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ProblemSet3-2009 - Econ 6202 Fall 2009 Dmitry Shapiro...

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Econ 6202, Fall 2009 Dmitry Shapiro Problem Set 3 Due Tuesday September 22 1. (JR 2.8) The consumer buys bundle x i at price p i , i = 0 , 1. Separately for parts (a) to (d), state whether these indicated choices satisfy WARP: (a) p 0 = (1 , 3) , x 0 = (4 , 2); p 1 = (3 , 5) , x 1 = (3 , 1). (b) p 0 = (1 , 6) , x 0 = (10 , 5); p 1 = (3 , 5) , x 1 = (8 , 4). (c) p 0 = (1 , 2) , x 0 = (3 , 1); p 1 = (2 , 2) , x 1 = (1 , 2). (d) p 0 = (2 , 6) , x 0 = (20 , 10); p 1 = (3 , 5) , x 1 = (18 , 4). 2. Consider the set outcome C = { c 1 , c 2 , c 3 } , and let L denote the set of simple lotteries over C . Suppose that the preference relation over L satisfies the independence axiom, and that c 1 c 2 c 3 . Show that c 1 L c 3 for every lottery L . 3. Suppose that U : L → R represents the preference relation . Show that if U has the expected utility form, then satisfies the independence axiom. 4. Consider the following lotteries: ( L 1 ) $5000 for sure; ( L 2 ) a 1 10 chance of $30,000 and a 89 100 chance of $5000 (and a 1 100 chance of nothing); ( L 3 ) a 11 100 chance of $5000 (and a 89 100 chance of nothing); and ( L 4 ) a 1 10 chance of $30,000 (and a 9 10 chance of nothing). Are the preferences L 1 ´ L 2 and L 4 ´ L 3 consistent with the independence axiom? (Assume that the preference relation is continuous.)
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