Consider an individual facing the risk of becoming ill and her willingness to in
ID: 1248129 • Letter: C
Question
Consider an individual facing the risk of becoming ill and her willingness to insure herself. The individual has a probability of 5% of getting seriously ill in a given year. If she gets ill, her yearly net income will amount to $20,000 (this amount takes into account the forgone income during her period of illness as well as the cost of hospitalization). With a probability of 95%, however, she will not get ill and will make a yearly income of $45,000. Assume her utility function is given by U(x)=x1/2. Compute the individual's expected utility.b. Find the certain level of income that would make the individual as well off as being
in the risky situation described above (this amount is called the “certainty
equivalent").
c. Use this to find the maximum premium she would be willing to pay to get rid of this
risk, i.e. to insure herself against the economic consequences of illness.
Explanation / Answer
Expected utility = .05 (20,000)^0.5 +.95(45,000)^.5= 208.6 Certainty equivalent 208.6= x^.5= 43,514 Maximum premium 45,000-43,514= 1,486