solution

Suppose you are a travelling account manager in Ontario. Your utility U depends upon your income I as follows: U = v I. You are making I = 900 each week, but if you are caught speeding on Ontario Highway 401 while making your rounds, you will receive a fine of $500. The probability of you being caught speeding in any given week is 50%.

(a) (1 point) What is your expected income?

(b) (3 points) What is your expected utility?

(c) (4 points) Suppose that your boss offers you a position in online account management that eliminates the risk of being caught speeding. What salary would provide you with the same utility you expected to receive as a travelling account manager? What is your “certainty equivalent”?

(d) (3 points) What is your risk premium?

(e) (4 points) Suppose instead that you are given the opportunity to purchase car insurance that would pay off all of your speeding fines. What is the most you would pay for this insurance? Explain.

(f) (6 points) How does the maximum amount you indicated in (e) compare to your expected loss? Why do people often want to be fully insured against uncertain situations even when the insurance premium exceeds the expected value of the loss?

(g) (2 points) If the insurance company convinces you to pay the maximum amount you indicated in (e), will the insurer earn a profit? If so, how much?