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Unformatted text preview: Economics 467 Spring 2010 Karl Dunz Problem Set 1 Answers 1. [6 points] Consider the following three lotteries: u1D43F 1 = [480 , . 5; 480 , . 5], u1D43F 2 = [850 , . 5; 200 , . 5], and u1D43F 3 = [1000 , . 5; 0 , . 5]. Each lottery represents the consumption an agent would receive if they invested in the corresponding project. (a) A risk-neutral agent will choose the lottery with the highest expected value, which is u1D43F 2 . (b) A risk-averse agent with a von Newmann-Morgenstern utility function of u1D462 ( u1D450 ) = u1D450 1 / 2 will choose lottery u1D43F 1 since u1D462 (480) > . 5 u1D462 (850) + . 5 u1D462 (200) > . 5 u1D462 (1000). How- ever, not all risk-averse agents would make the same choice since the other lotteries have higher expected values. So a person who is less risk averse might prefer u1D43F 2 . (c) A risk-loving agent with a von Newmann-Morgenstern utility function of u1D462 ( u1D450 ) = u1D450 2 will choose u1D43F 3 . However, it is possible that a risk-loving agent could prefer u1D43F 2 if they were less risk loving since that lottery has a higher expected value....
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