Suppose John's utility function is U = ln(2C) where C is the amount of consumption John has in any given period. John's income is $100,000 per year and there is a 3% chance that he will be involved in a catastrophic accident that will cost you $30,000 next year. (Assume John uses all of his income on consumption.)
a. What is John's expected utility?
b. What is the actuarially fair insurance premium for full insurance coverage?
c. What would John's expected utility be were he to purchase actuarially fair insurance?
d. What is John's risk premium?