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?
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?