Modeling population and technology: Why haven’t you starved to death?

2009 September 24
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By Navin Kumar
Article ID: 1338

Of all the interesting, insightful models produced in the last two or three hundred years of economics existence (I’m not including the models of financial markets: those are neither interesting nor insightful) few have achieved more long-range influence than the population model of Thomas Malthus.

The model (and the idea behind it) is so simple that it can be taught to school children. Human population – says the model – increases exponentially. Assuming every couple has three children, the growth in a population with 200 people grows like this: 200, 300, 450, 675. On the other hand, growth in the field of agricultural output is arithmetic and goes like this: 200, 300, 400, 500. At this rate, the growth in population will soon outstrip growth in food.

Malthus’ two-century-old prediction says that any increase in prosperity would soon be “consumed” by an increase in population. This is one reason why economics is labeled as ‘the dismal science’. This idea, though – that humanity’s increasing consumption of natural resources will outstrip our ability to raise those resources – is the driving idea behind modern concepts like sustainable development. This idea is also called a “Malthusian famine”.

Yet, in the 200 years of the theory’s existence, a famine caused by failure of food production has never occurred. Famines are typically caused by things like drought or flood, followed by a failure to deliver food to affected areas. For one thing, production has more than kept up with population growth. “Between 1820 and 1992,” writes Ronald Bailey in Earth Report 2000, “world population quintupled even as the world’s economies grew 40-fold.”

It’s worth asking where these predictions went wrong or – to put it in geeky terms – what systemic error in thinking lead to such incorrect conclusions? The short answer is that technological innovation is faster than population growth. But this is a hard idea to wrap one’s mind around, so an explanatory model is worth looking at.

Imagine a tiny little 14th century French village. The village has a population of 101 people: 100 wheat farmers (who own an acre of land each) and one guy who fancies himself as an alchemist but invents and sells fertilizer to pay the bills. Over the period of his life, he will increase the productivity of each acre of land by a bushel of wheat. Where the land was previously producing 10 bushels, it is now producing 11. Thus, where 100 farmers were producing 1000 bushels of wheat, they are now growing 1100 bushels. The change: +100 bushels.

Now imagine a village of 1010 people: 1000 wheat farmers and 10 inventors – the same ratio as the small village. Each of the inventors is just as productive as the alchemist was – that is, they all produce innovations which increase the productivity of each farmer by +1 bushels. But there are now ten alchemists. So the total increase in the productivity of each farmer is +10. And there are now a thousand farmers. So the total change: 1,000×10 = +10,000 bushels.

Notice the population grew tenfold but the change in production was a hundredfold. The reason: more innovators, whose productivity-enhancing techniques can be applied to everyone.

Note also that this model doesn’t factor in a whole bunch of stuff that might cause production to grow even faster. For example, the original alchemist sells to 100 people – but a person who goes into research in the larger village has a market of 1000. This increases the incentives to invest in research and more people will become fertilizer inventors. So instead of 1 inventor for every 100 farmers, you might get 3. Furthermore, collaboration is now possible. While a single inventor, by himself, might produce +1 bushels, two working together might manage +3 bushels, further increasing the rate of innovation.

To summarize: the larger a population is, the more innovators there are, the more incentive there is to invest in research (as the result of a larger market) or to become a researcher and to collaborate.

Of course, this over-simplification of reality (which is what all models essentially are) is loaded with flaws. For starters, I’ve completely ignored the question of whether or not the land has a ‘carrying capacity’: for example, if there’s a limit to which it can grow more wheat. I’ve ignored the question of whether there is a limit to how much we can extract from nature. I’ve ignored the possibility of patent wars between increasingly competitive innovators that would hinder innovation. I’ve ignored how a population must invest heavily in education to continue producing scientists (which is not happening in populous places like India). There’s even a possibility that there is a “limit to science”: that at some point in the future anything that can be invented, will be. If you can think of any more problems with the model, please let me know in the comment section.

All these are important, but I’m not going to deal with them right now. The value of a model lies in its’ ability to explain an idea – not to prove it. (The people who claim that they use a model to predict the outcomes of complicated social, financial or technological events are self-deluding frauds.) The point of this thought experiment was to explain how some researchers can get so far off the mark: they didn’t see innovation as a result of population. People solve problems. Problems are limited – but the number of people available to throw at problems increases constantly.


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8 Comments
2009 September 24
rc_moore permalink

“The people who claim that they use a model to predict the outcomes of complicated social, financial or technological events are self-deluding frauds.”
 
Ok,  your article from last week on global warming was naive.  Now you are just making gross assertions from extreme ignorance.
 
We constantly use, with great success, many models that do “predict the outcomes of social, financial, or technological events.”
 
Bayesian analysis, for instance in used in many endeavors such as commodity markets, spam filters, internet traffic loads, etc.
 
This is just a few examples very complex models that are quite successful.
 
What you mean to say is that we cannot predict, through models, all events, to the level of probability that we need.
 
And I would note that while Malthus was not entirely accurate (perhaps due to the mother on invention paradigm,  but this is not a perfect explanation, as technology can have as many deleterious effects as beneficial ones.  WW I and II for example),  Malthus is used in many types of modeling in various areas with success.

