Exam 16: Auctions

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 that the bidder's value for the object is $400 and a probability of 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?

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

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 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 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 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 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 that the bidder's value for the object is $500 and a probability of 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?

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

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.

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 that the bidder's value for the object is $600 and a probability of 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 seller knows that there are two bidders for the object she is selling. She believes that with probability , one has a buyer value of $5 and the other has a buyer value of $10 and, with probability , 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 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

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 of valuing it at $800,000, a probability of of valuing at $600,000, and a probability of 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.)

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).

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.

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 of valuing it at $700,000, a probability of of valuing at $400,000, and a probability of 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 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 that the bidder's value for the object is $600 and a probability of 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 seller knows that there are two bidders for the object he is selling. He believes that with probability , one has a buyer value of $5 and the other has a buyer value of $12 and, with probability , 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

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 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,

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.

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.