Consider Nick who has an income of $50,000. There is a 15% chance that he gets sick in the next year, in which case he will definitely need an operation and the operation will cost $30,000. a) What is the expected income of Nick? Now assume that there is an insurance company that offers Nick an insurance which will cover the entire costs of the operation. The insurance premium is $4,600 for the next year. b) Calculate how much is the difference between an insurance premium charged by a company and the actuarially fair premium (a premium that would make a risk neutral person indifferent between buying and not buying the insurance)? c) How much is Nick's expected income if he buys the insurance? Now assume that the utility function of Nick is U(X) = \\X , whereby X is the amount of available income after health expenditures (Assume that all taxes are 0%). d) What is the utility of Nick from buying the insurance and what is his utility from not buying the insurance