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eco331-04b-EUcalculations - Some practice EU calculations X...

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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 .
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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 .
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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 )]
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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)
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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 .
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