Solow Growth Model

Structure and the steady state

Proposed independently by Robert Solow (1956) and Trevor Swan (1956), the model resolved the "knife-edge" problem of the Harrod (1939) and Domar (1946) models by using a production function in which capital and labor can substitute for one another. Output Y = F(K, AL) has constant returns to scale and diminishing returns to capital. Capital per effective worker evolves as Δk = s·f(k) − (n + g + δ)k: if investment from the saving rate s exceeds the dilution of capital from population growth n, technological progress g and depreciation δ, k rises; otherwise it falls. Diminishing returns bring the economy to a "steady state" where the two forces balance, after which per capita income grows only at the rate of technological progress g. The model's central conclusion is that a higher saving rate raises the steady-state level of income but not the long-run growth rate. Phelps (1961) derived the "golden rule" capital stock that maximizes consumption per worker, where the marginal product of capital equals n + g + δ.

The Solow residual and growth accounting

Using U.S. data for 1909–1949, Solow (1957) computed the part of output growth not explained by growth in labor and capital inputs and found that about 87 percent of the growth in output per worker was this "residual." Called technical progress or total factor productivity (TFP), it became the basic framework for growth accounting. In the model, however, technological progress is exogenous, so the model cannot explain why technology advances; this limitation became the starting point for endogenous growth theory. Paul Krugman (1994) and Alwyn Young (1995) argued that East Asia's rapid growth came mainly from rising capital and labor inputs rather than TFP, recalling the Solow prediction that input-driven growth runs into diminishing returns.

Convergence and evidence

The Solow model predicts "convergence": poorer countries, with a higher marginal product of capital, should grow faster. Baumol (1986) found convergence among industrialized countries, but absolute convergence was weak in global samples. Barro (1991) showed "conditional convergence" once factors determining the steady state, such as saving rates, population growth and human capital, are controlled for. Mankiw, Romer and Weil (1992) argued that a Solow model augmented with human capital explains about 80 percent of cross-country income differences. Hall and Jones (1999), by contrast, found that much of the variation stems from TFP differences rooted in "social infrastructure" such as institutions and government policy. The Solow model remains the starting point of macroeconomics textbooks and the benchmark against which innovation theories such as creative destruction are compared.

FAQ

What is the Solow model in simple terms?

Adding capital such as factories and machines boosts growth at first, but with shrinking returns, so in the long run only technological progress can keep raising income per person.

What is the Solow residual?

It is the part of output growth not explained by increases in labor and capital inputs, usually interpreted as technological progress or total factor productivity.

Sources reviewed: 2026-10-26

References

1. Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics, 70(1), 65–94.
2. Swan, T. W. (1956). Economic growth and capital accumulation. Economic Record, 32(2), 334–361.
3. Solow, R. M. (1957). Technical change and the aggregate production function. Review of Economics and Statistics, 39(3), 312–320.
4. Harrod, R. F. (1939). An essay in dynamic theory. Economic Journal, 49(193), 14–33.
5. Domar, E. D. (1946). Capital expansion, rate of growth, and employment. Econometrica, 14(2), 137–147.
6. Phelps, E. S. (1961). The golden rule of accumulation. American Economic Review, 51(4), 638–643.
7. Mankiw, N. G., Romer, D., & Weil, D. N. (1992). A contribution to the empirics of economic growth. Quarterly Journal of Economics, 107(2), 407–437.
8. Barro, R. J. (1991). Economic growth in a cross section of countries. Quarterly Journal of Economics, 106(2), 407–443.
9. Baumol, W. J. (1986). Productivity growth, convergence, and welfare. American Economic Review, 76(5), 1072–1085.
10. Krugman, P. (1994). The myth of Asia's miracle. Foreign Affairs, 73(6), 62–78.
11. Young, A. (1995). The tyranny of numbers. Quarterly Journal of Economics, 110(3), 641–680.
12. Hall, R. E., & Jones, C. I. (1999). Why do some countries produce so much more output per worker than others? Quarterly Journal of Economics, 114(1), 83–116.
13. Jones, C. I., & Vollrath, D. (2013). Introduction to Economic Growth (3rd ed.). New York: W. W. Norton.