Adjust s, δ, n, and α to see the Solow steady-state diagram. Cobb-Douglas: f(k) = k^α.
Δk = sf(k) − (δ + n)k Steady state when Δk = 0
30%
5%
1.0%
0.40
k* (capital per worker)
7.95
y* (output per worker)
2.32
c* (consumption per worker)
1.62
Investment / break-even
0.70
Try this
Increase s. Both k* and y* rise — but consumption c* may NOT (you save more, consume less). Try lowering n: k* and y* rise. Try raising δ: k* falls (depreciation eats more capital).
Start the economy AWAY from steady state. Watch capital, output, and consumption converge over 100 years.
2.0
30%
6%
k after 10 yrs
3.4
k after 50 yrs
7.5
k* (steady state)
7.95
% of k* at year 50
94%
Convergence speed
Solow predicts CONDITIONAL convergence: countries with similar fundamentals converge to the same k*. Speed depends on (1−α)·(δ+n+g) — typically ~2%/year, meaning a 35-year half-life. Catch-up is SLOW.
For each saving rate, compute steady-state c*. Find the saving rate that MAXIMIZES consumption (the Golden Rule).
5%
1%
0.40
Golden-rule s_GR
0.40
k* at GR
25.6
y* at GR
3.73
c* at GR (max)
2.24
Cobb-Douglas result
For f(k) = k^α, the Golden Rule saving rate equals the capital share: s_GR = α. With α = 0.40, s_GR = 40%. Most countries SAVE LESS than the Golden Rule — meaning they're under-saving relative to long-run consumption. China saves ~45%, U.S. ~20% — China may be ABOVE Golden Rule.