Robert Solow has passed away at the age of 99. He was the 1987 winner of the Nobel prize in economics for his work on the study of economic growth. He first became a professor at MIT in 1949, and was still a professor emeritus there at the time of his death.

There are many coincidences of scientific advancement in history. Newton and Leibniz independently developed calculus at roughly the same time. Oxygen was discovered independently by Carl Wilhelm Scheele and Joseph Priestley. One of economics’ iterations of this phenomenon was the exogenous growth model, formulated independently by Solow and Australian economist Trevor Swan in 1956.

Maybe because Solow is American, it is commonly taught as the “Solow model” in the U.S. The Solow model is the basis for much of the modern understanding of how countries become wealthier, and what helps and hurts them as they grow.

Solow aggregated vast amounts of information into a relatively simple equation. The variable K is for capital, which is all the stuff people use to make stuff (factories, machines, vehicles, computers, etc.). The variable N is for labor, the number of workers in an economy. The variable A is for technology. Economic output, Y, is a function of K, N, and A. The Solow model has no foreign trade and no government.

This is a crazy oversimplification of the real world. But Solow demonstrated that doing such oversimplification can help to understand the real world better.

How does a country get capital? It invests. How does it get investment? It saves. Output can be consumed now or later, and consuming later is saving. Savings can then be invested to buy more capital.

Is more capital always better? No. There are diminishing returns to capital. The first sewing machine a person buys is way better than sewing by hand. Buying a second sewing machine doesn’t help as much. The same principle can be extrapolated to entire countries, for all machines and with much bigger numbers.

So the returns to capital diminish as capital grows. As capital grows, there are more costs to maintain capital. You have to repair sewing machines, and trucks and infrastructure and computers, and that costs money. The costs do not diminish like the returns do. If it costs $10 per year to maintain one machine, it costs $20 per year to maintain two, and $30 per year to maintain three, etc.

That constant depreciation is also paid for with savings. That means the old capital competes with new capital for investment. At low levels of capital, adding new capital is worth it, because you don’t have much capital depreciating that needs to be paid for. At higher levels of capital, the depreciation costs start swamping out the benefits of increasing the level of capital.

Eventually, an economy in the Solow model reaches what’s called the “steady state.” That’s when all the economy’s savings is used to maintain the existing level of capital. It’s an equilibrium point. There’s no output growth in the steady state.

The Solow model uses a few very elementary economic ideas — aggregation, diminishing returns, and equilibrium — to allow for powerful analysis.

If we know that there is a steady state to which an economy is headed, that means it doesn’t matter how much capital a country starts with. No matter where it starts, it will converge to that steady state, as a function of its savings rate and depreciation rate. Nothing else matters.

This seems fatalistic, and it is if you only consider K. But it’s much the same story with N. This one comes a little more intuitively: There’s basically no correlation between national wealth and population. And the population is basically a given for a country, so it’s impractical to look there for economic growth.

That leaves us with A, technology, and that’s the one that counts. “Technology” when economists use it in this context refers to ideas, innovations, and institutions that improve productivity.

If the value of K and N don’t matter to make a country richer or poorer than another, and countries in the real world are, obviously, richer or poorer than each other, that means the difference must be explained by A.

We see this result play out in the real world. Think of a wealthy country like Germany. A huge chunk of its K got destroyed during World War II. It lost millions of people, N. Yet Germany became a wealthy country again relatively quickly after the war. The war didn’t destroy A, i.e., it didn’t make Germans less productive.

The flip-side is that if you give a poor country, such as Liberia, a bunch of K (think of many development programs that provide capital to poor countries), it won’t become a wealthy country. Liberia’s A remains low, in the form of public corruption, the absence of the rule of law, and poor enforcement of property rights. It will still converge to the same steady state as long as A remains constant.

A is the thing that allows for economic growth. Higher levels of A allow for more investment and more capital accumulation over time. And it never has to stop, mathematically. It’s how we see modern economic growth, where countries expect to grow by a few percent every single year. It’s why new capital doesn’t cause mass unemployment, because there’s more output and more investment to go around. It’s why different regions within countries, where A is roughly equal but levels of K or N might vary, tend to converge with each other economically.

For a good video series that explains all this better than I can, with helpful graphics to illustrate, check out Alex Tabarrok of GMU at Marginal Revolution University here.

The Solow model is the basis for the modern understanding of economic growth. Solow was on the left politically, and advised several Democrats, but his political involvement will be forgotten long before his work on growth theory will be. Every economist who studies economic growth, and everyone who benefits from effective economic-development efforts around the world, is in some way indebted to Solow. R.I.P.