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 $6 or $16, 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 $16 Reserve Price
($)	($)	($)
$6	$6	0.25
$6	$16	0.25
$16	$6	0.25
$16	$16	0.25

Without a reserve price, the expected price is

. With a reserve price of $16, the expected price is

. Thus, the expected price is larger the reserve price.