1. 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.

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) = Y^1/2, where Y is 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) = Y^1/5?

d. Suppose that Bill and Ted instead have different utility functions: Bills utility is given by U^B(Y) = Y^1/2, and Teds is given by U^T(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?