Sorry, Cornucopianism is Silly
[This is a post in my series on Thomas Malthus’ “An Essay on the Principle of Population,” first published in 1798. I have put an overview with all the articles together that I will keep updated as I go along: Synopsis: What’s Wrong with the Malthusian Argument?]
My main contention in this series of posts is that the Malthusian argument fails as an explanation for how human populations behave (or also populations of many other species). It suffers from many internal problems and mostly rests on equivocations and logical leaps. There is an interpretation that is correct, but trivial and disconnected from reality, and another that would be interesting if it were true, but which is contradicted by the evidence.
That was so from the start. Still the Malthusian argument has had a long shelf-life and is still around. My explanation here is that there is an associated worldview that has a strong hold over our imagination and which has become a part of our culture. It is an intuitive understanding that is mostly immune to rational argument and empirical evidence. (If it is not clear what I mean by a “worldview,” you might want to read my general post on “Worldviews, Narratives, and Ideologies.”)
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The Malthusian worldview is deeply pessimistic: Human populations stubbornly grow at a fast pace when they can, and until they hit a binding constraint for the food supply, a wall of steeply rising mortality from starvation and famine, whether directly or indirectly. Population growth can only be stopped by brutal means. Improvements are only fleeting because soener than later a population finds itself again on the brink of starvation.
Obviously, this panorama is at odds with easily obtainable evidence, and it was so already in Malthus’ time. His solution was to point to various “checks” that kept population growth down. In his own words, this is a “struggle for existence” and a “war of extermination.” Improvements in living standards are only possible in a parodoxical way: via high mortality, eg. from wars, lethal pandemics, natural catastrophes, and so forth. Although Malthusians concede improvements for a population as possible, they are still convinced that their worldview is correct most of the time.
Of course, many people have felt that there is something wrong with the Malthusian argument. And so there have been plenty of criticisms over time. I would like to look at one of them here that in my experience is rather popular. It goes by the somewhat awkward name of “Cornucopianism.” As with the Mathusian worldview, there is also a Cornucopian worldview, which is as optimistic, as the former is pessimistic. That’s why Cornucopians think of themselves as the anti-thesis of Malthusianism.
However, as I will argue here: They are still Malthusians at heart. While they accept what is wrong in the Malthusian argument, they see a way out by specious arguments of their own. The alternative “Malthusian or Cornucopian” is misleading. It is like positing that the sun has to be either blue or red, then pointing out that blue would be depressing, and concluding from this that it must be red.
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The Malthusian argument rests on two claims (cf. I.18):
Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio.
On a continuous time scale this is equivalent to exponential and linear growth, respectively. Malthus ignores the important qualification “when unchecked” in the further development of his argument and treats it as if human populations generally grow exponentially when that is possible. He even thinks that they grow at the maximum rate possible. Malthusians have integrated this claim into their worldview as if it were a simple truism. Evidence that is at odds with it is then explained away on an adhoc basis.
As I will explain in more detail in another post, Malthus has no argument why “subsistence,” which is essentially the food supply, should grow linearly. Actually, he wavers between the claim and a weaker one that it can grow at most linearly, slopes are bounded above by some constant. However, linear growth is not possible because on a planet with finite resources, food production also has to be finite whereas a linear function goes to infinity.
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Cornucopians try to challenge the assertion that the food supply has to remain finite with a cringeworthy argument. They point to human ingenuity that has made ever higher productivity possible in the past. From this, they extrapolate to the future and want to conclude that there is hence no upper bound for what can be produced.
But that is silly. Malthus himself already makes the correct argument that a quantity can keep growing, ie. it is a monotonously increasing function, and still it can remain bounded. So it is false to conclude from ever more growth to growth beyond any bound, ie. to infinity. What is disingenous about Malthus’ point is that he plunders the argument from the Marquis de Condorcet, and then uses it in his argument against him and William Godwin as if it were his own.
The simple confusion that Cornucopians fall for here is that it may well be possible that food production could grow a lot from where it is now. But that only implies that it will become very large. Yet, it still remains finite! Infinity is not another word for “very large,” but the claim that a quantity is larger than any finite bound. And the amount of food that can be produced on our planet cannot grow beyond any bound.
The surface that could be used for agricultural production — and you may add the oceans to it if you like — is finite. There also has to be some upper bound for how much you can produce on a square meter. If you doubt that, you have to believe that you could feed a billion people from its produce, and also from that on a square centimeter, and then on a square millimeter, etc. And that would still not prove that the total amount can go to infinity, only that it can become very large.
