HW 6 - #2 U(w) = 3w^.5 W = 100 U(100) = 30 EU =...

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HW 6 #1 Alvin’s utility function is U = W Barry’s utility function is U = W^2 Carl’s utility function is U = W^0.5 Initial W = 100 Alvin U(100) = 100 Barry’s U(100)= 10,000 Carl’s U(100)= 10 Alvin’s EU = .9(U(0)) + .1(U(1000)) = .9(0) + .1(1000) = 100 Barry’s EU = .9(U(0)) + .1(U(1000)) = .9(0) + .1 (1,000,000) = 100,000 Carl’s EU = .9(U(0)) + .1(U(1000)) = .9(0) + .1(√1000) = 3.16 Alvin’s expected utility from the bet equals his certain utility from his wealth. He is indifferent to the investment. He is risk neutral. Barry’s expected utility from the bet = 100,000 compared to his certain utility from his current wealth of 10,000. He will invest and is risk loving. Carl’s expected utility from the bet is 3.16. This is less than his certain utility from his wealth of 10. He is risk adverse and will not invest.
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Unformatted text preview: #2 U(w) = 3w^.5 W = 100 U(100) = 30 EU = .03(U(25-5)) + .97(U(100-5)) = .03(13.416) + .97(29.24) = 28.765 Stephans certain utility is 30 from his current wealth. His expected utility from the bet is 28.765. He is risk adverse and will not take the bet. #3 U() = 0 runs it herself E() = E(U) .7(10) +.2(90) + .1(.790) = 90 Agent w = 10 L = w (1/2) 2 = 1.16 H = w (1/2) 3 = .16 Plan C1 effort 100 800 L 0.7 0.2 0.1 H 0.1 0.2 0.7 C2 W = 40 if = 800 L= ((40-2) *.1)) + ((-2) *. 7) + ((.2) * 2)) = -1.350 H = ((-3) *1) + ((-3)*.2) + (( 40) 2(.7)) = 1.43 E() = EU2 = .1(0) + 100(.2) + 760(.7) = 552 a) He would accept either compensation method. b) Bucarram would like C2 if he works hard because his Expected utility is highest. c) E(U2) > E(U1) so C2 is better for Sloan too....
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This note was uploaded on 04/11/2009 for the course ARE 100B taught by Professor Whitney during the Fall '08 term at UC Davis.

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HW 6 - #2 U(w) = 3w^.5 W = 100 U(100) = 30 EU =...

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