Why did Malthus assume linear increase in food?

JF comments on Malthus, which is my excuse for raising a question I’ve wondered about for a bit (without being sufficiently interested to actually read M, so for all I know I’m perpetuating common misreadings): M assumes exponential population growth (for which there is some basis) and linear food growth, for which there is no apparent basis at all. To first order (in an economy with little mech), it would seem to be natural to assume that food output is proportional to the number of people working the land. Or, if you assumed that land output and land area was fixed, you might assume that food output was fixed. What assumptions does M use to justify a linear increase in food production?


* [2018] CIP has a go at the subject.

15 thoughts on “Why did Malthus assume linear increase in food?”

  1. “Science of Discworld 3” gives IMO a good answer:

    “We suspect that Malthus plumped for linear growth of resources for a slightly silly reason. Victorian school-textbook mathematics distinguished two main types of sequence: geometric (exponential) and arithmetic (linear). There were plenty of other possibilities, but they didn’t get into the textbooks. Having already assigned geometric growth to organisms, Malthus was left with arithmetic growth for resources. His main point doesn’t depend on the actual growth rate, in any case, as long as it is less than exponential.”


  2. I am reminded of Kurzweil’s mantra; “We live in exponential times”. (Whatever the hell that is supposed to mean.)

    Anyway, food is a production process: we can add to the means of production but the means of production don’t add to themselves. Wheat doesn’t plant itself, milk doesn’t make more milk, etc. But human babies go on to have more babies. Could that have been what Malthus was thinking?


  3. I don’t know(and I’m not quite sure where to look, at least in the time I have before I need to go sleep); but it would be worth looking at the technological and social environment in which Malthus was writing. If food supplies had been increasing roughly arithmetically in the past, at the time he was writing, that could easily lead him to assume the same. I’d have to look up British agricultural data for the time to see. A pop-science consensus in favor of gradual agricultural improvement might have the same effect.

    I’d imagine that it would be something like an American of the present day, or near past, referring to the rate at which transistor density increases. Almost nobody has any real technical understanding of why exactly Moore’s law holds; but recent history and popular consensus both bear it out, so it is treated as wholly unremarkable.


  4. I’ll second phisrow. Malthus was writing in the 1790s and all the data leading up to his work probably supported his theory.

    Paul Krugman commented on this earlier this year:

    The fact is that Malthus was right about the whole of human history up until his own era.

    Sumerian peasants in the 30th century BC lived on the edge of subsistence; so did French peasants in the 18th century AD. Throughout history population growth had always managed to cancel out any sustained gains in the standard of living, just as Malthus said.

    It was only with the industrial revolution that we finally escaped from the trap.

    [Throughout history population growth had always managed to cancel out any sustained gains in the standard of living – err yes, thatss what *I*m saying: food proportional to population. So why then suddeny assume it would decouple in the future and become linear? -W]


  5. The industrial revolution didn’t help much in food production. There were better machines, but they only improved efficiency of the work force. For food production you also need fertilizers, and they weren’t available in the times of Malthus.

    Use of fertilizers – not just locally produced manure – didn’t spread until the chemistry (nitrogen and phosphorus) was worked out, and use of guano started. The green revolution came only after WW2, when artificial fertilizers became widely available. Not coincidentally, the global population explosion happened around the same time (but medicine was also involved).


  6. Krugman’s point is I think the correct one. Up until the point that Malthus was writing, it was true.

    [Don’t understand you. What was true? That food had increased linearly? I don’t see him saying that. K appears to say that food growth had matched population, which is what you would expect, since more people can grow more food -W]


  7. “Almost nobody has any real technical understanding of why exactly Moore’s law holds; but recent history and popular consensus both bear it out, so it is treated as wholly unremarkable.”

    Off topic but huh? We know why Moore’s law (the estimate that area size of features on silicon chips would half every two years or so – thus density double) has been (vaguely, within fairly large limits) accurate over the past several decades. I mean “we” as in modern society did the engineering to make it happen, so how could we NOT know? Moore’s law is an educated guess at engineering and production capability, based on knowledge of then current and possible technologies. It is not precise in any sense, or predicated directly on natural limits. In fact when the natural limits get felt Moore’s law will likely then start to be less accurate.


  8. More people grow slightly more food, but more additional arable land grows a lot more food. Perhaps his assumption was based upon a notion that all quality farmland was already in production.

    [It may have been based on some version of that; although (a) this was clearly not true abroad, and probably not true in England and (b) why should “slightly more” be linear?

    What I’m trying to say is that this appears to bee a major plank of his platform, but no-one has any good justification for it. Does no-one care? -W]


  9. I found the text of his reasoning, which amazingly doesn’t refer to the peer reviewed literature. 🙂


    Let us now take any spot of earth, this Island for instance,
    and see in what ratio the subsistence it affords can be supposed to increase. We will begin with it under its present state of cultivation.

    If I allow that by the best possible policy, by breaking up
    more land and by great encouragements to agriculture, the produce of this Island may be doubled in the first twenty-five years, I think it will be allowing as much as any person can well demand.

    In the next twenty-five years, it is impossible to suppose
    that the produce could be quadrupled. It would be contrary to all our knowledge of the qualities of land. The very utmost that we can conceive, is, that the increase in the second twenty-five years might equal the present produce. Let us then take this for our rule, though certainly far beyond the truth, and allow that, by great exertion, the whole produce of the Island might be increased every twenty-five years, by a quantity of subsistence
    equal to what it at present produces. The most enthusiastic
    speculator cannot suppose a greater increase than this. In a few centuries it would make every acre of land in the Island like a garden.


    Writers of that time seemed to be paid by the word. The quick summary is that the amount of arable land is limited and can only be pushed so far in terms of production. Of course this skips all types of possibilities, which is a common fault of people making predictions about the future.

    [Ah, thank you. Well there you have it I suppose. Argument from imagination -W]


  10. There is only so much humans can do to increase production on a given amount of arable land. With a given technology, if 40 people can maximize yield, having 41 may not squeeze out a single extra carrot.

    Other restrictions that existed in his world that we take for granted are food transportation and storage, and animal health.

    I’m just a cowboy, so I can’t do any more than guess.


  11. Somewhere I have a copy of Malthus’ longer form volume on the subject that I worked on for Project Gutenberg years ago. Anyway, comments up to this point seem to capture his thinking pretty well, such as it was. Obviously when human population is low, people and agriculture can grow exponentially together, under conditions that allow expansion of agriculture into new lands. When all the land is used up, though, that growth in food must stop. Malthus’ point then was that human population at that point contiunes to grow inexorably until forcibly constrained by abject poverty, war, starvation, or other “vices”, that bring them back into sync.


  12. WC,

    Referring to your comment to JCH. The quote that I included in my earlier post appears to be his entire logic on the point.

    In terms of caring. Malthus was wrong about essentially everything. This is only one point. The only thing that I find interesting about him is as an example of poor forecasting based on the prejudices of the forecaster.

    It was the same kind of thinking that forecast that England would run out of coal by 1900.


  13. “that forecast that England would run out of coal by 1900.”

    Yeah, but they probably knew there was plenty of it under Wales. 😉


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