Consider Bill and Ted, the two citizens in the country of Adventure land described in Problem 9 from Chapter 1. Suppose that Bill and Ted have the same utility function U(Y) = Y1/2, where Y is consumption (which is equal to net income).

a. Rank the three tax policies discussed in Problem 9 from Chapter 1 for a utilitarian social welfare function. Rank the three for a Rawlsian social welfare function.

b. How would your answer change if the utility function was instead U(Y) = Y1/5?

c. Suppose that Bill and Ted instead have different utility functions: Bill’s utility is given by UB(Y) = ¼ Y1/2, and Ted’s is given by UT(Y) = Y1/2. (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?