Risk and uncertainity.

[Meghanjalli Routh]

Suppose you are an expected utility maximizer and you place a bet of $50,000 on India winning World cup. Your utility function is U = ln(W) and current wealth is $200,000. What is the minimum probability you must place on India winning the World cup?
Please show the working. Answer is 0.563.

[Do bats eat cats?]

Let the required probability be p.
E(U) = pln(250,000) + (1-p)ln(150,000)
Since I want to maximise my expected utility, I will only place the bet if E(U)>= U(W) = ln(200,000)

I think that solving gives the answer you are looking for.

[duck]

Hi.. :)

"Do bats eats cats" has correctly pointed out that.
Or you can think of the question as:
Lottery 1: Giving 2,50,000 with probability "p"  and 1,50,000 with probability "1-p"
Lottery 2: Giving 2,00,000 with probability 1.
Now, given expected utility maximiser you'll prefer Lottery1 over lottery 2 only when Expected utility from lottery1 is greater than expected utility from lottery2.
ie. p*log(2,50,000)+(1-p)*log(1,50,000) > log(2,00,000)