In order to simplify their treatments-as we have seen in the course-some microeconomic models assume that firms don't exist. They model an exchange economy where there is only exchange from endowments, no production occurs, and all supply is from initial endowments. State the definition of competitive equilibrium and Pareto optimality that is appropriate for an exchange economy. Then prove the first fundamental theorem of welfare economics for an exchange economy. Use the same notation and make the same assumptions as in the Third Handout. Comment: Probably the most straightforward proof is a simple variant of the reductio ad absurdum proof from the Third Handout. However, in that handout I didn't include explanations of the two inequalities at the bottom of page 4 or the ten lines of algebra on page 5. Your answer will not require all of these lines, but should include explanations of any that you include