18 May 2008

Malthus is overrated

Malthus, the false prophet, from The Economist, and Costs of Living, a review of Common Wealth: Economics for a Crowded Planet by Jeffrey Sachs.

Sachs' book is about how to avert global economic catastrophe, which is obviously something worth worrying about. Basically, he seems to be saying that global cooperation is necessary, because "we're all in this together". He also argues, it seems, that population growth is bad; I found the article from Greg Mankiw's blog. Mankiw quotes the end of the review:
In an age when we don’t need to have lots of children to work the fields, or to compensate for high infant mortality, Sachs argues that it’s both economically rational — and crucial for a future of sustainable growth — for people to reproduce at a rate close to 2.1 children per family. In his acknowledgments, Sachs thanks his three children.

But Mankiw pointed out in 1998 that it's not necessarily true that population growth is bad. It seems like a lot of people like to quote Thomas Malthus on this, who said that population grows exponentially with time (true) but that food production ability only grows linearly. As far as I know Malthus had no reasonable argument for this; people talk about the Malthusian catastrophe. But if you actually look at the relevant section in An Essay on the Principle of Population, in chapter 1 Malthus just postulates these growth rates. In Chapter 2 he offers as justification for this basically that there's not enough room in England for the farms to feed an exponentially growing population. But there's not room for an exponentially growing population itself either!

It would be one thing if, say, farms fell from the sky at a constant rate. But farms are made by people; thus if people grow exponentially so will farms.

Now, I'm not saying that we aren't running out of room. It's obvious that some land is better for farming than other land, and people will tend to farm the better land first; as time goes on we will be obliged to farm more and more of the inferior land, therefore decreasing the amount of food grown per person.

But Malthus was writing in 1798. He assumes that the population is producing just enough food for itself in his time, and then goes on to say:
In two centuries and a quarter, the population would be to the means of subsistence as 512 to 10.
Two centuries and a quarter is 2023; roughly speaking, now. We clearly have much more than two percent of the food we need.

Of course, it's possible -- as is pointed out in every introductory computer science class -- that polynomial growth can outstrip exponential growth over some short time, and we're not in the limiting regime yet. But I don't think anybody is seriously saying this. And anyway, Malthus made the stronger claim that food production is growing linearly.

(Does Malthus get more sophisticated than this? I'm just cherry-picking, but skimming his work it seems to continue in roughly the same vein.)

Now, this is an obvious criticism -- but somehow it rarely gets pointed out. Mankiw pointed it out, though -- sure, people use resources. But they also create resources. People will eat food. But they will also figure out how to grow more food. That is, if we don't just disintegrate into a society of virtual reality addicts first.

edited, 11:08 am: Also from the NYT, Deaths are outpacing births in the Pittsburgh metropolitan area. I'm not sure how meaningful this is on a national level, because people move around.


Anonymous said...

Hmmm people don't really create resources we just convert one resource into another. Aside from sunlight which fuels our planet all other resources really are limited on this planet no matter how clever humans are.

Anonymous said...

Malthus also uses the assumption that food production is only proportional to allocated land, which we've seen to be untrue so far. New agricultural technology certainly has increased the production capacity of the land we use by a huge amount since Malthus' time.

However, new technology is inherently something that comes in fits and starts and can't be relied upon. In theory, if we had a long period of time when we had no major advances in agriculture, we could run into the situation where the population outstrips its ability to feed itself. Is that actually going to happen? Nobody knows, and I think most of the arguments about economic collapse basically boil down to one's opinion on that question.

Michael Lugo said...


you're right that we can't rely on new technology coming on a regular basis. I'm inclined to think that statistically we should see improvement over time in the amount of food per acre, but try telling that to people who don't have food NOW!

And many arguments about economic collapse actually just boil down to making whatever assumptions are necessary to get the consequences one desires. Whether someone predicts economic collapse or not really says a lot more about their personality and political leanings than the actual economy.

CarlBrannen said...

Most of the people who don't have food now will probably have food next year, when harvests in the southern hemisphere return to normal.

In the US, in school children nowadays are frequently told that the earth is being destroyed and that mankind will soon have a starve back. Then, at church, some of their preachers tell them that the 2nd coming shall arrive soon and that most of the planet will die in the conflagration. (When I was a kid, it was nuclear war.)

I see that people tell children these things because they want them to care about the environment, or be moral, or be afraid of the Communists, but I'm not sure that scaring the crap out of children is a good thing for them. When kids bring guns to school I wonder if they're thinking that "they're all going to be dead at 30 anyway, so why bother brushing their teeth?"

Adrienne said...

Never heard of Malthus until this post, but now I totally get the reference to the "Malthusian Belts," which are belts containing contraceptive dispensers, worn by the few women allowed to remain fertile in "Brave New World." Thanks!

misha said...

Malthus was right that the exponential population growth is unsustainable in a long run, but the population growth model that predicts unchecked exponential growth of the population is clearly wrong. The reproduction rate is dropping everywhere, for many reasons. For example, Isabel is busy studying math and blogging, not popping out babies.

Joseph said...

One problem with overpopulation predictions is that they assume that humans are animals. Animal populations often show a boom-and-bust pattern caused by overshoot. If humans are animals we must beware of overshoot, which means we must be concerned about overpopulation long before there is any real evidence of it.

On the other hand, ecologically speaking humans are plants. (Plants rarely have overshoot problems.) When there are more of a species of animal there is less of what that animal eats. When there are more of a species of plant, the resources the plant needs either increase (soil) or stay the same (sunlight).

For most resources, humans are like plants; when there are more humans, there is more of the resource. The only resources that humans treat the way animals do are fossil fuels and wild fish. Both of those should be obsolete soon.

Tree huggers have a point (but not the one they think they're making).

Anonymous said...

Have you read The Omnivore's Dilemma? This book suggests that even sustaining our present level of food production over the long term will not be easy, because currently large amounts of fossil fuel are used to produce food - typically 10 calories of fossil fuel energy for 1 calorie of food energy.

Sudipta Das said...

Well, by home loan I mean a home loan and not a personal property loan like on a trailer home/manufactured home in a trailer court. I qualified for a home loan and I want to keep it cheap, so I want to purchase a piece of land and a manufactured home. Can I take out a home loan for land and a manufactured loan? Will this work as a home loan if it’s on private land?

Sudipta das
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