## Mathematical Flaw In Caplan’s Exhortation To Have More Kids

I heard a radio interview this morning with Bryan Caplan (a professor of economics at George Mason University), who argues in his recent book Selfish Reasons to Have More Kids (which I have not read) that the average person ought to have more children. The book is apparently based on one of Caplan’s 2005 blog posts.

In his blog post, Caplan says

Contrary to organizations like Zero Population Growth, the externalities of another productive human being are positive, not negative.

and

There is however a purely selfish argument for making another baby that most people overlook. …  Basic microeconomics recommends a simple strategy. Have the number of children that maximizes average utility over your whole lifespan. When you are 30, you might feel like two children is plenty. But once you are 60, you are more likely to prefer ten sons and daughters to keep you company and keep the grandkids coming. A perfectly selfish and perfectly foresighted economic agent would strike a balance between these two states. For example, he might have four kids total – two too many at 30, six too few at 60.

This abhorrent perspective is perfectly in line with (my stereotype of) current economics ideology: If every “economic agent” behaves selfishly, then the unseen hand of the market will ensure the greatest utility for all.

The idea that the average economic agent ought to have more children, to “keep the grandkids coming” for his own selfish reasons, without any thought to what kind of world all these children and grandchildren will have if every other “economic agent” does the same, is so short-sighted, so lacking in heart, as to be breathtaking.

But leaving aside the emotional arguments, there is something seriously wrong with the idea that the externality (i.e., the net cost or benefit to the rest of society) is positive if I bring another productive human being into the world. If that is so, then the best thing for society is to produce as many children as possible, and definitely “keep the grandkids coming.” This is absurd, for if we repeat the argument, then by the same reasoning adding 20 billion productive human beings would also be a positive externality, which is clearly ridiculous. We would choke on our own wastes long before we added that many new inhabitants.

The simple mathematical point that, if understood, would prevent Caplan and people like him from making such egregious errors, can be phrased as follows:

If a resource is finite and non-renewable, then any amount of consumption whatsoever is unsustainable.

If there are 100 “scrunchies” left in the world, and the worldwide consumption rate is 1 per year, then in 100 years there will be no more scrunchies. If the rate of consumption is 2 per year, then in 50 years there will be no more scrunchies. There is no such thing as sustainable consumption when it comes to consumption of scrunchies; there is only a finite number of them, and if we keep consuming them, soon there will be none left.

Every additional human being consumes essential resources that must be considered non-renewable, because the time scales for renewal are very long compared to the time scales for consumption. For example, in North America we are chewing up and spitting out fertile soil at an alarming rate (go here and scroll down), and if we continue this practice we will soon be in trouble. The same goes for our rapid consumption of water resources. Petroleum is another popular example.

So the whole concept of sustainable consumption is suspect, and can be seen as an attempt to continue business as usual without really coming to grips with our serious problems. Our only hope is to change the way we live, which first requires changing the way we think; thinking that growth is essential to our well-being, or that bringing as many more “productive” human beings as we can into the world is a good thing, is a fast road to our doom.

We must learn how to truly recycle the resources that we use, instead of trashing them and then chewing up our environment as we desperately search for more, more, more.

We must also think in terms of stabilizing our population, then gradually, gracefully, and humanely decreasing it to levels that are truly sustainable. If we are lucky, we might be able to do this simply by slightly reducing our birth rates, and letting older generations die off naturally.

The alternatives are horrible; when populations exhaust their resources they typically collapse. And our consumption of all of our precious resources continues to increase, along with our population.

Let’s be conservatively sensible, and take prudent action while we still have a chance. And part of that prudent action must be to call out foolish exhortations to produce as many children as we can.

Update: Quite a number of gullible people believe that the rapture is starting later this month; if so, then never mind.

I am a former university prof, having taught mathematics and physics since the mid 1980s. I have also been a textbook writer/editor since then. Currently I am working independently on a number of writing and education projects. I love math and physics, and love teaching and writing about them. My blog also discusses education, science, environment, etc. http://qedinsight.wordpress.com Further resources, and online tutoring, can be found at my other site http://www.qedinfinity.com
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### 4 Responses to Mathematical Flaw In Caplan’s Exhortation To Have More Kids

1. Lawson says:

Very interesting post Santo!
I’ve been thinking about the idea of “growth” a lot since I took a class in macroeconomics last semester.

I’m wondering if you have ever seen this video: http://www.youtube.com/watch?v=F-QA2rkpBSY&feature=bf_prev&list=SP6A1FD147A45EF50D&index=1

• Santo says:

Hi Lawson,

I just finished watching Bartlett’s lecture … and it is very, very good, and very important. Thanks very much for sending the link, as I didn’t know about it!

I’ll write a post tomorrow and include the link.

The great thing about Bartlett’s lecture is how clear he makes his points by using extremely simple mathematics.

I recall reading a memorable article by Bartlett in Physics Today about 10 years ago, where he makes many of the same points. An additional point he made in the article is that any technological advance that makes life more comfortable for people actually makes our predicament even worse, because it allows the population to grow! This makes the possibility of a graceful decline in population to sustainable levels even more difficult.

Thanks again, Lawson!

• Lawson says: