2010_lecture_10_ho

# 2010_lecture_10_ho - Economics 101Lecture 10 Risk and...

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Economics 101—Lecture 10 Risk and Uncertainty II George J. Mailath February 17, 2011

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In our last episode 1 Consider two gambles, X = ( π 1 , x 1 ; π 2 , x 2 ; . . . ; π n , x n ) , π i = Pr ( x i ) , and ˆ X = ( ˆ π 1 , ˆ x 1 ; ˆ π 2 , ˆ x 2 ; . . . ; ˆ π m , ˆ x m ) , ˆ π j = Pr ( ˆ x j ) . Expected utility maximizer with utility function u for money: X ± ˆ X ⇐⇒ n i = 1 π i u ( x i ) m j = 1 ˆ π j u ( ˆ x j ) . 2 Decision maker with utility function u is risk neutral if for all gambles X , u ( EX ) = Eu ( X ) .
Risk Aversion Decision maker with utility function u is risk averse if for all gambles X satisfying Pr ( X ± = EX ) > 0, u ( EX ) > Eu ( X ) , that is, u ²² < 0.

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State-Contingent Wealth Two states, bad and good, with probabilities π b and π g . MRS bg = π b u ± ( x b ) π g u ± ( x g ) = π b π g on the certainty line x b = x g .
State-Contingent Wealth Two states, bad and good, with probabilities π b and π g . Initial situation (endowment):

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2010_lecture_10_ho - Economics 101Lecture 10 Risk and...

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