Consider the infinite-horizon model with IID returns and no labor income. Assume max E[log Rt+1] <

Consider the infinite-horizon model with IID returns and no labor income.

Assume max π E[logπ

Rt+1] < ∞.

(a) Calculate the unique constant γ such that J(w) = logw 1− δ + γ

solves the Bellman equation.

(b) Show that the transversality condition limT→∞ δTE[J(W∗

T)] = 0 holds.

(c) Show that the optimal portfolio is the one that maximizes E[logπ

Rt+1]

and the optimal consumption is Ct = (1 −δ)Wt.