Managerial Economics: A Problem Solving Approach
5th Edition
ISBN: 9781337106665
Author: Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher: Cengage Learning
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Question
Chapter 18, Problem 18.2IP
To determine
The reserve price set by the auctioneer.
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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 $21 or $56, 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 of 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 $56 Reserve Price
($)
($)
($)
$21
$21
0.25
$21
$56
0.25
$56
$21
0.25
$56
$56
0.25
Without a reserve price, the expected price is _______…
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 $39 or $104, 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 of 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 $104 Reserve Price?
($)
($)
($)
$39
$39
0.25
$39
$104
0.25
$104
$39
0.25
$104
$104
0.25
Without a reserve price, the expected price is…
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 Valerie places a value of $15,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Valerie simply bids $15,000/2=$7,500 and wins the piece of art.
The expected price paid by Valerie, with no other bidders present, is $________..
Suppose the owner of the artwork manages to recruit another bidder, Antonio, to the auction. Antonio is known to value the art piece at $12,000.
The expected price paid by Valerie, given the presence of the second bidder Antonio, is $_______.
.
Chapter 18 Solutions
Managerial Economics: A Problem Solving Approach
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