3. Answer the following questions related to choice under uncertainty and risk: (a) Consider an investor who must decide how much of his initial wealth w to put into a risky asset. The risky asset can have rate of return ri with probability pi for i = 1, 2. If B is the amount of wealth to be put into the risky asset, final wealth given ri would be (w - B) + (1 + ri)B. The investor's problem is to choose B E [0, w] to maximize his expected utility of final wealth. Let w = 1 and p1 = p2 = 2. Find the investor's optimal B if r1 = -2, r2 = 1, and u(x) = (x + 1)2. (b) Consider two individuals with VNM utility functions of wealth ul(x) and u2(x). Assume that u1(x) and u2(x) are strictly increasing and strictly concave. Show that individual 1's Arrow-Pratt measure of absolute risk aversion, Ra(x), is greater than individual 2's Arrow-Pratt measure of absolute risk aversion, Ra(x), if and only if there is a strictly concave function h(.) such that ul (x) = h(uz(x))