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 $144 or $192, with both values equally probable. Without a reserve price, the second highest bid will be the price paid by the winning bidder. The following table lists the four possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder with and without the stated reserve price. Bidder 1 Value Bidder 2 Value Price Without Reserve (3) ($) Probability ($) Price with $192 Reserve Price $144 5144 0.25 V 7 $144 $192 0.25 v v $192 5144 0.25 Y Y $192 $192 0.25 V v Without a reserve price, the expected price i_ . With a reserve price of $192, the expected price i- . Thus, the expected price is larger 7 the reserve price