Return to exercise 4.1. and assume that w = 10, h = 0.10 and d = 0.08. You should find that = 12.5. Now

Return to exercise 4.1. and assume that w = 10, h = 0.10 and d = 0.08.

You should find that α∗ = 12.5. Now assume that, besides his wealth of 10, the decision maker faces a background risk ˜ ε (independent of the other risk)

distributed as (+2, 1 2;−2, 1 2).

(a) Write the expected utility (Eu) of the decision maker.

(b) Compute dEu/dα, evaluate it at α = 12.5. What does the sign imply for the comparison between α∗ andα∗∗ (theoptimumwhenbackground risk is present)?

(c) Verify that for u = lnw conditions 2 and 3inProposition 4.3 are indeed satisfied.