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final10 - Name Final Exam Econ 210A December 2010 Answer...

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Name Final Exam, Econ 210A, December, 2010 Answer all five questions. Question 1. A) Define the Arrow-Pratt measure of absolute risk aversion. B) Consider the following von Neumann Morgenstern utility function u ( x ) = - 1 α e - αx . For what values of α is a consumer with this utility function risk-averse? Does this consumer display increasing, decreasing, or constant absolute risk aversion? Explain.
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C) Consider the following von Neumann Morgenstern utility function u ( x ) = 1 α x α . For what values of α is a consumer with this utility function risk-averse? Does this consumer display increasing, decreasing, or constant absolute risk aversion? Does this consumer display increasing, decreasing, or constant relative risk aversion? Explain D) Ulrich and Virgil have twice-differentiable von Neumann Morgenstern util- ity functions u ( x ) and v ( x ). Virgil’s utility function is given by v ( x ) = f ( u ( x )) where f ( · ) is a strictly increasing and strictly concave function. Prove that Virgil’s is strictly more risk averse than Ulrich by the Arrow-Pratt mea- sure of risk aversion.
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Question 2.
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