A seller decides to sell an object by means of a sealed-bid second-price auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $400 and a probability of 1/2 that the bidder's value is $300.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally, what is the seller's expected revenue from the auction?
A)$325
B)$400
C)$350
D)$320
E)$340

Question

Quizplus · Accepted Answer

The expected revenue is the sum of the expected payments from each bidder. The expected payment from a bidder is the probability that the bidder wins times the amount the bidder pays. The probability that a bidder wins is the probability that the bidder's bid is higher than the other bidder's bid. The amount the bidder pays is the second highest bid.The probability that a bidder's value is $400 is 1/2. The probability that a bidder's bid is higher than the other bidder's bid is 1/2. The amount the bidder pays is $300. Therefore, the expected payment from a bidder is (1/2) * (1/2) * $300 = $75.The expected revenue is the sum of the expected payments from each bidder. Therefore, the expected revenue is $75 + $75 = $150.

A Seller Decides to Sell an Object by Means of a Sealed-Bid