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Uniqueness, Stability, and Comparative Statics in Rationalizable Walrasian Markets

  • Donald J. Brown
  • Chris Shannon
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 604)

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 tâtonnement. 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 ttonnement. 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 tâtonnement, equilibrium prices are locally unique and equilibrium comparative statics are locally monotone are not refutable with a finite data set.

Key words

Local stability Monotone demand Refutability Equilibrium Manifold 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Donald J. Brown
    • 1
  • Chris Shannon
    • 2
  1. 1.Yale UniversityNew Haven
  2. 2.University of California at BerkeleyBerkeley

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