3 Arielle is a risk-averse traveler who is planning a trip to Canada. She is planning on carrying $400 in her backpack. Walking the streets of Canada, however, can be dangerous and there is some chance that she will have her backpack stolen. If she is only carrying cash and her backpack is stolen she will have no money ($0). The probability that her backpack is stolen is 1/5. Finally assume that her preferences over money can be represented by the utility function u(x) = x0.5 a) What is Arielle's expected utility? What is her expected income? b) What is her certainty equivalent? What is her risk premium? c) Illustrate her utility, expected utility, expected income, certainty equivalent and the risk premium in a diagram. Suppose that she has the option to buy traveler's checks. If her backpack is stolen and she is carrying traveler's checks then she can have those checks replaced at no cost. National Express charges a fee of $p per $1 traveler's check. In other words, the price of a $1 traveler's check is $(1+p). d) Given the price 1+p of a $1 traveler's check, what is the maximum number of checks that she can buy? If she buys the maximum then how much money will she have in the event her backpack is stolen? How much if the backpack is not stolen? e) If the purchase of traveler's checks is a fair bet then we know that the purchase of traveler checks will not change her expected income. Show that if the purchase is a fair bet then the price 1+p = 1.25. Hint: your answer to part (d) may be helpful. f) If the price is fair (so p = .25) then how many checks will she buy? Illustrate your answer in the diagram from part (c). For the last two parts assume that the price of a check is 1 + p and let a be the number of checks that she purchases. g) Write her expected utility function as a function of p and a. h) Find the a that maximizes her expected utility (your answer will be a function of p)