ECO 330T Final Exam

Jill and Bill sign a contract to make pudding and sell it at concerts for a total revenue of $2000, which they will split evenly. Jill will provide the pudding (at a cost of $500), and Bill will provide the bowls and spoons (at a cost of $100). After Jill spends $500 on pudding, Bill breaches the contract by not providing the bowls and spoons. In this case, how much are expectation damages?

$1000

Elephant, Hippo, Zebra, and Mouse must build a bridge strong enough to carry each of them, which costs $18,000. A bridge strong enough to carry Mouse (but not any of the others) would cost $8000. A bridge strong enough to carry Mouse or Zebra (but not any of the others) would cost $11,000. A bridge strong enough to carry Mouse, Zebra, or Hippo (but not Elephant) would cost $13,000. According to the Shapley value, what is Mouse's fair share of the $18,000 cost?

$2000

Hank, Iris, and Jo must split the $110 cost of sharing a taxi that drops them all at their homes. A taxi would cost $60 for Hank alone, $50 for Iris alone, and $50 for Jo alone. A taxi for would cost $80 for Hank and Iris together, $90 for Iris and Jo together, and $100 for Hank and Jo together. According to the Shapley value, what is Iris's fair share of the $110?

$30

Hank, Iris, and Jo must split the $110 cost of sharing a taxi that drops them all at their homes. A taxi would cost $60 for Hank alone, $50 for Iris alone, and $50 for Jo alone. A taxi for would cost $80 for Hank and Iris together, $90 for Iris and Jo together, and $100 for Hank and Jo together. According to the Shapley value, what is Hank's fair share of the $110?

$40

Elephant, Hippo, Zebra, and Mouse must build a bridge strong enough to carry each of them, which costs $18,000. A bridge strong enough to carry Mouse (but not any of the others) would cost $8000. A bridge strong enough to carry Mouse or Zebra (but not any of the others) would cost $11,000. A bridge strong enough to carry Mouse, Zebra, or Hippo (but not Elephant) would cost $13,000. According to the Shapley value, what is Hippo's fair share of the $18,000 cost?

$4000

Jill and Bill sign a contract to make pudding and sell it at concerts for a total revenue of $2000, which they will split evenly. Jill will provide the pudding (at a cost of $500), and Bill will provide the bowls and spoons (at a cost of $100). After Jill spends $500 on pudding, Bill breaches the contract by not providing the bowls and spoons. In this case, how much are reliance damages?

$500

There are 220 voters who must be put into 20 congressional districts of equal size. There are two political parties, Up and Down. Each congressional district chooses its winning party using majority voting. 66 of the voters prefer the Up party and 154 prefer the Down party. 1) If we assign voters to district in such a way as to maximize the number of districts that choose the Up party, how many of the districts will choose Up? 2) If we assign voters to district in such a way as to maximize the number of districts that choose the Down party, how many of the districts will choose Down?

1) 11 2) 20

We have 15 voters and four alternatives, and the individual preference lists are as follows: Voters 1-3: a d b c Voters 4-5: b d a c Voters 6-7: c d a b Voters 8-9: a d c b Voters 10-11: b d c a Voters 12-13: c d b a Voters 14-15: d b a c 1) The plurality voting procedure? 2) The Condorcet procedure? 3) The Hare (instant runoff) system? 4) The Borda count procedure? 5) Sequential pairwise voting with agenda bdac?

1) A 2) D 3) B 4) D 5) D

Phyllis values each painting at $200 and each statuette at $300. Quincy values each painting at $400 and each statuette at $100. Randolph values each painting at $300 and each statuette at $200. Consider the following three allocations: -Allocation 1: Phyllis has 5 paintings and 2 statuettes, Quincy has 2 paintings and 5 statuettes, and Randolph has 1 painting and 1 statuette. -Allocation 2: Phyllis has 1 painting and 1 statuette, Quincy has 5 paintings and 2 statuettes, and Randolph has 2 paintings and 5 statuettes. -Allocation 3: Phyllis and Randolph have nothing, Quincy has 8 paintings and 8 statuettes. 1) Rank the three allocations according to the Rawlsian criterion. 2) Rank the three allocations according to the total surplus criterion. 3) Rank the three allocations according to the Pareto criterion.

