Economics question

1. State Brouwer's Fixed Point Theorem; your answer should at least implicitly define a xed point in the setting of this theorem. 2. For each of the conditions you listed in the assumptions for Brouwer's Fixed Point Theorem, give an example that violates that assumption only and fails to have a fixed point. 3. Explain how Brouwer's Fixed Point Theorem can be sued to show that an economy specified by an aggregate excess demand function has an equilibrium price vector. Note that you are not asked to prove the theorem. 4. Discuss the following statement in terms of whether you agree or disagree and why: Regardless of how many commodities there are, existence of competitive equilibrium isn't a problem provided that the excess demand function for each good is continuous and satisfies the property that it's very large for low prices and very negative for high prices, you just need to nd a price where the excess demand function crosses the axis (or becomes zero) for each market in turn