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theoryfinalf07 - Name Final Exam Econ 210A Answer as many...

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Name Final Exam, Econ 210A Answer as many questions as you can. Enjoy. 1. A poor fellow is an expected utility maximizer with a von Neumann Mor- genstern utility function v ( x ) = x 1 / 2 . He has a wealth of $99 , 000. His shady brother-in-law has given him inside information on the outcome of an upcoming sports event. On the basis of this information, the poor fellow believes that the probability that Team A will defeat Team B is 2/3, despite the fact that Team B is two-to-one favorite to win among the betting community. It is possible for the poor fellow to bet as much money as he wishes on Team A to win at the prevailing odds. That is, for every dollar that he bets, he will get back $2 if Team A wins and will get back nothing if Team A does not win. a. Let x A be the contingent commodity “wealth if Team A wins” and let x B be “wealth if Team B wins.” Write a budget equation expressing the combinations of x A and x B that the poor fellow can afford by betting some amount of money on Team A. Draw a graph to show all of these combinations. b. If this poor fellow bets so as to maximize his expected utility, what will be his wealth if Team A wins? What will be his wealth if Team B wins? c. Another poor fellow has a von Neumann Morgenstern utility function v ( x ) = - x - 1 and he also has a wealth of $99 , 000. He has the same shady brother- in-law and the same inside information on the outcome of an upcoming sports event. This poor fellow also believes that the probability that Team A will
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