3. Work It Out. Consider an economy described by the production function Y = F(K, L) = K0.4 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 and depreciation rates.
3. Work It Out. Consider an economy described by the production function Y = F(K, L) = K0.4 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 and depreciation rates.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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answer questions a and b please
Transcribed Image Text:3. Work It Out • Consider an economy described by the production function
Y = F(K, L) = K0.4 L0.6
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 and depreciation
rates.
c. Assume that the depreciation rate is 15 percent 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. (You might find it easiest to use a
spreadsheet.) 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 capital and
steady-state consumption?
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