It is understandable why Cornucopians want to believe that it is possible to increase food production to infinity, namely because it would do away with a binding constraint from the food supply for a population that grows exponentially. But that makes them reject simple logic. To be blunt: This is just wishful thinking. And it would still not work because what Cornucopians need to establish is exponential growth that can keep up with exponential population growth, and not just any growth that goes to infinity.
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Also further attempts to obtain the conclusion via fancy assumptions do not work. Suppose the world were flat, an infinite Euclidean plane. That would mean that the surface available for agriculture is now infinite. However, humans could only expand the area under cultivation at a finite speed. That means they would live on balls with a diameter that grows linearly, ie. in line with time. But then the area under cultivation expands at most quadratically, a function as x², because there is still a finite upper bound on how much you can produce on a square meter.
Fantasies about space travel and colonization of other planets do not help here either. Suppose there were so many habitable planets in a ball with some diameter. Since they have to have some minimum size at least, there are only finitely many of them you can fit in the ball. Now, each planet has a surface that is finite. Times a finite number for the number of planets in the ball, this still implies only a finite area. Since humans could only expand at a finite speed, this leads to the conclusion that the area available for cultivation can at most expand cubically, a function like x³. And with still a finite produce on a square meter, that’s also how the food supply could at most grow in this fantastic scenario.
In principle, it is conceivable that an infinite non-Euclidean plane or space could have a curvature that goes to infinity fast enough as you move away from a starting-point that also exponential growth were feasible with a finite speed of expansion. However, there is no reason to believe that the universe has such a structure. And so exponential growth of the food supply is simply not possible. No amount of human ingenuity can overcome this. And singing odes to it is hence besides the point.
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Now, Malthus spends a lot of time on his attempted proof that an exponential function grows faster asymptotically, ie. as time goes to infinity, than a linear function. His approach is sorely inadequate even by the mathematical standards of his time and only shows his low level of sophistication. Nonetheless, the claim is correct and rather easy to prove in a rigorous sense although Malthus is unable to do it.
Actually, you can prove even more: An exponential function grows faster asymptotically than any polynomial, a finite sum of powers of x. However, even if we were on an infinite Euclidean plane, the food supply could at most grow quadratically, which is a polynomial. And so it cannot keep up with exponential growth for a population. The same is also true in the fancy scenario with space colonization because a cubic function is also a polynomial. It is not possible to keep up with an exponential function in this way. Malthus is unable to show this with an argument, but he is still right about it.
But if that is so, a human population that grows exponentially will inevitably hit a binding constraint from the food supply at some point in time. Cornucopians would like to avoid this, but it can only be avoided at the expense of logic, namely by assuming the absurd claim that the food supply could also grow exponentially, and strictly speaking at a rate at least as high as the exponential growth for population. Otherwise, food per capita has to fall to zero asymptotically until it hits a lower bound that humans can barely live on. That’s when steeply rising mortality from starvation and famine, both directly or indirectly, would stop population growth. And that would then be the Malthusian end-game where the population has to live on the brink of starvation.
To repeat the point: Cornucopians appeal to human ingenuity, which could devise ever better methods and expand the area of cultivation. But even if you are extremely optimistic about this, it does not show that humans could keep up with exponential population growth and avoid the Malthusian end-game. It is not possible. Stomping your foot does not change this.
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Cornucopians seem to sense the problem and that it cannot be solved by wishful thinking. One way they try to handle it is by plugging the optimism from their worldview in to get the conclusion that human ingenuity can at least keep up with exponential population growth for a long time. So, while it may not be possible to avoid the Malthusian end-game forever, it can be pushed out far into the future.
Many critics of Malthus have tried this route before, and the argument is even older than Malthus’ essay. The first to make it seems to have been Robert Wallace (1697–1771) in his “Dissertation on the numbers of mankind in antient and modern times,” published in 1753, ie. almost half a century before Malthus. If that is confusing: Malthus was by no means the first to think about population growth. He actually reacted to a debate that had gone on for centuries.
Still, Malthus’ argument, though deficient in many ways, is correct if you grant him certain assumptions. He thinks that a population “when unchecked” would grow at the maximum rate possible. I will explain in further posts why he has to do this. But basically, it is because he needs a fixed rate, and the only one around is the maximum rate. That that is his assumption becomes clear from his direct arguments: He derives a lower bound for the maximum rate, which he confusingly then identifies with it. And indirectly, it is also clear because Malthus can only think of “checks” that lower fertility or raise mortality versus a state of society “when unchecked.” Since this must lead to a lower rate of growth for actual populations than “when unchecked,” the latter have to have maximum exponential growth.
