1. Consider 2 countries, Avataria and Twilightia, which can be described by the Solow model. Avataria has a capital-labor ratio that is initially twice as big as that of Twilightia, but neither country is yet in a steady state. Both countries have the same production function,
Y(K,L) = 4(K)^1/2(L)^1/2.
Avataria has a 10% investment rate and 8% depreciation rate, while Twilightia has a 15%
investment rate and 12% depreciation rate.
(a) Calculate the steady-state capital-labor ratio for each country. Does the initial capital-labor ratio affect your results?
(b) Calculate output per worker and consumption per worker for each country. Which country has the highest output per worker? The highest consumption per worker?
(c) In general, do all the fundamental characteristics of different countries need to be identical for convergence of output per worker?
2. How long will it take for Avataria with a growth rate of 6% to triple its income? What about Twilightia with a growth rate of 18%? Will it be correct to say that Twilightia will triple its income 3 times faster than Avataria? If no, then what is the correct answer?