We begin with the tool of growth accounting. The growth accounting equation for our aggregate production function is as follows: [***Growth accounting is discussed in more detail in Chapter 5 "Globalization and Competitiveness".***]
output growth rate = [a × (capital growth rate)]
*
+[(1 − a) × (workforce growth rate + human capital growth rate)]
*
+technology growth rate.
Toolkit: Section 16.17 "Growth Accounting"
You can review growth accounting in the toolkit.
In this equation, a is just a number. For the US economy, a is approximately equal to 1/3. Remember that output is just another term for real gross domestic product (real GDP).
It turns out that, in the very long run, we expect the capital stock and the level of output to grow at exactly the same rate. We see why later in this section. Such a situation is called balanced growth. When this is true, the growth accounting equation then becomes [***You don’t need to worry about the mathematical details, but if you are interested, we obtain this equation by setting the capital growth rate equal to the output growth rate:output growth rate BG = [a × (output growth rate BG)] + [(1 − a) × (workforce growth rate + human capital growth rate)] + technology growth rate, which implies (1 − a) × output growth rate BG = [(1 − a) × (workforce growth rate + human capital growth rate)] + technology growth rate.****]
For example, suppose that a = 1/3, the human capital growth rate = 0.01, the technology growth rate = 0.02, and the workforce growth rate = 0.03. Then
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