HW XXXXXXXXXXModels and Welfare
XXXXXXXXXXA 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,
espectively. Which of these policy outcomes, if any, are Pareto efficient?
???? ???? ????
?? XXXXXXXXXX
?? XXXXXXXXXX
?? XXXXXXXXXX
?? XXXXXXXXXX
(+1) Is outcome ?? Pareto efficient?
(+1) Is outcome ?? Pareto efficient?
(+1) Is outcome ?? Pareto efficient?
(+1) Is outcome ?? Pareto efficient?
XXXXXXXXXXA computerized carnival game chooses a real number ?? ∈ [0,100] at
andom 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?
XXXXXXXXXXThree friends, Alice, Bart, and Chris, agree to eat lunch together at a
estaurant. There are three restaurants available for lunch: a diner (??), an ethnic
estaurant (??), 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.
. (+2) Rank the three restaurants according to the Rawlsian criterion.
c. (+4) By the Pareto criterion, which is better, ?? or ??? ?? or ??? ?? or ???
XXXXXXXXXXDescribe an example of a policy that:
a. (+2) A utilitarian planner favors but is not a Pareto improvement.
. (+2) A Rawlsian planner favors but is not a Pareto improvement.
c. (+2) A utilitarian planner favors but a Rawlsian planner opposes.
XXXXXXXXXXHow 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 XXXXXXXXXXModels and Welfare