1) Allocation 3 is the worst, Allocations 1 and 2 are tied. 2) Allocation 2 is the best, then Allocation 3, then Allocation 1. 3) No allocation Pareto dominates another.

Lemur, Monkey, and Chimpanzee must decide how to split up the three bedrooms (red, blue, and yellow) in the house that they are renting. -Lemur values the red bedroom at $700, the blue bedroom at $400, and the yellow bedroom at $100. -Monkey values the red bedroom at $500, the blue bedroom at $100, and the yellow bedroom at $300. -Chimpanzee values the red bedroom at $300, the blue bedroom at $200, and the yellow bedroom at $100. The bedrooms are indivisible. No animal can use more than one bedroom. (That is, the marginal value of a second or third bedroom is $0.) 1) Which of the following splits is efficient? 2) Now suppose that the rent for the different bedrooms is different: the rent on the red bedroom is $300, the rent on the blue bedroom is $100, and the rent on the yellow bedroom is $100. Which of the following splits is envy-free?

1) Lemur gets the blue bedroom, Monkey gets the red bedroom, and Chimpanzee gets the yellow bedroom. 2) Lemur gets the red bedroom, Monkey gets the yellow bedroom, and Chimpanzee gets the blue bedroom.

Ray, Brianna, and Ned must divide a ring, a brooch, a necklace, and a hat. They assign points to each item as follows: Ray: ring 35, brooch 17, necklace 30, hat 18. Brianna: ring 20, brooch 50, necklace 20, hat 10. Ned: ring 30, brooch 14, necklace 35, hat 21. 1) Which of the following splits is envy-free? 2) Which of the following splits is efficient? 3) Which of the following splits is equitable?

1) None of these splits are envy-free. 2) Ray gets the ring and the hat, Brianna gets the brooch, and Ned gets the necklace. 3) None of these splits are equitable.

There are 100 voters and three alternative restaurants: Dylan's Pizza, Elise's Thai, and Frank's Fish. In Situation 1, the individual preference lists are as follows: Voters 1-49: Dylan's Pizza, Frank's Fish, Elise's Thai Voters 50-75: Elise's Thai, Dylan's Pizza, Frank's Fish Voters 76-100: Frank's Fish, Elise's Thai, Dylan's Pizza Situation 2, the individual preference lists are as follows: Voters 1-47: Dylan's Pizza, Frank's Fish, Elise's Thai Voters 48-49: Frank's Fish, Dylan's Pizza, Elise's Thai Voters 50-75: Elise's Thai, Dylan's Pizza, Frank's Fish Voters 76-100: Frank's Fish, Elise's Thai, Dylan's Pizza 1) We can use those two situations to demonstrate which of the following statements? 2) We can also use those two situations to demonstrate which of the following statements? 3) We can also use those two situations to demonstrate which of the following statements?

1) The Hare (instant runoff) system fails to satisfy the monotonicity property. 2) The Condorcet procedure fails to satisfy the Always a Winner property. 3) The Hare (instant runoff) system is manipulable: in Situation 1 Voter 1 would get a better outcome for himself by falsely reporting that his preference list is Frank's Fish, Dylan's Pizza, Elise's Thai.

Voter 1: a b c d Voter 2: c a b d Voter 3: b d c a The social choice procedure being used is sequential pairwise voting with a fixed agenda, and you have agenda-setting power (that is, you get to choose the order). 1) What order should you choose if you want alternative c to be the social choice? 2) Which alternative does NOT arise as the social choice for ANY order?

1) a vs. b, then winner vs. d, then winner vs. c. 2) d

We have 11 voters and four alternatives, and the individual preference lists are as follows: Voters 1-3: a c d b Voters 4-5: b d a c Voters 6-7: d b c a Voters 8-9: c d a b Voter 10: b d a c Voter 11: a d b c 1) The Condorcet procedure? 2)The Hare (instant runoff) system?

