Theoretical Economics 7 (2012), 163–181

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### On the number of critical equilibria separating two equilibria

*Yves Balasko*

#### 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 one, 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.

Keywords: Equilibrium prices, equilibrium manifold, equilibrium path, critical equilibrium, catastrophe

JEL classification: D41, D51

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