13. The country of Adventureland has two citizens, Bill and Ted. Bill has a private legal business. He earns $50 per hour. At a tax rate of 0%, Bill works 20 hours per week. At a 25% tax rate he works only 15 hours per week, and at a 40% tax rate he works only 8 hours per week. Ted works a manufacturing job. He works 20 hours per week and earns $6 per hour, regardless of the tax rate. The government is considering imposing an income tax of either 25% or 40% on Bill and using the revenues to make transfer payments to Ted. The accompanying table summarizes the three possible policies. 0% 25% 40% Bill's pretax income $1000 $800 $400 Bill's taxes 0 $200 Bill's net income $1,000 $600 Ted's preetnx income $120 $ 120 Ted's transfer payment 0 $200 Ted's net income 5120 $320 $280 a. Compare the three policies. Are any of the policies obviously less than optimal? Now suppose that Bill and Ted have the same utility function U(Y) = Y1f2, where Yis consumption (which is equal to net income). b. Rank the three tax policies discussed in part (a) for a Rawlsian social welfare function. Rank the three for a utilitarian social welfare function. c. How would your answer change if the utility function was instead U(Y) = Y1I5? d. Suppose that Bill and Ted instead have different utility functions: Bill's utility is given by UB(Y) = 'AYHZ. and Ted's is given by LIT-(Y) = Y1\". (This might happen, for example, because Bill has signicant disabilities and therefore needs more income to get the same level of utility.) How would a Rawlsian rank the three tax policies now