Growth

We live in a time dominated by economics and economists. Every politician subscribes to a particular economic orthodoxy, even they have only a superficial grasp of it, because they need talking points. And those talking points are inevitable: jobs and growth. And trade, of course. Since NAFTA everyone talks about trade.

Ultimately everything comes down to economic growth. If the Soviet Union could have generated similar economic growth to the United States and its NATO allies it would still be functioning. Alas, the planned economy could not compete with the free market and the whole mess collapsed upon itself.

If you want growth you have to have a capitalist system. And we want growth. We want our wealth to increase, both individually and as a nation. Growth is the solution to every social problem. If worker productivity grows then the economy will grow and there will be more investment in the future and we will all get richer. Anything that gets in the way of economic growth is bad. Anything that sustains or encourages it is good.

I don’t mean to be simplistic but we rarely dispute the need for growth, so I won’t. Not this time. There are plenty of folks out there who think maybe continuous growth is a bad thing, especially for the environment, and they have arguments worth looking at. But I’m not going to do that. I’m just going to think about growth.

When I want to understand something I try to measure it or put a number on it. Lots of things are not amenable to numerical analysis but growth is obviously something that requires numbers. I remember my mom and dad marking my height on the wall and each year we’d see how much I grew from last year. I didn’t need numbers to see the change of course but I was measuring nonetheless.

How do we measure growth? I’ll give you one easy way. It’s one of those very few things from high school math class that you can actually use.

It’s called the Rule of 72. Sometimes you will see it called the Rule of 70 but it doesn’t really matter. The Rule of 72 (or 70) is a quick estimator. A rule of thumb. (If you wanna be fancy, call it a “heuristic” instead.)

We’ll use 72. This is a handy number because it is divisible by 12 and there are 12 months in a year. And the Rule of 72 is about time, and years is a unit of time.

Let’s say you put money in something like a Treasury note or a CD and you get 4% interest rate. How fast will your money grow? The Rule of 72 says “divide 72 by the rate” so that’s what we’ll do.

72 divided by 4 (from the 4% interest rate) is 18. That means your money will DOUBLE in 18 years!

What the Rule of 72 tells us is the DOUBLING TIME of any quantity expressed as a percent growth rate. (Note that 70/4 = 17.5 which is pretty close. You can use either 70 or 72 as either is a handy estimate.)

Let’s say your candidate for President argues that the country needs to grow the economy by 3% every year. Let’s take a quick look at that.

72 divided by 3 is 24. (70/3 = 23.3)

What the candidate is saying is that the economy should be TWICE AS BIG AS IT IS NOW in 24 years. Is that what you want? I’m not saying this is a good or bad political position. I’m saying we should all understand the implications. Do we want our economy to double in size in 24 years?

When you see something expressed as a rate percentage you are looking at a phenomenon called “fractional growth.” That means that over each time period the original amount will grow by the same fraction. That fraction is the same (4/100 in the case of 4%) but since the amount keeps growing the amount of new growth added on keeps growing. We know this as compound interest. This is the Holy Grail of capitalism. Here’s what steady fractional growth looks like:

Don’t you want your money to do this?

When you learn the growth equation in algebra class they use examples like bacteria growing in a petri dish because bacteria double (one splits into two) in a predictable way. So you get these nice graphs. Look how fast the population grows after the fifth hour! The growth rate is constant, but the amount added on in each interval increases rapidly. You learn this stuff in the chapter about “exponential functions.”

I once heard a speaker (a physics professor teaching science teachers) say “the greatest shortcoming of the human race is the inability to understand the exponential function.” (Albert Bartlett)

Growth can be good and growth can be bad. But the most important thing is to get a handle on what growth means. Now you have a tool for estimating the DOUBLING TIME of anything that grows at a constant rate. Doubling is a nice, intuitive way to visualize quantities.

Note that 72 can be divided by 36, 24, 18, 12, 9, 8, 6, 4, 3, and 2 so it is a handy number for quick math in your head. 70 is divisible by 14, 10, 7, 5 and 2 so it’s really a matter of how precise you want to get. The actual number is approximately 69.3 (that’s the natural logarithm of 2 times 100) and you can use that with your calculator. Of course the internet is chock full of websites with interest calculators and any spreadsheet program (like Excel) will have the exponential functions built in if you need an accountant’s level of precision.

But most of us don’t need that. We just need a “quick and dirty” estimate. That’s the Rule of 72—high school math you can actually use in real life!

Quick quiz: the world’s population is growing 1.2% per year. How many years will it take at this rate for the world’s population to double?

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