Economics question

4. This question concerns the existence of competitive equilibrium in an economy specified by its aggregate excess demand function. [30 points] (a) What mathematical tool is used to show that an economy with more than two commodities has a competitive equilibrium? Name and state the theorem. [15 points] (b) Briefly explain the role of the theorem in part (a) in the proof. Do not give a complete proof of the theorem, just discuss the role of the mathematical result you stated in part (a). [15 points]