3. Individual Problems 183 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 prot of SD for the auctioneer. If only one bidder values the item at or above the reserve pricef that bidder pays the reserve price. An auctioneer laces two bidders, each with a value of either $50 or 580, with both values equally probable. Without a reserve pricer 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. Oh the foliowrng tabie, 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) (:3) Probability (5') Price with $80 Reserve Price 560 $50 0.25 V V $50 $00 0.25 v v 580 560 0.25 V V $80 $00 0.25 v V Without a reserve pricef the expected price isl:l . With a reserve price of $80, the expected price isl:l. Thus, the expected price is larger V the reserve price