Small Changes In Growth Rates Add Up Over Time

In my macro courses we read a chapter in the book "The Economics of Macroissues." The chapter discussed how nations with common law systems, where property rights are better protected than in nations with civil law systems, have higher growth rates. I pointed out to my classes that even a small difference in growth rates ends up causing a very big difference in per capita incomes due to the annual compounding effect.

In early 2010, Paul Krugman mentioned that the per capita GDP since 1980 has grown 1.95% in the US and 1.83% in the EU. But we should also remember that small differences in growth rates compound over time. If per capita income was 20,000 in both the US and EU 29 years ago, the per capita income (or GDP) now would be 35,015 in the US and 33,839 in the EU, a difference of $1,176. Maybe not a big difference. But after 100 years the US income level would be 12% higher. After 200 years it would be 26% higher.

The table below shows how much per capita income would be at various rates after 100 and 200 years. Assume we start with a per capita income of $1,000. If we grow 2.0% per year, after 100 years it will be $7,245. At 2.1% per year, it would be $7,791 or about $700 more. That is how much that little .1% matters. The difference over 200 years is about $11,000. After 100 years at 2.5% per year, per capita income would be $11,814. That is $4,000 more than the 2.0% rate. Small differences in growth rates add up to big differences over time.

Per Capita Income After 100 and 200 Years At Various Annual Growth Rates (Starting With $1,000)