compounding of growth

A growth rate of 1 or 2 percent a year sounds tiny, almost not worth arguing about. But growth compounds: each year's gain builds on a slightly bigger base than the year before, so the effect snowballs. Over a human lifetime or a country's history, those small annual percentages stack into staggering differences. Understanding compounding is the difference between dismissing growth rates as trivial and seeing why economists fight so hard over a fraction of a percentage point.

Compounding means growth applies to an ever-larger total, the same mathematics that makes savings grow with compound interest. There is a handy shortcut called the rule of 70: divide 70 by the annual growth rate to get the rough number of years for something to double. At 2 percent a year, an economy doubles in about 70 divided by 2, which is 35 years; at 7 percent it doubles in only 10 years; at 1 percent it takes about 70 years, two human generations. The arithmetic is unforgiving in both directions: a country growing at 4 percent will, over a century, become vastly richer than one growing at 2 percent, not twice as rich but many times richer, because the gap itself keeps compounding.

Compounding matters because it explains why long-run growth rates are arguably the most important numbers in economics. As Robert Lucas wrote, once you start thinking about the consequences of growth differences for human welfare, it is hard to think about anything else. It is why a policy that nudges the growth rate up by even half a percentage point, sustained for decades, can matter more for living standards than almost any one-off program. And it is a double-edged lesson: the same relentless compounding that builds prosperity also drives concerns about whether resource use and environmental pressure can grow exponentially forever.