Provide an intuition for why countries grow at the same

Question

In the model of Section 18.2.2 with household optimization, suppose that preferences in country j are given by

where ρj differs across countries.

(a) Show that a unique steady-state world equilibrium still exists and all countries grow at the rate g.

(b) Provide an intuition for why countries grow at the same rate despite different rates of discounting.

(c) Show that this steady-state equilibrium is globally saddle-path stable.