Solow Growth Model
The Solow growth model explains long-run economic growth through capital accumulation and technology.
Learn the formula with examples.
The Formula
Steady state: k* = (sA / (n + δ))^(1/(1-α))
The Solow growth model (also called the Solow-Swan model) is a foundational model in macroeconomics that explains how capital accumulation, labor growth, and technological progress drive long-run economic growth. It was developed independently by Robert Solow and Trevor Swan in 1956. Solow received the Nobel Prize in Economics in 1987 for this work.
The production function Y = A × K^α × L^(1-α) is called the Cobb-Douglas production function. Output (Y) depends on technology (A), capital (K), and labor (L). The parameter α (typically around 0.3) represents capital's share of output.
A key prediction of the model is that economies converge to a steady state where capital per worker (k) stops growing. At the steady state, investment exactly offsets depreciation and population growth. The only source of sustained per-capita growth in the long run is technological progress (increases in A).
Variables
| Symbol | Meaning |
|---|---|
| Y | Total output (GDP) |
| A | Total factor productivity (technology level) |
| K | Total capital stock |
| L | Total labor force |
| α | Capital's share of output (typically ≈ 0.3) |
| s | Savings rate (fraction of output saved and invested) |
| n | Population growth rate |
| δ | Depreciation rate of capital |
| k* | Steady-state capital per worker |
Example 1
An economy has A = 1, K = 1000, L = 500, and α = 0.3. What is total output?
Y = A × K^α × L^(1-α) = 1 × 1000^0.3 × 500^0.7
1000^0.3 ≈ 7.943
500^0.7 ≈ 76.61
Y = 1 × 7.943 × 76.61
Y ≈ 608.5 units of output
Example 2
Find the steady-state capital per worker when s = 0.20, A = 1, n = 0.02, δ = 0.05, and α = 0.3.
k* = (sA / (n + δ))^(1/(1-α))
k* = (0.20 × 1 / (0.02 + 0.05))^(1/0.7)
k* = (0.20 / 0.07)^(1.4286) = (2.857)^1.4286
k* ≈ 2.857^1.4286 ≈ 4.41
k* ≈ 4.41 units of capital per worker at steady state
When to Use It
The Solow model is the starting point for understanding economic growth.
- Analyzing why some countries are richer than others
- Predicting the impact of higher savings rates on economic growth
- Understanding the role of technology in sustaining growth
- Policy analysis — evaluating the effects of investment and population changes