Exam 18:Auctions-Part A

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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. )

(Multiple Choice)
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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.

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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.

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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

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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.

(True/False)
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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

(Multiple Choice)
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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

(Multiple Choice)
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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

(Multiple Choice)
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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. )

(Multiple Choice)
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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?

(Multiple Choice)
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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

(Multiple Choice)
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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.

(True/False)
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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?

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

(True/False)
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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

(Multiple Choice)
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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.

(True/False)
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