A dealer decides to sell an oil painting by means of an English auction with a reservation price of slightly below $70,000.If she fails to get a bid as high as her reservation price, she will burn the painting.There are two bidders.The dealer believes that each bidder's willingness to pay will take one of the three following values: $80,000, $70,000, and $45,000.The dealer believes that each bidder has a probability of 1/3 of having each of these three values.The probability distribution of each buyer's value is independent of that of the other's.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the painting is slightly less than

A) $70,000.
B) $59,000.
C) $75,000.
D) $50,000.
E) $65,000.

Question

Patrick Kazehaya · Accepted Answer

Final Answer : A, Explanation :  The dealer's expected revenue is the sum of the probabilities of each possible outcome multiplied by the corresponding revenue. The possible outcomes are:1. Both bidders have a willingness to pay of $80,000. In this case, the dealer will sell the painting for $80,000. The probability of this outcome is (1/3) * (1/3) = 1/9.2. One bidder has a willingness to pay of $80,000 and the other has a willingness to pay of $70,000. In this case, the dealer will sell the painting for $70,000. The probability of this outcome is (1/3) * (1/3) * 2 = 2/9.3. Both bidders have a willingness to pay of $70,000. In this case, the dealer will sell the painting for $70,000. The probability of this outcome is (1/3) * (1/3) = 1/9.4. One bidder has a willingness to pay of $70,000 and the other has a willingness to pay of $45,000. In this case, the dealer will not sell the painting. The probability of this outcome is (1/3) * (1/3) * 2 = 2/9.5. Both bidders have a willingness to pay of $45,000. In this case, the dealer will not sell the painting. The probability of this outcome is (1/3) * (1/3) = 1/9.The dealer's expected revenue is therefore:(1/9) * $80,000 + (2/9) * $70,000 + (1/9) * $70,000 + (2/9) * $0 + (1/9) * $0 = $70,000Since the dealer's reservation price is slightly below $70,000, she will not burn the painting and will instead sell it for $70,000.

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