Risk doubttt

[Shefali]

Suppose there are two states of the world: good and bad. In the good state of the world your income is $250,000. In the bad state of the world your income is $40,000. The good state occurs with probably .25 and the bad state occurs with probably .75. Suppose your utility function is: u = y1/2 where y = income.

What would be an expected profit from“income insurance” contract if it took away all your income risk and left you indifferent between buying the insurance and taking the income gamble?
   
       
a 75,625
b 174,375
c 210,000
d 16875.

[Ankur9]

The expected utility is

E(U) = 0.25*(250000)^0.5 + 0.75*(40000) = 275

The certain income that gives us the same utility(indifferent b/w taking the insurance and not) is the certainty equivalent(CE).

U = 275 = (CE)^0.5
Hence, CE = 75625

Expected income without insurance

0.25*250000 + 0.75*40000 = 92500

Certain income = 75625

Expected profit = 92500-75625 = 16875

I think it should be (d)

 

[Shefali]

Thnxx..