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4. (More difficult question) Oscar is an exchange student at NUS from Sweden. He is about to travel to Johor Bahru for the weekend to explore the Malaysian city. He has $400 that he will take with him on the trip. His Singaporean friends tell him that Johor Bahru is a dangerous city and he could get mugged there. Oscar's utility is given by u(w) = x/W where w is his level of wealth. Muggers in Iohor Bahru always take $300 away from their victims. Let p denote the probability that Oscar gets mugged in Johor Bahru. Oscar has an annoying friend at NUS who sells travel insurance against such potential losses. Insurance is always offered at a fair rate, that is every dollar of insurance that Oscar wants to buy is always offered to him at a price of p. However, the insurance rm also charges an administrative fee of $16 for the purchase of insurance. a. How does the administrative fee change the nature of the budget constraint for insurance? b. We saw in lecture that when insurance is fair, an agent will fully insure. What will Oscar' 5 utility be if he fully insures (as a function of p)? c. If Oscar does not buy insurance, what is his expected utility? d. It turns out that Oscar will not purchase insurance for certain values of p. Determine those values using your answers in (b) and (c) to aid you in the process. e. Provide economic intuition for Oscar's behaviour in (d)