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Lecture18-2010 - Utility Functions Risk Aversion...

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Unformatted text preview: Utility Functions, Risk Aversion Coefficients and Transformations: Lecture XVIII Charles B. Moss October 6, 2010 I. An examination of the Arrow-Pratt Coefficients for particular func- tions. A. Quadratic Utility Function: To specify the appropriate shape of the utility function, the quadratic function becomes U ( w ) = aw − bw 2 U ( w ) = a − 2 bw U 00 ( w ) = − 2 b (1) Arrow-Pratt absolute risk aversion coefficient R A ( w ) = − − 2 b a − 2 bw ⇒ R A ( w ) = 2 b a − 2 bw dR A ( w ) dw = 2 b 2 b ( a − 2 bw ) 2 > ⇐ d dx 1 f ( x ) = − f ( x ) ( f ( w )) 2 (2) Arrow-Pratt relative risk aversion coefficient R R ( w ) = 2 b a − 2 bw w = 2 b a w − 2 b dR R ( w ) dw = 2 b 2 b ( a − 2 bw ) 2 + 2 b a − 2 bw > (3) 1 AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XVIII Fall 2010 B. Power Utility Function U ( w ) = w 1 − r 1 − r U ( w ) = w − r U 00 ( w ) = − rw − r − 1 (4) Arrow-Pratt absolute risk aversion coefficient R A ( w ) = − − rw − r − 1 w − r = r w dR A ( w ) dw = − r w 2 < (5) Arrow-Pratt relative risk aversion coefficient R R ( w ) = − rw − r − 1 w w − r = r dR R ( w ) dw = 0 (6) Constant relative risk aversion....
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Lecture18-2010 - Utility Functions Risk Aversion...

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