Consider a Samuelson model with one commodity in each period and where each consumer is endowed with one unit of the commodity in youth and none in old age. The utility function of each consumer is u(x0 , x1) = 2√x0 + 2√x1.
(a) Compute a stationary spot price equilibrium, (x0 , x1, P , r , G, T), with r = P = 1. Check that tax payments equal the interest on the government debt.
(b) Compute a stationary spot price equilibrium, (x0 , x1, P , r , G, T), with P = 1 and r = 0.
(c) Show that the allocation of the equilibrium of part (a) is Pareto optimal.
(d) Compute the utility of a typical consumer in each of the equilibria of parts (a) and (b).
(e) Why is the allocation of the equilibrium of part (a) not Pareto dominated by that of part (b)?
(f) Show the equilibrium allocations of parts (a) and (b) in a two- dimensional diagram.