Long-run dynamics of income per worker. Move the controls: the initial situation is dashed, the current one is solid, the arrows show what changed, and the charts below show the transition over time. Hover over the charts (or drag a finger across them) to read the values.
Equations: y = A·kα · Δk = s·f(k) − (n+g+δ)·k ·
k* = (s·A/(n+g+δ))1/(1−α) · c* = (1−s)·y* ·
Golden Rule: f'(k) = n+g+δ, i.e., s = α ·
speed of convergence λ = (1−α)(n+g+δ).
With g > 0, k, y, and c are measured per effective worker (K/EL), and output per worker Y/L grows at rate g in the long run.
The time path uses the exact solution of the Solow equation.