Friday and Robenson Crusoe have identical utility functions described by the following table:

a. Assume that there are 8 oranges to be divided between Friday and Crusoe. Take a utilitarian view and assume that social welfare is the sum of the utilities of individuals. Using the data above, what is the social welfare level corresponding to each possible allocation of oranges? What allocation maximizes the social welfare? Show that the allocation that maximizes the welfare has the property that the marginal utility of an extra orange given to each individual is the same.

b. Now take a Rawlsian welfare view and find the social welfare level associated with each allocation of oranges. What allocation maximizes the social welfare.

c. Now assume that initially Crusoe has 6 oranges and Friday has 2. Assume that for every 2 oranges taken away from Crusoe, Friday gets only 1, indicating the loss of an orange in the process. Which of the feasible allocations maximizes the social welfare with a utilitarian social welfare function? With a Rawlsian welfare function? What general conclusion can you draw from this exercise?

Table 2.1: Utility Function of Friday and Crusoe 2 Number of Oranges Utility Level 1 11 21 30 4 38 5 45 3 6 48 7 50 8 51