Question

Andy earns $100,000 annually. He also faces a 25% chance of getting sick during any given year. If Andy falls sick during the year, the cost to him will be $20,000. Andy has the option of purchasing health insurance to hedge against the risk of illness. Andy's total utility of income is given by U = ln(Y). Where Y denotes Andy's annual income. Use this information to answer the following questions. Be sure to show all your work. (Its safer to round to 4 decimal places for questions on expected utility)

a. Calculate Andy's expected utility if he chooses not to purchase an insurance policy.

b. Calculate the actuarially fair insurance premium.

c. Calculate Andy's expected utility if he chooses to purchase an insurance policy at the actuarially fair premium.

d. Should Andy purchase the insurance policy? Why or why not?

e. What is the maximum premium Andy would be willing to pay for the insurance policy?

f. What is Andy's risk premium?

Answer 1