1. Assume that Crusoe and Friday have identical utility functions described by the following table.

Utility Functions for Friday and Crusoe

NUMBER OF ORANGES UTILITY MARGINAL UTILITY

11 1

22 1

33 0

43 8

54 5

64 8

75 0

85 1

Draw the utility function. Fill in the marginal utility data in the table above, and draw the marginal utility function.

2. Assume that there are eight oranges to be divided between Friday and Crusoe. Take a utilitarian viewassume that social welfare is the sum of the utilities of the two individuals. Using the data from Problem 1, what is the social welfare corresponding to each possible allocation of oranges? What allocation maximizes social welfare? Show that it has the property that the marginal utility of an extra orange given to each individual is the same.

3. Now take a Rawlsian view and assume that the social welfare function is the level of utility of the individual with the lowest utility level. Using the data from Problem 1, and again assuming there are eight oranges, what is the social welfare associated with each allocation of oranges? What allocation maximizes social welfare?

4. Draw the utility possibilities schedule based on the data from Problem 1. Mark the points that maximize social welfare under the two alternative criteria from Problems 2 and 3.

5. Assume that Crusoe's and Friday's utility functions are described in Problem 1. Assume now, though, that initially Crusoe has six oranges and Friday two. Assume that for every two oranges taken away from Crusoe, Friday gets only one, an orange being lost in the process. What does the utility possibilities schedule look like now? Which of the feasible allocations maximizessocial welfare with a utilitarian social welfare function? With a Rawlsian social welfare function?