Unit 1 Prosperity, inequality, and planetary limits

1.7 Explaining the flat part of the hockey stick: The Malthusian trap, population, and the average product of labour

On its own, the diminishing average product of labour cannot explain the long, flat portion of the hockey stick. It just means that living standards depend on the size of the population. It doesn’t tell us why, over long periods, living standards and population didn’t change much. But Malthus’s model contains a second key idea:

• Population expands if living standards increase.

His logic was that, if agricultural technology improved and raised the productivity of labour, people would have more children as soon as they were somewhat better off. Because the quantity of land and other available natural resources would not expand along with population, the result would be to lower how much each person could produce. But as long as people were better off, population growth would continue until living standards fell to a sufficiently low level to halt the population increase. Among economists, Malthus’s idea of a poverty trap, illustrated in Figure 1.9, was widely accepted.

It provided an explanation of the world in which they lived, in which incomes might fluctuate from year to year (or even century to century), but not permanently trend upwards. This had been the case in many countries for at least 700 years before Malthus published his essay, as shown in the long flat part of the hockey stick in Figure 1.1.

His theory of population essentially regarded people as not that different from other animals. He was not the first person to have this idea. Years earlier, the Irish economist, Richard Cantillon had stated that, ‘Men multiply like mice in a barn if they have unlimited means of subsistence.’

Imagine a herd of antelopes on an otherwise empty plain (there are no predators). When the antelopes are better fed, they live longer and have more offspring. When the herd is small, the antelopes can eat all they want, and the herd gets larger.

Eventually the herd will get so large (relative to the size of the plain), that the antelopes can no longer eat all they want. As the quantity of land per animal declines, they have less to eat. This reduction in living standards will continue as long as the herd continues to increase in size.

subsistence level

The level of living standards (measured by consumption or income) below which the population will decline.

Since each antelope has less food, they will have fewer offspring and die younger. Population growth will slow down. Eventually, living standards will be so low that the herd no longer increases in size. The antelopes have filled up the plain. At this point, each animal will be eating an amount of food that we call the subsistence level.

Much of the same logic would apply, Malthus reasoned, to a human population with a fixed supply of agricultural land. While people were well fed, they would multiply like Cantillon’s mice; but eventually they would fill the country, and further population growth would push down the incomes of most people as a result of diminishing average product of labour. Falling living standards would slow population growth as death rates increased and birth rates fell; ultimately incomes would settle at the subsistence level.

In Figure 1.10, we have plotted the relationship between the average product of labour and the number of farmers in our model of an agricultural economy, using the table in Figure 1.8a. When the number of farmers is low, their average product is high: for example, if 200 farmers work the land, the output is 855 kg of grain per farmer. As the number of farmers increases, the average product falls. So the graph of the average product of labour is a downward-sloping line.

Suppose that the subsistence level of income in this economy is 500 kg of grain per farmer. In Figure 1.10, the average product is equal to subsistence income when there are 1,500 farmers, at point E. At this point the population neither grows nor falls: it remains constant. If the number of farmers is below 1,500, their income is above subsistence level—they have a higher standard of living, but then the population will rise. And as it rises, the number of farmers working the land will increase and their average product will fall. So eventually the economy will reach point E, with 1,500 farmers each receiving subsistence income. And if the number of farmers is above 1,500, the opposite will happen: since incomes are below subsistence level, the population will fall, until there are 1,500 farmers and incomes reach subsistence level.

equilibrium

An equilibrium is a situation or model outcome that is self-perpetuating: if the outcome is reached it does not change, unless an external force disturbs it. By an ‘external force’, we mean something that is determined outside the model.

Figure 1.10 captures the essence of Malthus’s argument: the economy will tend to return to an equilibrium level of population and income, at which income is equal to subsistence level. Equilibrium is an important concept in economics. In everyday language, something is in equilibrium if the forces acting on it are in balance, so it remains unchanged. The same is true here: point E is an equilibrium because if income and population take the values at point E, there is no tendency for them to change; they will remain constant at these values (unless something else in the economy changes).

Malthusian economics: The effect of technological improvement

We know that over the centuries before the Industrial Revolution, improvements in technology occurred in many regions of the world, including Britain, and yet living standards remained constant. Can Malthus’s model explain this?

Figure 1.11 shows what happens in our model following an improvement in agricultural technology—such as the new type of plough from China that came to England in the early seventeenth century. The average product of labour rises at each level of the labour input. In the figure, the line representing the average product of labour shifts upwards.

Suppose that the economy is initially in equilibrium at point E, with 1,500 farmers and subsistence income of 500 kg of grain per farmer. Follow the steps in Figure 1.11 to understand what happens when productivity rises.

Technological progress has raised living standards only temporarily. At the new equilibrium, the population is higher—but income has returned to subsistence level. Rather than raising living standards, a better technology provides subsistence income for a larger population.

The Malthusian model predicts that improvements in technology will not raise living standards if:

• the average product of labour diminishes as more labour is applied to a fixed quantity of land
• population grows in response to an increase in living standards.

Then in the long run, an increase in productivity will result in a larger population but not higher living standards. This depressing conclusion was once regarded as so universal and inescapable that it was called Malthus’s Law.

So we now have a possible explanation of the long, flat portion of the hockey stick. Human beings periodically invented better ways of making things, both in agriculture and in industry, and this periodically raised the incomes of farmers and employees above subsistence. The Malthusian interpretation was that higher incomes led couples to marry earlier and have more children, and they also led to lower death rates. Population growth eventually forced incomes back to subsistence levels, which might explain why China and India, with relatively sophisticated economies at the time, ended up with large populations but—until recently—very low incomes.

Looking for evidence

Can we find evidence to support the central prediction of the Malthusian model, that incomes will return to subsistence level?

Figure 1.12 is consistent with what Malthus predicted. Each point shows the population, together with an index of average wages—representing living standards—in England for a decade between 1280 and 1800. The index measures wages relative to the average wage in 1860.

The Black Death swept through Asia and Europe in the fourteenth century. It spread along trade routes, reaching Europe in the 1340s. An estimated 25 million people died: almost a third of the European population.

In 1280 the population was just under five million, and the wage index stood at 61 (that is, 61% of the wage in 1860). Then in the fourteenth century, as a result of the outbreak of bubonic plague known as the Black Death, the population fell dramatically. The decline in population and labour supply had an economic benefit for the farmers and workers who survived: it meant that farmers had more and better land, and workers could demand higher wages. Incomes rose as the plague abated. Work through the figure to see what happened next.

The seventeenth century was a period of technological progress in English agriculture.¹ New crops (including potatoes), new techniques (such as the Dutch system of crop rotation), and new equipment (like the Chinese plough) raised productivity. Figure 1.12 shows the corresponding rise in incomes. But, just as the model in Figure 1.11 predicts, the improvement in living standards was only temporary. Population rose further, and wages began to fall. By the time Malthus was studying the problem in the 1790s, wages were below the average level for the previous five centuries.