Answer:
Reserve price = $6.25
Approximately $7
Explanation:
Reserve price is the lowest set price that is acceptable by a seller at an auction.
With probability 1/2:
Buyer values = $5 and $7
Buyer values= $3 and $10
Since the seller knows there are two bidders for the object he is selling and he wants to maximize his expected profits. He also sells it in an English auction which he must set the reserve price before the commencement of the auction. His reserve price should be:
[tex] (\frac{5*1}{4}+\frac{7*1}{4}) + (\frac{3*1}{4}+\frac{10*1}{4}) [/tex]
= (1.25 + 1.75) + (0.75 + 2.5)
= 3 + 3.25
$6.25
The maximize his expected profit the buyer should set his reserve price at approximately $7
Answer:
$6
Explanation:
bidder 1:
50% chance paying $5
50% chance paying $7
expected value = ($5 x 50%) + ($7 x 50%) = $6
bidder 2:
50% chance paying $3
50% chance paying $10
expected value = ($3 x 50%) + ($10 x 50%) = $6.50
According to Myerson's optimal reserve price theory, the reserve price does not depend on the number of bidders, instead it depends on the distribution of the buyers' valuation. In this case, both buyers' valuations are very similar, $6 and $6.50, so one of them should be the reserve price. Since this is an open bid and the reserve price will probably serve as reference point, the reserve price should be $6 so that both bidders can participate and hopefully the price will exceed $7 (the highest second bid).
