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Problem 3: Auctioning the Business
After a long career as an entrepreneur, you have decided to sell your business and retire. You know that two businesspeople are interested in acquiring your firm. You know with certainty that one of the buyers, Ms. A, has a willingness-to-pay of $100 million. You have less information about the other prospective buyer, Mr. B, but you think that with probability 60% his WTP is $80m, with probability 20% it is $90m, and with probability 20% it is $110m.
Note: Be careful in your calculations of expected values in these questions. You may wish to refer to your notes from the Managerial Statistics class.
(a) (2 points) If you sell your business through a 2nd Price (Vickrey) auction, what is your expected revenue? Please explain how you arrived at your answer.
(b) (3 points) Suppose that, with probability 10%, Ms. C is also interested and she is willing to pay $1 billion ($1000 million) for your company. Assume that the probability that Ms. C enters the auction is uncorrelated with Mr. B’s WTP. How does this change your expected revenue from the auction? Please be sure to explain why.
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