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 16 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. Suppose that Bill and Ted have the same utility function U(Y) = Y 1/2 , where Y is consumption (which is equal to net income). Effects of Redistributive Policies in Adventureland on Incomes 0% 25% 40% Bill's pre-tax income $1,000 $800 $400 Bill's taxes 0 $200 $160 Bill's net income $1,000 $600 $240 Ted's pre-tax income $120 $120 $120 Ted's transfer payment 0 $200 $160 Ted's net income $120 $320 $280 1) Compare the three policies. Are any of the policies obviously less than social optimal? 2) Rank the three tax policies discussed in part (1) for a Rawlsian social welfare function. Rank the three for a utilitarian social welfare function. 3) How would your answer change if the utility function was instead U(Y) = Y 1/5? 4) Suppose that Bill and Ted instead have different utility functions: Bill's utility function is given by UB (Y) = Y 1/2, and Ted's is given by UT (Y) = Y 1/2. (This might happen, for example, because Bill has significant disabilities and therefore needs more income to get the same level of utility.) How would a Rawlsian rank the three tax policies now?