What to explore
Change parameters and watch the model adjust.
- Capital share, savings rate, depreciation, population growth, and TFP
- Initial capital and simulation horizon for transition paths
Exogenous growth foundations
Solow-Swan Growth Model
A classic long-run growth model showing how savings, depreciation, population growth, and productivity shape the steady state of an economy.
Focus
Steady state, golden rule, and transition dynamics
Use the sliders to compare current outcomes with the golden rule, inspect the Solow diagram, and see how capital accumulation converges over time.Interactive diagram
Solow — explore it instantly
How to read this
The Solow–Swan model explains why economies grow and why growth eventually slows. Output per worker depends on capital per worker through a production function with diminishing returns: each extra machine adds less than the one before.
A constant fraction of output is saved and invested — the saving curve s·f(k). Capital wears out and must be spread across a growing population — the break-even line (δ+n)·k. Where the two cross, investment exactly offsets depreciation and population growth, so capital per worker holds steady. That crossing is the steady state k*.
The golden-rule level k_gold is the capital stock that maximises long-run consumption. Saving more than the golden rule actually lowers steady-state consumption, because the extra output is used up just maintaining the larger capital stock. Move the sliders to see how patience (s), productivity (A), depreciation (δ), population growth (n), and the capital share (α) shift k* and k_gold.
Core ideas
Interpret the mechanics before you chase the graphs.
- The Solow diagram compares actual savings with break-even investment.
- The golden-rule benchmark shows when more saving raises or lowers steady-state consumption.
- Transition dynamics help explain convergence after a shock or policy change.
Learning goals
What this model should help students internalize.
- Solve for the steady state of the Solow model and relate it to savings and depreciation.
- Interpret the golden-rule benchmark for consumption-maximizing capital accumulation.
- Read transition dynamics and convergence paths after a parameter shock.
Prerequisites
Concepts to review before diving in.
- Comfort with algebra and simple growth notation
- Basic idea of a production function and capital accumulation
Open the full interactive notebook (Python · loads on demand)
Next models to study
Keep moving through the track.
Optimal growth with endogenous saving
Ramsey-Cass-Koopmans Model
Explore how preferences, technology, and depreciation alter the steady state and the planner's optimal transition path using a shooting algorithm.
Advanced macroeconomics
Diamond Overlapping-Generations Model
Study the steady state, compare it with the golden-rule benchmark, and see when an economy may overaccumulate capital and become dynamically inefficient.