1) d 2) a

Alfred's copy of "The Untold Legend of the Batman," which is autographed by Batman, is worth $1000 to Alfred and $5000 to Joe Chill. Unless Alfred buys a fancy safe that costs $300, Joe Chill is able to take the book. Suppose that Alfred has a liability right over the book. That is, Joe Chill chooses whether or not to take the book (unless Alfred prevents him by buying the safe), but he must compensate Alfred for the consequences of his choice. However, there are litigation problems. In particular, the court is mistaken about the value of the book to Alfred. There are also bargaining problems: Joe Chill and Alfred hate each other and refuse to negotiate. What outcome do we expect? Suppose that the court mistakenly believes that the value of the book to Alfred is $500. What outcome do we expect?

Alfred will buy the safe (so Joe Chill will not take the book), and no payments will be made.

Bigfoot has sold 10,000 copies of his new mystery novel. As part of a marketing scheme, 20% of them are personally autographed by Bigfoot. Used book dealers cannot tell whether or not a book is signed until after they purchase the book. The used book market is highly competitive, with many dealers. The current owners of signed copies of the book will sell their books if and only if they get at least $20, and the owners of unsigned copies will sell theirs if and only if they get at least $5. A signed copy is worth $70 to a dealer, and an unsigned one is worth $10. If used book dealers offer $22 for used books, what will happen?

All owners will sell; total profits for the dealers will be $0.

There are three students (Ron, Sally, and Tia) and three schools (Alligator, Bear, and Crawfish). Alligator and Crawfish have capacities of one student each, and Bear has a capacity of two students. The students' preference lists are as follows: Ron: Alligator, Bear, Crawfish, Ron Sally: Bear, Alligator, Sally, Crawfish Tia: Alligator, Bear, Tia, Crawfish The schools' priority rankings are as follows: Alligator: Sally, Tia, Ron Bear: Ron, Sally, Tia Crawfish: Tia, Ron, Sally What is the outcome of the Top Trading Cycles algorithm?

Alligator:Ron, Bear:Sally and Tia

There are three students (Ron, Sally, and Tia) and three schools (Alligator, Bear, and Crawfish). Alligator and Crawfish have capacities of one student each, and Bear has a capacity of two students. The students' preference lists are as follows: Ron: Alligator, Bear, Crawfish, Ron Sally: Bear, Alligator, Sally, Crawfish Tia: Alligator, Bear, Tia, Crawfish The schools' priority rankings are as follows: Alligator: Sally, Tia, Ron Bear: Ron, Sally, Tia Crawfish: Tia, Ron, Sally Which of the following assignments has no justified envy?

Alligator:Sally, Bear:Ron, Crawfish:Tia.

There are three students (Ron, Sally, and Tia) and three schools (Alligator, Bear, and Crawfish). Alligator and Crawfish have capacities of one student each, and Bear has a capacity of two students. The students' preference lists are as follows: Ron: Alligator, Bear, Crawfish, Ron Sally: Bear, Alligator, Sally, Crawfish Tia: Alligator, Bear, Tia, Crawfish The schools' priority rankings are as follows: Alligator: Sally, Tia, Ron Bear: Ron, Sally, Tia Crawfish: Tia, Ron, Sally What is the outcome of the student-proposing deferred acceptance algorithm?

Alligator:Tia, Bear:Ron and Sally

We have seven voters and five superhunks, and the individual preference lists are as follows: Voter 1: Tom Cruise, Mel Gibson, Leo Di Caprio, Clark Gable, Burt Reynolds Voter 2: Tom, Clark, Burt, Leo, Mel Voter 3: Tom, Clark, Mel, Leo, Burt Voter 4: Mel, Leo, Burt, Tom, Clark Voter 5: Leo, Clark, Burt, Mel, Tom Voter 6: Leo, Burt, Tom, Mel, Clark Voter 7: Clark, Burt, Tom, Leo, Mel What social preference list results from iterating sequential pairwise voting with agenda Mel, Leo, Clark, Tom, Burt?