As noted, Malthus’ identifies his estimate for a lower bound with the rate of growth “when unchecked,” which is illogical. If we gloss over this, it is understandable why he obtains this conclusion (cf. II.7):
That population, when unchecked, goes on doubling itself every twenty-five years or increases in a geometrical ratio.
But that implies that over 250 years, the population grows roughly by a factor of 1,000 (2¹⁰ = 1024). Over one millennnium it would be a factor of about: 1,000 * 1,000 * 1,000 * 1,000 = one trillion. So even if you are very optimistic about human ingenuity, the Malthusian end-game cannot be too far away.
An appeal to success in the past does not help here either. Humankind has grown over the past 100,000 years by a factor that is equivalent to only about 16 doublings. That would take only about 400 years with this fast rate for population growth. While it affords you some breathing-space in principle, that does not amount to much. Malthus hammers this point in over and over again. However, it is only convincing if his assumptions are correct, however that is exactly the question.
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Cornupocians, and also other critics of the Malthusian argument, now try to challenge the high rate of growth. Maximum population growth might not be necessary, and so the end-game could be farther out in the future. As I will develop in further posts, this is a reasonable point. Just look at the very slow growth of humankind over the past 100,000 years. Still this type of argument causes a problem of its own for Cornucopians who rely on human ingenuity. They tacitly exchange their argument for one about rather slow population growth, which has to do the heavy-lifting. If that is the point, then not a lot of human ingenuity might be needed. Population growth that is slow enough could mostly do the trick.
The assumption that slower than maximum, but still exponential growth is somehow the “natural” behavior of human populations creates a host of problems for the Malthusian argument, and that’s why it is consistent that Malthus himself avoids such a concession like the plague. Instead he insists on maximum exponential growth. The reason is that once you grant that population growth could be rather slow, then you also grant that fertility in the respective population is close to the replacement level. The replacement level is the fertiliy where only as many children are born as people die, and where hence the population remains stable.
To put numbers on this: Some populations have had fertility of about eight for some time. In principle, also higher fertility of ten or more seems feasible. Now, the replacement level depends on mortality until adulthood. Mortality is rather low by historical standards these days in developed countries, roughly 5%. Hence you need two children per woman to replace her and her husband in the next generation plus 10% more (times two because this is per woman), or a fertility of about 2.1.
In earlier times, mortality was higher, but not arbitrarily high. 50% until adulthood was rather extreme. That leads to a replacement fertility of 4 because half of the children do not survive long enough to have offspring. If we assume that fertility runs at eight and the replacement level is four, the population doubles from one generation to the next because each couple has four surviving children. With a generation length of 25 years that is just what Malthus thinks it is for a population “when unchecked.”
Population growth over the past 100,000 years was very slow, though. If it had been uniform over time, it would have been roughly 0.01% per year, or 0.25% per generation of 25 years, not 100% as Malthus assumes for a population “when unchecked.” With mortality of 50% until adulthood and the corresponding replacement level of four, this means that fertility would have to have been 4 * 1.0025 = 4.01 to produce the actual result over the past 100,000 years.
Hence you would have to think that human populations somehow stubbornly had fertility of 4.01 instead of 4, and not 8 as would be possible. They would hence have had the power to keep their fertility down by 3.99 (or more since 8 is not even the maximum). However, that leads to the simple question: If human populations could keep fertility down by 3.99, why not also by 4?
In that case, they would have been able to stabilize. And it is hard to see why they could not have done this. They would have even easily had to power to shrink sometimes with slightly lower fertility of 3.99 or a decrease from 8 by 4.01. The difference is so minimal that it is almost impossible to exclude that this would have been possible, or even larger deviations from a replacement level of four on both sides. But if that is so, it is no longer necessary that a population just cannot stop growing. It could simply not do this. And if it stabilizes or sometimes even shrinks, the Malthusian end-game is called off because the population might just not grow that far.
Malthus himself gets around this concession because he implicitly assumes that population growth can only stray slightly from 8 or more. In that case, exponential growth is still very fast and so the above argument goes through. It is notable though that Malthus never makes an explicit argument for small deviations from the maximum, which is probably so because he does not understand the concept of replacement fertility and equates “children being born” with “population growth.” That is totally silly, but plausibly indeed the case in the first edition of his essay. In the later editions, he seems to understand the point in a vague sense, but fails to address the problem it causes for his argument. I will get back to this in another post.
Slight deviations from the maximum would still ensure stubborn exponential growth and at a fast rate, which does not help Cornucopians a lot. Larger deviations could draw the Malthusian end-game out, but lead to the concession that human populations might have the power to stabilize and avoid it altogether. In that case, no appeal to human ingenuity is necessary. Even stagnant technology and fixed land under cultivation would work.
