Solow Growth Model

Y = K^α(AL)^1−α — watch capital per worker converge to steady state as you adjust savings, depreciation and technology growth

🇺🇦 UA

Savings rate s 0.30

Depreciation δ 0.05

Tech growth g 0.02

Pop. growth n 0.01

Capital share α 0.33

k* (steady): — y* (steady): — k (current): — y (current): — Golden s: — Year: 0

Output per worker y Capital per worker k Consumption per worker c Steady state k*

About the Solow-Swan Model

The Solow growth model (Robert Solow & Trevor Swan, 1956) is the foundation of modern macroeconomics. Effective capital per worker k̃ = K/(AL) evolves by: dk̃/dt = s·f(k̃) − (δ+g+n)·k̃, where f(k̃) = k̃^α is the Cobb-Douglas production function in intensive form.

The steady state k* is where investment s·f(k̃) exactly covers capital widening (δ+g+n)·k̃. Below k* the economy grows; above k* it contracts — guaranteeing convergence. The Golden Rule savings rate maximises steady-state consumption: s_gold = α (capital share).

The left panel shows time-series of y, k, and c = (1−s)y per effective worker. The right phase diagram shows the sf(k̃) (actual investment) curve and the (δ+g+n)k̃ (break-even) line; their intersection is k*.