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Nothing is more important for people’s standard of living than sustained economic growth. Even small changes in the rate of growth, when sustained and compounded over long periods of time, make an enormous difference in the standard of living. Consider [link] , in which the rows of the table show several different rates of growth in GDP per capita and the columns show different periods of time. Assume for simplicity that an economy starts with a GDP per capita of 100. The table then applies the following formula to calculate what GDP will be at the given growth rate in the future:
For example, an economy that starts with a GDP of 100 and grows at 3% per year will reach a GDP of 209 after 25 years; that is, 100 (1.03) 25 = 209.
The slowest rate of GDP per capita growth in the table, just 1% per year, is similar to what the United States experienced during its weakest years of productivity growth. The second highest rate, 3% per year, is close to what the U.S. economy experienced during the strong economy of the late 1990s and into the 2000s. Higher rates of per capita growth, such as 5% or 8% per year, represent the experience of rapid growth in economies like Japan, Korea, and China.
[link] shows that even a few percentage points of difference in economic growth rates will have a profound effect if sustained and compounded over time. For example, an economy growing at a 1% annual rate over 50 years will see its GDP per capita rise by a total of 64%, from 100 to 164 in this example. However, a country growing at a 5% annual rate will see (almost) the same amount of growth—from 100 to 163—over just 10 years. Rapid rates of economic growth can bring profound transformation. (See the following Clear It Up feature on the relationship between compound growth rates and compound interest rates.) If the rate of growth is 8%, young adults starting at age 20 will see the average standard of living in their country more than double by the time they reach age 30, and grow nearly sevenfold by the time they reach age 45.
| Growth Rate | Value of an original 100 in 10 Years | Value of an original 100 in 25 Years | Value of an original 100 in 50 Years |
|---|---|---|---|
| 1% | 110 | 128 | 164 |
| 3% | 134 | 209 | 438 |
| 5% | 163 | 338 | 1,147 |
| 8% | 216 | 685 | 4,690 |
The formula for growth rates of GDP over different periods of time, as shown in [link] , is exactly the same as the formula for how a given amount of financial savings grows at a certain interest rate over time, as presented in Choice in a World of Scarcity . Both formulas have the same ingredients:
Recall that compound interest is interest that is earned on past interest. It causes the total amount of financial savings to grow dramatically over time. Similarly, compound rates of economic growth, or the compound growth rate , means that the rate of growth is being multiplied by a base that includes past GDP growth, with dramatic effects over time.
For example, in 2013, the World Fact Book, produced by the Central Intelligence Agency, reported that South Korea had a GDP of $1.67 trillion with a growth rate of 2.8%. We can estimate that at that growth rate, South Korea’s GDP will be $1.92 trillion in five years. If we apply the growth rate to each year’s ending GDP for the next five years, we will calculate that at the end of year one, GDP is $1.72 trillion. In year two, we start with the end-of-year one value of $1.67 and increase it by 2%. Year three starts with the end-of-year two GDP, and we increase it by 2% and so on, as depicted in the [link] .
| Year | Starting GDP | Growth Rate 2% | Year-End Amount |
|---|---|---|---|
| 1 | $1.67 Trillion × | (1+0.028) | $1.72 Trillion |
| 2 | $1.72 Trillion × | (1+0.028) | $1.76 Trillion |
| 3 | $1.76 Trillion × | (1+0.028) | $1.81 Trillion |
| 4 | $1.81 Trillion × | (1+0.028) | $1.87 Trillion |
| 5 | $1.87 Trillion × | (1+0.028) | $1.92 Trillion |
Another way to calculate the growth rate is to apply the following formula:
Where “future value” is the value of GDP five years hence, “present value” is the starting GDP amount of $1.64 trillion, “g” is the growth rate of 2%, and “n” is the number of periods for which we are calculating growth.
Productivity, the value of what is produced per worker, or per hour worked, can be measured as the level of GDP per worker or GDP per hour. The United States experienced a productivity slowdown between 1973 and 1989. Since then, U.S. productivity has rebounded (the current global recession notwithstanding). It is not clear whether the current growth in productivity will be sustained. The rate of productivity growth is the primary determinant of an economy’s rate of long-term economic growth and higher wages. Over decades and generations, seemingly small differences of a few percentage points in the annual rate of economic growth make an enormous difference in GDP per capita. An aggregate production function specifies how certain inputs in the economy, like human capital, physical capital, and technology, lead to the output measured as GDP per capita.
Compound interest and compound growth rates behave in the same way as productivity rates. Seemingly small changes in percentage points can have big impacts on income over time.
An economy starts off with a GDP per capita of $5,000. How large will the GDP per capita be if it grows at an annual rate of 2% for 20 years? 2% for 40 years? 4% for 40 years? 6% for 40 years?
An economy starts off with a GDP per capita of 12,000 euros. How large will the GDP per capita be if it grows at an annual rate of 3% for 10 years? 3% for 30 years? 6% for 30 years?
Say that the average worker in Canada has a productivity level of $30 per hour while the average worker in the United Kingdom has a productivity level of $25 per hour (both measured in U.S. dollars). Over the next five years, say that worker productivity in Canada grows at 1% per year while worker productivity in the UK grows 3% per year. After five years, who will have the higher productivity level, and by how much?
Say that the average worker in the U.S. economy is eight times as productive as an average worker in Mexico. If the productivity of U.S. workers grows at 2% for 25 years and the productivity of Mexico’s workers grows at 6% for 25 years, which country will have higher worker productivity at that point?
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