Plz solve question 1

308 Chapter 11 GENERAL PRINCIPLES respect to the artificial (risk-neutral) probabilities. A set of risk-neutral probabilities can be found by multiplying the state prices by the total return R of the risk-free asset. Exercises I. (Certainty equivalent) An investor has utility function U(x) =x1/4 for salary. He has a new job offer which pays $80,000 with a bonus. The bonus will be $0, $10,000, $20,000, $30,000, $40,000, $50,000, or $60,000, each with equal probability. What is the certainty equivalent of this job offer? ealth independence) Suppose an investor has exponential utility function Ox) -e-ax and an initial wealth level of W. The investor is faced with an opportunity to invest an amount w-W and obtain a random payoff x. Show that his evaluati incremental investment is independent of W. 2. (W on of this 3. (Risk aversion invariance) Suppose U() is a utility function with Arrow-Pratt risk of v? aversion coefficient a(x). Let V(x) = c+bU(x). What is the risk aversion coefficient of V? 4. (Relative risk aversion) The Arrow-Pratt relative risk aversion coefficient is (x)-xU'(x)