please do not answer in hand writting

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 7 per insured sum K. The individual's preferences can be ropresented by the utility function 11(3) = 3*. 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 prot? (5 marks] (b) What is the individual's optimal choice of K if the insurance is actuariallv fair? (5 marks) (c) Assume the insurance company charges a premium 1 = 0.05. How much insurance would the individual purchase notv? (4 make) (d) Suppose the individual's utility is state dependent. In particular. in the "good state" in which the individuai does not suffer an accident, their utility can be represented as m9) = i. whereas in the \"bad state" their utility can be represented at up.) = :5. How much insurance would the individual now buv if the insurance is actuarially fair? (4 marks)