Consider the model in Section 18.4.2. Suppose that the world consists of two countries with constant and equal populations, and constant savings rates, s1 > s2. Suppose that the production function in each country is given by (18.15), with k' corresponding to the highest capital-labor ratio in any country experienced until then. There is no technological progress, and both countries start with the same capital-labor ratio.
(a) Characterize the steady-state world equilibrium (i.e., the steady-state capital-labor ratios in both countries).
(b) Characterize the output per capita dynamics in the two economies. How does an increase in γ affect these dynamics?
(c) Show that the implied income per capita differences (in steady state) between the two countries are increasing in γ. Interpret this result.
(d) Do you think this model provides a plausible mechanism for generating large income differences across countries? Substantiate your answer with theoretical or empirical arguments.