1. Anny is deciding whether to bet on a volleyball match. A friend offers to giv

Question

1. Anny is deciding whether to bet on a volleyball match. A friend offers to give her 64 dollars if the lower ranked team wins provided that she pays him 11 dollars when the higher ranked team wins. The utility that she derives from a (positive or negative) cash transfer of x dollars is determined by the following utility function, Anny believes that the probability of the lower ranked player winning the match is p. (a) Find the expected value of this lottery. For what values of p is the expected value positive? (4 marks) (b) Find Anny's expected utility when betting on the match. For what values of p would she accept the bet? (6 marks) (c) Find Anny's certainty equivalent for this lottery when p-2/5. (5 marks)

Explanation / Answer

ANs a)

Lets assume "p" be the probability

Expected value of lottary =Prob. of winning* Outcome from winning +Prob. of Losing * Outcone from Losing=p*64+(1-p)*(-11)=64p-11+11p=75p-11

Expected Value of Lottary = E(X)=75p-11>0 when p>11/75

Ans b)

Simlar method to find expected value of utility

E(U)=pU(64)+(1-p)U(11)=p(36+64)^(1/2)+(1-p)(36+11)^(1/2)=p*10+(1-p)(47)^1/2=10p+6.86-6.86p=3.14p+6.86

E(U)=3.14p+6.86>0

Then p>=0 will do to accept the bet

Ans c)

Certainty premium=EMV-EU^(-1)=EV-EU^(-1)=75p-11-EU^(-1)

Now E(U)=3.14p+6.86

(36+x)^1/2=3.14p+6.86

we need to find x in p terms

(3.14p+6.86)^2-36=x=9.8596p^2+21.5404p+47.0596

x=9.86p^2+21.54p+47.06

Hence Certainity Equivalent will be

CE=75p-11-9.86p^2-21.54p-47.06=53.46p-47.06-9.86p^2

When p=2/5

CE=-27.2536

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