Suppose there is a single asset that is risk free with return Rf > 1. Consider an investor with an infinite horizon, utility function u

(c) =

c, and discount factor δ = 1/Rf . Suppose she is constrained to consume 0 ≤ Ct ≤ Wt.

(a) Show that the value function for this problem is J(w) = w.

(b) Show that the value function solves the Bellman equation.

(c) Show that J

ˆ(w) = 2w also solves the Bellman equation.

(d) Show that, using the true value function J

ˆ(w) = w in the Bellman equation, the suboptimal policy Ct = 0 for every t achieves the maximum for every value of w.