midterm_Winter2008

midterm_Winter2008 - Econ 51 Midterm Instructions This is a...

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Econ 51: Midterm February 11, 2008 Instructions: ° This is a closed book, closed-notes exam. You are allowed to use a hand-held calculator (i.e. no laptop). ° You have 110 minutes. ° Please answer all 3 questions. Please use a separate blue book for each question . Please write the name of your TA and section number (or section time) on each blue book. ° Note that throughout the midterm (and the class) log implies the natural logarithm. ° Always remember: think before you do the math ! ° Good luck! 1. Short questions (32 points) (a) (16 points, 4 points for each utility function) Let x and y be the consumption in two states of the world. Consider four utility functions: I. u ( x; y ) = exp(70 log(2 + x ) + 12 log(2 + y )) II. u ( x; y ) = log(70 exp(2 + x ) + 12 exp(2 + y )) III. u ( x; y ) = exp(70 exp(2 + x ) + 12 exp(2 + y )) IV. u ( x; y ) = exp(70 log(2 + x ) + 12 exp(2 + y )) For each of these utility functions, answer the following questions: (i) Does u ( x; y ) represent vNM preferences? Explain (in no more than two sentences). (ii) If the answer to (i) is yes, is an individual with such preferences exhibit risk aversion, risk neutrality, or risk loving? Explain in a single sentence. (iii) Regardless of the answer to (i), would an individual with this utility function be willing to participate (for free) in a lottery in which he gains 0.2 in the °rst state of the world (so x
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