eco331-04b-EUcalculations

Eco331-04b-EUcalcula - Some practice EU calculations X = R X = 100 1 3 1 2 3 Preferences u x = log 10 x Expected Value E X = 1 3 100 2 3 1 = 34

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Unformatted text preview: Some practice EU calculations X = R + X = ( 100 , 1 3 ; 1 , 2 3 ) . Preferences: u ( x ) = log 10 x Expected Value : E [ X ] = 1 3 · 100 + 2 3 · 1 = 34. Expected Utility : E [ u ( X )] = 1 3 log 10 100 + 2 3 log 10 1 = 2 3 . Some practice EU calculations X = R + X = ( 100 , 1 3 ; 1 , 2 3 ) . Preferences: u ( x ) = log 10 x Expected Value : E [ X ] = 1 3 · 100 + 2 3 · 1 = 34. Expected Utility : E [ u ( X )] = 1 3 log 10 100 + 2 3 log 10 1 = 2 3 . Certainty Equivalent : x such that δ x = ( x , 1) ∼ X . Some practice EU calculations X = R + X = ( 100 , 1 3 ; 1 , 2 3 ) . Preferences: u ( x ) = log 10 x Expected Value : E [ X ] = 1 3 · 100 + 2 3 · 1 = 34. Expected Utility : E [ u ( X )] = 1 3 log 10 100 + 2 3 log 10 1 = 2 3 . Certainty Equivalent : x such that δ x = ( x , 1) ∼ X . Therefore must have E [ u ( δ x )] = E [ u ( X )] Some practice EU calculations X = R + X = ( 100 , 1 3 ; 1 , 2 3 ) . Preferences: u ( x ) = log 10 x Expected Value : E [ X ] = 1 3 · 100 + 2 3 · 1 = 34. Expected Utility : E [ u ( X )] = 1 3 log 10 100 + 2 3 log 10 1 = 2 3 . Certainty Equivalent : x such that δ x = ( x , 1) ∼ X . Therefore must have E [ u ( δ x )] = E [ u ( X )], i.e. 1 · log 10 x = 2 3 (as computed above) Some practice EU calculations X = R + X = ( 100 , 1 3 ; 1 , 2 3 ) ....
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This note was uploaded on 11/17/2009 for the course ECONOMICS 331 taught by Professor Marciano during the Spring '09 term at Northwestern.

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Eco331-04b-EUcalcula - Some practice EU calculations X = R X = 100 1 3 1 2 3 Preferences u x = log 10 x Expected Value E X = 1 3 100 2 3 1 = 34

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