Derive the explicit-form solution

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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

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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.

Reference no: EM131136029

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