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A reserve price is a minimum price set by the auctioneer. If no bidder is willing to pay the reserve price, the item is unsold at a profit of $0 for the auctioneer. If only one bidder values the item at or above the reserve price. An auctioneer faces two bidders, each with a value of either $30 or $80, with both values equally probable. What reserve price should the auctioneer set, and what is the expected revenue from auctioning the item with and without a reserve price?

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Answer:

Reserve price = $55

Expected revenue with a reserve price = $55

Expected revenue without a reserve price = $55

Explanation:

The auctioneer should set the reserve price siguiente:

Reserve price = ($30x0.5) + ($80x0.5) = $15 + $40 = $55

In the case of the expected revenue with the reserve price, only the bidder who has set a $80 value will pay the reservation fee, then the expected revenue will be the reserve fee of $55.

In the case of the expected revenue without the reserve price, both of the bidders will enter the auction for the item. Since the values are equally probable the expected profit without the reservation fee is equally $55.  

Hope this helps!

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