Letting c 0 denote optimal consumption in the previous exercise, define the precautionary premium by

Letting c

∗

0 denote optimal consumption in the previous exercise, define the precautionary premium π by u

((w0 −π − c

∗

0)Rf) = E[u

((w0 − c

∗

0)Rf + ˜y)].

(a) Show that c

∗

0 would be the optimal consumption of the investor if she had no labor income and had initial wealth w0 −π.

(b) Assume the investor has CARA utility. Show that the precautionary premium is independent of initial wealth (again, no wealth effects with CARA utility).