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Assignmenttwo

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

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Economics 206 Spring 2007 (Prof. G. Loury) Assignment 2: Risk and Information 1. Concerning Measures of Risk Aversion: Let u i : < -→ < , i = 1 , 2 , be two strictly increasing, strictly concave, twice differentiable Bernoulli utility functions; and, let F : < -→ [0 , 1] be a cumulative distribution function for some real-valued random variable, ˜ y , which is the (positive or negative) reward from accruing some risky situation. So, agent i ’s preferences over gambles can be represented as follows: U i ( F ) = R u i ( y ) dF ( y ) , i = 1 , 2. Define c ( F ; u i ) to be the certainty equivalent of the gamble represented by F for agent i : c ( F ; u i ) u - 1 i [ R u i ( y ) dF ( y )] . We say that agent 1 is “more risk averse than agent 2” if and only if: F : c ( F ; u 1 ) 5 c ( F ; u 2 ). Prove that the following three claims are equivalent: (a) Agent 1 is more risk averse than agent 2. (b) There exists an increasing concave function v : < -→ < such that, y ∈ < : u 1 ( y ) = v ( u 2 ( y )) . (c) y ∈ < : - u 00 1 ( y ) u 0 1 ( y ) = - u 00 2 ( y ) u 0 2 ( y ) 2. Concerning Blackwell’s Theorem: Let C = { c 1 , ...c N }

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Assignmenttwo - Economics 206 Spring 2007(Prof G Loury...

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