On the number of critical equilibria separating two equilibria - Yves Balasko (Theoretical Economics, 2012)
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: D41; D51; 330; Equilibrium prices; equilibrium manifold; equilibrium path; critical equilibrium; catastrophe