Investor A whose utility function is U(x) = x^1/3, x > 0 and initial wealth is $7, is offered an investment that generates a random payoff of $X, where P(X = 20) = p, P(X = 1) = p and P(X = 6) = 1 2p. (1) Find the range of p for which investor A will avoid this investment. Investor B has utility function V(x) = U(x) + ax + b where a > 0 and b R. Let R_A and R_B be the absolute risk aversion function of investor A and B respectively (2) Show that R_A is a decreasing function. (3) By finding and simplifying an expression for R_A R_B, prove that investor A is globally more risk averse than investor B.