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Still, as I have said, Cornucopians are Malthusians at heart. They believe that populations cannot avoid growing. That leads to their puzzlement how humankind could pull it off that the food supply grew in line with increasing population sizes. Population growth comes first in the Malthusian worldview, and then people have to scramble to feed the extra people.
In addition, Corucopians also implicitly grant the Malthusian claim that populations were almost always at the maximum size in the past that is feasible at a certain technological level. So any further growth without technological progress would immediately lead to starvation and famine. In line with this thinking, Cornucopians tell a story of a desperate race to increase food production to match population growth.
What Cornucopians need at this point is some deus ex machina, a trick that fixes the problem. Their solution is that a growing population somehow pulls itself out of the swamp by its own hair like the Baron von Münchhausen. Their contention is, therefore, that a larger population somehow produces the technological progress that can stave off otherwise inevitable starvation and famine. The history of humankind appears from this vantage point as an amazing race where human ingenuity somehow managed to beat population growth.
However, the problem for Cornucopians that they try to solve in this way stems from their own Malthusian worldview. The only thing they add is a baseless belief that human ingenuity will supply what is necessary, just because it has to. And that makes it possible to cast the Malthusian worldview in an optimistic light as a Cornucopian worldview. Apart from this differnt spin, Cornucopians are still Malthusians.
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How could it be otherwise? If I find both Malthusianism and Cornucopianism silly, what then? Could the sun be neither blue nor red?
As I have noted above and also in other posts, the Malthusian worldview is part of our culture. We take it for granted. It hence takes mental effort to suspend it only for a short time. I include myself here. Anything else seems patently absurd. But then please bear with me. It might take some time to sink in, and then the Malthusian worldview might still make it counter-intuitive. But the answer to the question is actually quite simple.
Cornucopians are right that food production has kept pace with population growth over time. Production, not only of food, has even outstripped it. But since they assume, like the unreformed Malthusians they are, that population growth at an exponential rate is a given, they are driven into an argument how human ingenuity pulled this off.
The crucial point to understand here is that population growth might not be primary, but the growth of food production, or rather the potential to produce further food. In that case, there is no race to beat population growth. When a population grows slowly enough to match primary growth for food production, there is nothing to chase. If food production does not increase, then a population simply does not grow. And if population growth is slower than the growth of food production, it is also easily possible to have both population growth and that people are better off at the same time.
Of course, there can be technological progress or new fertile land may become available when you discover, for example, the Americas. But this is primary, and population growth then follows. When there is no technological progress or no new fertile land is discovered, the population just does not grow. It also does not have to grow to a maximum if it has the power to stabilize. It can stabilize at any level below it.
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There is another twist here that I will explore in a further post. A fundamental fallacy in Malthus’ thinking is that he equates the amount of food with the living standard. But that is false. People in modern societies in the developed world are not better off because they eat ten times as much than others. Human beings need pretty much the same amount of calories whether they are hunter-gatherers or live in an industrial society if you correct for features like height, weight, or activity level. This is effectively a constant of human nature.
It makes no more sense to expect that calorie intake should go up as people are better off than that their body temperatures should go up. And this means that food production per capita has to remain essentially stable. What can change, of course, is food quality, variety, and security. Still broadly there should always be a rough correspondence, after correcting for other features, between population size and food production. This is not the outcome of some race, but because it has to be so.
That’s also why I write about a potential. If technological progress makes twice as much food production possible than before, that does not mean that people will now grow twice as much food and eat twice as much. Barring food production for a market, they will grow as much food as before and will now produce other goods on top which make them better off. Part of that may be better food, eg. more meat, more variety or most importantly greater security, eg. via storage. And they can also expand their population and tap into the potential to feed the extra people.
Malthus has the silly idea that to make people better off you have to produce more food. But that makes no sense. If you produced twice as much food, people could still only eat as much as before, and the other half would have to rot away. You could perhaps use some of it to build up reserves, and that is an important point that I will explore in still another post. Or they could grow extra food to trade for other goods. But then this is just another way of producing those other goods directly. Since Malthus gets this wrong, he draws all kinds of fallacious conclusions, eg. that the production of luxury goods edges food production out and hence starves a part of the population. But that is not so, or if it is, that is for other reasons.
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Now back to the argument after this digression: Let’s work through this step by step, so I can hammer my argument in against the knee-jerk reflexes from the Malthusian worldview:
The first observation is simple. Malthus thinks he can prove that human populations “when unchecked” will have very high fertility and hence population growth. The maximum is the “natural” behavior. However, if you look at any modern population in a developed country, it is clear that it is closer to being “unchecked” than any population in Malthus’ time. There is practically no constraint on population growth from the food supply. We have perfect food security, and more people could easily be fed. But then populations in developed countries do not grow stubbornly because of it. Instead they have fertility around the replacement level that is now lower than in earlier times because of lower mortality until adulthood.
