Hello! I would really appreciate if you could help me out with this problem... T

Question

Hello! I would really appreciate if you could help me out with this problem... Thanks very much.

Sotheby's plans to auction a famous Picasso. There are 5 bidders with values distributed uniformly between $0 and $50 million. (a) Suppose that Sotheby's holds a second-price sealed bid auction with no reserve price. What is the expected revenue? (b) The seller proposes to hold an all-pay auction to try to get as much money as possible. In an all-pay auction, each bidder places a bid, the bidder with the highest bid wins the object, but all bidders pay their bids. Bids must be non-negative. (i) In an all-pay auction what should a bidder with the lowest possible value ($0) bid? (ii) In equilibrium, bids in an all-pay auction are a strictly increasing function of a bidder's value. Explain why this fact, and yours answer to (a) and (b)(i), imply that the expected revenue from the all-pay auction is $33.3 million. (c) Suppose that Sotheby's now plans to hold a second-price auction with a reserve price. (i) What is the optimal reserve price if Sotheby's knows that there will be 5 bidders? (ii) What is the optimal reserve price if Sotheby's thinks that there will be 5 bidders with probability 0.5 and 10 bidders with probability 0.5? Explain.

Explanation / Answer

a)given range is 0 to 50 million and for the 5 bidders

the expected revenue is between 0 to 50 ie o+50/5=50/5=10 milllion

b)the lowest auction value must be 5 million

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