Anna's Antiques expects to get two bidders for the unique china teacup it sells.Each of the bidders can either have a high-value of $100 or a low-value of $70 with equal probability.If Anna instead holds an oral auction between the two bidders and one bidder of each type shows up,she earn ___ from the auction.
A)Just above $100
B)$100
C)Just above $70
D)$70

Question

Anna's Antiques expects to get two bidders for the unique china teacup it sells.Each of the bidders can either have a high-value of $100 or a low-value of $70 with equal probability.If Anna instead holds an oral auction between the two bidders and one bidder of each type shows up,she earn ___ from the auction.
A)​Just above $100
B)$100
C)Just above $70
D)​$70

Quizplus · Accepted Answer

If Anna sells the teacup to one of the bidders randomly, she can expect an average revenue of $(0.5)(100)+(0.5)(70)=$85. However, if she holds an oral auction, the bidder with the high-value of $100 will bid $100 and the bidder with the low-value of $70 will bid up to the point where the expected value of the teacup is equal to their bid (i.e. $85). Therefore, Anna can expect to earn just above $70 from the oral auction.

Anna's Antiques Expects to Get Two Bidders for the Unique