The introduction of new manufacturing technologies generally affects economic growth by

Automated assembly process

History, instability, and growthInnovation

How improvements in technology happen, and how they sustain growth in living standards

• Economic models help explain the Industrial Revolution, and why it started in Britain.
• Wages, the cost of machinery, and other prices all matter when people make economic decisions.
• In a capitalist economy, innovation creates temporary rewards for the innovator, which provide incentives for improvements in technology that reduce costs.
• These rewards are destroyed by competition once the innovation diffuses throughout the economy.
• Population, the productivity of labour, and living standards may interact to produce a vicious circle of economic stagnation.
• The permanent technological revolution associated with capitalism allowed some countries to make a transition to sustained growth in living standards.

In 1845, a mysterious disease appeared for the first time in Ireland. It caused potatoes to rot in the ground, but by the time it became clear that a plant was infected, it was too late. The ‘potato blight’, as it became known, devastated Irish food supplies for the rest of the decade. Starvation spread. By the time the Irish famine ended, about a million people out of an initial total of 8.5 million had died, which in percentage terms is equivalent to the mortality suffered by Germany through defeat in the Second World War.

The Irish famine sparked a worldwide relief effort. Former slaves in the Caribbean, convicts in Sing Sing prison in New York, Bengalis both rich and poor, and Choctaw Native Americans all donated money, as did celebrities such as the Ottoman Sultan Abdulmecid and Pope Pius IX. Then, as now, ordinary people felt empathy for others who were suffering, and acted accordingly.

But many economists were much more hard-hearted. One of the best-known, Nassau Senior, consistently opposed British government famine relief, and was reported by a horrified Oxford University colleague as saying that ‘he feared the famine of 1848 in Ireland would not kill more than a million people, and that would scarcely be enough to do much good.’

Senior’s views are morally repulsive, but they did not reflect a genocidal desire to see Irish men and women die. Instead, they were a consequence of one of the most influential economic doctrines of the early nineteenth century, Malthusianism. This was a body of theory developed by an English clergyman, Thomas Robert Malthus, in An Essay on the Principle of Population, first published in 1798.1

Malthus held that a sustained increase in income per capita would be impossible.

His logic was that, even if technology improved and raised the productivity of labour, people would still have more children as soon as they were somewhat better off. This population growth would continue until living standards fell to subsistence level, halting the population increase. Malthus’ vicious circle of poverty was widely accepted as inevitable.

There is evidence that Victorian colonial administrators thought that famine was nature’s response to overbreeding. Mike Davis argues that their attitudes caused an avoidable and unprecedented mass extinction, which he calls a ‘cultural genocide’.2

It provided an explanation of the world in which Malthus lived, in which incomes might fluctuate from year to year or even century to century, but not trend upwards. This had been the case in many countries for at least 700 years before Malthus published his essay, as we saw in Figure 1.1a.

Unlike Adam Smith, whose book The Wealth of Nations had appeared just 22 years earlier, Malthus did not offer an optimistic vision of economic progress—at least as far as ordinary farmers or workers were concerned. Even if people succeeded in improving technology, in the long run the vast majority would earn enough from their jobs or their farms to keep them alive, and no more.

But in Malthus’ lifetime something big was happening all around him, changes that would soon allow Britain to escape from the vicious circle of population growth and income stagnation that he described. The change that had sprung Britain from the Malthusian trap, and would do the same for many countries in the 100 years that followed, is known as the Industrial Revolution—an extraordinary flowering of radical invention that allowed the same output to be produced with less labour.

In textiles, the most famous inventions involved spinning (traditionally carried out by women known as spinsters, meaning female spinner, a term which has come to mean an older unmarried woman), and weaving (traditionally carried out by men). In 1733, John Kay invented the flying shuttle, which greatly increased the amount a weaver could produce in an hour. This increased the demand for the yarn that was used in weaving to the point where it became difficult for spinsters to produce sufficient quantities using the spinning wheel technology of the day. James Hargreaves’ spinning jenny, introduced in 1764, was a response to this problem.

Technological improvements in other areas were equally dramatic. James Watt’s steam engine, introduced at the same time as Adam Smith published The Wealth of Nations, was a typical example. These engines were gradually improved over a long period of time and were eventually used across the economy: not just in mining, where the first steam engine powered water pumps, but also in textiles, manufacturing, railways and steamships. They are an example of what is termed a general-purpose innovation or technology. In recent decades the most obvious equivalent is the computer.

Coal played a central role in the Industrial Revolution, and Great Britain had a lot of it. Prior to the Industrial Revolution, most of the energy used in the economy was ultimately produced by edible plants, which converted sunlight into food for both animals and people, or by trees whose wood could be burned or transformed into charcoal. By switching to coal, humans were able to exploit a vast reserve of what is effectively stored sunlight. The cost has been the environmental impact of burning fossil fuels, as we saw in Unit 1 and will return to in Unit 20.

These inventions, alongside other innovations of the Industrial Revolution, broke Malthus’ vicious circle. Advances in technology and the increased use of non-renewable resources raised the amount that a person could produce in a given amount of time (productivity), allowing incomes to rise even as the population was increasing. And as long as technology continued improving quickly enough, it could outpace the population growth that resulted from the increased income. Living standards could then rise. Much later, people would prefer smaller families, even when they earned enough to afford to have a lot of children. This is what happened in Britain, and later in many parts of the world.

