An investor has preferences represented by the following utility function: u(c) = ln c. He receives an initial endowment w > 0 at time 0 and nothing at time 1. He invests at time 0 and consumes at time 1 only. He can invest an amount x in a risky asset that pays 1.5 (for each unit invested) with probability = 0.7 and 0 with the complementary probability. He can also invest in a risk-free asset that pays 1.1 for sure.

a) Does the investor have decreasing, constant or increasing absolute risk aversion?

b) Is the investor willing to invest a positive amount x in the risky asset, for any level of w?

c) Suppose w = 10. Compute the optimal investment in the two assets.

d) Suppose w = 20. Is the amount x of the risky asset higher, the same or lower than that computed for question (c)? Explain.