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?
What will be an ideal response?
| (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: |
| (b) | y = 6k1/2 = 24 for both countries. c = (1 - s)y, so country A has c = 0.9y = 21.6, while country B |
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