(a) Draw the tree that represents together the two risks.

(b) Show that if is sufficiently small, u = 1 2 pu00(w1) 2 pu0 (w1) + (1 p)u 0 (w2) (2) [Hint: just as in the lecture notes, take Taylor series expansions of appropriate orders on both sides of (1) - first-order on the left and second-order on the right.]

(c) Let u(w) = expaw and v(w) = expbw. Compute the absolute risk-aversion measure for u and v.

(d) Suppose a > b. Show that if p < 1 then there exists a value w1 w2 large enough to make v > u. What does this suggest about the usefulness of the absolute risk-aversion measure for problems where risk is only partially reduced?