with u (c, h) = 1 1 (c h)1 . (a) Can optimal consumption follow a

with u

(c, h) = 1 1−γ (c − h)1−γ .

(a) Can optimal consumption follow a geometric Brownian motion under these assumptions?

(b) Assume that the excess consumption rate cˆt = ct − ht follows a geometric Brownian motion. Show that the state-price deflator will be of the form ζt = f(t)e−δt cˆ

−γ

t for some deterministic function f(t) (and find that function). Find an expression for the equilibrium interest rate and the market price of risk. Compare with the

‘simple model’ with no habit, CRRA utility, and consumption following a geometric Brownian motion.