\"U\""\"\"\"'\" ' \\\" \"*\"* \"\"1 Consider a risk averse individual with a Bernoulli utility function for wealth u : R++ > [R given by u(c) : log 0, where log means the natural log or log to the base e. (1) What is the ArrowPratt measure of absolute risk aversion for this individual? (4 marks) (2) Suppose that this individual initially has a level of wealth of 1000 but that she is exposed to a risk of losing and amount 200 with probability %. Suppose that she can purchase any amount of insurance at a price p. That is, if she purchases 56 units of insurance and the loss occurs her nal wealth will be 1000 7 200 + SE 7 p32 and if the loss does not occur her final wealth will be 1000 7 pm. Find the amount of insurance this individual will buy if she can 1 buy the insurance at an actuarially fair price, that is, if p = fr Carefully explain how you nd this amount. (6 marks) Now, consider a decision maker who, when confronted with a choice between a lottery that would give her 4 for sure and a lottery that would give her 10 with probability i, 4 with probability %, and 0 with probability i, would strictly prefer the first lottery and, when confronted with a choice between a lottery that would give her 4 with probability % and 0 with probability % and a lottery that would give her 10 with probability i and 0 with probability 2, would strictly prefer the second lottery. (3) Show that these preferences violate the independence axiom. (10 marks)