5 3 2
PA R T N I N E
T H E R E A L E C O N O M Y I N T H E L O N G R U N
relative to others. One country that has fallen behind is the United Kingdom. In
1870, the United Kingdom was the
richest country in the world, with average
income about 20 percent higher than that of the United States and about twice that
of Canada. Today, average income in the United Kingdom is below average
income in its two former colonies.
These data show that the world’s richest countries have no guarantee they will
stay the richest and that the world’s poorest countries are not doomed forever to
remain in poverty. But what explains these changes over time? Why do some
countries zoom ahead while others lag behind? These are precisely the questions
that we take up next.
Q U I C K Q U I Z :
What is the approximate growth rate of real GDP per person
in the United States? Name a country that has had
faster growth and a country
that has had slower growth.
P R O D U C T I V I T Y : I T S R O L E A N D D E T E R M I N A N T S
Explaining the large variation in living standards around the world is, in one
sense, very easy. As we will see, the explanation can be summarized in a single
word—
productivity.
But, in another sense, the international
variation is deeply
It may be tempting to dismiss
differences in growth rates as
insignificant. If one countr y
grows at 1 percent while anoth-
er grows at 3 percent, so what?
What difference can 2 percent
make?
The answer is: a big differ-
ence. Even growth rates that
seem small when written in per-
centage terms seem large after
they are compounded for many
years.
Compounding
refers to
the
accumulation of a growth
rate over a period of time.
Consider an example. Suppose that two college gradu-
ates—Jerr y and Elaine—both take their first jobs at the age
of 22 earning $30,000 a year. Jerr y lives in an economy
where all incomes grow at 1 percent per year, while Elaine
lives in one where incomes grow at 3 percent per year.
Straightfor ward calculations show what happens. For ty
years later, when both are 62 years old, Jerr y earns
$45,000 a year, while Elaine earns $98,000. Because of
that difference of 2 percentage
points in the growth rate,
Elaine’s salar y is more than twice Jerr y’s.
An old rule of thumb, called the
rule of 70,
is helpful in
understanding growth rates and the effects of compounding.
According to the rule of 70, if some variable grows at a rate
of
x
percent per year, then that variable doubles in approxi-
mately 70/
x
years. In Jerr y’s economy, incomes grow at 1
percent per year, so it takes about 70 years for incomes to
double. In Elaine’s economy, incomes grow at 3 percent per
year, so it takes about 70/3, or 23, years for incomes to
double.
The rule of 70 applies not only to a growing economy
but also to a growing savings account. Here is an example:
In 1791, Ben Franklin died and left $5,000 to be invested
for a period of 200 years to benefit medical students and
scientific research. If this money had earned 7 percent per
year (which would, in fact, have been ver y possible to do),
the investment would have doubled in value ever y 10 years.
Over 200 years, it would have doubled 20 times. At the end
of 200 years of compounding, the investment would have
been worth 2
20
⫻
$5,000, which is about $5 billion. (In fact,
Franklin’s $5,000 grew to only $2 million over 200 years
because some of the money was spent along the way.)
As these examples show, growth rates compounded
over many years can lead to some spectacular results. That
is probably why Alber t Einstein once called compounding
“the greatest mathematical discover y of all time.”
F Y I
The Magic of
Compounding
and the
Rule of 70
C H A P T E R 2 4
P R O D U C T I O N A N D G R O W T H
5 3 3
puzzling. To explain why incomes are so much higher in some countries than in
others, we must look at the many factors that determine a nation’s productivity.
W H Y P R O D U C T I V I T Y I S S O I M P O R TA N T
Let’s begin our study of productivity and economic growth by developing a sim-
ple model based loosely on Daniel DeFoe’s famous novel
Robinson Crusoe.
Robin-
son Crusoe,
as you may recall, is a sailor stranded on a desert island. Because
Crusoe lives alone, he catches his own fish, grows his own vegetables, and makes
his own clothes. We can think of Crusoe’s activities—his production and con-
sumption of fish, vegetables, and clothing—as being a simple economy. By exam-
ining Crusoe’s economy, we can learn some lessons that also apply to more
complex and realistic economies.
What determines Crusoe’s standard of living? The answer is obvious. If Cru-
soe is good at catching fish, growing vegetables, and making clothes, he lives well.
If he is bad at doing these things, he lives poorly. Because
Crusoe gets to consume
only what he produces, his living standard is tied to his productive ability.
The term
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