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

<p>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 <a href="https://i.sstatic.net/nXcte.jpg" rel="nofollow noreferrer"><img src="https://i.sstatic.net/nXcte.jpg" alt="enter image description here"></a></p>

<p>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? </p>

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2018-12-09T21:31:32.900Z
I am not sure what you mean by "regular economies". Could you please link to an exact definition?
Giskard
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2018-12-09T22:39:27.580Z
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
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<general-equilibrium><competitive-equilibrium>
Equilibria in non regular economies
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# Equilibria in non regular economies

(Asked by: username_0 on 2018-12-09)

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 [![enter image description here](https://i.sstatic.net/nXcte.jpg)](https://i.sstatic.net/nXcte.jpg)

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?

**Tags:** general-equilibrium, competitive-equilibrium

> **Comments:**
> **username_1**: I am not sure what you mean by "regular economies". Could you please link to an exact definition?  
> **username_0**: 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  

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