73, January.
  11. 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.
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  13. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  14. repec:dgr:kubrem:1982118 is not listed on IDEAS
  15. Movshovich, Solomon M., 1994. "A price adjustment process in a rationed economy," Journal of Mathematical Economics, Elsevier, vol. 23(4), pages 305-321, July.
  16. Doup, T.M. & Talman, A.J.J., 1987. "A new simplicial variable dimension algorithm to find equilibria on the product space of unit simplices," Other publications TiSEM 398740e7-fdc2-41b6-968f-4, Tilburg University, School of Economics and Management.
  17. Keisler, H Jerome, 1996. "Getting to a Competitive Equilibrium," Econometrica, Econometric Society, vol. 64(1), pages 29-49, January.
  18. repec:cup:cbooks:9780521265140 is not listed on IDEAS
  19. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July.
  20. repec:dgr:kubrem:1985174 is not listed on IDEAS
  21. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.
  22. 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.
  23. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November.
  24. Mukherji, Anjan, 1995. "A Locally Stable Adjustment Process," Econometrica, Econometric Society, vol. 63(2), pages 441-48, March.
  25. repec:ner:tilbur:urn:nbn:nl:ui:12-148734 is not listed on IDEAS
  26. Laroque, G, 1981. "A Comment on "Stable Spillovers among Substitutes."," Review of Economic Studies, Wiley Blackwell, vol. 48(2), pages 355-61, April.
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