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The Transition from a Drze Equilibrium to a Walrasian Equilibrium

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Author Info
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)

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Abstract

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
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Handle: RePEc:ctl:louvir:1996013

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Related research
Keywords: Adjustment processes; price rigidities; simplicial algorithms;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C68 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computable General Equilibrium Models
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Keisler, H Jerome, 1995. "Approximate Tatonnement Processes," Economic Theory, Springer, vol. 5(1), pages 127-73, January.
  2. Day, Richard H. & Pianigiani, Giulio, 1991. "Statistical dynamics and economics," Journal of Economic Behavior & Organization, Elsevier, vol. 16(1-2), pages 37-83, July. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. Laroque, G, 1981. "A Comment on "Stable Spillovers among Substitutes."," Review of Economic Studies, Blackwell Publishing, vol. 48(2), pages 355-61, April. [Downloadable!] (restricted)
  6. Movshovich, Solomon M., 1994. "A price adjustment process in a rationed economy," Journal of Mathematical Economics, Elsevier, vol. 23(4), pages 305-321, July. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. Mukherji, Anjan, 1995. "A Locally Stable Adjustment Process," Econometrica, Econometric Society, vol. 63(2), pages 441-48, March. [Downloadable!] (restricted)
  9. Herings, P.J.J., 1994. "A Globally and Universally Stable Quantity Adjustment Process for an Exchange Economy with Price Rigidities," Discussion Paper 111, Tilburg University, Center for Economic Research. [Downloadable!]
  10. Veendorp, E C H, 1975. "Stable Spillovers among Substitutes," Review of Economic Studies, Blackwell Publishing, vol. 42(3), pages 445-56, July. [Downloadable!] (restricted)
  11. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September. [Downloadable!] (restricted)
  12. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation, Yale University. [Downloadable!]
  13. Keisler, H Jerome, 1996. "Getting to a Competitive Equilibrium," Econometrica, Econometric Society, vol. 64(1), pages 29-49, January. [Downloadable!] (restricted)
  14. Kamiya, Kazuya, 1990. "A Globally Stable Price Adjustment Process," Econometrica, Econometric Society, vol. 58(6), pages 1481-85, November. [Downloadable!] (restricted)
  15. Van Der Laan, G. & Talman, A. J. J., 1987. "A convergent price adjustment process," Economics Letters, Elsevier, vol. 23(2), pages 119-123. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Herings, P.J.J. & Elzen, A. van den, 1998. "Computation of the Nash equilibrium selected by the tracing procedure in n-person games," Discussion Paper 4, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Herings, P.J.J. & Laan, G. van der & Talman, D., 1998. "Price-quantity adjustment in a Keynesian economy," Discussion Paper 118, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  3. Herings,P. Jean-Jacques, 2002. "Universally Stable Adjustment Processes - A Unifying Approach -," Research Memoranda 006, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
    Other versions:
  4. Sander van der Hoog, 2004. "Credit and Cash-in-Advance in Disequilibrium Models," Computing in Economics and Finance 2004 294, Society for Computational Economics. [Downloadable!]
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