7.5 Ms. Fogg is planning an around-the-world trip on which she plans to spend $10,000. The utility from the trip is a function of how much she actually spends on it (Y), given by UðYÞ ¼ ln Y:

a. If there is a 25 percent probability that Ms. Fogg will lose $1,000 of her cash on the trip, what is the trip’s expected utility?

b. Suppose that Ms. Fogg can buy insurance against losing the $1,000 (say, by purchasing traveler’s checks) at an ‘‘actuarially fair’’ premium of $250. Show that her expected utility is higher if she purchases this insurance than if she faces the chance of losing the $1,000 without insurance.

c. What is the maximum amount that Ms. Fogg would be willing to pay to insure her $1,000?