# The Growth Rate of Output per Worker in a Balanced-Growth Economy

When we are comparing living standards across countries, it is better to adjust for differences in the size of the workforce to obtain output per worker. This is a measure of the overall productivity of an economy—that is, the effectiveness of an economy for producing output. (Of course, output per worker and output per person are very closely related. For the US economy, the workforce is roughly half the total population, so output per person is therefore approximately half as much as output per worker.) The growth rate of output per worker equals the growth rate of output minus the growth rate of the workforce:

balanced-growth output-per-worker growth rate = human capital growth rate + 1

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1−a × technology growth .

This equation tells us that, in the end, the secret to economic growth is the development of knowledge and skills. Invention, innovation, education, training, and improvements in social infrastructure are the drivers of economic growth in the very long run. Perhaps surprisingly, the growth rate of the capital stock is not a fundamental determinant of the growth rate. When we have balanced growth, the capital stock grows, which contributes to the overall growth of output. But if we ask what determines the overall growth rate in an economy, it is the growth of technology and human capital. The capital stock then adjusts to keep the economy on its balanced-growth path. By the definition of balanced growth, the growth rate of the capital stock is equal to the output growth rate. Figure 6.13 Output and Capital Stock in a Balanced-Growth Economy This picture shows an example of an economy on a balanced-growth path. Both variables grow at 3 percent per year and the capital stock is always equal to exactly twice the level of GDP.

Figure 6.13 “Output and Capital Stock in a Balanced-Growth Economy” illustrates balanced growth. Look first at output. Notice that even though the growth rate of output is constant, the graph is not a straight line. Instead, it curves upward: the change in the level of output increases over time. This is because a growth rate is a percentage change. In our example, output in 2000 is \$10 trillion, and the growth rate is 3 percent. From 2000 to 2001, output increases by \$300 billion (= \$10 trillion × 0.03). By 2050, output is equal to \$44 trillion. Between that year and the next, output increases by \$1.3 trillion (= \$44 trillion × 0.03). Even though the growth rate is the same, the change in the level of output is more than four times as large. When output and the capital stock grow at the same rate, the ratio of the capital stock to GDP does not change. In Figure 6.13 “Output and Capital Stock in a Balanced-Growth Economy”, the value of the capital stock is always twice the value of output. The capital stock and real GDP both grow at the same rate (3 percent per year), so the ratio of the capital stock to GDP does not change over time.

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