1. a. Explain why indifference curves slope downward and are convex to the origin. b. What would your consumption of, say, hamburgers and sweet tea be if your indifference curve for hamburgers and sweet tea was concave to the origin? 2. Using indifference analysis and income constraints (use mathematical equations as well), explain why you don't just eat lobster every day for breakfast, lunch, and dinner. (Assuming you love lobster. If you don't, substitute lobster with something else that is expensive and that you like to consume.) 3. Suppose Nathan's budget constraint is based on him having $50 to spend on movie theater tickets and Chick-fil-A sandwiches. Movie theater tickets are on the x-axis and the sandwiches are on the y-axis. If for $10 Nathan buys a movie theater ticket, which moves him to a point on his indifference curve where he is maximizing his utility, and the marginal rate of substitution is 2.5, what must be the price of Chick- fil-A sandwiches? 4. Suppose your state was considering a tax in order to increase spending on education. If maximizing utility in light of this tax (i.e., you cannot stop it from passing or avoid paying it) was your only concern, would you rather be taxed a percentage of your income or assessed a lump sum tax assessed on each household? Why?