Schumpeter brought to economics the idea of the entrepreneur as the central actor in the capitalist economic system. The entrepreneur is the agent of change who introduces new products, new methods of production, and opens up new markets. Imitators follow, and the innovation is diffused through the economy. A new entrepreneur and innovation launch the next upswing.

For Schumpeter, creative destruction was the essential fact about capitalism: old technologies and the firms that do not adapt are swept away by the new, because they cannot compete in the market by selling goods at a price that covers the cost of production. The failure of unprofitable firms releases labour and capital goods for use in new combinations.

This decentralized process generates a continued improvement in productivity, which leads to growth, so Schumpeter argued it is virtuous.9 Both the destruction of old firms and the creation of new ones take time. The slowness of this process creates upswings and downswings in the economy. The branch of economic thought known as evolutionary economics (you can read articles on the subject in the Journal of Evolutionary Economics) can clearly trace its origins to Schumpeter’s work, as well as most modern economic modelling that deals with entrepreneurship and innovation. Read Schumpeter’s ideas and opinions in his own words.10 11

Schumpeter was born in Austro-Hungary, but migrated to the US after the Nazis won the election in 1932 that led to the formation of the Third Reich in 1933. He had also experienced the First World War and the Great Depression of the 1930s, and died while writing an essay called ‘The march into socialism’, recording his concerns about the increasing role of government in the economy and the resulting ‘migration of people’s economic affairs from the private into the public sphere’. As a young professor in Austria he had fought and won a duel with the university librarian to ensure that students had access to books. He also claimed that as a young man he had three ambitions in life: to become the world’s greatest economist, the world’s greatest lover, and the world’s greatest horseman. He added that only the decline of the cavalry had stopped him from succeeding in all three.

History, instability, and growthInequalityInnovation

2.6 The British Industrial Revolution and incentives for new technologies

Before the Industrial Revolution, weaving, spinning, and making clothes for the household were time-consuming tasks for most women. Single women were known as ‘spinsters’ because spinning was their primary occupation.

Eve Fisher, a historian, calculated that making a shirt at this time required 500 hours of spinning, and 579 hours of work in total—costing $4,197.25 at today’s minimum wage in the US.

What did inventions such as the spinning jenny do? The first spinning jennies had eight spindles. One machine operated by just one adult therefore replaced eight spinsters working on eight spinning wheels. By the late nineteenth century, a single spinning mule operated by a very small number of people could replace more than 1,000 spinsters. These machines did not rely on human energy, but were powered first by water wheels, and later by coal-powered steam engines. Figure 2.9 summarizes these changes that happened in the Industrial Revolution.

Figure 2.9 The change in spinning technology during the Industrial Revolution.

The model in the previous section provides a hypothesis (potential explanation) for why someone would bother to invent such a technology, and why someone would want to use it. In this model, producers of cloth chose between technologies using just two inputs—energy and labour. This is a simplification, but it shows the importance of the relative costs of inputs for the choice of technology. When the cost of labour increased relative to the cost of energy, there were innovation rents to be earned from a switch to the energy-intensive technology.

This is just a hypothesis. Is it actually what happened? Looking at how relative prices differed among countries, and how they changed over time, can help us understand why technologies such as the spinning jenny were invented in Britain rather than elsewhere, and in the eighteenth century rather than at an earlier time.

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Figure 2.10 Wages relative to the price of energy (early 1700s).

Page 140 of Robert C. Allen. 2008. The British Industrial Revolution in Global Perspective. Cambridge: Cambridge University Press.

Figure 2.10 shows the price of labour relative to the price of energy in various cities in the early 1700s—specifically, the wages of building labourers divided by the price of 1 million BTU (British Thermal Units, a unit of energy equivalent to slightly more than 1,000 joules). You can see that labour was more expensive relative to the cost of energy in England and the Netherlands than in France (Paris and Strasbourg), and much more so than in China.

Wages relative to the cost of energy were high in England, both because English wages were higher than wages elsewhere, and because coal was cheaper in coal-rich Britain than in the other countries in Figure 2.10.

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Figure 2.11 Wages relative to the cost of capital goods (late sixteenth to the early nineteenth century).

Page 138 in Robert C. Allen. 2008. The British Industrial Revolution in Global Perspective. Cambridge: Cambridge University Press.

Figure 2.11 shows trends in the cost of labour relative to the cost of capital goods in England and France, from the late sixteenth to the early nineteenth century. It shows the wages of building labourers divided by the cost of using capital goods. This cost is calculated from the prices of metal, wood, and brick, the cost of borrowing, and takes account of the rate at which the capital goods wear out, or depreciate.

As you can see, wages relative to the cost of capital goods were similar in England and France in the mid-seventeenth century but from then on, in England but not in France, workers became steadily more expensive relative to capital goods. In other words, the incentive to replace workers with machines was increasing in England during this time, but this was not true in France. In France, the incentive to save labour by innovating had been stronger during the late sixteenth century than it was 200 years later, at the time the Industrial Revolution began to transform Britain.

