Assume that Friday and Crusoe have identical utility functions described by the following table. Number of Oranges Utility Marginal Utility
1 11
2 21
3 30
4 38
5 45
6 48
7 50
8 51
(1) Assume that there are eight oranges to be divided between Friday and Crusoe. Take a utilitarian view. What is the social welfare corresponding to each possible allocation of orange? What allocation maximizes the utilitarian social welfare? Show that it has the property that the marginal utility of an orange given to each individual is the same.
(2) Now take a Rawlsian view while assuming again that there are eight oranges to be divided between Friday and Crusoe. What is the social welfare corresponding to each possible allocation of orange? What allocation maximizes the Rawlsian social welfare?
(3) Now assume that initially, Crusoe has six oranges and Friday two. Assume also that for every two oranges taken from Crusoe, Friday gets only one, an orange being lost in the process. What does the utility possibility frontier look like now? Which of the feasible allocations maximizes social welfare with a utilitarian social welfare function? Which of the feasible allocations maximizes social welfare with a Rawlsian social welfare function?