Question

Suppose Ashok's utility function is u={r/1000}1/2. His initial income when healthy is36000 . however there is 50% chance that he will face financial loss on being ill and income is likely to reduce by 20000.1) find the expected value of his income? 2) what expected utility he will have given the possible state of his health? 3) what is the risk premium he will be willing to pay to cover the risk of sickness.

Answer 1

u = {I/1000}1/2. I1 = 36000, I2 = 16000.
1) The expected value of his income is:
I = 0.5*36000 + 0.5*16000 = 26000.
2) Expected utility he will have given the possible state of his health is:
u = 26000/1000*1/2 = 13.
3) The risk premium is 50% to cover the possibility of illness.