Consider an economy described by the production function: Y = F(K,L) = K^0.4 L^0.6
a. What is the per-worker production function?
b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.
c. Assuming that the depreciation rate is 15% per year, make a table showing steady state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
d. Use information from Chapter 3 to find the marginal product of capital. Add to your table, from part (c) the marginal product of capital net of depreciation for each of the saving rates. What does your table show about the relationship between the net marginal product of capita and steady-state consumption?
Consider an economy described by the production function: Y = F(K,L) = K^0.4 L^0.6
a. What is the per-worker production function?
b. Assuming no population growth or technological progress, find the steady-state capital stock per worker, output per worker, and consumption per worker as a function of the saving rate and the depreciation rate.
c. Assuming that the depreciation rate is 15% per year, make a table showing steady state capital per worker, output per worker, and consumption per worker for saving rates of 0 percent, 10 percent, 20 percent, 30 percent, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
d. Use information from Chapter 3 to find the marginal product of capital. Add to your table, from part (c) the marginal product of capital net of depreciation for each of the saving rates. What does your table show about the relationship between the net marginal product of capita and steady-state consumption?
