Wilbur is an airline pilot who currently has income of $60,000. If he gets sick and loses his flight medical certificate, he loses his job and has only $10,000 income. His probability of staying healthy is 0.6, and his probability of getting sick is 0.4. Wilbur's utility function is given in the accompanying table.
Income Total utility (utils)
$0……………………………. 0
10,000……………………….. 60
20,000……………………….. 110
30,000……………………….. 150
40,000……………………….. 180
50,000……………………….. 200
60,000……………………….. 210
a. What is the expected value of Wilbur's income?
b. What is Wilbur's expected utility? Wilbur thinks about buying "loss-of-license" insurance that will compensate him if he loses his flight medical certificate.
c. One insurance company offers Wilbur full compensation for his income loss (that is, the insurance company pays Wilbur $50,000 if he loses his flight medical certificate), and it charges a premium of $40,000. That is, regardless of whether he loses his flight medical certificate, Wilbur's income after insurance will be $20,000. What is Wilbur's utility? Will he buy the insurance?
d. What is the highest premium Wilbur would just be willing to pay for full insurance (insurance that completely compensates him for the income loss)?