Why Some Countries Are Rich: The Solow Model

Why building more factories and roads makes a country richer — for a while. The Solow model explains why saving more is a one-shot boost, not a permanent path to faster growth.

The puzzle

In 1960, South Korea and Ghana had roughly the same GDP per person. By 2025 South Korea’s was about twenty times Ghana’s. Both countries gained access to similar technology. Both have hard-working people. So what happened?

A useful first model says: it’s mostly about capital per worker — how much equipment, how many machines, how much infrastructure each worker has. Build more of that, and each worker produces more.

US real GDP per capita, quarterly, 1947 to 2024, log scale. — US real GDP per capita on a log scale since 1947. A straight line on a log plot is constant percent growth — and the US has run remarkably close to ~2% per year for nearly 80 years. The Solow model is the simplest framework that explains why that line has a slope at all (capital accumulation + technology growth) and why it's roughly straight (diminishing returns pulling the economy back to its steady-state path).Source: FRED, St. Louis Fed (A939RX0Q048SBEA)

One key idea: diminishing returns

Here’s the catch. The hundredth machine added to a factory adds less output than the first one. There are only so many places to put a robot arm before they start tripping over each other. The same principle applies at a country level: doubling capital per worker doesn’t double output per worker.

In math: if output per worker is $y$ and capital per worker is $k$ , the relationship looks like $y = k^{\alpha}$ with $\alpha$ between zero and one (roughly $\alpha \approx 1/3$ for the US). Plot it and the curve bends over as $k$ gets large.

The balance

A country adds new capital every year through investment (a fraction $s$ of its income, where $s$ is the saving rate). It also loses capital through depreciation (machines wear out) and through population growth (the existing capital has to be spread over more workers). Call the combined “drag” $(n + \delta) \cdot k$ .

Capital grows when saving exceeds drag. It shrinks when drag exceeds saving. They balance at a steady state $k^\*$ where the curve $s \cdot k^{\alpha}$ meets the straight line $(n + \delta) \cdot k$ .

Play with it

Savings s: 0.25Pop. growth n: 0.020Depreciation δ: 0.050Capital share α: 0.33

Steady-state k* ≈ 6.69, y* ≈ 1.87

Investment vs break-even

Transition path

Try doubling the savings rate from 0.25 to 0.50. Two things happen:

The country’s capital and output rise toward a new, higher steady state. This is real and matters — a 30% gain in output per worker is a generation of higher living standards.
Once it gets there, growth slows back to roughly zero. The economy is now richer, but it’s no longer growing.

That second observation is the Solow model’s most important insight.

What this means

Long-run growth — the kind that turns a country from poor to rich over generations — has to come from something the model treats as separate: technology $A$ . Better methods of producing, not just more inputs. Innovations let the same $k$ yield a higher $y$ .

This is why South Korea’s industrial policy after 1960 wasn’t just about saving and investing (though it was about that, a lot). It was about acquiring, copying, and eventually inventing better production technologies — semiconductors, shipbuilding, automobiles. Ghana hasn’t had the same trajectory; the model points us toward asking why its technology-adoption story has been different.

Quick check

Take the practice quiz when you’re ready, and try the guided IS-LM walkthrough next for the short-run counterpart to this long-run model.