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Midterm1Ans

Midterm1Ans - Midterm Answers to Midterm Problems Econ 100C...

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1. There are three bidders in an auction for a single object. Each individual knows his own value for the object, but nobody knows anyone’s value but their own. The other bidders and the seller think of any bidder’s value as a random variable which is equally likely to be any amount between 0 and \$100. As it turns out, the actual values are as follows. Bidder 1 values the object at \$90, bidder 2 values it at \$75 and bidder 3 values it at \$45. A) If the object is sold in an English auction and bidders all behave rationally, approximately what price will the seller get for it? \$75 B) If the object is sold in a second-price sealed bid auction and all bidders bid rationally, approximately what price will the seller get for it? \$75 C) If the object is sold in a ﬁrst-price sealed bid auction, and each bidder uses an equilibrium strategy, how much will each bidder bid? What price does the seller receive for the object? Each will bid 2/3 of his value. Seller will get \$60. 2. A) What is the ”revenue equivalence theorem?” The revenue equivalence theorem is the result that in a private values auction where a single object is sold and where the probability distribution of individual values is continuous and independent among individuals, the ex- pected revenue in a Nash equilibrium between bidders is the same for any type of auction that has the following characteristics. a) In equilibrium the object is sold to the person with highest buyer value. b) The expected winnings or losses of the person with lowest buyer value is zero. The ﬁrst price sealed bid auction, the English auction, the Dutch auction, and the second price sealed bill auction all have these properties and hence yield the same expected revenue under the above assumptions. 1

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Midterm1Ans - Midterm Answers to Midterm Problems Econ 100C...

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