Instrument 06 · Robert M. Solow · 1956
Capital deepening raises the level. Then the curve runs out of slope.
Investment adds capital, but depreciation subtracts from a stock whose extra units produce progressively less additional output.
Move the saving rate and the destination changes. The economy approaches a higher capital level, not permanent acceleration. Solow disciplined accumulation precisely by leaving sustained technological progress outside the machine.
- Production
- y = k0.35
- Depreciation
- 8% per period
- Technology
- Held fixed
More saving raises the destination, not the long-run slope.
At a 18% saving rate, capital approaches an illustrative steady state of 3.48 per worker.
Exact representative values and equation
| Period | Capital | Output | Investment | Depreciation |
|---|---|---|---|---|
| 0 | 0.60 | 0.84 | 0.15 | 0.05 |
| 10 | 1.57 | 1.17 | 0.21 | 0.13 |
| 20 | 2.30 | 1.34 | 0.24 | 0.18 |
| 30 | 2.76 | 1.43 | 0.26 | 0.22 |
| 40 | 3.05 | 1.48 | 0.27 | 0.24 |
| 50 | 3.23 | 1.51 | 0.27 | 0.26 |
| 60 | 3.33 | 1.52 | 0.27 | 0.27 |
y_t = k_t^0.35; k_(t+1) = k_t + s y_t - 0.08 k_t; k* = (s / 0.08)^(1 / (1 - 0.35)).
Illustrative capital and output per worker; model period is not calendar time. The Cobb-Douglas parameters, saving rate, depreciation rate, and periods are authored teaching values. Technology and population are held fixed; the path is not a country estimate or forecast.