From the model in the previous section we learned that the technology chosen depends on relative input prices. Combining the predictions of the model with the historical data, we have one explanation for the timing and location of the Industrial Revolution:

• Wages relative to the cost of energy and capital goods rose in the eighteenth century in Britain compared with earlier historical periods.
• Wages relative to the cost of energy and capital goods were higher in Britain during the eighteenth century than elsewhere.

No doubt it helped, too, that Britain was such an inventive country. There were many skilled workmen, engineers and machine makers who could build the machines that inventors designed.

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Technology in the 1600s

In the 1600s, the relative prices are shown by isocost line HJ. The B-technology was used. At those relative prices, there was no incentive to develop a technology like A, which is outside the isocost line HJ.

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Technology in the 1700s

In the 1700s, the isocost lines such as FG were much steeper, because the relative price of labour to coal was higher. The relative cost was sufficiently high to make the A-technology lower cost than the B-technology.

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Why is technology A lower cost?

We know that when the relative price of labour is high, technology A is lower cost because the B-technology lies outside the isocost line FG.

Watch our video in which Bob Allen, an economic historian, explains his theory of why the Industrial Revolution occurred when and where it did.

1. Summarize Allen’s claim using the concept of economic rents. Which ceteris paribus assumptions are you making?
2. What other important factors may explain the rise of energy-intensive technologies in Britain in the eighteenth century?

The relative prices of labour, energy and capital can help to explain why the labour-saving technologies of the Industrial Revolution were first adopted in England, and why at that time technology advanced more rapidly there than on the continent of Europe, and even more rapidly compared with Asia.

What explains the eventual adoption of these new technologies in countries like France and Germany, and ultimately China and India? One answer is further technological progress, where a new technology is developed that dominates the existing one in use. Technological progress would mean that it would take smaller quantities of inputs to produce 100 metres of cloth. We can use the model to illustrate this. In Figure 2.13, technological progress leads to the invention of a superior energy-intensive technology, labelled A′. The analysis in Figure 2.13 shows that once the A′-technology is available, it would be chosen both in countries using A, and in those using B.

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Energy- or labour-intensive?

Where the relative price of labour is high, the energy-intensive technology, A, is chosen. Where the relative price of labour is low, the labour-intensive technology, B, is chosen.

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An improvement in technology

Improvements in cloth-making technology occur, resulting in a new technology, labelled A′. This technology uses only half as much energy per worker to produce 100 metres of cloth. The new technology dominates the A-technology.

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A′ is least-cost

The A′ technology is cheaper than both A and B, both in countries where wages are relatively high (isocost line FG) and in low-wage, expensive-energy economies (isocost line HJ). The new labour- and energy-saving technology, A′, is inside FG and HJ, so it will be adopted in both economies.

A second factor that promoted the diffusion across the world of the new technologies was wage growth and falling energy costs (due, for example, to cheaper transportation, allowing countries to import energy cheaply from abroad). This made isocost lines steeper in poor countries, again providing an incentive to switch to a labour-saving technology.12

Either way, the new technologies spread, and the divergence in technologies and living standards was eventually replaced by convergence—at least among those countries where the capitalist revolution had taken off.13

Nevertheless, in some countries we still observe the use of technologies that were replaced in Britain during the Industrial Revolution. The model predicts that the relative price of labour must be very low in such situations, making the isocost line very flat. The B-technology could be preferred in Figure 2.13 even when the A′-technology is available if the isocost line is flatter than HJ, so that it goes through B but below A′.

Look again at Figure 2.12 which depicts isocost lines for the 1600s and the 1700s in Britain.

Which of the following is true?

• The flatter isocost line HJ for 1600s Britain indicates higher wages relative to the price of coal.
• The increase in wages relative to the cost of energy in the 1700s is represented by the outward shift of the isocost line from HJ to the parallel isocost line going through A.
• Had the wage level fallen together with the falling energy costs (due for example to cheaper transportation), then 1700s Britain would definitely have stayed with technology B.
• The comparison between isocost line FG and the parallel isocost going through B suggests that an innovation rent was earned in 1700s Britain when firms moved from technology B to A.

• The slope of the isocost line is the negative of the price ratio, −(wage/price of coal). A flatter isocost line indicates lower wages relative to the price of coal.
• An increase in the level of wages relative to the cost of energy would lead to a steeper isocost line.
• The relative price matters, not the absolute level. So if wages fall, but by relatively less than the energy costs so that the price ratio still increases, then technology A may still be the better choice.
• The comparison between these two lines shows that that the cost of producing is lower at A than at B. Therefore, firms adopting technology A enjoy some profit in excess of that which they earned with the alternative: an innovation rent.

Read David Landes’ answer to this question, and this summary of research on the great divergence to discuss why the Industrial Revolution happened in Europe rather than in Asia, and in Britain rather than in Continental Europe.

1. Which arguments do you find most persuasive, and why?
2. Which arguments do you find least persuasive, and why?

2.7 Malthusian economics: Diminishing average product of labour

The historical evidence supports our model that uses relative prices and innovation rents to provide a simple account of the timing and the geographical spread of the permanent technological revolution.14

This is part of the explanation of the upward kink in the hockey stick. Explaining the long flat part of the stick is another story, requiring a different model.