So what if fertility around the replacement level were the natural behavior of human populations, not maximum fertility? As I have shown for the slow growth of humankind over the past 100,000 years, that must have been the case on average for most of the time in the past anyway. It cannot be a blip over the past century, it was always so. Hence the extraordinary behavior in the past must have been population growth and not stabilization.
Now, if populations can and do often stabilize, they may do this at any level. There is no necessity that they have to grow to a maximum size where a binding constraint bites that can only be overcome by technological progress. That is just a Malthusian idée fixe, contrary to all evidence.
Suppose a population stabilizes at half the maximum size. In this case, there is still plenty of land not under cultivation. If the population then grows, it is rather easy to produce more food without technological progress. Of course, this cannot continue at a fixed rate, ie. with exponential growth. But if the population can stabilize, it does not have to keep growing. It can grow a little and then stop. That would lead to a higher population size, but that should generally still be below the maximum. It would also be possible for the population to shrink somewhat. Once you concede this, inevitable population growth until stopped by brutal means is anything but necessary.
If that sounds strange for any time in the past apart from our times: It was practically always so. Humankind has never grown to the maximum size possible at the respective technological level. It is hard to find a country that has ever been populated to the maximum. There were almost always forests that could have been chopped down or other wastelands that could have been taken into cultivation. If you read Malthus’ essay closely, he, too, know this is. Here is how he explains it away (cf. XVII.6):
The superior encouragement that has been given to the industry of the towns, and the consequent higher price that is paid for the labour of artificers, than for the labour of those employed in husbandry, are probably the reasons why so much soil in Europe remains uncultivated.
If you want to object “But there were many famines in the past!” keep in mind that a famine can happen at any population size, not only at maximum size. All it takes is an unexpectedly bad harvest and no way to obtain food from elsewhere, eg. via trade. This is about the volatility and not the average level of agricultural production. Of course, in earlier times people found it much harder to handle this. But this does not prove maximum population. (For more on this, please read my post: “A Very Simple, But Common Mistake.”)
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To explain the many observations that contradict the Malthusian argument, eg. people being better off with more population, it is not necessary to postulate a mystical mechanism that first the population grows and then it finds some way to keep up with food production. All it takes is that the population usually stabilizes at some level that leaves room for some growth although that may not be realized. And that the population generally only grows when the potential for food production increases, be it because new fertile land becomes available or technology progresses. In the latter case, this is what happens first, and then the population follows, not the other way around.
There is now no need that the population has to follow in lockstep with (potential) food production. As you can see in developed countries nowadays, it might not do this at all. In that case, the population just puts all extra production into being better off via other goods, among them perhaps also higher quality, more variety, and before all: more security for food. If it grows more slowly than the food supply could expand, it has leeway to produce other goods and be better off at the same time.
Technological advances, like the domestication of animals and then of plants, come first, then the population grows into the potential more or less, or not at all. If there are no technological advances, the population just remains where it is. There are hunter-gatherers that have preserved their way of life until our times. Their populations have not grown for 100,000 years apart from geographical expansion.
There is indeed a tight connection between technological progress and population growth as Cornucopians rightly point out. And there can also be an unexpected connection between more population and being better off, unexpected only if you are trapped in the Malthusian worldview. But there does not have to be any magic how the increased population forces technological progress.
Human ingenuity plays a role, but not in the sense that it has to win a race with inevitable population growth. If there is no technological progress, the size of a population just remains where it is. And if there is technological regression, as has sometimes happened, then the population shrinks along with it. That has, for example, happened after the demise of the Roman Empire when the population of Italy fell from seven to five million people.
Of course, there is a connection between more population and technological progress. However, the direction of causation might be from technological progress to more population and not the other way around. This does not have to preclude also a feedback from more population to technological progress. But you have to be careful here because it may prove too much, namely extremely explosive population growth.
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I will explore this line of thought in further posts after I have demolished the Malthusian argument and its associated worldview further. I have to do this first because as long as the Malthusian worldview is assumed as an obvious truth it is hard to even understand my argument. However, once you are able to leave the worldview behind, it is actually quite simple. And you don’t need an appeal to human ingenuity as a deus ex machina either, which is so astonishing because it is probably not true. All you need is just the fact that human ingenuity has led to some technological progress in the past and that then induced also some population growth.
Stay tuned …
