Let us return to Example 6.4.
(a) Prove that the law of motion of capital stock given by (6.37) monotonically converges to a unique steady-state value of k∗ starting with any k0 > 0. What happens to the level of consumption along the transition path?
(b) Now suppose that instead of (6.37), you hypothesize that
Verify that the same steps lead to the conclusion that b = c = 0 and a = βa.
(c) Now let us characterize the explicit solution by guessing and verifying the form of the value function. In particular, make the following guess: V (x) = A log x, and using this form together with the first-order conditions, derive the explicit-form solution.