Deck 18: A: Auctions

Question 1

The optimal strategy for a bidder in a private-values Vickrey auction is to bid his true valuation.

Answer 1

True

Question 2

An antique cabinet is being sold by means of an English auction.There are four bidders,Zelda,Clara,Anneli,and Diana.These bidders are unacquainted with each other and do not collude.Zelda values the cabinet at $800,Clara values it at $550,Anneli values it at $1,300,and Diana values it at $300.If the bidders bid in their rational self-interest,the cabinet will be sold to

A) Anneli for about $1,300.
B) Zelda for about $800.
C) either Anneli or Zelda for slightly more than $800.Which of them actually gets it is randomly determined.
D) Anneli for slightly more than $800.
E) None of the above.

Answer 2

Anneli for slightly more than $800.

Question 3

An antique cabinet is being sold by means of an English auction.There are four bidders,Holly,Penelope,Minnie,and Sheila.These bidders are unacquainted with each other and do not collude.Holly values the cabinet at $1,600,Penelope values it at $1,350,Minnie values it at $2,100,and Sheila values it at $1,100.If the bidders bid in their rational self-interest,the cabinet will be sold to

A) Holly for about $1,600.
B) Minnie for about $2,100.
C) either Minnie or Holly for slightly more than $1,600.Which of them actually gets it is randomly determined.
D) Minnie for slightly more than $1,600.
E) None of the above.

Answer 3

Minnie for slightly more than $1,600.

Question 4

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house,Ernie,Minnie,and Betsy.First Fiddler's does not know the willingness to pay of these three bidders for the house,but on the basis of its previous experience,the bank believes that each of these bidders has a probability of 1/3 of valuing it at $700,000,a probability of 1/3 of valuing at $400,000,and a probability of 1/3 of valuing it at $300,000.First Fiddler's believes that these probabilities are independent among buyers.If First Fiddler's sells the house by means of a second-bidder,sealed-bid auction (Vickrey auction),what will be the bank's expected revenue from the sale? (Choose the closest option. )

A) $400,000
B) $451,852
C) $466,667
D) $700,000
E) $300,000

Question 5

The reserve price in an auction is the lowest price at which the seller of a good will part with it.

Question 6

An antique cabinet is being sold by means of an English auction.There are four bidders,Penelope,Marilyn,Irene,and Betsy.These bidders are unacquainted with each other and do not collude.Penelope values the cabinet at $1,600,Marilyn values it at $1,350,Irene values it at $2,100,and Betsy values it at $1,100.If the bidders bid in their rational self-interest,the cabinet will be sold to

A) Irene for about $2,100.
B) either Irene or Penelope for slightly more than $1,600.Which of them actually gets it is randomly determined.
C) Penelope for about $1,600.
D) Irene for slightly more than $1,600.
E) None of the above.

Question 7

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house,Ernie,Teresa,and Marilyn.First Fiddler's does not know the willingness to pay of these three bidders for the house,but on the basis of its previous experience,the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000,a probability of 1/3 of valuing at $500,000,and a probability of 1/3 of valuing it at $200,000.First Fiddler's believes that these probabilities are independent among buyers.If First Fiddler's sells the house by means of a second-bidder,sealed-bid auction (Vickrey auction),what will be the bank's expected revenue from the sale? (Choose the closest option. )

A) $433,333
B) $448,148
C) $600,000
D) $500,000
E) $200,000

Question 8

A stamp dealer is holding an auction for an English Penny Black postage stamp,issued in 1840.Potential buyers are asked to submit written bids for this stamp,and it will be sold to the highest bidder at a price equal to the bid submitted by the second-highest bidder.If bidders understand the logic of this auction and bid in their own self-interest,

A) bidders will shade their bids by approximately 10%,and hence the stamp will be sold for about 10% less than the second-highest willingness to pay.
B) bidders will bid more than their true valuation,since they only have to pay the second-highest bid and not their own bid.
C) bidders will bid exactly their true valuation.
D) the highest bidder will overstate his valuation and the second-highest bidder will understate his valuation.
E) bidders will all bid (n 2 1/2)of their true valuations,where n is the number of bidders.

Question 9

It is often the case that a seller can increase his profit from an auction by setting a reserve price even if he has to destroy the object being auctioned if nobody bids as high as the reserve price.

