CHAPTER 18: Auctions
MULTIPLE CHOICE
1. First Fiddler’s Bank has foreclosed on a home mortgage and is selling the house at auction. There are
three bidders for the house, Jesse, Shelia, and Elsie. First Fiddler’s does not know the willingness to
pay of any of these bidders but on the basis of its previous experience believes that each of them has a
probability of 1/3 of valuing the house at $600,000, a probability of 1/3 of valuing it at $500,000, and a
probability of 1/3 of valuing it at $200,000. First Fiddler’s believes that these probabilities are
independent between 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
answer.)
a.
$500,000
b.
$550,000
c.
$433,333.33
d.
$350,000
e.
$366,666.67
2. First Fiddler’s Bank has foreclosed on a home mortgage and is selling the house at auction. There are
three bidders for the house, Jesse, Shelia, and Elsie. First Fiddler’s does not know the willingness to
pay of any of these bidders but on the basis of its previous experience believes that each of them has a
probability of 1/3 of valuing the house at $800,000, a probability of 1/3 of valuing it at $300,000, and a
probability of 1/3 of valuing it at $100,000. First Fiddler’s believes that these probabilities are
independent between 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
answer.)
a.
$300,000
b.
$200,000
c.
$550,000
d.
$400,000
e.
$366,666.67
3. First Fiddler’s Bank has foreclosed on a home mortgage and is selling the house at auction. There are
three bidders for the house, Jesse, Shelia, and Elsie. First Fiddler’s does not know the willingness to
pay of any of these bidders but on the basis of its previous experience believes that each of them has a
probability of 1/3 of valuing the house at $900,000, a probability of 1/3 of valuing it at $700,000, and a
probability of 1/3 of valuing it at $200,000. First Fiddler’s believes that these probabilities are
independent between 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
answer.)
a.
$700,000
b.
$800,000
c.
$450,000
d.
$600,000
e.
$533,333.33
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, Jesse, Shelia, and Elsie. First Fiddler’s does not know the willingness to
pay of any of these bidders but on the basis of its previous experience believes that each of them has a
probability of 1/3 of valuing the house at $800,000, a probability of 1/3 of valuing it at $500,000, and a
probability of 1/3 of valuing it at $300,000. First Fiddler’s believes that these probabilities are
independent between 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
answer.)
a.
$400,000
b.
$533,333.33
c.
$650,000
d.
$500,000
e.
$433,333.33
5. First Fiddler’s Bank has foreclosed on a home mortgage and is selling the house at auction. There are
three bidders for the house, Jesse, Shelia, and Elsie. First Fiddler’s does not know the willingness to
pay of any of these bidders but on the basis of its previous experience believes that each of them has a
probability of 1/3 of valuing the house at $900,000, a probability of 1/3 of valuing it at $700,000, and a
probability of 1/3 of valuing it at $400,000. First Fiddler’s believes that these probabilities are
independent between 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
answer.)
a.
$800,000
b.
$700,000
c.
$666,666.67
d.
$550,000
e.
$533,333.33
6. An antique cabinet is being sold by means of an English auction. There are four bidders, Kitty, Gloria,
Judy, and Cindy. These bidders are unacquainted with each other and do not collude. Kitty values the
cabinet at $800, Gloria values it at $500, Judy values it at $1,700, and Cindy values it at $700. If the
bidders bid in their rational self-interest, the cabinet will be sold to
a.
Judy for about $1,700.
b.
Kitty for about $800.
c.
either Judy or Kitty for about $800. Which of these two buyers gets it is randomly
determined.
d.
Judy for slightly more than $800.
e.
either Judy or Kitty for about $500. Which of these two buyers gets it is randomly
determined.
7. An antique cabinet is being sold by means of an English auction. There are four bidders, Arabella,
Gloria, Desiree, and Cindy. These bidders are unacquainted with each other and do not collude.
Arabella values the cabinet at $1,000, Gloria values it at $800, Desiree values it at $1,300, and Cindy
values it at $700. If the bidders bid in their rational self-interest, the cabinet will be sold to
a.
