Mr. Fogg is planning an around-the-world trip. The utility from the trip is a function of how much he spends on it (Y) given by
U(Y)=log(Y)
a. If there is a 25 percent probability that Mr. Fogg will lose $1,000 of his cash on the trip, what is the trip's expected utility?
b. Suppose that Mr. Fogg can buy insurance against losing the $1,000 (say, by purchasing traveler's checks) at an actuarially fair premium of $250. Show that his utility is higher if he purchases this insurance than if he faces the chance of losing the $1,000 without insurance.
c. What is the maximum amount that Mr. Fogg would be willing to pay to insure his $1,000?
d. Suppose that people who buy insurance tend to become more careless with their cash than those who donât, and assume that the probability of their losing $1,000 is 30 percent. What will be the actuarially fair insurance premium? Will Mr. Fogg buy insurance in this situation? (This is another example of the moral hazard problem in insurance theory.)