Theoretical Economics, Volume 7, Number 1 (January 2012)

Theoretical Economics 7 (2012), 163–181

On the number of critical equilibria separating two equilibria

Yves Balasko


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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