Consider the model analyzed in Section 13.4.
(a) Show that the allocation described in Proposition 13.6 always involves finite utility and satisfies the transversely condition.
(b) Show that in this model there are no transitional dynamics.
(c) Characterize the Pareto optimal allocation, and show that the equilibrium growth rate in Proposition 13.6 is less than the growth rate in the Pareto optimal allocation.