Stability Questions and the Number of Equilibria

Abstract

Imagine an economy with two commodities only and assume that the demand for a good exceeds its supply if the price of the good tends to zero . If the economy is regular we see that the number c_o of locally stable equilibria exceeds the number c₁ of locally unstable equilibria by one . We have : c_o ≥ 1, c_o-c₁=1= x(s) ( cf. p.22 ) , because excess demand must be a gradient field on S if dim S= 1.