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Unformatted text preview: ECN 712 Fall 2007 Edward Schlee Final Exam 1. (20 points) Risk aversion and risk . Two consumers, A and B, satisfy the expected utility hypothesis over money lotteries; consumer t s preferences are represented by the strictly increasing vN-M utility u t on R + for t = A,B . Consumer A weakly prefers the sure wealth of y &gt; 0 to the lottery L with two equally likely outcomes, z 1 or z 2 , with 0 &lt; z 1 &lt; z 2 . Consumer B is strictly more risk averse than A : u B ( z ) = T ( u A ( z )), for some strictly increasing, strictly concave real-valued function T on Range ( u A ). (a) (10) Prove that consumer B strictly prefers the sure wealth of y to the lottery L . (b) (10) Suppose that u A is strictly concave and differentiable everywhere (and that A still weakly prefers the sure thing to the lottery L ). Show that consumer A strictly prefers the sure wealth of y to a lottery with gives two equally likely outcomes, z 1- or z 2 + , where 0 &lt; &lt; z 1 . 2. (30 points) Technology Choice . A monopoly produces and sells a single output under constant returns to scale. Its technology, hence its unit production cost, depends on how much it invests before production; if the firm spends I 0 dollars, then its...
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