Desiree for slightly more than $1,000.
b.
Desiree for about $1,300.
c.
Arabella for about $1,000.
d.
either Desiree or Arabella for about $1,000. Which of these two buyers gets it is randomly
determined.
e.
either Desiree or Arabella for about $800. Which of these two buyers gets it is randomly
determined.
8. An antique cabinet is being sold by means of an English auction. There are four bidders, Gloria, Elise,
Judy, and Arabella. These bidders are unacquainted with each other and do not collude. Gloria values
the cabinet at $800, Elise values it at $500, Judy values it at $1,800, and Arabella values it at $600. If
the bidders bid in their rational self-interest, the cabinet will be sold to
a.
Gloria for about $800.
b.
either Judy or Gloria for about $800. Which of these two buyers gets it is randomly
determined.
c.
Judy for slightly more than $800.
d.
Judy for about $1,800.
e.
either Judy or Gloria for about $500. Which of these two buyers gets it is randomly
determined.
9. An antique cabinet is being sold by means of an English auction. There are four bidders, Arabella,
Desiree, Gloria, and Flora. These bidders are unacquainted with each other and do not collude.
Arabella values the cabinet at $1,100, Desiree values it at $600, Gloria values it at $1,700, and Flora
values it at $700. If the bidders bid in their rational self-interest, the cabinet will be sold to
a.
Gloria for slightly more than $1,100.
b.
either Gloria or Arabella for about $1,100. Which of these two buyers gets it is randomly
determined.
c.
Arabella for about $1,100.
d.
Gloria for about $1,700.
e.
either Gloria or Arabella for about $600. Which of these two buyers gets it is randomly
determined.
10. An antique cabinet is being sold by means of an English auction. There are four bidders, Arabella,
Lana, Hester, and Betsy. These bidders are unacquainted with each other and do not collude. Arabella
values the cabinet at $1,000, Lana values it at $500, Hester values it at $1,300, and Betsy values it at
$800. If the bidders bid in their rational self-interest, the cabinet will be sold to
a.
Hester for slightly more than $1,000.
b.
Hester for about $1,300.
c.
Arabella for about $1,000.
d.
either Hester or Arabella for about $1,000. Which of these two buyers gets it is randomly
determined.
e.
either Hester or Arabella for about $500. Which of these two buyers gets it is randomly
determined.
11. 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 that each
bidder’s willingness to pay might take, $6,500, $3,600, and $900. Each bidder has a probability of 1/3
of having each of these willingnesses to pay, and the probabilities 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 automobile is
a.
$5,050.
b.
$3,666.67.
c.
$3,600.
d.
$3,100.
e.
$6,500.
12. A dealer decides to sell an antique automobile by means of an English auction with a reservation price
of $200. There are two bidders. The dealer believes that there are only three possible values that each
bidder’s willingness to pay might take, $7,700, $3,100, and $200. Each bidder has a probability of 1/3
of having each of these willingnesses to pay, and the probabilities 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 automobile is
a.
$2,600.
b.
$5,400.
c.
$3,666.67.
d.
$3,100.
e.
$7,700.
13. A dealer decides to sell an antique automobile by means of an English auction with a reservation price
of $100. There are two bidders. The dealer believes that there are only three possible values that each
bidder’s willingness to pay might take, $7,300, $2,600, and $100. Each bidder has a probability of 1/3
of having each of these willingnesses to pay, and the probabilities 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 automobile is
a.
$3,333.33.
b.
$2,100.
c.
$2,600.
d.
$4,950.
e.
$7,300.
14. 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 that each
bidder’s willingness to pay might take, $6,700, $3,400, and $900. Each bidder has a probability of 1/3
of having each of these willingnesses to pay, and the probabilities 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 automobile is
a.
$5,050.
b.
$3,400.
c.
$2,900.
d.
$3,666.67.
e.
$6,700.
