Simulator · Macro · Growth Theory · ~10 min

Solow-Swan Growth Model

The workhorse model of long-run growth, augmented with human capital following Mankiw, Romer & Weil (1992). Set savings rates, population growth, and technology — see steady states, the golden rule, and convergence dynamics.

Output per worker

—

y* at steady state

Physical capital

—

k* per worker

Human capital

—

h* per worker

Consumption

—

c* per worker

Analysis

Parameters

Physical savings s_k 0.25

Human-capital investment s_h 0.10

Share of output invested in schooling & training.

Capital share α 0.33

Human-capital share β 0.33

α + β < 1 (must have diminishing returns to all reproducible factors).

Population growth n 1.5%

Tech growth g 2.0%

Depreciation δ 5.0%

Country calibrations

MRW-style stylized values, not current data. Click to load.

The MRW-augmented Solow model in one paragraph

Mankiw, Romer & Weil (1992) added human capital to the standard Solow model, arguing that if you interpret capital broadly enough to include schooling and skills, the Solow framework does surprisingly well at explaining cross-country income differences. Output per effective worker is y = k^α h^β with α + β < 1. Physical capital grows when saved output s_k·y exceeds effective depreciation (n + g + δ)k, and human capital grows when s_h·y exceeds (n + g + δ)h. Setting both to zero gives closed-form steady states:

k* = ( s_k^1-β · s_h^β / (n+g+δ) )^1/(1-α-β) · h* = ( s_k^α · s_h^1-α / (n+g+δ) )^1/(1-α-β)

Two implications drive most policy debate: (1) countries with the same technology but different savings/investment rates converge to different steady states — no automatic catch-up. (2) The golden-rule savings rate that maximizes long-run consumption is s_k=α. Save less and you're leaving consumption on the table. Save more and you're dynamically inefficient — building capital that pays back less than it costs to maintain.