**Exercise 3.1.**** **Benevolent Dictators

Two friends, Bob and Ann, cannot agree on how to spend the evening. To solve this problem, the ask a friend, Dan, to act as a benevolent dictator. There are four things to do.

{ Cinema Football Television Theatre }

Ann and Bob`s preferences are given by

*U**A*(Cinema)1*U **B*(Cinema)4

*U**A*(Football)3*U **B*(Football)1

*U**A*(Television)2.5*U **B*(Television)0.5

*U**A*(Theatre)1.5*U **B*(Theatre)2 Answer the following questions. (Hint: draw the set of feasible utilities)

◼Which options Dan *cannot *choose if he wants to be a benevolent dictator?

◼Which options should he choose to maximize a utilitarian Social Welfare Function?

◼Which options should he choose to maximize a Rawlsian Social Welfare Function?

◼Which option he *cannot *choose to maximize a Bergsonian social welfare function?

◼Among the options you just excluded, is the one which is Pareto efficient?

◼Change either Ann or Bob utility function so that you obtain different results. For example, can you change their utilities so that all SWF choose Theater?

Robinson and Friday consume coconuts and fish. They have 10 units of fish and 5units of coconuts. They have the same preferences that are represented by the following utility function

◼Draw the Edgeworth box and the corresponding contract curve. Be careful: the contract curve goes through the points in which Robinson or Friday consume the entire endowment of the two goods. The contract curve is also continuous...

◼Would it be correct to say that, within limits, there is a distribution of fish which is optimal, independently from the way we divide coconuts? What are these limits?

(Hint: before you do any calculation, sketch the level curve for the SWF of the exercise. You will see that these curves have a kink on the line in which the utilities of the two individuals are the same.)