Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
What is the per-worker production function?
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.
k* = _________
y* = _________
c* = _________
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Consider an economy described by the production function:
Y = F(K, L) = K0.3L0.7.
Assume that the depreciation rate is 5 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. Round your answers to two decimal places. (You might find it easiest to use a computer spreadsheet then transfer your answers to this table.)
Steady State Values for Various Saving Rates | ||||
s | k* | y* | c* | |
Depreciation Rate: | 0.0 | |||
(0.05) | 0.1 | |||
0.2 | ||||
0.3 | ||||
0.4 | ||||
0.5 | ||||
0.6 | ||||
0.7 | ||||
0.8 | ||||
0.9 | ||||
1.0 |
What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?
A saving rate of percent maximizes output per worker. A saving rate of percent maximizes consumption per worker.
Use information from Chapter 3 to find the marginal product of capital. Round your answers to three decimal places. Add to your table the marginal product of capital net of depreciation for each of the saving rates.
s | k* | y* | c* | MPK* - d | |
Depreciation Rate: | 0.0 | 0.00 | 0.00 | 0.00 | ∞ |
0.05 | 0.1 | 2.69 | 1.35 | 1.21 | |
0.2 | 7.25 | 1.81 | 1.45 | ||
0.3 | 12.93 | 2.16 | 1.51 | ||
0.4 | 19.50 | 2.44 | 1.46 | ||
0.5 | 26.83 | 2.68 | 1.34 | ||
0.6 | 34.81 | 2.90 | 1.16 | ||
0.7 | 43.38 | 3.10 | 0.93 | ||
0.8 | 52.50 | 3.28 | 0.66 | ||
0.9 | 62.12 | 3.45 | 0.35 | ||
1.0 | 72.21 | 3.61 | 0.00 |
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