Lesson preview · Growth Basics
Growth Facts & Patterns
~12 min · Free to read
Two countries start in the same place. One grows its income per person by 1% a year. The other grows by 2% a year. After a century, the second country is not twice as rich as the first. It is more than twice as rich — far more. Tiny differences in the yearly growth rate pile up into enormous gaps in how people live. This is the most important fact in the study of growth.
Here is a quick way to feel it. Take the growth rate, in percent, and divide it into 70. The answer is roughly how many years it takes for income to double. This shortcut is called the rule of 70. At 1% a year, income doubles in about 70 years — one long lifetime. At 2%, it doubles in about 35 years. At 3%, about 23 years. At 4%, about 18 years. Each extra percentage point roughly halves the wait.
Key Term
The rule of 70
The rule of 70 is a shortcut for how long something takes to double when it grows at a steady percentage rate. Doubling time in years is about 70 divided by the growth rate in percent.
- 1% a year → doubles in about 70 years
- 2% a year → doubles in about 35 years
- 3% a year → doubles in about 23 years
- 4% a year → doubles in about 18 years
Why 70 and not 100? Because growth compounds — each year you grow on top of last year’s gain, not on the starting amount. That compounding makes doubling faster than simple addition would suggest.
Doubling once is just the start. Over a long stretch, income doubles again and again, and the gaps explode. Start every country at an income index of 100. After 100 years, a country growing at 1% reaches about 270 — roughly 2.7 times richer. At 2% it reaches about 724 — about 7.2 times richer. At 3%, about 1922 — about 19 times. At 4%, about 5050 — about 50 times.
Read those numbers again. The jump from 1% to 2% is a single percentage point. Yet over a century it is the difference between ending up 2.7 times richer and 7.2 times richer. That is not a small edge. Over generations, a growth rate that looks dull on paper decides whether a country stays poor or becomes wealthy.
Key Term
The Great Divergence
For almost all of human history, nearly everyone everywhere was poor. Living standards barely budged from one generation to the next — a farmer in the year 1500 lived much like a farmer in the year 1000.
Then, around 1800, the Industrial Revolution changed the pattern. A handful of countries began growing income per person at roughly 2% a year and kept it up for about 200 years. Two percent sounds modest. But sustained for two centuries, it compounds into staggering wealth.
Those countries pulled away from the rest. The result is the Great Divergence: the gap between the richest and poorest countries today is roughly 50 times. That gap did not exist before sustained growth began. It is compounding, playing out across history.
Tip
The catch-up puzzle
Here is a hopeful twist. A poor country has an advantage the rich ones never had: it can copy. It does not need to invent new technology from scratch — it can adopt machines, methods, and ideas that rich countries already proved work. In principle this lets poorer countries grow faster and converge — close the gap by catching up.
Some did exactly that. South Korea was poorer than many African countries in 1960 and is now wealthy. China lifted hundreds of millions out of poverty in a few decades. But others started poor and stayed poor, with no catch-up at all.
So convergence is not a law that automatically pulls every poor country upward. It is a possibility some seize and others miss. Why some catch up and others do not is one of the biggest open questions in economics.
Tip
So what?
A one-percentage-point difference in the growth rate, compounded over a century, is the difference between a country that ends up about 2.7 times richer and one that ends up about 7.2 times richer.
Worked Example
A country grows its income per person at a steady 2% a year. Roughly how long until income doubles? And after 100 years, starting from an index of 100, will it be about twice as rich, or much more?
Check yourself · no marks
Country A grows at 1% a year and Country B at 2% a year, both starting from an income index of 100. People sometimes say B will end up “twice as well off” as A. Why is that wrong, and what is the real gap after 100 years?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 4
A country’s income per person grows at a steady 2% a year. Using the rule of 70, about how long until its income doubles?
Next
Like what you read?
Sign up free to save your progress, get spaced reviews tuned to you, and unlock all 50 microeconomics knowledge points with interactive graphs and adaptive practice.