Malthus provided a model of the economy that predicts a pattern of economic development consistent with the flat part of the GDP per capita hockey stick from Figure 1.1a in Unit 1. His model introduces concepts that are used widely in economics. One of the most important concepts is the idea of diminishing average product of a factor of production.

Diminishing average product of labour

To understand what this means, imagine an agricultural economy that produces just one good, grain. Suppose that grain production is very simple—it involves only farm labour, working on the land. In other words, ignore the fact that grain production also requires spades, combine harvesters, grain elevators, silos, and other types of buildings and equipment.

Labour and land (and the other inputs that we are ignoring) are called factors of production, meaning inputs into the production process. In the model of technological change above, the factors of production are energy and labour.

We will use a further simplifying ceteris paribus assumption: that the amount of land is fixed and all of the same quality. Imagine that the land is divided into 800 farms, each worked by a single farmer. Each farmer works the same total hours during a year. Together, these 800 farmers produce a total of 500,000 kg of grain. The average product of a farmer’s labour is:

This describes the relationship between the amount of output produced and the amounts of inputs used to produce it.

To understand what will happen when the population grows and there are more farmers on the same limited space of farmland, we need something that economists call the production function for farming. This indicates the amount of output produced by any given number of farmers working on a given amount of land. In this case, we are holding constant all of the other inputs, including land, so we only consider how output varies with the amount of labour.

In the previous sections, you have already seen very simple production functions that specified the amounts of labour and energy necessary to produce 100 metres of cloth. For example, in Figure 2.3, the production function for technology B says that if 4 workers and 2 tonnes of coal are put into production, 100 metres of cloth will be the output. The production function for technology A gives us another ‘if-then’ statement: if 1 worker and 6 tonnes of coal are put into production using this technology, then 100 metres of cloth will be the output. The grain production function is a similar ‘if-then’ statement, indicating that if there are X farmers, then they will harvest Y grain.

Figure 2.14a lists some values of labour input and the corresponding grain production. In the third column we have calculated the average product of labour. In Figure 2.14b, we draw the function, assuming that the relationship holds for all farmers and grain production amounts in between those shown in the table.

Leibniz: Malthusian Economics: Diminishing Average Product of Labour

We call this a production function because a function is a relationship between two quantities (inputs and outputs in this case), expressed mathematically as:

We say that ‘Y is a function of X’. X in this case is the amount of labour devoted to farming. Y is the output in grain that results from this input. The function f(X) describes the relationship between X and Y, represented by the curve in the figure.

Figure 2.14a Recorded values of a farmer’s production function: Diminishing average product of labour.

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The farmers’ production function

The production function shows how the number of farmers working the land translates into grain produced at the end of the growing season.

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Output when there are 800 farmers

Point A on the production function shows the output of grain produced by 800 farmers.

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Output when there are 1,600 farmers

Point B on the production function shows the amount of grain produced by 1,600 farmers.

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The average product diminishes

At A, the average product of labour is 500,000 ÷ 800 = 625 kg of grain per farmer. At B, the average product of labour is 732,000 ÷ 1,600 = 458 kg of grain per farmer.

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The slope of the ray is the average product

The slope of the ray from the origin to point B on the production function shows the average product of labour at point B. The slope is 458, meaning an average product of 458 kg per farmer when 1,600 farmers work the land.

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The ray to A is steeper than the ray to B

The slope of the ray to point A is steeper than to point B. When only 800 farmers work the land there is a higher average product of labour. The slope is 625, the average product of 625 kg per farmer that we calculated previously.

In Unit 1 we explained that the economy is part of the biosphere. Think of farming biologically.

1. Find out how many calories a farmer burns, and how many calories are contained in 1 kg of grain.
2. Does farming produce a surplus of calories—more calories in the output than used up in the work input—using the production function in Figure 2.14b?

Our grain production function is hypothetical, but it has two features that are plausible assumptions about how output depends on the number of farmers:

Labour combined with land is productive. No surprises there. The more farmers there are, the more grain is produced; at least up to a certain point (3,000 farmers, in this case).

As more farmers work on a fixed amount of land, the average product of labour falls. This diminishing average product of labour is one of the two foundations of Malthus’ model.

Remember that the average product of labour is the grain output divided by the amount of labour input. From the production function in Figure 2.14b, or the table in Figure 2.14a (both show the same information) we see that an annual input of 800 farmers working the land brings an average per-farmer output of 625 kg of grain, while increasing the labour input to 1,600 farmers produces an average output per farmer of 458 kg. The average product of labour falls as more labour is expended on production. This worried Malthus.

To see why he was worried, imagine that, a generation later, each farmer has had many children, so that instead of a single farmer working each farm, there are now two farmers working. The total labour input into farming was 800, but is now 1,600. Instead of a harvest of 625 kg of grain per farmer, the average harvest is now only 458 kg.

You might argue that in the real world, as the population grows, more land can be used for farming. But Malthus pointed out that earlier generations of farmers would have picked the best land, so any new land would be worse. This also reduces the average product of labour.

So diminishing average product of labour can be caused by:

• more labour devoted to a fixed quantity of land
• more (inferior) land brought into cultivation

Because the average product of labour diminishes as more labour is devoted to farming, their incomes inevitably fall.

Look again at Figure 2.14b which depicts the production function of grain for farmers under average growing conditions with the currently available technology.

