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solution

Auctions (Part 1)
(a) Suppose there is an oral/English auction for an item with three bidders who come from
two pools of buyers: high-value buyers and low-value buyers. High-value buyers are
willing to pay $100 for the item being auctioned. Low-value buyers are willing to pay
$50. For each bidder who joins the auction, there is an equal probability (50% chance)
that he/she comes from either pool of buyers. What is the expected revenue from this
auction?
(b) Re-do part (a), but now calculate the expected revenue if the auction were a Vickrey, or
second-price, auction.
(c) Compare your answers in parts (a) and (b). Discuss what you found. What does this
imply about oral/English auctions and Vickrey auctions?
(d) Suppose after analyzing the results in parts (a) and (b), the seller decides to conduct a
sealed-bid first-price auction with a $75 reservation price. The reservation price means
that the item would only be sold if the maximum bid was $75 or higher. If the maximum
bid was below $75, the item would not be sold and the seller would collect $0 in
revenue. What is the expected revenue from this auction?

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