State the First Welfare Theorem (FWT). What are the implicit assumptions? What is the importance of the FWT? (5 points) 2. State the Second Welfare Theorem (SWT). What are the implicit assumptions? What is the importance of SWT? (5 points) 3. Optimal choice - 15 points Suppose that a consumer's income is 100 dollars which can be spent on either food (x) or clothes (y). One unit of food costs px and a unit of clothes costs py dollars, where px = 2 and py = 5 dollars. Suppose that consumer's preferences can be represented by a utility function