The Malthusian Trap
An Extremely Short Introduction
If you’ve read much about the pre-industrial world, you’ve probably run into Malthus. The English parson whom Keynes dubbed “the first of the Cambridge economists” has had an outsized and wholly unintended impact on the study of income and demography thanks to his 1798 classic, An Essay on the Principle of Population, in which he argued that any increase in wages above a bare minimum would be curtailed by a corresponding rise in birth rates. This prediction, which had just become invalid at the time of writing,1 was nevertheless a fairly accurate characterization of human history. to that point. Between 1250 and 1650, for example, England’s GDP per capita rose by just 27 percent. Malthusianism is so useful and illustrative in explaining the relative stagnation of pre-modern living standards that historians, economists, and anthropologists of all stripes invoke it casually. We’re all familiar with implicit or explicit versions of the “Malthusian Trap.” But familiarity has bred contempt—contempt as in disregard, as we appear to have forgotten what exactly it means.
As we’ll see, using the word “Malthusian” to describe an economy doesn't define its standard of living. Instead, the term refers to a hypothetical relationship between population and income, which can be characterized using a simple model. The focus of this essay is thus straightforward: explaining how economic historians use the basic Malthusian model.2 Once we’re familiar with the assumptions, mechanisms, and predictions, we can then discuss how and when the framework should be applied to the pre-industrial world.
To start, however, let’s take our cue from the Cambridge curate himself. In Chapter II of the Essay, Malthus wrote that
[I]n all societies… there is a constant effort towards an increase of population… [This] increases the number of people before the means of subsistence are increased. The food therefore which before supported seven millions must now be divided among seven millions and a half or eight millions. The poor consequently must live much worse, and many of them be reduced to severe distress. The number of labourers also being above the proportion of the work in the market, the price of labour must tend toward a decrease, while the price of provisions would at the same time tend to rise. The labourer therefore must work harder to earn the same as he did before.
Once incomes had fallen sufficiently as a result of this increased pressure on productive and natural resources, however, corrective machinery operated to return the worker’s status back to subsistence conditions.
During this season of distress, the discouragements to marriage, and the difficulty of rearing a family are so great that population is at a stand. In the mean time the cheapness of labour, the plenty of labourers, and the necessity of an increased industry amongst them, encourage cultivators to employ more labour upon their land, to turn up fresh soil, and to manure and improve more completely what is already in tillage, till ultimately the means of subsistence become in the same proportion to the population as at the period from which we set out. The situation of the labourer being then again tolerably comfortable, the restraints to population are in some degree loosened, and the same retrograde and progressive movements with respect to happiness are repeated.
With the halt in population growth and fall in incomes, in other words, employment would increase and push wages back up again. But they could not rise too high; exceeding subsistence would activate forces tending to return living standards to the basic supportable level. Positive checks, including famines, plagues, and wars, increased mortality; preventative checks—late marriage, celibacy, birth control—lowered fertility. In the second edition, Malthus allowed that the subsistence income varied between countries, and the cross-national data has borne out this modification. He did not, however, abandon the essential negative feedback loop.
The best-known co-optation of the Malthusian mechanism into economic history is that of Greg Clark, who uses it prominently in his 2007 book A Farewell to Alms. The stripped-down model involves three assumptions:
The birth rate (measured as births per year per thousand persons) was constant or rising with real incomes. However, the birth rate for any given income varied across societies depending on social conventions concerning reproduction.
The death rate (deaths per year per thousand persons) fell as living standards rose; the specific level, however, varied between regions as a result of environmental or cultural factors.
Material living standards fell when population rose.
A simple diagram (see below) illustrates how Malthusian mechanisms kept population and living standards in relative stasis. The top panel relates birth and death rates with income levels; the bottom, population with income. At y*, subsistence income, birth rates are equal to death rates, and population growth is zero. Higher incomes imply higher birth rates (positive slope) and lower death rates (negative slope). Larger populations lead to lower incomes, so the curve in the bottom panel is negatively sloping.
Suppose that population collapsed abruptly from N* to N0, the classic reason being a plague. Decreased pressure on the resource base moves real incomes to y0. At y0, however, birth rates exceed death rates, so population will start to rise. As the number of laborers grows, incomes decrease, and so does the gap between birth and death rates. Population growth slows until N* is reached, at which point birth and death rates are equal and income per person has returned to subsistence. This is the Malthusian trap: higher living standards cause population growth, which lowers living standards until population growth stops. These dynamics broadly characterized the period after the Black Death; mortality temporarily increased living standards, but by the sixteenth century, wages across Europe were in free fall, bottoming out across the continent in 1600.
