Sydney and Simon both like coffee and pie. Their utility functions are identical: ?where C? is the

Question:

Sydney and Simon both like coffee and pie. Their utility functions are identical: ?where C?is the number of cups of coffee and?P is the number of slices of pie.

Sydney?s and Simon?s allocations of coffee and pie are illustrated in the accompanying Edgeworth box. The current allocation of coffee and pie occurs at point?A: Simon has 2 cups of coffee and 3 slices of pie; Sydney has 4 cups of coffee and 6 slices of pie.

a. Is the current allocation of coffee and pie Pareto-optimal? How do you know?

b. Suppose that the social welfare function is given by?Show that the allocation at?A is less socially desirable than the allocation at?B.

c. Is the allocation at?B Pareto-optimal?

d. Comment: Just because an allocation is Pareto-efficient doesn?t mean it must produce the most welfare; just because a different allocation produces a lot of welfare doesn?t mean it is Pareto-efficient.