ndividual Problems 18-3
A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price, that bidder pays the reserve price. An auctioneer faces two bidders, each with a value of either $126 or $168, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder.
The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur.
On the following table, indicate the price paid by the winning bidder with and without the stated reserve price.
|Bidder 1 Value||Bidder 2 Value||Probability||Price Without Reserve||Price with $168 Reserve Price|
Without a reserve price, the expected price is .
With a reserve price of $168, the expected price is .
Thus, the expected price is larger (with / without_) the reserve price.
Individual Problems 18-4
In Sweden, firms that fail to meet their debt obligations are immediately auctioned off to the highest bidder. (There is no reorganization through Chapter 11 bankruptcy.) The current managers are often the high bidders for the company. (Hint: Assume these auctions are common-value auctions.)
Suppose for a particular auction, the current managers have placed a bid of $15 million.
True or False: To avoid the winner’s curse, you should avoid bidding in such auctions.
Individual Problems 18-5
When a famous painting becomes available for sale, it is often known which museum or collector will be the likely winner. Yet, the auctioneer actively woos representatives of other museums that have no chance of winning to attend anyway.
Suppose a piece of art has recently become available for sale and will be auctioned off to the highest bidder, with the winner paying an amount equal to the second highest bid. Assume that most collectors know that Alex places a value of $125,000 on the art piece and that he values this art piece more than any other collector. Suppose that if no one else shows up, Alex simply bids $125,0002=$62,500$125,0002=$62,500 and wins the piece of art.
The expected price paid by Alex, with no other bidders present, is
Suppose the owner of the artwork manages to recruit another bidder, Brian, to the auction. Brian is known to value the art piece at $100,000.
The expected price paid by Alex, given the presence of the second bidder Brian, is
Individual Problems 18-6
Bob Green estimates the cost of future projects for a large contracting firm. Bob uses precisely the same techniques to estimate the costs of every potential job and formulates bids by adding a standard profit markup. For some companies, to which the firm offers its services, there are no competitors also seeking their business, so Bob’s company is almost certain to get these companies as clients. For these jobs, Bob finds that his cost estimates are right, on average. For jobs where competitors are also vying for the business, Bob finds that they almost always end up costing more than he estimates.
True or False: Bob is less likely to win the jobs where he underestimates the costs, causing him to experience the winner’s curse.
Individual Problems 19-1
In the late 1990s, car leasing was very popular in the United States. A customer would lease a car from the manufacturer for a set term, usually two years, and then have the option of keeping the car. If the customer decided to keep the car, the customer would pay a price to the manufacturer, the “residual value,” computed as 60% of the new car price. The manufacturer would then sell the returned cars at auction. In 1999, manufacturers lost an average of $480 on each returned car (the auction price was, on average, $480 less than the residual value).
Suppose two customers have leased cars from a manufacturer. Their lease agreements are up, and they are considering whether to keep (and purchase at 60% of the new car price) their cars or return their cars. Two years ago, Rosa leased a car valued new at $12,000. If she returns the car, the manufacturer could likely get $8,400 at auction for the car. Tim also leased a car, valued new at $19,000, two years ago. If he returns the car, the manufacturer could likely get $9,880 at auction for the car.
Use the following table to indicate whether each buyer is more likely to purchase or return the car.
|Buyer||Keep and Purchase Car||Return Car|
The manufacturer will lose money (at auction, relative to the residual value of the car) if returns the car instead of keeping and purchasing it.
True or False: Setting a more accurate residual price of each car would help attenuate the problems of adverse selection.
Individual Problems 19-2
Many police officer positions require the applicant to have a college degree, even though the tasks of a police officer rarely call upon college course material.
Suppose two individuals who do not have college degrees are considering applying to the police force. Ginny is considering applying for an officer position and plans on working for the police force for a period of time, over which she would earn approximately $7,000 (in present discounted value) in earnings while in the position. Cho is also considering applying, and plans on working as an officer for a period of time, over which she would earn approximately $420,000 (in present discounted value) in lifetime earnings while in the position. Also suppose that present value of obtaining a college degree, which is required to submit a job application to the police department, is $70,000.
Use the following table to indicate whether each individual would likely apply, or not, given the cost of obtaining a college degree.
|Buyer||Would Apply||Would Not Apply|
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