Consider 2 countries, Avataria and Twilightia, which can be described by the Sol

Question

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?

Explanation / Answer

Using the formula sf(k) = (n + d)k, country Avataria: 0.1 x 4k^1/2 = 0.08k, or k^1/2 = 5, so k = 25;

country Twilightia: 0.15 x 4k1/2= 0.12k, or k1/2= 5, so k = 25 also. The initial capital-labor ratios have no effect on the steady-state capital-labor ratios.

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