Country A and country B both have the production function Y= F(K,L)= K 1/2 L 1/2 Assume that neither country experiences population growth nor technological progress and that 5% of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 20% of output each year. Using your answer from part (a) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the steady-state levels of income per worker and consumption per worker. (b) Suppose that both countries start off with a capital per stock per worker of 2. What are the levels of income per worker and consumption per worker? Rememberi
- Country A and country B both have the production function
Y= F(K,L)= K 1/2 L 1/2
Assume that neither country experiences population growth nor technological progress and that 5% of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 20% of output each year. Using your answer from part (a) and the steady-state condition that investment equals
(b) Suppose that both countries start off with a capital per stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator to show how the capital stock per worker will evolve over time in both countries. For each year, calculate income per worker and consumption per worker. How many years will it be before the consumption in country B is higher that the consumption in country A?
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