If an economy is not yet on its balanced-growth path, it will tend to go toward that path. If a country has a small capital stock relative to GDP, then its capital stock will grow faster than real GDP. Countries that are still developing may well be in this position. Countries that are further along in the development process are likely to be (approximately) on their balanced-growth paths. For such countries, the ratio of capital stock to output is unchanging.
Economies that have not yet accumulated enough capital to be on their balanced-growth paths will have a growth rate that equals the balanced-growth rate plus an additional factor due to the growth rate of capital relative to GDP. [***If you are interested in the mathematical derivation of this equation, you can find it in the toolkit.***]
The first term is the growth rate along the balanced-growth path. The second term is the additional component to growth that comes about whenever the capital stock is growing faster than output.
***Table 6.6 "Approaching the Balanced-Growth Path" gives an example of an economy that is approaching a balanced-growth path. Like the economy in ***Figure 6.13 "Output and Capital Stock in a Balanced-Growth Economy", the balanced-growth output growth rate is 3 percent. The workforce grows at 1 percent, so output per worker grows at 2 percent along the balanced-growth path. However, this economy starts off (in the year 2000) with a smaller capital stock than is needed for balanced growth. Looking at the first row of the table, you can see that the capital stock grows at 14.4 percent, while output grows at 6.8 percent. Because capital grows faster than output, there is an additional component to growth, as we have just explained. This contributes an extra 3.8 percentage points to the growth rate, so output per worker grows at 5.8 percent.
As time goes on, the capital stock grows relative to output, and the economy gets closer to the balanced-growth path. As this happens, the additional component of growth becomes smaller. For example, in 2010, the capital stock grows at 6.8 percent, and output grows at 4.3 percent. The growth rate of output per worker is 3.3 percent—2 percentage points being the balanced-growth contribution and 1.3 percent due to the faster growth rate of capital stock compared to output. By 2050, the economy is close to balanced growth: output per worker grows at 2.3 percent, with capital stock growing only a little bit faster than output.
Table 6.6 Approaching the Balanced-Growth Path
|
Year |
Balanced-Growth Output Growth Rate (%) |
Balanced-Growth Output per Worker Growth Rate (%) |
Capital Growth Rate (%) |
Output Growth Rate (%) |
Output per Worker Growth Rate (%) |
|
2000 |
3.0 |
2.0 |
14.4 |
6.8 |
5.8 |
|
2005 |
3.0 |
2.0 |
9.3 |
5.1 |
4.1 |
|
2010 |
3.0 |
2.0 |
6.8 |
4.3 |
3.3 |
|
2015 |
3.0 |
2.0 |
5.5 |
3.8 |
2.8 |
|
2020 |
3.0 |
2.0 |
4.7 |
3.6 |
2.6 |
|
2025 |
3.0 |
2.0 |
4.1 |
3.4 |
2.4 |
|
… |
… |
… |
… |
… |
… |
|
2050 |
3.0 |
2.0 |
3.8 |
2.3 |
Countries that are well below their growth path will see their capital stock grow rapidly relative to GDP. They will experience relatively rapid GDP growth. Countries that are close to their balanced-growth path will see their capital stock grow more slowly relative to GDP and have a GDP growth rate that is only slightly bigger than the balanced-growth rate. Although the economy will eventually reach its balanced-growth value, this adjustment may take decades. For this reason, we say that the economy will achieve balanced growth only in the very long run. [***To be mathematically precise, the economy gets closer and closer to its balanced-growth path but never quite gets there. Over a period of decades, it gets close enough that it makes no practical difference.****]
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