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 $60 or $160, 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.

Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter20: The Problem Of Adverse Selection Moral Hazard
Section: Chapter Questions
Problem 3MC
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2. Individual Problems 18-2

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 $60 or $160, 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 $160 Reserve Price
($)
($)
($)
$60 $60 0.25          
$60 $160 0.25          
$160 $60 0.25          
$160 $160 0.25          
 
Without a reserve price, the expected price is  $________?
 
. With a reserve price of $160, the expected price is $________?
 
. Thus, the expected price is larger (with? or without?)   the reserve price.
 
 

3. Individual 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 $228 or $304, 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 $304 Reserve Price
($)
($)
($)
$228 $228 0.25          
$228 $304 0.25          
$304 $228 0.25          
$304 $304 0.25          
 
Without a reserve price, the expected price is ______?
 
. With a reserve price of $304, the expected price is ________?
 
. Thus, the expected price is larger (with? or without? )    the reserve price.
 

4. 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 $7 million.
True or False: To avoid the winner's curse, your bid should be larger than $7 million.
 
True
or
False
 
 

5. 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 Simone places a value of $65,000 on the art piece and that she values this art piece more than any other collector. Suppose that if no one else shows up, Simone simply bids $65,0002=$32,500$65,0002=$32,500 and wins the piece of art.
The expected price paid by Simone, with no other bidders present, is ___$___?
 
.
 
Suppose the owner of the artwork manages to recruit another bidder, Yakov, to the auction. Yakov is known to value the art piece at $52,000.
The expected price paid by Simone, given the presence of the second bidder Yakov, is _____$____?
 
.
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