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Behavioural economics.pdf - Problem set 2 Due date This...

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Problem set 2 Due date This problem set is due at the beginning of class on Monday September 18th. Alternatively, you can email the problem set to the TA on the same date. Remember, there is a 10% per day penalty for late problem sets. Questions 1. Show that von-Nuemann Morgenstern utility functions are invariant under affine transfor- mation. i.e. Show that if U ( L ) = i p i u ( x i ) represents the preference relation then U 0 ( L ) = i p i ( au ( x i ) + b ) also represents . What does this imply about normalizations of utility functions? 2. Consider the following lotteries over three outcomes, where x 0 < x 1 < x 2 . A = ( x 0 , 0; x 1 , 0 . 5; x 2 , 0 . 5) , B = ( x 0 , 0 . 2; x 1 , 0 . 3; x 2 , 0 . 5) , C = ( x 0 , 0 . 1; x 1 , 0 . 2; x 2 , 0 . 7) , D = ( x 0 , 0 . 1; x 1 , 0 . 6; x 2 , 0 . 3). Plot the lotteries in a Marschack-Machina triangle. Identify all FOSD relationships between the 4 lotteries. Shade the region of the triangle that contains all of the lotteries that are FOSD by lottery B. 3. Consider each of the following paradoxes. For each one, discuss whether you think your mother’s preferences would generate the paradox (use
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