Before we analyze the sources of long-run economic growth, it’s useful to have a sense of just how much the U.S. economy has grown over time and how large the gaps are between wealthy countries like the United States and countries that have yet to achieve a comparable standard of living. So let’s take a look at the numbers.

The key statistic used to track economic growth is real GDP per capita—real GDP divided by the population size. We focus on GDP because, as we have learned, GDP measures the total value of an economy’s production of final goods and services as well as the income earned in that economy in a given year. We use real GDP because we want to separate changes in the quantity of goods and services from the effects of a rising price level. We focus on real GDP per capita because we want to isolate the effect of changes in the population. For example, other things equal, an increase in the population lowers the standard of living for the average person—there are now more people to share a given amount of real GDP. An increase in real GDP that only matches an increase in population leaves the real GDP per capita unchanged.

Although we learned that growth in real GDP per capita should not be a policy goal in and of itself, it does serve as a very useful summary measure of a country’s economic progress over time. Figure 37.1 shows real GDP per capita for the United States, India, and China, measured in 2005 dollars, from 1910 to 2010. (We’ll talk about India and China in a moment.) The vertical axis is drawn on a logarithmic scale so that equal percentage changes in real GDP per capita across countries are the same size in the graph.

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To give a sense of how much the U.S. economy grew during the last century, Table 37.1 shows real GDP per capita at 20-year intervals, expressed two ways: as a percentage of the 1910 level and as a percentage of the 2010 level. In 1930, the U.S. economy already produced 125% as much per person as it did in 1910. In 2010, it produced 614% as much per person as it did in 1910. Alternatively, in 1910, the U.S. economy produced only 16% as much per person as it did in 2010.

The income of the typical family normally grows more or less in proportion to per capita income. For example, a 1% increase in real GDP per capita corresponds, roughly, to a 1% increase in the income of the median or typical family—a family at the center of the income distribution. In 2010, the median American household had an income of about $45,600. Since Table 37.1 tells us that real GDP per capita in 1910 was only 16% of its 2010 level, a typical family in 1910 probably had purchasing power only 16% as large as the purchasing power of a typical family in 2010. That’s around $7,400 in today’s dollars, representing a standard of living that we would now consider severe poverty. Today’s typical American family, if transported back to the United States of 1910, would feel quite deprived.

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Yet many people in the world have a standard of living equal to or lower than that of the United States a century ago. That’s the message about China and India in Figure 37.1: despite dramatic economic growth in China over the last three decades and the less dramatic acceleration of economic growth in India, China has only recently attained the standard of living that the United States enjoyed in 1910, while India is still poorer than the United States was in 1910. And much of the world today is poorer than China or India.

You can get a sense of how poor much of the world remains by looking at Figure 37.2, a map of the world in which countries are classified according to their 2013 levels of GDP per capita, in U.S. dollars. As you can see, large parts of the world have very low incomes. Generally speaking, the countries of Europe and North America, as well as a few in the Pacific, have high incomes. The rest of the world, containing most of its population, is dominated by countries with GDP less than $7,000 per capita—and often much less. In fact, today more than 50% of the world’s people live in countries with a lower standard of living than the United States had a century ago.

In 2013, the United States was much richer than it was in 1953; in 1953, it was much richer than it had been in 1903. But how did 1853 compare with 1803? Or 1753? How far back does long-run economic growth go?

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The answer is that long-run growth is a relatively modern phenomenon. The U.S. economy was already growing steadily by the mid-nineteenth century—think railroads. But if you go back to the period before 1800, you find a world economy that grew extremely slowly by today’s standards. Furthermore, the population grew almost as fast as the economy, so there was very little increase in output per person. According to the economic historian Angus Maddison, from 1000 to 1800, real aggregate output around the world grew less than 0.2% per year, with population rising at about the same rate. Economic stagnation meant unchanging living standards. For example, information on prices and wages from sources such as monastery records shows that workers in England weren’t significantly better off in the early eighteenth century than they had been five centuries earlier. And it’s a good bet that they weren’t much better off than Egyptian peasants in the age of the pharaohs. However, long-run economic growth has increased significantly since 1800. In the last 50 years or so, real GDP per capita worldwide has grown at a rate of about 2% per year. Let’s examine the implications of high and low growth rates.

How did the United States manage to produce nearly seven times more per person in 2010 than in 1910? A little bit at a time. Long-run economic growth is normally a gradual process in which real GDP per capita grows at most a few percent per year. From 1910 to 2010, real GDP per capita in the United States increased an average of 2.1% each year.

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To have a sense of the relationship between the annual growth rate of real GDP per capita and the long-run change in real GDP per capita, it’s helpful to keep in mind the Rule of 70, a mathematical formula that tells us how long it takes real GDP per capita, or any other variable that grows gradually over time, to double. The approximate answer is:

(Note that the Rule of 70 can only be applied to a positive growth rate.) So if real GDP per capita grows at 1% per year, it will take 70 years to double. If it grows at 2% per year, it will take only 35 years to double. Applying the Rule of 70 to the 2.1% average growth rate in the United States implies that it should have taken 33.3 years for real GDP per capita to double; it would have taken 100 years—three periods of 33.3 years each—for U.S. real GDP per capita to double three times. That is, the Rule of 70 implies that over the course of 100 years, U.S. real GDP per capita should have increased by a factor of 2 × 2 × 2 = 8. And this does turn out to be a pretty good approximation of reality. Between 1910 and 2013—a period of 103 years—real GDP per capita rose just about eightfold.

Figure 37.3 shows the average annual rate of growth of real GDP per capita for selected countries from 1980 to 2012. Some countries were notable success stories: we’ve already mentioned China, which has made spectacular progress. India, although not matching China’s performance, has also achieved impressive growth.

Some countries, though, have had very disappointing growth. This includes many of the countries in Africa and South America, where growth rates below 1% are common. A few countries, such as Zimbabwe, have actually slid backward.

What explains these differences in growth rates? To answer that question, we need to examine the sources of long-run growth.