1. Suppose that Eleanor has utility function u(w) = In(w) and initial wealth wo = 450. She has the opportunity to invest in two different assets, one risky and one safe. . The safe asset yields a return of 1.02 dollar for every dollar invested with probability 1 (so that r = 0.02). . The risky asset yields a return of 1 + x for every dollar invested, where a is the lottery 3 10 10 x = 0.42 -0.58 (a) Solve Eleanor's portfolio problem to find the optimal amount of money invested in the risky asset, given by a, and the optimal amount of money invested in the safe asset, given by wo - a. (b) Eleanor's neighbor, Janet, has utility function u(w) = 2000w - w2.* She also has initial wealth wo = 450. Janet also has the opportunity to invest in the two different assets Eleanor does. Solve Janet's portfolio problem to find the optimal amount of money invested in the risky asset and in the safe asset. (c) Now suppose that Eleanor's initial wealth increased and is now equal to 560. Find the optimal amount of money invested in the risky asset and in the safe asset in this case. What happened to o? Explain how you can use whether Eleanor's utility function exhibits DARA/IARA/CARA to make sense of what happens to a. (d) Now suppose that Janet's initial wealth increased and is now equal to 560. Find the optimal amount of money invested in risky and safe assets. What happened to a