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Unformatted text preview: outcomes. U(P A )= U(P B ) => .4+.1U($50)+.4U($20)=.56 U(P C )= U(P D ) => .1+.4U($50)+.1U($20)=.44 So that, U($50)=.8 and U($20)=.2 Therefore, U((p,0,0,1p))= p =U($50)=.8; U((q,0,0,1q))= q =U($20)=.2 (d) P=(a, b, c, d) with a+b+c+d=1 and a, b, c, d in [0,1]. U(P)=a+.8b+.2c 3. Jiongs preference: alpha=.668 U($400)=1, U($0)=0 A~$300, B~$200 and C~$100 => U(P A )=U($300)=.75+.25U($200), U(P B )=U($200)=.6, U(P C )= U($100)=.55U($200) 2 U($100)=.33, U($200)=.6 and U($300)=.9 U(P D )=.35U($400)+.18U($300)+.15U($200)+.2U($100)+.12U($0)=.668= alpha 4. Dutta, Ch. 27: 19 U(x)=log(10+x) U(A)=.5log(10+1)+.5log(101)=.9978 U(B)=.5log(10+5)+.5log(105)=.9375 5. Dutta, Ch. 27: 20 U(C)=.25log(10+13)+.25log(10+16)+.5log(104)=1.083 Since U(C)>U(A)>U(B), the ranking of preference is C>A>B. Lottery C is the most preferred. 6. E.g. $100 $0 $50...
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 Spring '11
 econ
 Game Theory

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