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Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets

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Author Info
Donald J. Brown (Department of Economics, Yale University)
Chris Shannon (Department of Economics, University of California, Berkeley)

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Abstract

This paper studies the extent to which qualitative features of Walrasian equilibria are refutable given a finite data set. In particular, we consider the hypothesis that the observed data are Walrasian equilibria in which each price vector is locally stable under tatonnement. Our main result shows that a finite set of observations of prices, individual incomes and aggregate consumption vectors is rationalizable in an economy with smooth characteristics if and only if it is rationalizable in an economy in which each observed price vector is locally unique and stable under tatonnement. Moreover, the equilibrium correspondence is locally monotone in a neighborhood of each observed equilibrium in these economies. Thus the hypotheses that equilibria are locally stable under tatonnement, equilibrium prices are locally unique and equilibrium comparative statics are locally monotone are not refutable with a finite data set.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 9802003.

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Date of creation: 23 Feb 1998
Date of revision: 02 Mar 1998
Handle: RePEc:wpa:wuwpge:9802003

Note: LaTex .dvi, This is an version updated Feb 1998.
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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
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

References listed on IDEAS
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  1. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August. [Downloadable!] (restricted)
  2. Quah, J-K-H, 1996. "The Monotonicity of Individual and Market Demand," Economics Papers 127, Economics Group, Nuffield College, University of Oxford.
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  3. Chiappori, Pierre-Andre & Rochet, Jean-Charles, 1987. "Revealed Preferences and Differentiable Demand: Notes and Comments," Econometrica, Econometric Society, vol. 55(3), pages 687-91, May. [Downloadable!] (restricted)
  4. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November. [Downloadable!] (restricted)
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  5. Herbert E. Scarf, 1959. "Some Examples of Global Instability of the Competitive Equilibrium," Cowles Foundation Discussion Papers 79, Cowles Foundation, Yale University. [Downloadable!]
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(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. P.A. Chiappori & I. Ekeland & F. Kubler & H.M. Polemarchakis, 2002. "Testable Implications of General Equilibrium Theory: a differentiable approach," Working Papers 2002-10, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  2. Fabrice Talla Nobibon & Laurens Cherchye & Bram De Rock & Jereon Sabbe & Frederic Vermeulen, 2008. "Heuristics for Deciding Collectively Rational Consumption Behavior," ECARES Working Papers 2008_028, Université Libre de Bruxelles, Ecares. [Downloadable!]
    Other versions:
  3. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2008. "The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery and Welfare Analysis," ECARES Working Papers 2008_029, Université Libre de Bruxelles, Ecares. [Downloadable!]
    Other versions:
  4. Donald J. Brown & Ravi Kannan, 2005. "Two Algorithms for Solving the Walrasian Equilibrium Inequalities," Cowles Foundation Discussion Papers 1508R, Cowles Foundation, Yale University, revised Oct 2006. [Downloadable!]
    Other versions:
  5. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2008. "An Afriat Theorem for the Collective Model of Household Consumption," IZA Discussion Papers 3794, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  6. Anat Bracha & Donald J Brown, 2007. "Affective Decision Making: a Behavioral Theory of Choice," Levine's Bibliography 122247000000001676, UCLA Department of Economics. [Downloadable!]
  7. Donald J. Brown & Ravi Kannan, 2005. "Decision Methods for Solving Systems of Walrasian Inequalities," Cowles Foundation Discussion Papers 1508, Cowles Foundation, Yale University. [Downloadable!]
  8. Anat Bracha & Donald J. Brown, 2007. "Affective Decision Making: A Behavioral Theory of Choice," Cowles Foundation Discussion Papers 1633, Cowles Foundation, Yale University. [Downloadable!]
  9. Donald J. Brown & Ravi Kannan, 2003. "Indeterminacy, Nonparametric Calibration and Counterfactual Equilibria," Cowles Foundation Discussion Papers 1426, Cowles Foundation, Yale University. [Downloadable!]
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