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.
Y = K0.3L0.7
Output per worker (y) = Y / L = (K/L)0.3 = k0.3 where k = K/L
When s: Savings rate, in steady state,
s /
= k / y
s /
= k / k0.3
s /
= k0.7
Capital per worker (k*) = [s /
](1/0.7) = [s /
]1.43
Output per worker (y*) = k0.3 = [s /
](0.3/0.7) = [s /
]0.43
Consmption per worker (c*) = yY - sy* = y* x (1 - s) = [s /
]0.43 x (1 - s)
When
= 0.05,
k* = (s / 0.05)1.43
y* = (s / 0.05)0.43
c* = (s / 0.05)0.43 x (1 - s)
Therefore:
s | k* | y* | c* |
0 | 0 | 0 | 0 |
0.1 | 2.69 | 1.35 | 1.21 |
0.2 | 7.26 | 1.82 | 1.45 |
0.3 | 12.96 | 2.16 | 1.51 |
0.4 | 19.56 | 2.45 | 1.47 |
0.5 | 26.92 | 2.69 | 1.35 |
0.6 | 34.93 | 2.91 | 1.16 |
0.7 | 43.55 | 3.11 | 0.93 |
0.8 | 52.71 | 3.29 | 0.66 |
0.9 | 62.38 | 3.47 | 0.35 |
1 | 72.52 | 3.63 | 0.00 |
A savings rate of 100% maximizes output per worker.
A savings rate of 30% maximizes consumption per worker.
Get Answers For Free
Most questions answered within 1 hours.