CHAPTER 18: Auctions
TRUE/FALSE
1. 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).
2. In an English auction, with rational bidders, the object being sold always goes to the bidder who values
it most highly.
3. 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.
4. In a private-values auction with rational bidders, we can expect the same outcome from an English
auction as from a Vickrey auction.
5. 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.
6. The reserve price in an auction is the lowest price at which the seller of a good will part with it.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. The optimal strategy for a bidder in a private-values Vickrey auction is to bid his true valuation.
13. 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.
MULTIPLE CHOICE
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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
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
8. 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
9. 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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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