A seller knows that there are two bidders for the object he is selling. He belie
ID: 3181348 • Letter: A
Question
A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of $10 and the other has a buyer value of $15 and, with probability 1/2, one has a buyer value of $7 and the other has a buyer value of $24. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must set before the auction starts. To maximize his expected profits, he should set the reserve price at
Explanation / Answer
Answer
He should set the reserve price at $19.5
Justification
The first bidder is likely to bid $10 with probability ½ and $7 with probability ½. So, the expected bid from the first bidder = (½ x 10) + (½ x 7) = $8.5.
Similarly, the expected bid from the second bidder = (½ x 15) + (½ x 24) = $19.5.
Thus, the seller can expect $19.5 and hence he must quote the reserve price as $19.5.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.