We can ascertain that:

• In a year with exceptionally good weather conditions, the production function curve will be higher and parallel to the curve above.
• A discovery of new high-yielding crop seeds would tilt the production function curve higher, pivoted anti-clockwise at the origin.
• In a year of bad drought, the production curve can slope downwards for large numbers of farmers.
• If there is an upper limit on the amount of grain that can be produced, then the curve will end up horizontal for large numbers of farmers.

• Zero farmers means zero output. Therefore, all curves must start at the origin, and cannot shift upwards or downwards in a parallel manner.
• Such a discovery would increase the kilogrammes of grain produced for any given number of farmers (except zero); this can be represented graphically as an anti-clockwise pivot in the production function curve.
• A downward-sloping curve implies decreasing output as the number of farmers increases. This would only be the case if the additional labourers have negative effects on the productivity of the existing labourers, which we normally rule out.
• An upper limit implies that additional farmers would not yield any additional kilogrammes of grain, which would be represented graphically by a flat production function past the upper limit.

History, instability, and growthInnovation

2.8 Malthusian economics: Population grows when living standards rise

On its own, the diminishing average product of labour does not 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 say anything about why, over long periods, living standards and population didn’t change much. For this we need the other part of Malthus’s model: his argument that increased living standards create a population increase.

Malthus was not the first person to have this idea. Years before Malthus developed his theories, Richard Cantillon, an Irish economist, had stated that, ‘Men multiply like mice in a barn if they have unlimited means of subsistence.’

Malthusian theory essentially regarded people as being not that different from other animals:

Elevated as man is above all other animals by his intellectual facilities, it is not to be supposed that the physical laws to which he is subjected should be essentially different from those which are observed to prevail in other parts of the animated nature.15

So the two key ideas in Malthus’ model are:

• the law of diminishing average product of labour
• population expands if living standards increase

Imagine a herd of antelopes on a vast and otherwise empty plain. Imagine also that there are no predators to complicate their lives (or our analysis). 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 amount of land per animal declines, their living standards will start to fall. This reduction in living standards will continue as long as the herd continues to increase in size.

Since each animal has less food to eat, the antelopes will have fewer offspring and die younger so population growth will slow down. Eventually, living standards will fall to the point where the herd is no longer increasing in size. The antelopes have filled up the plain. At this point, each animal will be eating an amount of food that we will define as the subsistence level. When the animals’ living standards have been forced down to subsistence level as a result of population growth, the herd is no longer getting bigger.

If antelopes eat less than the subsistence level, the herd starts to get smaller. And when consumption exceeds the subsistence level, the herd grows.

Much of the same logic would apply, Malthus reasoned, to a human population living in a country with a fixed supply of agricultural land. While people are well-fed they would multiply like Cantillon’s mice in a barn; 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.

Malthus’s model results in an equilibrium in which there is an income level just sufficient to allow a subsistence level of consumption. The variables that stay constant in this equilibrium are:

• the size of the population
• the income level of the people

If conditions change, then population and incomes may change too, but eventually the economy will return to an equilibrium with income at subsistence level.

Malthus wrote: ‘[I]t is not to be supposed that the physical laws to which [mankind] is subjected should be essentially different from those which are observed to prevail in other parts of the animated nature.’

Do you agree? Explain your reasoning.

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’ model explain this?

Figure 2.15 illustrates how the combination of diminishing average product of labour and the effect of higher incomes on population growth mean that in the very long run, technological improvements will not result in higher income for farmers. In the figure, things on the left are causes of things to the right.

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Figure 2.15 Malthus’ model: The effect of an improvement in technology.

Beginning from equilibrium, with income at subsistence level, a new technology such as an improved seed raises income per person on the existing fixed quantity of land. Higher living standards lead to an increase in population. As more people are added to the land, diminishing average product of labour means average income per person falls. Eventually incomes return to subsistence level, with a higher population.

Why is the population higher at the new equilibrium? Output per farmer is now higher for each number of farmers. Population does not fall back to the original level, because income would be above subsistence. A better technology can provide subsistence income for a larger population.

The Einstein at the end of this section shows how to represent Malthus’ model graphically, and how to use it to investigate the effect of a new technology.

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 amount of land
• population grows in response to increases in real wages

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

Malthus’s argument is summarized in Figure 2.16, using two diagrams.

The downward-sloping line in the left-hand figure shows that the higher the population, the lower the level of wages, due to the diminishing average product of labour. The upward-sloping line on the right shows the relationship between wages and population growth. When wages are high, population grows, because higher living standards lead to more births and fewer deaths.

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Left-hand diagram: How wages depend on the population level

At a medium population level, the wage of people who work the land is at subsistence level (point A). The wage is higher at point B, where the population is smaller, because the average product of labour is higher.

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Right-hand diagram: How population growth depends on living standards

The line in the right-hand diagram slopes upward, showing that when wages (on the vertical axis) are high, population growth (on the horizontal axis) is positive (so the population will rise). When wages are low, population growth is negative (population falls).

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Linking the two diagrams

At point A, on the left, population is medium-sized and the wage is at subsistence level. Tracing across to point A′ on the right shows that population growth is equal to zero. So if the economy is at point A, it is in equilibrium: population stays constant and wages remain at subsistence level.

