You are planning a trip to Livingstone after your exams and you have a utility function for the trip and it is a function of how much you spends on it, given by U(Y ) = ln(Y ) . You have K10,000 kwacha to spend on the trip and a 25% probability that you will lose K1500 of your money on the trip.

a. Calculate your expected value of your money and the expected utility. (10marks)

b. Suppose you can buy insurance against losing K1500 at an actuarially fair premium. Show that your utility is higher if you purchases this insurance than if you face the chance of losing the money without insurance. (10marks)

c. What is the maximum amount of premium that you would be willing to pay? (10marks)

d. Suppose that people who buy insurance tend to become more careless with their cash than those who don't, and assume that the probability of losing K1500 is 30%. What would be the actuarially fair premium? will you buy insurance in this situation?