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On the number of critical equilibria separating two equilibria

Authors

  • Yves Balasko

    1. Department of Economics, University of York; yves.balasko@york.ac.uk
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    • The author is grateful to Ed Green and a referee for valuable comments and suggestions. He also gratefully acknowledges the hospitality of IMPA in Rio de Janeiro where part of this research was done.


Abstract

It is shown that two arbitrary equilibria in the general equilibrium model without sign restrictions on endowments can be joined by a continuous equilibrium path that contains at most two critical equilibria. This property is strengthened by showing that regular equilibria having an index equal to 1, a necessary condition for stability, can be joined by a path containing no critical equilibrium. These properties follow from the real-algebraic nature of the set of critical equilibria in any fiber of the equilibrium manifold.

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