A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $900.There are two bidders.The dealer believes that there are only three possible values that each bidder's willingness to pay might take, $6,700, $3,400, and $900.Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the automobile is

A) $5,050.
B) $3,400.
C) $2,900.
D) $3,666.67.
E) $6,700.

Question

shamma AlAmiri · Accepted Answer

Final Answer : D, Explanation :  To find the expected revenue, we need to consider all possible outcomes of the auction.If both bidders have a willingness to pay of $6,700, the highest possible value, then the bidding will continue until one drops out. The other bidder will win with a price of $6,800 ($100 above the other bidder's final bid).If one bidder has a willingness to pay of $6,700 and the other has a willingness to pay of $3,400, then the auction will end at $6,700.If both bidders have a willingness to pay of $3,400, then the auction will end at $900, since neither will bid more than the reservation price.Using the probabilities given, there is a 1/9 chance of both bidders having a willingness to pay of $6,700, a 2/9 chance of one having $6,700 and the other having $3,400, and a 2/9 chance of both having $3,400.Therefore, the expected revenue is (1/9)($6,800) + (2/9)($6,700) + (2/9)($900) = $3,666.67.Therefore, the answer is (D).

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