assignmentthree

assignmentthree - Economics 206 Spring 2007 (Prof. G....

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Economics 206 Spring 2007 (Prof. G. Loury) Assignment 3: Applications of Stochastic Dominance 1. Let α 0 be a random variable representing a worker’s true ability. Consider two tests of worker ability, i =1 , 2 , with test scores t 1 and t 2 given by: t 1 = α + ε and t 2 = α + ε + η, where ε and η are real-valued, zero mean, statistically independent random variables representing error in the testing process. Suppose that a worker with test score t is paid a wage equal to his conditional mean ability, given that test score. Thus: μ i ( t )= E [ α | t i = t ] ,i =1 , 2 . gives the wage of a worker whose score on test i is t. Show that the population dis- tribution of wages under test i =1 is “more unequal” (i.e., “riskier” in the sense of second-order stochastic dominance) than is the population distribution of wages under test i =2 . 2. Consider an expected utility maximizing agent who does not know how much money is in his bank account. Let ˜ y 0 be this uncertain balance, with
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assignmentthree - Economics 206 Spring 2007 (Prof. G....

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