Question 10

An auction in which some bidders have different information about the value of an object than others is said to be an auction with private values.

Question 11

In a Dutch auction with rational bidders,it sometimes happens that the object being sold goes to someone whose value for the object is not as high as that of some other bidder(s).

Question 12

If a good is sold in a Dutch auction and the bidders bid rationally,the price paid for the good will always be equal to the second-highest willingness to pay of auction participants.

Question 13

In a private-values auction with rational bidders,we can expect the same outcome from an English auction as from a Vickrey auction.

Question 14

The "winner's curse" refers to the fact that in a sealed-bid auction with private values,the winning bidder often pays more than he would have to in order to win the object auctioned.

Question 15

A first edition of Adam Smith's Wealth of Nations (published in 1776)is being auctioned via the Internet.The current owner starts by posting his own "bid" for it.Bidders are allowed to submit bids at any time during a one-week interval.For the following week,bids will be accepted only if they exceed the currently posted high bid.Throughout the week,the highest bid that anyone has made so far will be posted.At the end of the week,the book will be sold to the highest bidder at the price that he or she bid for it.Assuming that bidders understand the rules of the auction,the outcome of this auction will be similar to that for

A) an English auction with a reserve price equal to the owner's bid.
B) a Dutch auction with a reserve price equal to the owner's bid.
C) a sealed-bid auction in which the book is sold to the highest bidder at the highest bidder's bid price.
D) a common-value auction.
E) an English auction with no reserve price.

Question 16

The profit-maximizing strategy for a bidder in a Vickrey auction where there are common values for the object being sold is to bid less than her estimated value for the object,and the more bidders there are,the more the profit-maximizing bidder should shade her bid below her estimated value.

Question 17

An auctioneer allows bidders to examine a jar of pennies,but he does not allow them to open the jar and count the pennies.The jar is then sold by means of an English auction.Economists call an auction of this type a private-values auction,since opinions differ.

Question 18

It is never a profit-maximizing strategy for a seller in an English auction to set a reserve price for the good he is selling so high that he might not be able to sell it at all.

Question 19

In a common-value auction,the bids of other bidders can influence the maximum amount that one is willing to pay for an object,while in a private-value auction this is not the case.

Question 20

In an English auction,with rational bidders,the object being sold always goes to the bidder who values it most highly.

Question 21

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house,Zeke,Fanny,and Heidi.First Fiddler's does not know the willingness to pay of these three bidders for the house,but on the basis of its previous experience,the bank believes that each of these bidders has a probability of 1/3 of valuing it at $800,000,a probability of 1/3 of valuing at $600,000,and a probability of 1/3 of valuing it at $300,000.First Fiddler's believes that these probabilities are independent among buyers.If First Fiddler's sells the house by means of a second-bidder,sealed-bid auction (Vickrey auction),what will be the bank's expected revenue from the sale? (Choose the closest option. )

A) $566,667
B) $600,000
C) $800,000
D) $574,074
E) $300,000

Question 22

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $900.There are two bidders.The dealer believes that there are only three possible values,$7,200,$3,600,and $900,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the car is approximately

A) $3,600.
B) $2,500.
C) $3,900.
D) $5,400.
E) $7,200.

Question 23

Herb's Auction House in Purloined Hubcap,Oregon,holds sealed-bid used-car auctions every Wednesday.Each car is sold to the highest bidder at the second-highest bidder's bid.On average,two-thirds of the cars that are auctioned are lemons and one-third are good used cars.A good car is worth $1,500 to any buyer.A lemon is worth only $150 to a buyer.Most buyers can do no better than random at picking good cars from the lot.There is only one exception,Al Crankcase.Al can sometimes but not always detect lemons by means of a subtle test.A good car will never fail Al's test,but approximately half of the lemons fail his test.Al attends every auction,tests every car,and always bids his expected value.Normal bidders bid less than the expected value for a randomly selected car but more than the value of a lemon.

