Since the Industrial Revolution, economists have attempted to explain why certain countries economies grow at greater rates than others. The post-Keynesian era saw the introduction of the Harrod-Domar model of economic growth. This model explained an economy’s growth rate by observing the level of saving and productivity of capital in the economy. The neo-classical Solow-Swann model, however, superseded this, as claims of instability in the solution of the Harrod-Domar model arose. On top of analyzing an economy in terms of it’s capital stock and productivity, the Solow Swann model took labour input into account as well. Both models, however, concluded that countries that were able to accumulate capital at greater rates than others generally saw faster growth rates up until their steady state was reached.
Solow (1956) introduced his version of the neoclassical theory of growth using the production function Y=F(K,AL), where Y is output, K is capital, L is labour, and A is a measure of the level of technology. AL can be seen as the labor force measured in efficiency units, which incorporates both the amount of labor and the productivity of labor as determined by the available technology. Assuming the production function has constant returns to scale, we can write the production function as y=f(k) where y=Y/AL, k=K/AL and f(k)=F(k,1). This production function relates output per effective worker to the amount of capital per effective worker. Ultimately, the neoclassical model emphasizes how growth arises from the accumulation of capital. The capital stock per effective worker, k, evolves according to: dk/dt=sf(k)-(n+g+δ)k, where s is the rate of saving, n is the rate of population growth, g is the rate of growth in technology, δ is the rate at which capital depreciates and dk/dt resembles the change in capital over time t.
The law of motion of capital (or the capital accumulation equation) stipulates that dK/dt=sY-δK. Meaning, the change in capital stock between t and t+1 is equal to investment minus the depreciation on capital. Therefore, high rates of saving in an economy (and therefore high levels of investment) will result in greater changes in capital. Thus, when observing the Hicks Neutral (Labour augmenting) Cobb-Douglas function; Y=K^α AL^1−α, we observe that countries with greater rates of saving, and thus greater levels of investment resulting in greater accumulation levels of capital, will have a greater input of K in their production function. A larger value of K ultimately results in greater levels of Y, or output. Thus, economies that can accumulate more capital at greater rates than others, ceteris paribus, should see faster growth rates.
The diagram above shows us that, given an increase in capital per effective worker from k(0) to k* (due to s>n+g+δ), output levels in that economy (per effective worker) will have increased from sy* to y*. This is due to the fact that the saving of income (or investment), defined by sf(k), is greater in this period, than break-even investment, defined by the line (n+g+δ)k. Countries that accumulate capital will see growth in output up until the point where sy=(n+g+δ)k. At this point, the economy has reached its steady state, k*, whereby any increase in capital accumulated will not have a long-run impact on output.
However, as assumed by the Inada conditions, certain countries that already hold large amounts of capital at time (t) will not gain large returns from extra units of capital added, due to the diminishing marginal product of capital. Smaller countries that hold far less capital at time (t) will see far greater returns from accumulating capital. Therefore, we cannot put different growth rates of nations solely down to different rates of capital accumulation. The UK, for example, could accumulate far greater levels of capital than say, Mongolia. However because Mongolians do not have access to as much capital per worker as people in the UK, one extra unit of capital will have a much greater impact on growth (or output, Y) in Mongolia.
Taking this into account, countries with similar capital/output ratios would certainly grow at different rates to each other given differing levels of capital accumulation. However, when an economy has reached its steady state, or is close to having reached it, other factors determine why certain countries grow faster than others.
According to various literatures, growth can be divided into two alternative types, extensive growth (resulting from factor accumulation) which is subject to diminishing returns, and intensive growth which results from technological progress. This type of growth allows continuous increases in output, labour productivity and living standards whilst contributing to welfare (Krugman 1994). Technological progress, or changes in Total Factor Productivity, defined as A(t) in the Cobb-Douglas function used in our Solow model, can be used to describe differences in rates of growth across developed economies. Growth in A alters due to unobservable factors such as institutional change, (quality of institutions is another major source of long run economic growth), changes in returns to scale, impacts of R&D discoveries etc. Large advances in technology enable the labour force to operate more efficiently, (boosting the marginal product of labour) and also enable capital efficiency improvements (increasing MPK).
Additionally, Mankiw, Romer and Weil (1992) introduce human capital as an extension to Solow’s model which solely observed physical capital and effective labour. Rapid accumulation of human capital through large investment in education has contributed to ‘an education miracle’ in East Asian economies. Other factors that contribute to differing rates of economic growth among countries include risk taking entrepreneurial activities and organizational skills.
To conclude, varying rates of capital accumulation has a part to play in understanding why certain countries grow at faster rates than others. However, Krugman (1994) predicted that output growth, dominated by physical capital accumulation, is short-lived and not sustainable. We can therefore not put growth disparities solely down to this, as when the steady state is reached, technological progress becomes much more telling as to why certain countries grow faster than others.