Ms. Fogg is planning an around-the-world trip on which she plans to spend $10,00

Question

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.

Explanation / Answer

a) Given, U(Y)= ln Y

E[U(Y)]= .25 ln(9,000) +.75 ln(10,000) = 9.184.25 ln(9,000) +.75 ln(10,000) = 9.184

b) With Insurance U(9,750) =     9.185. Since, the espected utility of going with insurance is more, hence she would go with insurance.

c)ln(X) = 9.184, or . e9.184 = 9,740.   Hence, she will pay a maximum of $260

d) E[U(Y)]= .30 ln(9,000) +.60 ln(10,000) = 8.258

Since, the price here is lower hence, she will not buy insurance.

e) This is a case of moral hazard wherein the insured act in a way so that the insured event becomes more likely.

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