15. A dealer decides to sell an antique automobile by means of an English auction with a reservation price
of $600. There are two bidders. The dealer believes that there are only three possible values that each
bidder’s willingness to pay might take, $6,400, $3,000, and $600. Each bidder has a probability of 1/3
of having each of these willingnesses to pay, and the probabilities 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 automobile is
a.
$2,500.
b.
$4,700.
c.
$3,333.33.
d.
$3,000.
e.
$6,400.
16. A dealer decides to sell an oil painting by means of an English auction with a reservation price of
slightly below $100,000. If she fails to get a bid as high as her reservation price, she will burn the
painting. There are two bidders. The dealer believes that each bidder’s willingness to pay will take one
of the three following values: $110,000, $100,000, and $25,000. The dealer believes that each bidder
has a probability of 1/3 of having each of these three values. The probability distribution of each
buyer’s value is independent of that of the other’s. 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.
$89,000.
b.
$100,000.
c.
$105,000.
d.
$80,000.
e.
$78,333.33.
17. A dealer decides to sell an oil painting by means of an English auction with a reservation price of
slightly below $75,000. If she fails to get a bid as high as her reservation price, she will burn the
painting. There are two bidders. The dealer believes that each bidder’s willingness to pay will take one
of the three following values: $90,000, $75,000, and $30,000. The dealer believes that each bidder has
a probability of 1/3 of having each of these three values. The probability distribution of each buyer’s
value is independent of that of the other’s. 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.
$75,000.
b.
$69,000.
c.
$60,000.
d.
$82,500.
e.
$65,000.
18. A dealer decides to sell an oil painting by means of an English auction with a reservation price of
slightly below $85,000. If she fails to get a bid as high as her reservation price, she will burn the
painting. There are two bidders. The dealer believes that each bidder’s willingness to pay will take one
of the three following values: $100,000, $85,000, and $25,000. The dealer believes that each bidder
has a probability of 1/3 of having each of these three values. The probability distribution of each
buyer’s value is independent of that of the other’s. 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.
$79,000.
b.
$92,500.
c.
$85,000.
d.
$70,000.
e.
$70,000.
19. A dealer decides to sell an oil painting by means of an English auction with a reservation price of
slightly below $100,000. If she fails to get a bid as high as her reservation price, she will burn the
painting. There are two bidders. The dealer believes that each bidder’s willingness to pay will take one
of the three following values: $120,000, $100,000, and $25,000. The dealer believes that each bidder
has a probability of 1/3 of having each of these three values. The probability distribution of each
buyer’s value is independent of that of the other’s. 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.
$110,000.
b.
$100,000.
c.
$89,000.
d.
$80,000.
e.
$81,666.67.
20. A dealer decides to sell an oil painting by means of an English auction with a reservation price of
slightly below $70,000. If she fails to get a bid as high as her reservation price, she will burn the
painting. There are two bidders. The dealer believes that each bidder’s willingness to pay will take one
of the three following values: $80,000, $70,000, and $45,000. The dealer believes that each bidder has
a probability of 1/3 of having each of these three values. The probability distribution of each buyer’s
value is independent of that of the other’s. 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.
$70,000.
b.
$59,000.
c.
$75,000.
d.
$50,000.
e.
$65,000.
21. Jerry’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, 2/3
of the cars that are auctioned are lemons and 1/3 are good used cars. A good used car is worth $1,200
to any buyer. A lemon is worth $270 to any buyer. Most buyers can do no better than picking at
random from among these used cars. The only exception is Al Crankcase. Recall that Al can
sometimes detect lemons by tasting the oil on the car’s dipstick. A good car never fails Al’s test, but
half of the lemons fail his test. Al attends every auction, licks every dipstick, and bids his expected
value of every car given the results of his test. Al will bid
a.
$735 for cars that pass his test and $270 for cars that fail his test. Normal bidders will get
only lemons.
b.
$600 for cars that pass his test and $400 for cars that fail his test. Normal bidders will get
only lemons.
c.
$400 for cars that pass his test and $270 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
d.
$580 for cars that pass his test and $370 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
e.
$540 for cars that pass his test and $270 for cars that fail his test. Normal bidders will get
good cars only 1/12 of the time.