This is your second article where you have presented  some well known arguments of no great import with a supercilious attitude that detracts from the innocuous point you are trying to make.
But my biggest objection at this point, is that while you post, you do respond to comments.  Are you looking for a skeptical discussion or a pulpit?

2009 September 24
rc_moore permalink

Sorry, please read my previous comment as “you do *not* respond to comments. “

2009 September 25
Andy Kaiser permalink

rc_moore,

You raise a good point about Navin not responding to comments. I didn’t realize that until now, when I checked a bunch of his old articles to verify. If he doesn’t respond to this or the previous article comments soon, I’ll email him directly and see what’s up. As you see, I’m willing to post articles from people with different opinions than you. But not if those people aren’t willing to – at least some of the time – respond to fairly solid and honest critiques. This isn’t a drive-by opinion site. I want things to be more interactive than that.

Andy

2009 September 26
Chris permalink

 
Well, I hardly need to criticise this since the author did so himself:
 
“I’ve completely ignored the question of whether or not the land has a ‘carrying capacity’”
 
I might as well make an argument that oil supply is unlimited and will last forever, with the qualification that I will ignore the issue of oil being a finite commodity.
 
 

2009 September 28
Brigitte permalink

Another source of food: solyent green.

Let’s multiply and pollute, everything has been taken care of.

2009 September 29
David Annis permalink

I take issue with the statement:
Yet, in the 200 years of the theory’s existence, a famine caused by failure of food production has never occurred.
There have been famines in Africa, North Korea, China, etc. not caused by weather.  Some, in fact, I would argue are caused by people innovating (Mao and Kim Jong Il), though in the model presented innovation only increases production.
 

2009 October 1
Navin Kumar permalink

Hello, everyone. Again: I’m sorry about the delay in replies. I’m staying in Bombay for anouther 3 weeks and the nearest cyber is quite far from my place. So there will be a gap on 2-3 days between rebuttals.
I’m going to start with David, because I find it the most interesting.
>>There have been famines in Africa, North Korea, China, etc. not caused by weather.  Some, in fact, I would argue are caused by people innovating (Mao and Kim Jong Il), though in the model presented innovation only increases production.
I agree: not all famines are caused by weather. I feel like an idiot for having forgotten the pain caused by ideas spawned by the Mao and Lysenko in Russia.
But I argue that this pain – like most famines – are more political than than technological. Typically, a progress in technology spreads slowly: there are people who take risks and try in out first and people who follow after seeing the positive results. This means only technology that works gets adopted.
In the case of Mao etc. an idea was forced upon farmers without proper verification resulting in the mess we saw. The problem was with the political and market structure.
Anywhere else only that technology which improves production/reduces costs would be adopted. (Again: I’m ignoring the technology – such as scrubbers – which is adopted to protect the environment etc.)
>>We constantly use, with great success, many models that do “predict the outcomes of social, financial, or technological events.”

Bayesian analysis, for instance in used in many endeavors such as commodity markets, spam filters, internet traffic loads, etc.
This comment would seem more appropriate on the GW section but I’ll deal with it.
I can’t see what problem you have with the model I presented in this article, so I assume this is sorta-kinda a question on when and where you can use models.
My purpose in this article wasn’t to attack predictive models. That was simply an aside. But as Andy said, I shouldn’t say something if I’m not ready to defend it.
I hardly need to point out these models are far from perfect: spam gets through and every once in a while a page or website suddenly generates so much traffic, it has to shut down for a while. But these are social phenomenon where a) a failure doesn’t equal disaster and b) there is constant real-time improving of the model.
Also, these are hardly predictive models, the main focus of my contempt. And commodity prices aren’t heavily subject to social (i.e. human free will generated) fluctuations. They *are* subject to whether changes: see how fast the prices of futures change when the meteorological department makes a mistake. Another source of fluctuations (for some commodities) is political. Sugar in my country, for example. The government recently (i.e. a year or two ago) tried to reduce the price of sugar by banning exports. That worked too well and there was a glut and a huge fall in prices, forcing the government to subsidize exports to help farmers. Shame the governments’ commodities model couldn’t figure out that was going to happen. After this fiasco a lot of farmers simply switched to other crops. Show me a commodities model that saw that coming.
Although I didn’t mention it, my main focus of attack here was the models used by Wall Street firms. These generate decent returns for a while and then blow up. The most recent blow up was caused because these considered a fall in prices in multiple real estate markets unlikely enough to ignore. Idiots.

2009 October 1
Navin Kumar permalink

>>And I would note that while Malthus was not entirely accurate (perhaps due to the mother on invention paradigm,  but this is not a perfect explanation, as technology can have as many deleterious effects as beneficial ones.  WW I and II for example),  Malthus is used in many types of modeling in various areas with success.
My curiousity is piqued. Could you give me an example?
Also, WWI and WWII weren’t caused by technology, but by politics. You can, of course argue, that it made killing easier and therefore increased the death toll. But prehaps the war would have gone on much longer had tech not existed to provide decisive victories and defeats, increasing the death toll. So I’m not sure how many people would have died if the tech hadn’t existed, so I find the question of how benefits of tech v/s costs of tech to be speculative instead of empirically or logically provable. I personally would rather have technological improvemment than not have it. I think I’m better off in 2009 – with a century of advancement as well as violence – behind me than I would have been in 1909. What about you?

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