Short Answer 1: Consumer Theory Under Perfect Competition, Tax Policy. 30 points all together. In class we learned to evaluate Whether a consumer with well-behaved preferences is better off from a lump sum tax or a quantity tax (conditional on the same amount of government revenue raised). In this problem, we will explore the meaning of well-behaved preferences and its relation to tax policy. Assume Daryl has the following utility functiOn U = (x1 10:)2 (x2 1002 a.. Graph a representative indifference curve, show several arrows over which preferences are increasing. [5 points] b. Are Daryl's preferences convex? Use the graph above and the denition of convexity to clearly demonstrate why or why not. [5 points] c. Now we will consider optimization and tax policy. Assuming Daryl has the above utility function but faces the following prices and income: p1 = 1, p2 = 1, m = 8. c.i. Solve for Daryl's optimal bundle? Explain the relation with where Daryl optimizes on the indifference curve and well-behaved preferences in a sentence. [5 points] cii. Does he prefer a lump sum tax of 1 dollar, or a per unit tax that raises the same level of revenue or is he indifferent between the two? Explain in a sentence using what you know about tax theorylS points] d. Instead, Assume Daryl has the same utility function as above but faces the following prices and income: p1 = 1, p2 = 1, m = 30. d.i. Solve for Daryl's optimal bundle. What type of preferences does Daryl have that ensures this must be the optimal bundle in this case? [5 points] dii. Does Daryl prefer a lump sum tax of 1 dollar, or per unit tax on good 1 that raises the same level of revenue, or is he indifferent between the two? Explain in a sentence [5 points]