Exam 16: A: Auctions

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 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

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 of valuing the house at $900,000, a probability of of valuing it at $700,000, and a probability of 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 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 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

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, of the cars that are auctioned are lemons and 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

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 of valuing the house at $800,000, a probability of of valuing it at $500,000, and a probability of 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.)