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A lower population

Suppose the economy is at B, with a higher wage and lower population. Point B′, on the right, shows that the population will be rising.

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The economy returns to equilibrium

As the population rises, the economy moves down the line in the left diagram: wages fall until they reach equilibrium at A.

The two diagrams together explain the Malthusian population trap. Population will be constant when the wage is at subsistence level, it will rise when the wage is above subsistence level, and it will fall when the wage is below subsistence level.

Figure 2.17 shows how the Malthusian model predicts that even if productivity increases, living standards in the long run do not.

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Initially the economy is in equilibrium

The economy starts at point A, with a medium-sized population and wage at subsistence level.

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An advance in technology—wages rise

A technological improvement (for example, better seeds) raises the average product of labour, and the wage is higher for any level of population. The real wage line shifts upward. At the initial population level, the wage increases and the economy moves to point D.

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Population begins to rise

At point D, the wage has risen above subsistence level and therefore the population starts to grow (point D′).

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Population increases

As population rises, the wage falls, due to the diminishing average product of labour. The economy moves down the real-wage curve from D.

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C is the equilibrium with the new technology

At C, the wage has reached subsistence level again. The population remains constant (point C′). The population is higher at equilibrium C than it was at equilibrium A.

Imagine that the population growth curve in the right panel of Figure 2.16 shifted to the left (with fewer people being born, or more people dying, at any level of wages). Explain what would happen to living standards describing the transition to the new equilibrium.

History, instability, and growthInnovation

2.9 The Malthusian trap and long-term economic stagnation

The major long-run impact of better technology in this Malthusian world was therefore more people. The writer H. G. Wells, author of War of the Worlds, wrote in 1905 that humanity ‘spent the great gifts of science as rapidly as it got them in a mere insensate multiplication of the common life’.

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 real wages led young couples to marry earlier and have more children, and they also led to lower death rates. Population growth eventually forced real wages 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.

As with our model of innovation rents, relative prices and technological improvements, we need to ask: can we find evidence to support the central prediction of the Malthusian model, that incomes will return to subsistence level?

Figure 2.18 is consistent with what Malthus predicted. From the end of the thirteenth century to the beginning of the seventeenth century, Britain oscillated between periods of higher wages, leading to larger populations, leading to lower wages, leading to smaller populations, leading to … and so on, a vicious circle.

We get a different view of the vicious circle by taking Figure 2.18 and focusing on the period between 1340 and 1600, shown in Figure 2.19. As a result of the outbreak of bubonic plague known as the Black Death, from 1349 to 1351 between a quarter and a third of Europe’s population died. The lower part of the figure shows the causal linkages that led to the effects we see in the top part.

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Figure 2.18 The Malthusian trap: Wages and population (1280s–1600s).

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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A Malthusian economy in England (1300–1600)

In this figure, we examine the Malthusian economy that existed in England between the years 1300 and 1600, highlighted above.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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The Black Death (1348–50)

The bubonic plague of 1348–50 was known as the Black Death. It killed 1.5 million people out of an estimated English population of 4 million, leading to a dramatic fall in labour supply.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Wages rose following the plague

This decline in the population 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.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Farmers and workers used their power

In 1351, King Edward III of England tried to limit wage rises by law, helping to cause a period of rebellions against authority, notably the Peasants’ Revolt of 1381. Despite the King’s actions, incomes continued to increase.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Population increased in the sixteenth century

By the middle of the fifteenth century, the real wages of English building workers had doubled. Increased wages helped the population to recover in the sixteenth century, but Malthus’ law asserted itself: as the population increased, incomes fell.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Malthusian stagnation (1350–1600)

By 1600, real wages had fallen to the level they were 300 years previously.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Cause and effect in Malthusian economics

Our model of Malthusian economics helps to explain the rise and fall of incomes between 1300 and 1600 in England.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

The decline of the number of people working on farms during the Black Death raised agricultural productivity according to the principle of diminishing average product of labour. Farmers were better off, whether they owned their land or paid a fixed rent to a landlord. Employers in cities had to offer higher wages too, to attract workers from rural areas.

The causal links in Figure 2.19 combine the two features of the Malthusian model with the role of political developments as responses to, and causes of changes in, the economy. When, in 1349 and 1351, King Edward passed laws to try to restrain wage increases, economics (the reduced labour supply) won out over politics: wages continued to rise, and peasants began to exercise their increased power, notably by demanding more freedom and lower taxes in the Peasants’ Revolt of 1381.

But when the population recovered in the sixteenth century, labour supply increased, lowering wages. Based on this evidence, the Malthusian explanation is consistent with the history of England at this time.

Look again at Figure 2.1 and Figure 2.19 showing graphs of real wages in England between 1300 and 2000.

You are also told the following facts:

During the bubonic plague of 1348 and 1351, between one-quarter and one-third of Europe’s population died.

In the seventeenth and eighteenth centuries, the wages of unskilled workers relative to the incomes of land owners were only one-fifth of what they had been in the sixteenth century.

What can we conclude from this information?

• According to the Malthusian model, the fall in the population due to the bubonic plague would have led to an increase in the average productivity of workers, causing the observed rise in the real wage post-plague.
• The doubling and halving of the real wage index over 250 years from around 1350 is contrary to the Malthusian model.
• The fall in the unskilled workers’ share of total output in the seventeenth and eighteenth centuries was due to the fall in their average product of labour.
• The fall in the relative wages of the unskilled workers in the seventeenth and eighteenth centuries was one of the factors that led to the eventual shooting up of the real wage in the nineteenth century, seen in the graph.

