Countries grow at different rates because they accumulate capital at different rates. Is this true? Explain your answer
Introduction
Economic growth can be interpret as an increase in output or wealth of an economy over a period of time. An economy may grow with capital accumulation because with the accumulated capital, more output will be produced. It is possible that countries grow at different rates because they accumulate capital differently. However, that’s not all because there are many other reasons why countries grow differently. In the next section the idea of capital accumulation leads to economic growth and conditional convergence will be explained using neoclassical growth model. In the third section, together with some limitations, some extended ideas except physical capital accumulation will be discussed. And in the last section, a conclusion will be given.
Economic Growth through Capital Accumulation
Assuming a diminishing marginal product of capital and constant saving rate s and capital depreciation rate δ, the capital accumulation equation is:


K  s Y  K
This equation shows that the net change in capital stock,or say, net investment, equals to gross saving minus depreciation. Saving which can be used in investment is a crucial way to finance the acquisition of physical capital because without it, capital stock will decrease over time due to depreciation. Capital stock will be increasing when investment is greater than depreciation. By dividing all terms by K we get,


K
 sY / K    g K  sf ( k ) / k  
K

We also know that and gK=gk+g+n because of K=ALk, then by equating gk the growth version equation will be:

g

k



sf (k )
 (n  g  ） k 

k

Then because of gk  k , multiply both side of the above equation,


k  sf (k )  (n  g   )k
The above is the fundamental equation of neoclassical growth model. The growth version equation can be illustrated in figure 1, which includes a horizontal line and a downward sloping curve. For any economy starting below the steady state value k*, which can be defined here as a point where capital accumulation alone will not increase output any further[1], the two lines do not hit and the gap between them will be gk, the growth rate of capital per effective labor. As long as gk is positive, the economy will be growing because the growth rate of capital per effective worker will be higher than it need to keep pace with capital depreciation. The additional units of physical capital will increase output.

1

Figure 1

This idea can be extended into two or more countries . Assuming two countries with same rate of population growth, technological progress，depreciation rate and saving rate, then the further away an economy is from the steady state value of capital per effective labor, the higher the growth rate of it, i.e., the faster the economy grows. As is shown in figure 2 below,

Figure 2

The “poorer” country with a lower capital per effective labor k1has a higher growth rate gk,1 than the “richer”one and over time it will catch up with the rich country. In this case, it is clearly shown that countries with different capital accumulation rate will have different growth rate. The idea that the economy’s growth rate is greater when it is further away from its steady state is know as conditional convergence.
Some Limitations and Economic Growth through Human Capital Accumulation
However, there are some limitation about the above explanation. The most obvious one is that when using this model, it is assumed that countries have the same population growth rate and technological progress. However, in reality this is quite unlikely. For example, in the last few decades, the population in some less developed countries like China has grown dramatically fast, while in some rich countries such as those in north Europe, population grows much slower and even negatively. Fast growth of population has put lots of pressure on fixed physical asset such as land. This