But what about technological change—the invention to which we attribute our present enrichment? Alas, Malthusian theory remains negative. Technical progress shifts up the population-income curve (lower panel, second figure) to the dotted line, which causes incomes to increase to y1. But once again, a wedge is driven between birth and death rates, so population starts to rise. When the number of laborers reaches n2, the birth and death schedules are back in equilibrium… and real income per worker is back at subsistence, albeit for a larger population. A single burst of ingenuity can’t liberate a civilization from the Malthusian fetters.
The level of subsistence, as Malthus noted in his second edition, varied widely in time and space. The most notable example is the European Marriage Pattern (EMP), which prevailed in the northwest part of the continent. The EMP has four characteristics: a late average age of first marriage for women (24–26); high fertility within marriage; 10–25 percent of women never marrying; and low illegitimacy rates (3–4 percent of births). As a consequence, fertility rates were well below the biological maximum—27 per 1000 circa 1650, at which time the average woman gave birth to just 3.6 children. Combined with relatively high mortality rates, fertility limitation led to living standards well in excess of the biological level of subsistence. Notice that on the real wage graph shown above, London’s real wages fell from the post-plague maximum, but stopped at a level twice that prevailing in Southern and Eastern Europe.
We have our model, and we have our predictions. A country or region caught in the Malthusian trap should experience little growth in population and real incomes over time. Any change in either of these two variables would produce a reaction tending to return both to subsistence equilibrium. Such patterns turn out to apply reasonably well to Europe before 1800. Ronald Lee called continental populations “weakly homeostatic,” the strongest feedback being the response of wages to population: a 10 percent rise in the latter decreased the former by 16 percent. The response of population to income was weaker. While the short-run effects of income effects—to harvest failures—were significant, but they dwindled after about five years. 107 years had elapsed before the English population recovered even halfway from the Black Death, leaving room for large swings in real income. Equilibration certainly did occur, but on the scale of centuries, not decades. Fortunately (for Malthus?), Europe spent millennia in the Trap.
What, then, would constitute an end to the Malthusian regime? Not population growth; as we have seen, slow technical advances over time would lead to an increasing population. Not higher-than-subsistence standards of living—a plague or elevated mortality might persistently depress population and inflate wages, while deliberate fertility limitation could push up y*.
The answer: simultaneously rising population and constant or increasing incomes for a prolonged period. This occurred first in Europe after 1750, and probably even earlier in Britain and the Netherlands.3 After growing slowly from 1500 to 1600, and practically stagnating up to 1700, the continent’s population exploded from 1750 to 1900—doubling over the century 1800-1900. Britain look the lead, seeing growth hit 13.2 persons per thousand in the first half of the nineteenth century. By 1850, her population was three times what it had been a century before. Lower, but still significant, increases took place across the continent.4 But the crisis predicted by the Malthusian model never materialized. Europe’s economies, gripped by the Industrial Revolution, grew even faster than did population. The ascent of the “inverted hockey curve” of GDP per capita began amidst the greatest labor-supply surge history. Rising incomes delinked mortality from harvest failures, advances in vaccination and sanitation ameliorated epidemic diseases, and better markets and transportation networks staved off famine. Malthus’s demon was banished—and once the demographic transition to lower birth rates set in, was chained and locked away.
That’s it! Malthusianism posits nothing more than a negative feedback loop between income and population. If incomes rise, population follows, which cuts incomes back to the no-growth subsistence level. If population continuously rises without decreasing living standards, we no longer exist in a Malthusian world. The same goes for a world in which population doesn’t respond to rising incomes. Do not be distracted by red herrings: there is no “Malthusian” standard of living, economic or biological. The model describes relationships, not prespecified levels.
If you find yourself talking about anything other than population and income, you may be having an interesting and valuable conversation. I might want to join you! But you won’t be talking about Malthus.
The Industrial Revolution, and all that.
I say “economic historians” to distinguish the use of the simple model in works like A Farewell to Alms and The Roman Market Economy from the far more complex unified growth models of Oded Galor and David Weil.
Robert Allen (2003) suggests that “escape from the Malthusian trap” occurred sometime between 1500 and 1800 in these two countries. The real wage chart certainly suggests that this may have occurred in England after 1600 or so. Whether the economic expansion of the commercial era would have weathered the early stages of the demographic transition, however, is another question entirely.