The demographic transition and the population debate

Thomas Robert Malthus published An Essay on the Principle of Population anonymously in 1798. His claim has two halves. First, population, unchecked, grows geometrically (1, 2, 4, 8, 16, …). Second, the food supply can grow only arithmetically (1, 2, 3, 4, 5, …), because land is limited. The gap closes in one way or another: the positive checks (famine, disease, war) raise the death rate, and the preventive checks (delayed marriage and restraint) lower the birth rate. In the second edition (1803) he added “moral restraint” as a preventive check.

The arithmetic is easy to test. If population doubles every 25 years and food adds the same amount each 25 years, then after 200 years population has multiplied by 2⁸ = 256 while food has multiplied by 9, so food per head has fallen to 9/256, about 3.5% of what it was. The unsettling implication is that income per head cannot rise for long: any gain in technology is eaten by population growth, and wages return to subsistence. For most of human history that was close to the truth (Galor and Weil’s model of the escape from this “Malthusian trap” is in the growth module).

Malthus was wrong about the nineteenth century and after: in Britain and then everywhere industrialisation, agricultural innovation and trade raised food output faster than population, and living standards rose. The critics differ in why.

• Boserup (1965) turned the causation round: population pressure does not just press on food, it induces farmers to intensify (shorter fallow, more labour, new tools), so agriculture changes because there are more mouths.
• Julian Simon (1981) argued that people are “the ultimate resource”, because more people produce more ideas. He won a famous wager against Paul Ehrlich (author of The Population Bomb, 1968) on whether the prices of five metals would rise between 1980 and 1990; they fell.
• The demographic transition itself is the best reply: Malthus assumed that higher income would raise births. Beyond a point it lowers them, which is the subject of this lesson.

What survives is the idea of a resource constraint: when land, water or the atmosphere is scarce, extra people impose costs on others. That returns in Lessons 15 and 16.

In 1929 the American demographer Warren Thompson sorted the countries of the world into three groups according to their birth and death rates and saw that they lay along a path. Adolphe Landry (1934) described the same shift in France, and Frank Notestein (1945) and Kingsley Davis (1945) gave it the form that is taught today. The pattern is that death rates fall first, because food, clean water and medicine reach a population, while birth rates, tied to custom and to the costs and benefits of children, fall later. The gap between them is the growth of population.

Textbooks differ over how many stages there are: four (stationary, early expanding, late expanding, stationary) in most Indian textbooks, five with Blacker, who added a stage in which deaths exceed births. The exam questions follow the same pattern: match the features to the stages, or arrange Blacker’s phases in order. Keep the rule in mind: death rate falls first, birth rate second, growth is highest in between.

The panel below plots World Bank data for ten countries from 1960. Start with the birth and death rates of one country: India’s death rate fell from 19.4 per 1,000 in 1960 to 6.6 in 2023, and its birth rate from 42.9 to 16.2. The gap, which is the natural rate of increase (divide by ten to get per cent), was about 2.3% a year in both 1960 and 1980 and about 0.95% in 2023. The birth rate began to fall decisively only in the 1980s and 1990s, which is why India’s population grew so much.

Compare countries. Niger still had a total fertility rate of 6.1 births per woman in 2023 and a birth rate of 41.9, with a death rate of 8.9: it is in the early expanding stage, growing about 3.3% a year. South Korea went from a TFR of 6.0 in 1960 to 0.72 in 2023, a collapse that took about forty years and put it in Blacker’s fifth stage. China’s death rate dropped far more suddenly (the famine of 1959–61 shows as a spike), and its TFR was 1.0 in 2023. Japan had 46.7 dependants per 100 people of working age in 2000 and 70.1 in 2023.

Why do families get smaller as countries get richer? Several explanations are asked in the exams, and they fit together.

Quantity and quality (Becker). Gary Becker (1960) treated children as something parents “buy”, with a price (the cost of food, schooling and, above all, the parents’ time) and an income. If a rise in income raised the number of children, richer families would be larger; they are not. Becker and Lewis (1973) resolve this: parents care about the number of children (quantity) and the amount spent on each (quality), and the two are linked, because the cost of an extra child rises with the quality chosen for the others. As incomes rise and returns to education grow, parents shift towards quality, and the demand for quantity falls. (JNU 2018 asked exactly this: the trade-off between quantity and quality of children.)

Opportunity cost. The main cost of raising a child is the time of the parent, usually the mother. As women’s wages rise, that time becomes dearer and births fall: a substitution effect. The same logic works in reverse: in JNU 2019, assuming away any income effect, high unemployment lowers the opportunity cost of childbearing, so fertility tends to rise.

