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. Suppose that Oscar's utility is given by utility is given by u(w) = √w where w is his level of wealth. Suppose also that muggers in Johor 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 firm also charges a fixed administrative fee of $16 for any purchase of insurance. For what range of values of p will Oscar purchase insurance? Provide economic intuition for this result.
Can you please provide a detailed and elaborate working?