A) Al will bid $825 for cars that pass his test and $150 for cars that fail his test.Normal bidders will get only lemons.
B) Al will bid $750 for cars that pass his test and $500 for cars that fail his test.Normal bidders will get only lemons.
C) Al will bid $500 for cars that pass his test and $150 for cars that fail his test.Normal bidders will get good cars only 1/6 of the time.
D) Al will bid $600 for cars that pass his test and $250 for cars that fail his test.Normal bidders will get good cars only 1/6 of the time.
E) Al will bid $300 for cars that pass his test and $150 for cars that fail his test.Normal bidders will get good cars 1/12 of the time.

Question 24

A seller decides to sell an object by means of an English auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $400 and a probability of 1/2 that the bidder's value is $100.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $175
B) $220
C) $400
D) $250
E) $100

Question 25

A seller knows that there are two bidders for the object she is selling.She believes that with probability 1/2,one has a buyer value of $5 and the other has a buyer value of $10 and,with probability 1/2,one has a buyer value of $8 and the other has a buyer value of $15.She knows that bidders will want to buy the object so long as they can get it for their buyer value or less.She sells it in an English auction with a reserve price which she must set before the auction starts.To maximize her expected profits,she should set the reserve price at

A) $5.
B) $10.
C) $8.
D) $13.
E) $15.

Question 26

A seller decides to sell an object by means of a sealed-bid second-price auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $400 and a probability of 1/2 that the bidder's value is $300.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $325
B) $400
C) $350
D) $320
E) $340

Question 27

A seller decides to sell an object by means of a sealed-bid second-price auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $600 and a probability of 1/2 that the bidder's value is $200.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $600
B) $400
C) $300
D) $280
E) $360

Question 28

A seller knows that there are two bidders for the object he is selling.He believes that with probability 1/2,one has a buyer value of $5 and the other has a buyer value of $12 and,with probability 1/2,one has a buyer value of $10 and the other has a buyer value of $30.He knows that bidders will want to buy the object so long as they can get it for their buyer value or less.He sells it in an English auction with a reserve price which he must set before the auction starts.To maximize his expected profits,he should set the reserve price at

A) $30.
B) $5.
C) $12.
D) $10.
E) $20.

Question 29

A seller decides to sell an object by means of an English auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $600 and a probability of 1/2 that the bidder's value is $200.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $300
B) $360
C) $400
D) $600
E) $200

Question 30

A dealer decides to sell an oil painting by means of an English auction with a reservation price just slightly below $45,000.If he fails to get his reservation price for the painting,he will burn it.There are two bidders.The dealer believes that there are only three possible values,$90,000,$45,000,and $18,000,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the painting is slightly less than

A) $40,000.
B) $45,000.
C) $18,000.
D) $31,500.
E) $51,000.

Question 31

A dealer decides to sell an oil painting by means of an English auction with a reservation price just slightly below $72,000.If he fails to get his reservation price for the painting,he will burn it.There are two bidders.The dealer believes that there are only three possible values,$117,000,$72,000,and $27,000,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the painting is slightly less than

A) $72,000.
B) $69,000.
C) $49,500.
D) $27,000.
E) $78,000.

Question 32

A seller decides to sell an object by means of an English auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $500 and a probability of 1/2 that the bidder's value is $200.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $320
B) $350
C) $275
D) $500
E) $200

Question 33

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $2,700.There are two bidders.The dealer believes that there are only three possible values,$5,400,$3,600,and $2,700,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingness to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the car is approximately

A) $4,500.
B) $3,900.
C) $3,600.
D) $3,300.
E) $5,400.

Question 34

A seller decides to sell an object by means of a sealed-bid,second-price auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $600 and a probability of 1/2 that the bidder's value is $300.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally,what is the seller's expected revenue from the auction?

A) $360
B) $450
C) $375
D) $600
E) $420

Question 35

A dealer decides to sell an oil painting by means of an English auction with a reservation price just slightly below $54,000.If he fails to get his reservation price for the painting,he will burn it.There are two bidders.The dealer believes that there are only three possible values,$90,000,$54,000,and $45,000,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the painting is slightly less than

A) $54,000.
B) $52,000.
C) $49,500.
D) $45,000.
E) $63,000.

Question 36

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $1,800.There are two bidders.The dealer believes that there are only three possible values,$6,300,$3,600,and $1,800,that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the car is approximately

A) $4,950.
B) $3,600.
C) $2,900.
D) $3,900.
E) $6,300.