finalexamspring2003

finalexamspring2003 - Your Name: _ Final Exam: 16 May 2003...

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1 Your Name: ____________________________ Final Exam: 16 May 2003 Econ 431 David Reiley You have 120 minutes to take this exam There are a total of 100 points possible, plus one extra-credit question worth 15 points. Please make sure to pace yourself, so that you answer all questions, even incompletely. I do give partial credit for incomplete work, but I give zero credit for blank pages. In order to get partial credit in case you make an error, you will want to explain carefully what you are doing. 1) Lucy van Pelt offers to play the following game with Charlie Brown: “Let us each simultaneously reveal pennies to each other, each separately choosing either heads or tails. If we both show heads, I pay you $3. If we both show tails, I pay you $1. If the two don’t match, you pay me $2.” 1 a) (10 points) Provide a normal-form payoff matrix for this game, with Charlie Brown as the row player and Lucy as the column player. 1 This problem comes from course materials developed by Avinash Dixit at Princeton University.
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2 b) (10 points) Charlie Brown reasons as follows: “The probability of both heads is 1/4, in which case I get $3. The probability of both tails is 1/4, in which case I get $1. The probability of no match is 1/2, and in that case I pay $2. So the expected value is 0, making it a fair game.” What is the flaw in Charlie Brown’s reasoning? What is Lucy’s expected profit in equilibrium?
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3 2) You are the Dean of the Faculty at St. Anford University. You hire Assistant Professors for a probationary period of 7 years, after which they come up for tenure and are either promoted, to gain a job for life, or turned down, in which case they must find another job elsewhere. Your Assistant Professors come in two types, Good and Brilliant. Any types worse than Good have already been weeded out in the hiring process, but you cannot directly distinguish between Good and Brilliant types. Each individual Assistant Professor knows whether he/she is Brilliant or merely Good. You would like to tenure only the Brilliant types. The payoff from a tenured career at St. Anford is $2 million; think of this as the expected discounted present value of salaries, consulting fees, and book royalties, plus the monetary equivalent of the pride and joy that the faculty member and his/her family would get from being tenured at St. Anford. Anyone denied tenure at St. Anford will get a faculty position at Boondocks College, and the present value of that
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finalexamspring2003 - Your Name: _ Final Exam: 16 May 2003...

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