## Economic Growth

This chapter analyzes economic growth by examining the aggregate production function. Sources of economic growth are identified and growth rates of different countries are compared.

### The Significance of Economic Growth

#### The Rule of 72 and Differences in Growth Rates

The Case in Point
on presidents and growth at the end of this section suggests a startling
fact: the U.S. growth rate began slowing in the 1970s, did not recover
until the mid-1990s, only to slow down again in the 2000s. The question
we address here is: does it matter? Does a percentage point drop in the
growth rate make much difference? It does. To see why, let us
investigate what happens when a variable grows at a particular
percentage rate.

Suppose two economies with equal populations
start out at the same level of real GDP but grow at different rates.
Economy A grows at a rate of 3.5%, and Economy B grows at a rate of
2.4%. After a year, the difference in real GDP will hardly be
noticeable. After a decade, however, real GDP in Economy A will be 11%
greater than in Economy B. Over longer periods, the difference will be
more dramatic. After 100 years, for example, income in Economy A will be
nearly three times as great as in Economy B. If population growth in
the two countries has been the same, the people of Economy A will have a
far higher standard of living than those in Economy B. The difference
in real GDP per person will be roughly equivalent to the difference that
exists today between Great Britain and Mexico.

Over time, small
differences in growth rates create large differences in incomes. An
economy growing at a 3.5% rate increases by 3.5% of its initial value in
the first year. In the second year, the economy increases by 3.5% of
that new, higher value. In the third year, it increases by 3.5% of a
still higher value. When a quantity grows at a given percentage rate, it
experiences **exponential growth**. A variable that grows exponentially
follows a path such as those shown for potential output in Figure 8.1 "A
Century of Economic Growth" and Figure 8.2 "Cyclical Change Versus
Growth". These curves become steeper over time because the growth rate
is applied to an ever-larger base.

A variable growing at some
exponential rate doubles over fixed intervals of time. The doubling time
is given by the** rule of 72**, which states that a variable's approximate
doubling time equals 72 divided by the growth rate, stated as a whole
number. If the level of income were increasing at a 9% rate, for
example, its doubling time would be roughly 72/9, or 8 years.Notice the
use of the words roughly and approximately. The actual value of an
income of $1,000 growing at rate r for a period of n years is $1,000 ×
(1 + r)^{n}. After 8 years of growth at a 9% rate, income would thus be
$1,000 (1 + 0.09)^{8} = $1,992.56. The rule of 72 predicts that its value
will be $2,000. The rule of 72 gives an approximation, not an exact
measure, of the impact of exponential growth.

Let us apply this
concept of a doubling time to the reduction in the U.S. growth rate. Had
the U.S. economy continued to grow at a 3.5% rate after 1970, then its
potential output would have doubled roughly every 20 years (72/3.5 =
20). That means potential output would have doubled by 1990, would
double again by 2010, and would double again by 2030. Real GDP in 2030
would thus be eight times as great as its 1970 level. Growing at a 2.4%
rate, however, potential output doubles only every 30 years (72/2.4 =
30). It would take until 2000 to double once from its 1970 level, and it
would double once more by 2030. Potential output in 2030 would thus be
four times its 1970 level if the economy grew at a 2.4% rate (versus
eight times its 1970 level if it grew at a 3.5% rate). The 1.1%
difference in growth rates produces a 100% difference in potential
output by 2030. The different growth paths implied by these growth rates
are illustrated in Figure 8.3 "Differences in Growth Rates".**Figure 8.3** Differences in Growth Rates

*The
chart suggests the significance in the long run of a small difference
in the growth rate of real GDP. We begin in 1970, when real GDP equaled
$2,873.9 billion. If real GDP grew at an annual rate of 3.5% from that
year, it would double roughly every 20 years: in 1990, 2010, and 2030.
Growth at a 2.4% rate, however, implies doubling every 30 years: in 2000
and 2030. By 2030, the 3.5% growth rate leaves real GDP at twice the
level that would be achieved by 2.4% growth.*