A society has three types of individuals, type I (one person in this type), type II (90 persons in this type) and type III (9 persons in this type),...

1. A society has three types of individuals, type I (one person in this type), type II (90 persons in this type) and type III (9 persons in this type), and is considering two policies, x and y. The utility information of the three policies is given below: 

 Each of type I Each of type II  Each of type III                               

Policy x  0  25  10   

Policy y  180  28  10  

a). How would a utilitarian evaluate these two policies? Remember that there are 90 individuals of type II, one individual of type I and 9 individuals of type III. 

b). Suppose the one individual of type I is the wealthiest individual in the society, the 90 individuals of type II are the middle class, and the 9 individuals of type III are at the very bottom of the income ladder. Would this information change the answer to a) above? Why or why not? 

c). Suppose we have the following information about Policy x and Policy y:  

 Background: the person of type I has a huge firm that benefits him and other individuals in the society; the firm is currently in financial distress due to mismanagement on the part of the person of type I; without any help from other individuals, the firm is bound to fail.  

Policy x: given the above Background, Policy x is the proposal that no action is going to be taken to save the firm; as a consequence, the firm will fail, the type I individual will incur a huge loss (so that his utility will be 0), and each of the 90 individuals of type II will incur a modest loss (so that each will get a utility of 25), though each of type III will not be affected much (each's utility will remain at 10). 

Policy y: given the Background above, Policy y is the proposal that the big firm will be bailed out by the public; as a consequence, the firm will be saved, and the utilities of various individuals are given in the table above. 

Would the above information change the answer to a)? Why or why not? 

d). Suppose the trouble of the firm in c) is not due to mismanagement on the part of the person of type I, but due to the economy-wide recession which could not be anticipated. Suppose everything else remains the same as described in c). 

Would this change the answers to a) and to d)? Why or why not? 

e). (This is just for you to think a bit further and you are not required to answer this part.) Think about the Too-Big-To-Fail (TBTF) regulation practiced in many countries. "TBTF is a doctrine postulating that 

the government cannot allow very big firms (particularly major banks and financial institutions) to fail, for the very reason that they are big (and hence systemically important)." The regulation can be justified on the basis of systemic risk—the risk of adverse consequences of the failure of one firm for the underlying sector or the economy at large.  The possibility of bailing out (using taxpayers' money) a large firm to prevent its failure or limit the losses caused by the failure is often on the table for policy makers to adopt.  

Is it a good regulation? Why or why not?    

2. A society has two individuals, A and B, and is considering three policies x, y, and z. The individuals' utility information of the three policies are given below: 

  x y z  

Individual A     10 3 2 

Individual B 3 0 7 

a). Suppose you subscribe to a utility-based evaluation principle in assessing the three policies. Do you need any further information about the three policies? Why or why not? 

b). How would a utilitarian rank the three policies? Explain.  

c). Suppose that you have just learned some details about the three policies x, y and z: under policy x: A practices no religion, B practices religion ????, under policy y: A practices religion ????, B practices no religion, 

 under policy z: neither A nor B practice any religion.  

c.1) With these details about the three policies, would you agree with the utilitarian's assessment in b)? 

c.2) Would you think Sen's minimal liberalism applicable in ranking the three policies? Why or why not? 

c.3) If you use Sen's minimal liberalism and the weak Pareto principle, whenever possible, to rank the three policies, what would be the ranking? Do you observe Sen's liberal paradox in this case? 

d). Explain Sen's liberal paradox and its significance in policy evaluations. 

3. (This is more a review question than an exercise.) What are the problems of inclusion and the problems of exclusion of the utilitarian principle that we discussed in class? How would a utilitarian respond to and deal with those problems?     

4. A society has two individuals, A and B, and is considering two possible institutions x and y for the purpose of allocating recourses. The individuals' utility information from the outcomes of the two institutions are given below: 

  x y   

Individual A     5 5  

Individual B 6 6  

a). Suppose you subscribe to a utility-based evaluation principle in assessing the two institutions. Do you need any further information about the two institutions? Why or why not? How would you rank the two institutions in this case? 

b). Suppose that you have just learned some details about the two institutions: 

 x is the market system as we have discussed and have become to know, 

y is the "command system" in which each individual is `planned' by the planning board a bundle that happens to be her/his most preferred bundle (the planning board has all the information about individuals' preferences for the purpose of planning).  

c. With these details about the two institutions, would you change your ranking obtained in a)? Why or why not? 

5. Consider the following games played between two players, A and B.  

Game 1: A and B have reached a verbal agreement: A would deliver a case of beer to B, and B would deliver a bag of beer nuts to A. Now, each player needs to take an action: keep the promise (to deliver the goods), break the promise. If both keep their promises, then each player gets a payoff of 5; if both break their promises, then each player gets a payoff of 1; if one keeps the promise and the other breaks the promise, then the one who keeps the promise gets a payoff of 0 and the other gets a payoff of 8.  

Game 2: A and B have each deposited $1000 with a bank. The bank has invested these deposits in a long-term project. If both investors make withdrawals now then each receives $600; if only one investor makes a withdrawal now then that investor receives $1000, the other receives $200, and if neither investors makes a withdrawal now, then the project matures and each gets $1400. 

a). Illustrate the above two games in game tables. 

b). For each game, find Nash equilibrium outcomes. 

c). For each game, is there any inefficient Nash equilibrium outcome?  

c). Is either game a prisoner's dilemma game or a stag hunt game? Explain. 

d). From your analysis above, compare and contrast the role of the state in resolving an inefficient Nash equilibrium outcome.