Ms. Fogg is planning an around-the-world trip on which she plans to spend $10,000. Her utility from the trip is a function of how much she actually spends on it (Y), given by:
U(Y) = ln Y.
(a) If there is a 25% probability that Ms. Fogg will lose $1000 of her cash on the trip, what is her expected utility from the trip?
(b) Suppose that Ms. Fogg can buy insurance against losing the $1000 at an actuarially fair premium of $250. Will Ms. Fogg purchase the insurance?
(c) What is the maximum amount that Ms. Fogg would be willing to pay to insure her $1000?
(d) Suppose that people who buy insurance tend to become more careless with their cash and that their probability of losing $1000 rises to 30%. What is the actuarially fair price of insurance in this situation? Will Ms. Fogg buy insurance now?
(e) Have we illustrated a case of adverse selection or moral hazard? Explain.