Consider the following continuous-time neoclassical growth model:
(a) Define a competitive equilibrium for this economy.
(b) Set up the current-value Hamiltonian for the representative household. Characterize the solution. Combine this solution with equilibrium factor prices, and derive the equilibrium path. Show that the equilibrium path displays nontrivial transitional dynamics.
(c) Determine the evolution of the labor share of national income over time.
(d) Analyze the impact of an unanticipated increase in B on the equilibrium path.
(e) Prove that the equilibrium is Pareto optimal.