Ann is deciding whether to bet on a tennis match. A friend offers to give her 20

Question

Ann is deciding whether to bet on a tennis match. A friend offers to give her 20 dollars if the lower ranked player wins, while she has to pay him 12 dollars otherwise. The utility that she derives from a (positive or negative) cash transfer of x dollars is determined by the following utility function, u(x) = (16+ x)^1/2. Ann 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? (b) Find Ann's expected utility when betting on the match. For what values of p would she accept the bet? (c) Find Ann's certainty equivalent for this lottery when p = 3/4.

Explanation / Answer

Solution:

a) Expected value of this lottery is P(20)-(1-P)12=32P-12

Expected value of lottery is positive when P>12/32 thus P>0.375

b)expected utility of betting =P(36)^1/2+(1-P)4^1/2=6P+2(1-P)=2+4P

He will accept the bet when Expectwd utility is greater than 4 which implies P>0.5

c)when P=3/4,Expected utility from lottery=5

And U(X)=5 when X=9=certainity equivalence

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