Burt, Tom, Leo, Clark, Mel

Ed, Fred, and Gloria must divide a table, a chair, a desk, and an umbrella. They assign points to each item as follows: Ed: table 40, chair 30, desk 20, umbrella 10. Fred: table 30, chair 40, desk 15, umbrella 15. Gloria: table 20, chair 20, desk 40, umbrella 20. Which of the following splits is efficient?

Ed gets the table, Fred gets the chair, Gloria gets the desk and the umbrella.

Ed, Fred, and Gloria must divide a table, a chair, a desk, and an umbrella. They assign points to each item as follows: Ed: table 40, chair 30, desk 20, umbrella 10. Fred: table 30, chair 40, desk 15, umbrella 15. Gloria: table 20, chair 20, desk 40, umbrella 20. Which of the following splits is envy-free?

Ed gets the table, Fred gets the chair, Gloria gets the desk and the umbrella.

Which of the following situations most closely corresponds to a two-sided, one-to-one matching environment?

Every ten-year-old in France needs a ten-year-old pen pal in the U.S., and every ten-year-old in the U.S. needs a ten-year-old pen pal in France.

What does a liability right to something mean?

If it is taken, the taker owes you compensation.

What is the main difference between fair division and the two-sided, one-to-one assignment model with public endowments?

In fair division, a person may be assigned more than one object.

Alfred's copy of "The Untold Legend of the Batman," which is autographed by Batman, is worth $1000 to Alfred and $5000 to Joe Chill. Unless Alfred buys a fancy safe that costs $300, Joe Chill is able to take the book. Suppose that Alfred has a liability right over the book. That is, Joe Chill chooses whether or not to take the book (unless Alfred prevents him by buying the safe), but he must compensate Alfred for the consequences of his choice. However, there are litigation problems. In particular, the court is mistaken about the value of the book to Alfred. There are also bargaining problems: Joe Chill and Alfred hate each other and refuse to negotiate. What outcome do we expect? Suppose that the court mistakenly believes that the value of the book to Alfred is $6000. What outcome do we expect?

Joe Chill will not take the book, Alfred will not buy the safe, and no payments will be made.

Consider two-sided, one-to-one matching between singers and musicians. What does it mean for Sue the Singer to be "unacceptable" to Mark the Musician?

Mark prefers being unmatched to being matched with Sue

Consider two-sided, one-to-one matching between four witches (Meg, Nancy, Ophelia, and Peg) and four cats (Whiskers, Fluffy, Toonces, and Rover). Their rankings are as follows: Meg: Whiskers, Fluffy, Toonces, Rover, Meg Nancy: Toonces, Fluffy, Whiskers, Rover, Nancy Ophelia: Fluffy, Toonces, Whiskers, Rover, Ophelia Peg: Whiskers, Rover, Peg, Toonces, Fluffy Whiskers: Ophelia, Nancy, Meg, Peg, Whiskers Fluffy: Meg, Nancy, Ophelia, Peg, Fluffy Toonces: Nancy, Ophelia, Meg, Peg, Toonces Rover: Meg, Nancy, Ophelia, Rover, Peg Which of the following matchings is stable?

Meg:Fluffy, Nancy:Toonces, Ophelia:Whiskers, Peg:Peg, Rover:Rover

Consider two-sided, one-to-one matching between four witches (Meg, Nancy, Ophelia, and Peg) and four cats (Whiskers, Fluffy, Toonces, and Rover). Their rankings are as follows: Meg: Whiskers, Fluffy, Toonces, Rover, Meg Nancy: Toonces, Fluffy, Whiskers, Rover, Nancy Ophelia: Fluffy, Toonces, Whiskers, Rover, Ophelia Peg: Whiskers, Rover, Peg, Toonces, Fluffy Whiskers: Ophelia, Nancy, Meg, Peg, Whiskers Fluffy: Meg, Nancy, Ophelia, Peg, Fluffy Toonces: Nancy, Ophelia, Meg, Peg, Toonces Rover: Meg, Nancy, Ophelia, Rover, Peg What matching does the witch-proposing Deferred Acceptance algorithm yield?

