1. An individual owns a car worth 40,000. The probability of an accident is p 0.02....

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1. An individual owns a car worth £40,000. The probability of an accident is p 0.02. An insurance company offers insurance at a premium y per insured sum K. The individual's preferences can be represented by the utility function u(x) = x. We assume there is no scrap value of the car if there is an accident, that is, the individual would own nothing in the "bad state". (a) How large is the insurance premium at which the insurance company makes zero profit? (5 marks) (b) What is the individual's optimal choice of K if the insurance is actuarially fair? (5 marks) (c) Assume the insurance company charges a premium y = 0.05. How much insurance would the individual purchase now? (4 marks) (d) Suppose the individual's utility is state dependent. In particular, in the "good state" in which the individual does not suffer an accident, their utility can be represented as u(x,) = x3, whereas in the "bad state" their utility can be represented as u(xb) = x. How much insurance would the individual now buy if the insurance is actuarially fair? (4 marks) 1. An individual owns a car worth £40,000. The probability of an accident is p 0.02. An insurance company offers insurance at a premium y per insured sum K. The individual's preferences can be represented by the utility function u(x) = x. We assume there is no scrap value of the car if there is an accident, that is, the individual would own nothing in the "bad state". (a) How large is the insurance premium at which the insurance company makes zero profit? (5 marks) (b) What is the individual's optimal choice of K if the insurance is actuarially fair? (5 marks) (c) Assume the insurance company charges a premium y = 0.05. How much insurance would the individual purchase now? (4 marks) (d) Suppose the individual's utility is state dependent. In particular, in the "good state" in which the individual does not suffer an accident, their utility can be represented as u(x,) = x3, whereas in the "bad state" their utility can be represented as u(xb) = x. How much insurance would the individual now buy if the insurance is actuarially fair? (4 marks)

Answer rating: 100% (QA)

1a In this case the total worth of the car owned by the individual is 40000 pounds and the utility function of the individual is given as uxx05 where u and x represent the total utility and the wealth ... View the full answer