Kara has a utility function of U = ln (2I), where I is the amount if income she receives in a year. Her income is $40,000 per year and there is a 2 percent chance that she will have a health emergency that will cause her income to drop to $10,000.
a. With this risk, what is her expected utility?
b. Calculate an actuarially fair insurance premium.
c. If Kara purchases this insurance, what would her expected utility be?
d. What is the most that Kara would be willing to pay for insurance?