• In the Malthusian model, fewer workers means higher average productivity, increasing output per capita. Given that their bargaining power did not remain constant but actually increased, workers claimed a larger share of this output and real wages rose.
• According to the Malthusian model, the increase in population caused by the rise in real wages would have led to a decrease in average productivity, leading to an eventual fall in the real wage back down to subsistence level. This seems to be what is observed in the graph.
• The average product of labour determines the size of the pie (the total output), but what share of this is claimed by the workers is determined by their bargaining power, which diminished over the Malthusian cycles in the graph.
• On the contrary, wage growth happened in spite of the low wages relative to the incomes of the land owners. The key to this process was that wages remained high compared to the prices of energy and capital goods, leading to innovation for less labour-intensive technology.

Real wages also rose sharply following the Black Death in other places for which we have evidence, such as Spain, Italy, Egypt, the Balkans, and Constantinople (present-day Istanbul).16

1. How does the growth of real wages compare with the growth of real GDP per capita as a measure of economic progress?
2. Try out your arguments on others. Do you agree or not? If you disagree, are there any facts that could resolve your disagreement, and what are they? If there are not, why do you disagree?

We have focused on farmers and wage earners, but not everyone in the economy would be caught in a Malthusian trap. As population continues to grow, the demand for food also grows. Therefore the limited amount of land used to produce the food should become more valuable. In a Malthusian world, a rising population should therefore lead to an improvement in the relative economic position of landowners.

This occurred in England: Figure 2.19 shows that real wages did not increase in the very long run (they were no higher in 1800 than in 1450). And the income gap between landowners and workers increased. In the seventeenth and eighteenth centuries, the wages of unskilled English workers, relative to the incomes of landowners, were only one-fifth of what they had been in the sixteenth century.

But while wages were low compared to the rents of landlords, a different comparison of relative prices was the key to England’s escape from the Malthusian trap: wages remained high compared to the price of coal (Figure 2.10) and even increased compared to the cost of using capital goods (Figure 2.11), as we have seen.

History, instability, and growthInequalityInnovation

2.10 Escaping from Malthusian stagnation

Nassau Senior, the economist who lamented that the numbers perishing in the Irish famine would scarcely be enough to do much good, does not appear compassionate. But he and Malthus were right to think that population growth and a diminishing average product of labour could create a vicious circle of economic stagnation and poverty. However, the hockey-stick graphs of living standards show they were wrong to believe that this could never change.

They did not consider the possibility that improvements in technology could happen at a faster rate than population growth, offsetting the diminishing average product of labour.

The permanent technological revolution, it turns out, means that the Malthusian model is no longer a reasonable description of the world. Average living standards increased rapidly and permanently after the capitalist revolution.

Figure 2.20 shows the real wage and population data from the 1280s to the 1860s. As we saw in Figure 2.18, from the thirteenth to the sixteenth century there was a clear negative relationship between population and real wages: when one went up the other went down, just as Malthusian theory suggests.

Between the end of the sixteenth and the beginning of the eighteenth century, although wages rose there was relatively little population growth. Around 1740, we can see the Malthusian relationship again, labelled ‘18th century’. Then, around 1800, the economy moved to what appears to be an entirely new regime, with both population and real wages simultaneously increasing. This is labelled ‘Escape’.

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Figure 2.20 Escaping the Malthusian trap.

Robert C. Allen. 2001. The Great Divergence in European Wages and Prices from the Middle Ages to the First World War. Explorations in Economic History 38 (4): pp. 411–447.

Figure 2.21 zooms in on this ‘great escape’ portion of the wage data.

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Escaping the Malthusian trap

In the eighteenth century, the Malthusian relationship persisted. In the nineteenth century, the economy appears to become a non-Malthusian regime, with real wages rising while population was increasing.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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The permanent technological revolution

The story begins with technological improvements, such as the spinning jenny and the steam engine, that increased output per worker. Innovation continued as the technological revolution became permanent, displacing thousands of spinsters, weavers and farmers.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Urban unemployment

The loss of employment reduced workers’ bargaining power, keeping wages low, seen in the flat line between 1750 and 1830. The size of the pie was increasing, but the workers’ slice was not.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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New opportunities

In the 1830s, higher productivity and low wages led to a surge in profits. Profits, competition, and technology drove businesses to expand. The demand for labour went up. People left farming for jobs in the new factories.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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Workers’ bargaining power

The supply of labour fell when business owners were stopped from employing children. The combination of higher labour demand and lower supply enhanced workers’ bargaining power.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

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The escape from Malthusianism

The power of working people increased as they gained the right to vote and formed trade unions. These workers were able to claim a constant or rising share of the increases in productivity generated by the permanent technological revolution.

Robert C. Allen. 2001. ‘The Great Divergence in European Wages and Prices from the Middle Ages to the First World War’. Explorations in Economic History 38 (4): pp. 411–447.

The story of the permanent technological revolution demonstrates that there are two influences on wages.

