The Harrod-Domar model suggests that “economies should spend most of their time experiencing either prolonged episodes of increasing or falling unemployment rates and/or prolonged periods of rising or falling capacity utilization … [but] … that is not what the record of the main capitalist economies looks like” (Solow 1994, p.46).

Robert Solow (1956, p.66) was uncomfortable with the knife-edge instability proposal derived by Harrod. Solow attacked Harrod for assuming fixed factor proportions and tried to show that growth does converge to the economy’s balanced growth path (Thirlwall 2003, p.142).

If capital grows faster than labour then *gw > gn*, the price of capital will fall and economies, via the price mechanism, will switch to more capital intensive techniques and long-run economic growth will return to *gn* (Solow 1994, p.47).

Let’s take the aggregate production function:

Where Y is output, K is the capital stock, A is technology or knowledge and L is labour.

Rewriting the production function in terms of output and capital per effective unit of labour we get:

Where y=Y/AL and k=K/AL.Where y=Y/AL and k=K/AL.

The Solow model then makes numerous assumptions mainly to restrict the shape of the production function and allow capital and labour to be infinitely substituted so that the economy converges to an equilibrium:

- There is only one good, Y, which can be consumed or invested (Solow 1956, p.66).
- All markets are perfectly competitive and there are no externalities (Jones 1998, p.20).
- All capital and labour are fully employed (Thirlwall 2002, p.20).
- All savings are invested (Thirlwall 2002, p.20). Let s be the savings ratio, S be savings and I be investment then sY = S = I.
- An infinitely flexible factor substitutability and an infinitely flexible capital-labour ratio. Basically, firms can choose any combination of capital and labour to produce Y.
- There is a decreasing marginal productivity of capital (MPk). As per unit of effective labour increases, ceteris paribus, capital becomes less productive and MPk declines. So as k increases, each additional unit of k adds less to y.
- The production function satisfies the Inada conditions, so a low capital stock means a high MPk and a high capital stock means a low MPk (Romer 2006, p.11).
- The production function exhibits constant returns, so doubling capital and labour leads to a doubling of output (Solow 1956, pp.66-67).
- The Euler theorem holds, so every factor is paid its marginal product (Jones 1998, p.21).
- There is Harrod-neutral technology, so as the capital stock increases, labour becomes more productive (Romer 2006, p.9).
- Technology is exogenous, manna from heaven, it is determined outside the model (Jones 1998, p.31).

After taking these assumptions we can look at the key Solow equation:

Where ∆k is the change in the capital stock per effective unit of labour. sf(k) is the actual level of savings or investment. n denotes the labour force growth rate, M is the exogenously determined technological growth rate and d is capital depreciation. Break-even investment, that is, the amount of investment that must be done just to keep the capital stock at its existing level is (n+M+d)k.

Basically then, the key Solow equation shows that the capital stock adjusts based on the difference between actual and break-even investment, k changes by sf(k) – (n+M+d)k until the economy reaches equilibrium at its balanced growth path.

At k’, capital deepening occurs. Actual investment is greater than break-even investment, more capital is being invested in than that required to keep the capital-labour ratio constant so k rises. At k’’, capital widening occurs because actual investment is less than break-even investment, less capital is being invested in than that required to keep the capital-labour ratio constant so k falls. So no matter where the economy starts from, it inevitably converges to its balanced growth path at the steady state level of k*. At k*, actual investment equals break-even investment, Δk = 0, and equilibrium is reached. At k*, income and consumption grow at rate , the labour force grows at rate , so income per capita and consumption per capita grow at the exogenous rate .

An important point must be highlighted here, the Solow model contends that long-run economic growth is determined by technology and this itself is determined exogenously. Technological progress is the source of sustained per capita growth and R&D spending does not affect technology (Jones 1998, pp.19-34). Any disturbance to the system will only induce short-run disequilibrium per capita growth and, in the long-run, per capita growth will return to the exogenous rate M once a new steady state is reached. Any change in savings or investment will not affect long-run economic growth. A rise in savings means investment rises, more capital is accumulated so k rises and economic growth rises in the short-run. But because of decreasing MPk, economic growth slows down and, in the long-run, returns back down to the exogenous rate M. Similarly, Ricardo (1817 cited in Thirlwall 2003, p.133) asserts that, due to diminishing returns in agriculture, capitalist economies will end up in a steady state with growth determined by technological change. Thus, policy measures like R&D tax cuts or investment subsidies can change short-run growth rates and alter the long-run steady state level of output but not the long-run growth rate.

Jones, C., (1998), Introduction to Economic Growth, London: W.W. Norton and Company.

Romer, D., (2006), Advanced Macroeconomics, New York: McGraw-Hill.

Solow, R., (1956), A Contribution to the Theory of Economic Growth, The Quarterly Journal of Economics, 70(1).

Solow, R., (1994), Perspectives on Growth Theory, Journal of Economic Perspectives, 8(1).

Thirlwall, A.P., (2002), The Nature of Economic Growth: An Alternative Framework for Understanding the Performance of Nations, Cheltenham: Edward Elgar.

Thirlwall, A.P., (2003), Growth and Development: With Special Reference to Developing Countries, London: MacMillan.