Child mortality. When many children die, parents have extra births to replace them (the replacement effect) and some have more than they want as insurance (the hoarding effect). When mortality falls, fertility follows, but with a lag, because parents take time to learn that the survival rate has changed. JNU 2015 asked a subtle version: if the total number of child deaths stays the same but they move from late to early childhood, parents are more able to replace them, so fertility rises.

Wealth flows and old-age support. John Caldwell (1976) argued that in traditional societies the flow of wealth runs from children to parents, so large families are rational; when the flow reverses, as the family becomes nuclear and children need schooling, large families are not. Where there are no pensions, children are old-age insurance; pensions, banks and insurance reduce the need. Supply and demand. Easterlin (1975) adds that fertility falls when the demand for children has dropped and the costs of limiting births, in knowledge, money and social disapproval, are small enough for parents to act on it.

The simulator follows a stylised country year by year through every age group. Life expectancy rises from 30 to 78 and the total fertility rate falls from 6.0 to 1.8; you choose when mortality starts to fall, how long fertility lags behind it, and how fast fertility then falls. Everything else, the peak of growth, the final size of the population, the changing share of workers, comes out of the age structure. It is a teaching model, not a forecast: the numbers are illustrative, but the mechanism is the one in the data.

Try the three presets. A long lag between the fall in mortality and the fall in fertility, as in Europe, gives growth that lasts for generations. A short lag, as in East Asia, gives a lower, earlier peak and a steeper rise in the working-age share. A very long delay gives the highest growth and a population many times its starting size.

The demographic dividend. When fertility falls, the generation of children shrinks relative to the generation of adults, and for a time the share of the population of working age rises. The dependency ratio (children and the elderly per 100 people of working age) falls. In the simulator, with the default settings it falls from about 87 to about 49 over some 55 years. If the extra workers find jobs, and the saving that fewer dependants allow is invested, income per head rises faster than output: the dividend. Bloom and Williamson (1998) estimated that this accounted for a large part of the growth of East Asia between 1965 and 1990. In India, with a median age under thirty, the working-age population is still rising as a share (UOH 2017 asked where India’s dividend comes from: a large and growing share of people of working age).

Three points to remember. It is a window, not a permanent gain: once fertility has stabilised the working-age population ages, and the dependency ratio rises again, now with the elderly (the shaded band in the third chart ends, and Japan in the data panel shows what comes next). It is an opportunity, not a guarantee: workers need productive jobs, and the benefit depends on health, education and flexible labour markets; Bloom, Canning and Sevilla (2003) stress that the same age structure gave very different results in East Asia and Latin America. The timing depends on the speed: a country whose fertility falls quickly has a bigger but shorter dividend, which is the contrast between the East Asia and Europe presets.

Population momentum. A population with a young age structure keeps growing even after fertility has dropped to replacement level (2.1 births per woman in low-mortality countries), because there are many girls about to become mothers. Keyfitz (1971) gave the idea its name. In the model of this lesson, with life expectancy of 70 and a total fertility rate of 4, an immediate fall to replacement fertility still leaves the population about 1.49 times its size when the fall begins; from 2.5 births per woman the figure is 1.06, and from 6 it is 1.82. (JNU 2016: the rate of population growth has great inertia because, when growth rates are high, a large share of the population is of child-bearing age.) Slowing a country’s fertility therefore takes decades to be seen in its population.

The old question is whether population growth raises or lowers income per head. The answers depend on the model.

• Solow: faster population growth raises the break-even investment per worker, so capital per worker and income per head are lower in the long run. The costs are those of “capital dilution”: more congestion, more pressure on land and public services (JNU 2021 lists increased congestion and a faster growing labour force with higher unemployment as costs; more resources per head is not a cost).
• Malthus: the same effect through land: more people on a fixed amount of land lowers output per head.
• Boserup and Simon: more people induce innovation and new ideas, which raises productivity (see the Romer model in the growth module).
• Age structure: the effect depends less on the size of population than on its age. Children and the elderly consume without producing, so a young population holds back saving, while a rising working-age share helps.

Empirical work over the last decades has found a weak overall link between population growth and growth per head, with the age-structure channel stronger. The policy conclusion is not that people are a burden or a resource, but that the benefit depends on the jobs, schools and clinics they find.

Questions on Malthus, the stages, the economics of fertility, the dividend and momentum. Questions that depend on Indian census figures or on the arithmetic of rates are in Lesson 9.