Argue without solving this problem that there exists a

Question

Consider the following discrete-time optimal growth model with full depreciation:

(a) Formulate this maximization problem as a dynamic programming problem.

(b) Argue without solving this problem that there exists a unique value function V (k) and a unique policy rule c = π(k) determining the level of consumption as a function of the level of capital stock.

(c) Solve explicitly for V (k) and π(k).