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Economics 1956

A Contribution to the Theory of Economic Growth

Robert M. Solow

Capital accumulation alone runs into diminishing returns; lasting growth comes from technology.

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In depth · the introduction

Save and invest all you like — a country built on capital alone eventually stops getting richer per person. What keeps living standards rising is something else entirely: better ideas.

The big idea

Solow asked a simple question: what makes a country grow richer over decades? The obvious answer is to build more — more factories, machines, roads, tools. And that works, for a while. But Solow showed that capital runs into diminishing returns: the hundredth machine in a workshop adds far less than the first. Each new dose of capital lifts output by a little less than the last.

So an economy that only piles up capital eventually reaches a plateau — a steady state where new investment just barely replaces what wears out and equips the extra workers being born. Income per person stops climbing. To keep it climbing forever, you need a different fuel: technological progress — knowing how to get more out of the same workers and machines. Saving sets how high the plateau is; technology decides whether the plateau itself keeps rising.

How it came about

In the early 1950s the leading theory of growth came from Roy Harrod and Evsey Domar. In their picture, steady growth was a knife-edge: an economy had to grow at exactly one rate or spiral into ever-worsening booms and slumps. That felt wrong to a young MIT economist named Robert Solow — real economies don't teeter on a razor's edge.

He found the hidden culprit: the Harrod–Domar model assumed factories needed capital and labor in fixed proportions, like a recipe that can never be adjusted. Solow let the recipe flex — use a bit more capital and a bit less labor, or the reverse — and the knife-edge vanished. The economy now glided smoothly toward a stable resting point. He published it in 1956; an Australian economist, Trevor Swan, reached almost the same model independently that same year. In 1987 Solow won the Nobel Memorial Prize.

Why it mattered

This one paper founded modern growth theory and changed what governments aim at. If saving and investment alone could make a nation permanently richer per person, the recipe for prosperity would be simple: save more. Solow showed that this only buys a temporary spurt and a higher plateau — the lasting driver is productivity, the technology and know-how that let people produce more from the same effort. It also predicted that poorer countries, starting with little capital, should grow faster and catch up — a claim economists have tested ever since.

A way to picture it

Think of watering a plant. The first cup of water does wonders; the second still helps; by the tenth you are just making mud. More water — more capital — gives less and less, until the plant is as big as that much water can support. To grow a bigger plant you do not add yet more water; you need better soil, more sun, a hardier seed. In Solow's economy, capital is the water and technology is the soil and sun — the thing that lets the same effort yield a taller plant year after year.

A Solow diagram: a rising, flattening saving curve crosses a straight line at one point — the steady state. Sliding the saving rate up shifts the crossing point higher, but a marker always glides back to rest on it, showing capital per worker settling at a plateau.

Where it sits

Adam Smith asked how nations grow rich and answered with the division of labor; Solow turned that question into a clean mathematical model with a single equation. His framework set the terms for everything after: the endogenous-growth theorists of the late 1980s (Paul Romer, Robert Lucas) tried to explain the technology that Solow had left as an outside gift, and growth accounting — splitting growth into capital, labor and a leftover «residual» — became a standard tool. Today's debates about why some nations stay poor, and whether rich economies are running out of new ideas, are still being argued on the diagram Solow drew.

The original document
Original source text
Robert M. Solow · A Contribution to the Theory of Economic Growth · The Quarterly Journal of Economics, 70(1), 1956 · pp. 65–94
I. Introduction
All theory depends on assumptions which are not quite true. That is what makes it theory.
The art of successful theorizing is to make the inevitable simplifying assumptions in such a way that the final results are not very sensitive. A “crucial” assumption is one on which the conclusions do depend sensitively, and it is important that crucial assumptions be reasonably realistic.
When the results of a theory seem to flow specifically from a special crucial assumption, then if the assumption is dubious, the results are suspect.
I wish to argue that something like this is true of the Harrod-Domar model of economic growth. The characteristic and powerful conclusion of the Harrod-Domar line of thought is that even for the long run the economic system is at best balanced on a knife-edge of equilibrium growth.
[ … ]
But this fundamental opposition of warranted and natural rates turns out in the end to flow from the crucial assumption that production takes place under conditions of fixed proportions. There is no possibility of substituting labor for capital in production. If this assumption is abandoned, the knife-edge notion of unstable balance seems to go with it.
II. A Model of Long-Run Growth
There is only one commodity, output as a whole, whose rate of production is designated Y(t). Thus we can speak unambiguously of the community's real income. Part of each instant's output is consumed and the rest is saved and invested. The fraction of output saved is a constant s, so that the rate of saving is sY(t).
[ … ]
Output is produced with the help of two factors of production, capital and labor. Technological possibilities are represented by a production function Y = F(K, L), assumed to show constant returns to scale. Hence, if we divide through by L, output per head of labor is a function of capital per head of labor alone.
Robert M. Solow · Massachusetts Institute of Technology · 1956