Meg:Whiskers, Nancy:Toonces, Ophelia:Fluffy, Peg:Peg, Rover:Rover

Consider two-sided, one-to-one matching between four witches (Meg, Nancy, Ophelia, and Peg) and four cats (Whiskers, Fluffy, Toonces, and Rover). Their rankings are as follows: Meg: Whiskers, Fluffy, Toonces, Rover, Meg Nancy: Toonces, Fluffy, Whiskers, Rover, Nancy Ophelia: Fluffy, Toonces, Whiskers, Rover, Ophelia Peg: Whiskers, Rover, Peg, Toonces, Fluffy Whiskers: Ophelia, Nancy, Meg, Peg, Whiskers Fluffy: Meg, Nancy, Ophelia, Peg, Fluffy Toonces: Nancy, Ophelia, Meg, Peg, Toonces Rover: Meg, Nancy, Ophelia, Rover, Peg Which of the following matchings has no blocking pairs?

Meg:Whiskers, Nancy:Toonces, Ophelia:Fluffy, Peg:Rover

Consider the following two-sided, one-to-one assignment model with public endowments: there are three people (Cindy, Mindy, and Wendy) and three objects (a flower, a goat, and a harmonica). Suppose that individual preference lists are as follows: Cindy: goat, harmonica, flower Mindy: flower, harmonica, goat Wendy: harmonica, goat, flower Suppose that the assignment is chosen using the serial dictatorship algorithm with order Cindy, Mindy, Wendy. Can anyone get a better outcome for herself by lying about her ranking?

No

Consider two-sided, one-to-one matching between four witches (Meg, Nancy, Ophelia, and Peg) and four cats (Whiskers, Fluffy, Toonces, and Rover). Their rankings are as follows: Meg: Whiskers, Fluffy, Toonces, Rover, Meg Nancy: Toonces, Fluffy, Whiskers, Rover, Nancy Ophelia: Fluffy, Toonces, Whiskers, Rover, Ophelia Peg: Whiskers, Rover, Peg, Toonces, Fluffy Whiskers: Ophelia, Nancy, Meg, Peg, Whiskers Fluffy: Meg, Nancy, Ophelia, Peg, Fluffy Toonces: Nancy, Ophelia, Meg, Peg, Toonces Rover: Meg, Nancy, Ophelia, Rover, Peg Suppose that the matching will be determined by the cat-proposing Deferred Acceptance algorithm. Can any cat get a better outcome for itself by lying about its ranking?

No

We have five voters and four alternatives, and the individual preference lists are as follows: Voter 1: d b c a Voter 2: d b c a Voter 3: c d b a Voter 4: b d c a Voter 5: a d b c Suppose that the social choice procedure used is Condorcet's method. Can any voter get a better outcome for him/herself by lying about his/her ranking (assuming that the other voters report their rankings truthfully)?

No

What does the "What Problem Do You Want? Theorem" say?

No social choice procedure satisfies the Always a Winner property, the monotonicity property, the Pareto property, the Condorcet property, and the Independence of Irrelevant Alternatives property.

There are four patients (P1, P2, P3, and P4), each of whom has a donor kidney (K1, K2, K3, and K4). The patients' preference lists are as follows: P1: K4, K3, K2, waitlist, K1 P2: K4, K1, K3, waitlist, K2 P3: waitlist, K4, K3, K2, K1 P4: waitlist, K4, K1, K3, K2 What is the outcome of the Top Trading Cycles with Chains algorithm if we use the following chain selection rule: pick the shortest chain (in case of a tie, pick the chain starting with the lowest-numbered kidney) and remove it?

P1:K2, P2:K1, P3:waitlist, P4:waitlist, K3:waitlist, K4:waitlist

There are four patients (P1, P2, P3, and P4), each of whom has a donor kidney (K1, K2, K3, and K4). The patients' preference lists are as follows: P1: K4, K3, K2, waitlist, K1 P2: K4, K1, K3, waitlist, K2 P3: waitlist, K4, K3, K2, K1 P4: waitlist, K4, K1, K3, K2 What is the outcome of the Top Trading Cycles with Chains algorithm if we use the following chain selection rule: pick the longest chain (in case of a tie, pick the chain starting with the lowest-numbered kidney) and leave the kidney at the start of the chain available?

