Question

2. The probability that James is involved in a car accident is 0.3 and the probability that he is not in a car accident is 0.7. The value of his car is $10000, which is lost if he is in an accident. That is, his wealth is $20000 if he does not have an accident and $10000 if he is involved in an accident. James utility function is U(M)-10-1000/Mo, where M is his wealth. (a) What are the expected value and standard deviation of James' wealth? (b) Is James risk averse, risk neutral or risk loving? Explain. (c) Suppose that James can purchase one of the following two automobile insurance packages: (i) He pays a premium of $2500 and is given the full value of the car if there is an accident or(ii) he pays a premium of S500 and is given S3000 if there is an accident. Will James purchase one of the insurance packages or will he choose not to insure? If he purchases insurance, which policy will he purchase? (d) What is the highest premium James is willing to pay for an insurance package that pays him the full value of the car in the event of an accident?

Answer 1

The expected value of wealth is E(w) = 0.3 (10000) + 0.7 (20000) = 17000 The standard derivation of wealth SD = squareroot sigma^2 = [E(w - E(w)]^2]^1/2 = [0.3 times (10000 - 17000)^2 + 0.7 (20000 - 17000)^2]^1/2 = 4582.58 A person attitude towards risk is determined through its Mu. If partial differential Mu/partial differential w < 0: the person is risk averse, it partial differential Mu/partial differential w = 0: w is risk neutral if partial differential Mu/partial differential w > 0: w is risk lover. W is wealth Here the utility is: is = 10 - 1000/squareroot M Mu = 500/M^3/2 therefore partial differential Mu/partial differential M = -3/2 middot 500/M^5/3 < 0 The person is risk averse. The insurance policy can be sold only if the person is risk averse. Here as the person is risk averse w will buy insurance. H is expected utility for option (i) is E(n) = 10 - 1000/squareroot 20000 - 2500 = 2.44