2. Suppose that there are three possible future states of the world, and the utility function is u(x) = log x. Let the probability of state 1, T,, be 1/2 , and T12 = 1/3 . The prices of the pure securities, P1, P2, P3, equal 0.8, 0.6, 0.4 in dollar, respectively. An individual has an initial wealth, Wo, of 50,000. a. What amounts will the risk-averse individual invest in pure securities 1, 2, and 3? b. How will the individual divide his or her initial endowment between current and future consumption