P1:K4, P2:K1, P3:waitlist, P4:waitlist, K2:waitlist, K3:waitlist

There are four patients (P1, P2, P3, and P4), each of whom has a donor kidney (K1, K2, K3, and K4). The patients' preference lists are as follows: P1: K4, K3, K2, waitlist, K1 P2: K4, K1, K3, waitlist, K2 P3: waitlist, K4, K3, K2, K1 P4: waitlist, K4, K1, K3, K2 What is the outcome of the Top Trading Cycles with Chains algorithm if we use the following chain selection rule: pick the shortest chain (in case of a tie, pick the chain starting with the lowest-numbered kidney) and leave the kidney at the start of the chain available?

P1:K4, P2:K1, P3:waitlist, P4:waitlist, K2:waitlist, K3:waitlist

There are four patients (P1, P2, P3, and P4), each of whom has a donor kidney (K1, K2, K3, and K4). The patients' preference lists are as follows: P1: K4, K3, K2, waitlist, K1 P2: K4, K1, K3, waitlist, K2 P3: waitlist, K4, K3, K2, K1 P4: waitlist, K4, K1, K3, K2 What is the outcome of the Top Trading Cycles with Chains algorithm if we use the following chain selection rule: pick the longest chain (in case of a tie, pick the chain starting with the lowest-numbered kidney) and remove it?

P1:K4, P2:K3, P3:waitlist, P4:waitlist, K1:waitlist, K2:waitlist

What does Arrow's Impossibility Theorem say?

The only social welfare function that satisfies the Pareto condition, the monotonicity condition, and the Independence of Irrelevant Alternatives condition is a dictatorship.

We have seven voters and five superhunks, and the individual preference lists are as follows: Voter 1: Tom Cruise, Mel Gibson, Leo Di Caprio, Clark Gable, Burt Reynolds Voter 2: Tom, Clark, Burt, Leo, Mel Voter 3: Tom, Clark, Mel, Leo, Burt Voter 4: Mel, Leo, Burt, Tom, Clark Voter 5: Leo, Clark, Burt, Mel, Tom Voter 6: Leo, Burt, Tom, Mel, Clark Voter 7: Clark, Burt, Tom, Leo, Mel What social preference list results from iterating plurality voting?

Tom, Clark, Mel, Leo, Burt

A "list exchange" is where a donor's kidney is given to some patient on the waiting list, and in return the patient associated with the donor obtains a high-priority position on the waiting list. What group of patients might suffer from allowing list exchanges?

Type O patients on the waitlist

We have three voters and four alternatives, and the individual preference lists are as follows: Voter 1: a b c d Voter 2: c a b d Voter 3: b a c d Suppose that the social choice procedure used is sequential pairwise voting with the fixed agenda acbd. Can any voter get a better outcome for him/herself by lying about his/her ranking (assuming that the other voters report their rankings truthfully)?

Yes, Voter 3 would do better to report b c a d.

We have three voters and four alternatives, and the individual preference lists are as follows: Voter 1: a b c d Voter 2: c a b d Voter 3: b a c d Suppose that the social choice procedure used is the Borda count. Can any voter get a better outcome for him/herself by lying about his/her ranking (assuming that the other voters report their rankings truthfully)?

Yes, Voter 3 would do better to report b d c a.

A penalty clause in a contract is

a private version of a property rule.

Natalie and Oscar must divide a mosaic, a car, a statuette, and a ring. They assign points to each item as follows: Natalie: mosaic 40, car 40, statuette 10, ring 10. Oscar: mosaic 30, car 50, statuette 15, ring 5. What items does Natalie receive according to the adjusted winner procedure?

mosaic, ring, 1/6 of the car.

The concept of "strategy-proof" in the assignment model corresponds most closely to which concept in fair division?

non-manipulable