Consider the canonical OLG model with log preferences and a Cobb-Douglas production function (as in Exercise 9.8).
(a) Define a competitive equilibrium.
(b) Characterize the competitive equilibrium, and derive explicit conditions under which the steady-state equilibrium is dynamically inefficient.
(c) Using plausible numbers discuss whether dynamic inefficiency can arise in "realistic" economies.
(d) Show that when there is dynamic inefficiency, it is possible to construct an unfunded social security system that creates a Pareto improvement relative to the competitive allocation.
Exercise 9.8
Consider the canonical model with log preferences, log(c1(t)) + β log(c2(t)), and the general neoclassical technology F(K, L) satisfying Assumptions 1 and 2 (see Chapter 2). Show that multiple steady-state equilibria are possible in this economy.