Solow-Swan Growth Model: Capital Convergence (2D)

Production & Savings

Savings rate (s) 25%

Capital share (α) 0.33

Total-factor productivity (A) 2.00

Depreciation & Population

Depreciation rate (δ) 5.0%

Population growth (n) 2.0%

Initial capital/worker (k₀) 1.00

Live Readout

Elapsed time

0.0 yr

GDP/worker (y)

0.00

Capital/worker (k)

0.00

Growth rate (ẏ/y)

0.00%

Steady-state k*

0.00

Steady-state y*

0.00

% to steady state

0.0%

Investment s·y

0.00

How it works

The Solow–Swan model is the standard growth-theory account of how an economy accumulates capital per worker. Output follows a Cobb–Douglas production function and capital per worker evolves under savings, depreciation and population growth:

y = A · k^α                (output per worker)
k̇ = s · y − (δ + n) · k    (capital accumulation per worker)
k* = ( s·A / (δ+n) )^(1/(1−α))   (steady-state capital)
y* = A · k*^α                    (steady-state output)

Because α < 1, the production function has diminishing marginal returns to capital: each extra unit of k raises y by less than the last. That is why the growth-rate curve on the right starts high and decays toward zero — the "catch-up growth" phenomenon at the heart of development economics, where economies far below their steady state grow fastest and growth slows automatically as k approaches k*.

GDP-per-capita chart — y(t) rising and flattening toward the dashed y* line.
Capital tank — investment s·y flows in, depreciation (δ+n)·k flows out; the tank's fill level is k relative to k*.
Growth-rate curve — ẏ/y over time, falling as diminishing returns bite; it never reaches the steady state, only approaches it asymptotically.

GDP per capita y(t) Steady state y* Growth rate ẏ/y