midterm+_winter2007

midterm+_winter2007 - Econ 51: Midterm February 12, 2007...

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Econ 51: Midterm February 12, 2007 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 on each blue book. Always remember: think before you do the math ! Good luck! 1. Short questions (36 points, 6 points each) (a) Let x and y be the consumption in two states of the world. Let u ( x; y ) = ± 10 + 2 log( x ) + 6 log( y ) + 21 y 3 + 7 x 3 . Does u ( x; y ) represent vNM preferences? If yes, express these preferences with a utility function that has the vNM form. (b) There are apples ( a ) and bananas ( b ). Rob’s utility function is u R ( a; b ) = log( a )+log( b ). Tom’s utility function is u T ( a; b ) = e log( a )+log( b ) + b . There are 20 apples and 20 bananas (c) There are apples ( a ) and bananas ( b ). Rob’s utility function is u R ( a; b ) = log( a )+log( b ). Tom’s utility function is u T ( a; b ) = 2 log( a )+2 log( b ). There are 3 apples and 3 bananas on the island. Derive the contract curve.
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midterm+_winter2007 - Econ 51: Midterm February 12, 2007...

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