Your utility function is U = log(2C), where C is the amount of consumption that you have in any given period. Your income is $40,000 per year and there is a 2% chance that you will be involved in a catastrophic accident that will cost you $30,000 next year.
a. What is your expected utility?
b. Calculate an actuarially fair insurance premium. What would your expected utility be were you to purchase the actuarially fair insurance premium?
c. What is the most that you would be willing to pay for insurance, given your utility function?