(a) Verify that Theorem 7.14 from Chapter 7 can be applied to the optimal growth problem in the baseline Schumpeterian model of Section 14.1.
(b) Show that the solution to this problem is unique. [Hint: recall Exercise 8.11 in Chapter 8.]
(c) Derive (14.27).
Exercise 8.11
Use an argument similar to that of the proof of Mangasarian's sufficiency result (Theorem 7.5) to show that because the representative household's Hamiltonian in the neoclassical growth model, H (t, a, c, μ), is concave in (a, c) and strictly concave in
c, the path of consumption and assets given by (8.17)-(8.19) is the unique solution to the household's maximization problem.