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ECON 206

# ECON 206 - Economics 206 Spring 2007(Prof G Loury...

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Economics 206 Spring 2007 (Prof. G. Loury) Assignment 1: Choice under Uncertainty 1. Concerning the Independence Axiom: L L 0 ⇐⇒ ∀ α [0 , 1] , L 00 : αL + (1 - α ) L 00 αL 0 + (1 - α ) L 00 (a) ( The Axiom extends to strict preference and to indifference. ) Show that the In- dependence Axiom implies: (i) L ´ L 0 ⇐⇒ ∀ α (0 , 1] , L 00 : αL + (1 - α ) L 00 ´ αL 0 + (1 - α ) L 00 (ii) L L 0 ⇐⇒ ∀ α [0 , 1] , L 00 : αL + (1 - α ) L 00 αL 0 + (1 - α ) L 00 (b) ( The Axiom implies there is a best and a worst lottery .) Let the set of consequences be finite: C = { c 1 , ..., c N } , and let L n be the lottery giving consequence c n with probability 1, n = 1 , ..., N . Assume, WLOG, that L 1 L 2 ... L N . Then, show that the Independence Axiom implies: lotteries L : L 1 L L N 2. Try to work through the following exercises from the text: page 208 number 6.B.4; and, page 209 number 6.B.6. 3. ( The demand for insurance .) An expected utility maximizing agent with wealth W either suffers a loss, D , reducing his wealth to W - D ; or, loses nothing and maintains his wealth at W . Let
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