"The greatest shortcoming of the human race is our inability to understand the exponential function."
-Albert A. Bartlett
Exponential growth is often widely underestimated. Here are a few issues where many people make mistakes because they don’t understand the simple math of exponential growth.
- Economic Growth: When there are trade offs between efficiency and equality, many people today think that the taxes, regulation and redistribution are worth a slightly lower growth rate. However, when this trade off is applied over a long time period, the results can be staggering. If the choice was made in 1870 to have more equality at a cost of 1 percentage point of growth a year, America in 1990 would be no richer than Mexico.
- Entitlement Spending and National Debt: As I have pointed out previously, the United States is headed for very high debt levels if entitlement spending is not reformed. One very simple way to fix this is to index entitlement benefits to inflation and not income. The growth of the economy would make it easy to pay for a safety net at today’s living standards. Unfortunately, this would only work for Social Security and not Medicare as the medical system is structured in a way that leads to health care inflation greater than that of the real economy. Additionally, there is another problem when the net national debt reaches 100% of GDP. If the market perception of the debt turns negative and nominal interest rates remain higher than nominal GDP growth, then there is no way for the economy to grow itself out of debt. This is the current situation with Greece, and Japan isn’t doing too much better.
- Personal Finance and Pension Plans: If a prudent investor can make 10% real returns in a year, then they can turn 50 thousand dollars into over 1.6 million dollars after 35 years. This simple math explains how many of the rich people today consist of those who have saved and invested prudently. On the other hand, a supposedly fully funded pension fund planning on a world of 8% real returns that finds itself in a world of 4% real returns will find itself underfunded by over 75% 35 years later (In this case, the people making pension return assumptions are underestimating how much they matter, they just know that their books look better if they assume a higher return). Robin Hanson has been proposing that people don't give to the future because they don't care about it, but it may also be that they do not fully understand the impact of exponential growth*.
- Overpopulation and increasing Resource Consumption: Overpopulation does not seem to be the exponential problem that we once thought it was. Once become rich enough, their population growth rate slows down. The UK’s Ministry of Defense 2008 Strategic Trends report expects the population to level out at around 9 billion people between 2050 and 2100 (page 25). While overpopulation is itself not a problem, the exponential economic growth of these emerging economies are coincident with an exponential increase in demand for resources and these limited resources present constraints on growth.
Having established that exponential growth rates are important, here is a handy rule of thumb that will give an intuitive understanding of exponential growth. To calculate the doubling time of an exponentially growing series, take 70 (or 69.3 to be exact) and divide it by the growth rate. This means that a 10% growth rate leads to a doubling every 7 years, a 7% growth rate is a doubling every 10 years and a 3.5% growth rate is a doubling every 20 years.
*It is also possible that someone who both cares about the future and understands exponential growth might think that there were existential problems for the current society that are significant enough to reduce the probability of a far future donation from ever paying off.