# Equilibria in non regular economies

We know that in regular economies general equilibrium theory predicts a finite and odd number of equilibria, using the properties of the excess demand function and the index theorem.

How about the non-regular economies? From my understanding, these are the economies in which at least one price vector equilibirum generates a singular matrix of price effects. Geometrically, this can be interpreted as the excess demand function having a zero slope at one of the equilibria as shown in the picture below Can we say something more about the equilibria, in case they are a finite number? Do they need to be even, odd or there is no restriction?

• I am not sure what you mean by "regular economies". Could you please link to an exact definition? – Giskard Dec 9 '18 at 21:31
• On MWG p.591, a regular economy is defined as an economy where every equilibrium price vector is regular, i.e. the matrix of price effects Dz(p) is nonsingular, i.e. its rank is L-1 – PhDing Dec 9 '18 at 22:39
• According to the picture, such economies have a 'continuum' of equilibria - which implies that the number is infinite. However, I should admit that I am basing this answer simply on the graph you provide, not any prior knowledge. – user17900 Dec 13 '18 at 2:59

## 1 Answer

@Afreelunch gave you the right intuition. Non-regular economies will exhibit an infinite amount of equilibrium points. Intuitively since there is no local uniqueness, the continuum can be expressed as an interval on the real line so there is an infinite number of such points.