Country A has a capital—labor ratio that is initially twice as big as that of country B, but neither is yet in a steady state. Both countries have the same production function, f(k) = 6k1/2
Country A has a 10% saving rate, 10% population growth rate, and 5% depreciation rate, while country B has a 20% saving rate, 10% population growth rate, and 20% 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?
(a) Using the formula sf(k) = (n + d)k, country A: 0.1 × 6k1/2 = 0.15k, or k1/2 = 4, so k = 16; country B: 0.2 × 6k1/2 = 0.3k, or k1/2 = 4, so k = 16 also. The initial capital—labor ratios have no effect on the steady-state capital—labor ratios.
(b) y = 6k1/2 = 24 for both countries. c = (1 - s)y, so country A has c = 0.9y = 21.6, while country B has c = 0.8y = 19.2. The two countries have the same capital—labor ratio and output per worker, but different consumption per worker.
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