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

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**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?

**Exercise 3.3. Contract Curves**

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

*U*(*c*,*f*)*c*+

◼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?

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**Exercise 3.4. Social Welfare Functions**. **Solve Kreps, prob. 2 Chapter 5. Page 182,183 a&b.**

(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.)

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