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HW 1 (+22) Models and Welfare 1. (+4) A policy outcome is Pareto efficient if no other policy outcome is Pareto superior to it. In a certain society, there are four possible policy outcomes, ??, ??,??, and ??, which give the following utilities to Abe, Betty, and Cindy, respectively. Which of these policy outcomes, if any, are Pareto efficient? ???? ???? ???? ?? 100 100 100 ?? 30 100 0 ?? 100 0 101 ?? 31 101 1 (+1) Is outcome ?? Pareto efficient? (+1) Is outcome ?? Pareto efficient? (+1) Is outcome ?? Pareto efficient? (+1) Is outcome ?? Pareto efficient? 2. (+2) A computerized carnival game chooses a real number ?? ∈ [0,100] at random from a uniform distribution (density function ??(??) = .01), and pays the player of the game ??(??) = ??2 dollars. If utility ??(??) = 2?? is linear in prize money, what is the expected utility ??�??�??(??)�� associated with this game? 3. (+8) Three friends, Alice, Bart, and Chris, agree to eat lunch together at a restaurant. There are three restaurants available for lunch: a diner (??), an ethnic restaurant (??), and a fast-food place (??). Taking prices into account, individual preferences over the three restaurant options are given by the following utility functions: ????(??) = 5 ????(??) = 5 ????(??) = 6 ????(??) = 6 ????(??) = 10 ????(??) = −2 ????(??) = 4 ????(??) = 3 ????(??) = 3 a. (+2) Rank the three restaurants according to the Utilitarian criterion. b. (+2) Rank the three restaurants according to the Rawlsian criterion. c. (+4) By the Pareto criterion, which is better, ?? or ??? ?? or ??? ?? or ??? 4. (+6) Describe an example of a policy that: a. (+2) A utilitarian planner favors but is not a Pareto improvement. b. (+2) A Rawlsian planner favors but is not a Pareto improvement. c. (+2) A utilitarian planner favors but a Rawlsian planner opposes. 5. (+2) How would you, personally, define a “good” or “bad” policy or policy outcome? Which of the social welfare functions that we discussed in class is closest to your personal definition? (Note: if you submit homework as a group, each should answer this question individually.) HW 1 (+22) Models and Welfare