22. Jerry’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, 2/3
of the cars that are auctioned are lemons and 1/3 are good used cars. A good used car is worth $1,800
to any buyer. A lemon is worth $270 to any buyer. Most buyers can do no better than picking at
random from among these used cars. The only exception is Al Crankcase. Recall that Al can
sometimes detect lemons by tasting the oil on the car’s dipstick. A good car never fails Al’s test, but
half of the lemons fail his test. Al attends every auction, licks every dipstick, and bids his expected
value of every car given the results of his test. Al will bid
a.
$900 for cars that pass his test and $600 for cars that fail his test. Normal bidders will get
only lemons.
b.
$780 for cars that pass his test and $370 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
c.
$1,035 for cars that pass his test and $270 for cars that fail his test. Normal bidders will
get only lemons.
d.
$600 for cars that pass his test and $270 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
e.
$540 for cars that pass his test and $270 for cars that fail his test. Normal bidders will get
good cars only 1/12 of the time.
23. Jerry’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, 2/3
of the cars that are auctioned are lemons and 1/3 are good used cars. A good used car is worth $2,700
to any buyer. A lemon is worth $240 to any buyer. Most buyers can do no better than picking at
random from among these used cars. The only exception is Al Crankcase. Recall that Al can
sometimes detect lemons by tasting the oil on the car’s dipstick. A good car never fails Al’s test, but
half of the lemons fail his test. Al attends every auction, licks every dipstick, and bids his expected
value of every car given the results of his test. Al will bid
a.
$1,470 for cars that pass his test and $240 for cars that fail his test. Normal bidders will
get only lemons.
b.
$1,060 for cars that pass his test and $340 for cars that fail his test. Normal bidders will
get good cars only 1/6 of the time.
c.
$1,350 for cars that pass his test and $900 for cars that fail his test. Normal bidders will
get only lemons.
d.
$900 for cars that pass his test and $240 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
e.
$480 for cars that pass his test and $240 for cars that fail his test. Normal bidders will get
good cars only 1/12 of the time.
24. Jerry’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, 2/3
of the cars that are auctioned are lemons and 1/3 are good used cars. A good used car is worth $3,000
to any buyer. A lemon is worth $150 to any buyer. Most buyers can do no better than picking at
random from among these used cars. The only exception is Al Crankcase. Recall that Al can
sometimes detect lemons by tasting the oil on the car’s dipstick. A good car never fails Al’s test, but
half of the lemons fail his test. Al attends every auction, licks every dipstick, and bids his expected
value of every car given the results of his test. Al will bid
a.
$1,500 for cars that pass his test and $1,000 for cars that fail his test. Normal bidders will
get only lemons.
b.
$1,100 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.
c.
$1,575 for cars that pass his test and $150 for cars that fail his test. Normal bidders will
get only lemons.
d.
$1,000 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.
e.
$300 for cars that pass his test and $150 for cars that fail his test. Normal bidders will get
good cars only 1/12 of the time.
25. Jerry’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, 2/3
of the cars that are auctioned are lemons and 1/3 are good used cars. A good used car is worth $1,800
to any buyer. A lemon is worth $240 to any buyer. Most buyers can do no better than picking at
random from among these used cars. The only exception is Al Crankcase. Recall that Al can
sometimes detect lemons by tasting the oil on the car’s dipstick. A good car never fails Al’s test, but
half of the lemons fail his test. Al attends every auction, licks every dipstick, and bids his expected
value of every car given the results of his test. Al will bid
a.
$1,020 for cars that pass his test and $240 for cars that fail his test. Normal bidders will
get only lemons.
b.
$900 for cars that pass his test and $600 for cars that fail his test. Normal bidders will get
only lemons.
c.
$760 for cars that pass his test and $340 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
d.
$600 for cars that pass his test and $240 for cars that fail his test. Normal bidders will get
good cars only 1/6 of the time.
e.
$480 for cars that pass his test and $240 for cars that fail his test. Normal bidders will get
good cars only 1/12 of the time.