# Arrow-Debreu model of general equilibrium having many equilibria

I am just beginning to study some stuffs outside introductory/sophomore(?) micro/macroeconomics. And I met with a stuff called Arrow-Debreu model.

The question is,

1) What would be the proof that Arrow-Debreu model has many equilibra in general case? Can anyone also explain the criteria required for the model to have a unique equilibrium? (thorough explanation would be appreciated)

2) Can introductory model of basic supply and demand curve/model (so not Arrow-Debreu model, but the model used for economics beginners) have many equilibria? I do not think so, but unsure. If not, or if so, can anyone show me the proof?

Edit:

3) Can anyone also thoroughly explain what Sonnenschein-Mantel-Debreu theorem is mathematically?

4) If a model has many equilibria, does this mean that the model has unstable solutions?

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2. No there cannot be multiple equilibria under the usual assumption that demand is strictly decreasing in price and supply strictly increasing. If the supply equals demand, we have $S(p)-D(p)=0$ and $S-D$ is a strictly increasing function which cannot have more than one zero.