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Ec701Midterm2SolutionsF05

Ec701Midterm2SolutionsF05 - Name[Last[First EC 701 Michael...

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Name: [Last], [First] EC 701 Microeconomics Michael Manove 18 November 2005 Midterm Examination 2 Solutions Instructions: Do not open the exam booklet until you are told to do so. Answer all of the following problems. Think before you write. Your grade will be based on your reasoning, not on your formal calculations. You will have 100 minutes to complete an 80-minute exam. If you fi nish before 10:10, you may leave. Otherwise please wait quietly until the end of the exam at 10:20. Do not write outside the answer boxes. You may use the backs of the sheets as scratch paper, or if necessary, continue your answers there, but do not write within 1 cm of the paper edge. Problem 1. [30 minutes] Suppose that Jonathan has a [Bernoulli] utility function given by u = log( y ) , where y is his wealth in money. a) [15 minutes] Suppose Jonathan has wealth y and is o ff ered a bet with a 50/50 chance of winning or losing βy dollars, where 0 < β < 1 . Write down the lottery that Jonathan faces if he accepts the bet. Find the expected utility of the lottery and its certainty equivalent c . EU = 1 2 log((1 + β ) y ) + 1 2 log((1 β ) y ) log c = 1 2 log(1 + β ) + 1 2 log(1 β ) + log y c = y q 1 β 2 b) [10 minutes] Why does the value of c that you derived suggest that Jonathan has constant relative risk aversion? The ratio ( y c ) /y 1 p 1 β 2 is the fraction of wealth that Jonathan is willing to pay to avoid the bet. The ratio is constant all levels of y . c) [5 minutes] Find the coe cient of relative risk aversion at wealth y . The coe cient of relative risk aversion r R ( y ) at outcome y is given by r R ( y ) ≡ − yu 00 ( y ) u 0 ( y ) = y μ 1 y 2 1 y = 1 .
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EC701 Midterm Exam 2 November 18, 2005 page 2 Problem 2. [50 minutes + 10 minutes extra credit]
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