• How much is produced: we can think of this as the size of the pie to be divided between workers and the owners of other inputs (land or machines).
• The share going to workers: This depends on their bargaining power, which in turn depends on how wages are determined (individually, or through bargaining with trade unions, for example) and the supply and demand for workers. If many workers are competing for the same job, wages are likely to be low.

After 1830, the pie continued growing, and the workers’ share grew along with it.

Britain had escaped from the Malthusian trap. This process would soon be repeated in other countries, as Figures 1.1a and 1.1b showed.

Look again at Figure 2.20, which plots real wages against population in England from the 1280s to the 1860s.

According to Malthus, with diminishing average product of labour in production and population growth in response to increases in real wages, an increase in productivity will result in a larger population but not higher real wages in the long run. Based on the information above, which of the following statements is correct?

• Between the 1800s and the 1860s, population grows as real wages rise. This is entirely in line with Malthus’s description of the economy’s growth.
• There is a clear evidence of a persistent and continuous Malthusian trap between the 1280s and the 1800s.
• The Malthusian traps seem to occur in a cycle of 60 years.
• The Malthusian model does not take into account the possibility of a persistent positive technology shock that may offset the diminishing average product of labour.

• It is true that Malthus assumes population growth in response to real wage increases. However, as population increases the average per capita output falls, resulting in a fall in real wages back to subsistence level. This is not evident in the graph post-1800s.
• There are actually two periods—between the 1280s and the 1590s, and between the 1740s and the 1800s—when a Malthusian trap is evident. There is, however, the period in between when the negative relationship between the real wage and population seems to break down (no population growth despite the wage increase).
• Though the second cycle of the Malthusian trap lasted about 60 years (between the 1740s and the 1800s), the first cycle seems to have lasted around 300 years.
• If technological developments increase the average productivity of labour faster than population growth decreases it, then population growth and real wages can coexist. This is what is shown by the escape trajectory of the English economy after the eighteenth century.

The escape from the Malthusian trap, in which technological progress outstripped the effects of population growth, took place following the emergence of capitalism. Consider the three basic institutions of capitalism in turn:

1. Why is private property important for technological progress to occur?
2. Explain how markets can provide both carrots and sticks to encourage innovation.
3. How can production in firms, rather than families, contribute to the growth of living standards?

2.11 Conclusion

We have introduced an economic model in which firms’ choice of production technologies depends on the relative prices of inputs, and the economic rent from adopting a new technology provides an incentive for firms to innovate. Testing this model against historical evidence shows that it could help to explain why the Industrial Revolution occurred in Britain in the eighteenth century.

We showed how the Malthusian model of a vicious circle, in which population growth offset temporary gains in income, could explain stagnation in living standards for centuries before the Industrial Revolution, until the permanent technological revolution allowed an escape due to improvements in technology.

Before you move on, review these definitions:

2.12 References

Consult CORE’s Fact checker for a detailed list of sources.

• Allen, Robert C. 2009. ‘The Industrial Revolution in Miniature: The Spinning Jenny in Britain, France, and India’. The Journal of Economic History 69 (04) (November): p. 901.
• Allen, Robert C. 2011. Global Economic History: A Very Short Introduction. New York, NY: Oxford University Press.
• Clark, Gregory. 2007. A Farewell to Alms: A Brief Economic History of the World. Princeton, NJ: Princeton University Press.
• Davis, Mike. 2000. Late Victorian holocausts: El Niño famines and the Making of the Third World. London: Verso Books.
• Landes, David S. 1990. ‘Why are We So Rich and They So Poor?’. American Economic Review 80 (May): pp. 1–13.
• Landes, David S. 2003. The Unbound Prometheus: Technological Change and Industrial Development in Western Europe from 1750 to the Present. Cambridge, UK: Cambridge University Press.
• Landes, David S. 2006. ‘Why Europe and the West? Why not China?’. Journal of Economic Perspectives 20 (2) (June): pp. 3–22.
• Lee, James, and Wang Feng. 1999. ‘Malthusian models and Chinese realities: The Chinese demographic system 1700–2000’. Population and Development Review 25 (1) (March): pp. 33–65.
• Malthus, Thomas R. 1798. An Essay on the Principle of Population. London: J. Johnson, in St. Paul’s Church-yard. Library of Economics and Liberty.
• Malthus, Thomas R. 1830. A Summary View on the Principle of Population. London: J. Murray
• McNeill, William Hardy H. 1976. Plagues and Peoples. Garden City, NY: Anchor Press.
• Mokyr, Joel. 2004. The Gifts of Athena: Historical Origins of the Knowledge Economy, 5th ed. Princeton, NJ: Princeton University Press.
• Pomeranz, Kenneth L. 2000. The Great Divergence: Europe, China, and the Making of the Modern World Economy. Princeton, NJ: Princeton University Press.
• Schumpeter, Joseph A. 1949. ‘Science and Ideology’. The American Economic Review 39 (March): pp. 345–59.
• Schumpeter, Joseph A. 1962. Capitalism, Socialism, and Democracy. New York: Harper & Brothers.
• Schumpeter, Joseph A. 1997. Ten Great Economists. London: Routledge.
• Skidelsky, Robert. 2012. ‘Robert Skidelsky—portrait: Joseph Schumpeter’. Updated 1 December 2007.