THEMES AND CAPSTONE UNITS
17: History, instability, and growth
18: Global economy
19: Inequality
21: Innovation
UNIT 2
TECHNOLOGY, POPULATION,
AND GROWTH
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.
Automated assembly process
43
Industrial Revolution A wave of
technological advances and
organizational changes starting in
Britain in the eighteenth century,
which transformed an agrarian and
craft-based economy into a
commercial and industrial eco-
nomy.
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 Popula-
tion, first published in 1798.
Malthus held that a sustained increase in income per capita would be
impossible.
His logic was that, even if technology improved and raised the pro-
ductivity 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’.
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 Indus-
trial 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.
Thomas R. Malthus. 1798. An Essay
on the Principle of Population
(https://tinyco.re/8473883). Library
of Economics and Liberty. London:
J. Johnson, in St. Paul’s Church-
yard.
Mike Davis. 2000. Late Victorian
holocausts: El Niño famines and
the making of the Third world.
London: Verso Books.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
44
general-purpose technologies
Technological advances that can
be applied to many sectors, and
spawn further innovations. Inform-
ation and communications
technology (ICT), and electricity are
two common examples.
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 Revolu-
tion, 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.
Figure 2.1 shows an index of the average real wage (the money wage in
each year, adjusted for changes in prices) of skilled craftsmen in London
from 1264 to 2001, plotted together with the population of Britain over the
same period. There is a long period in which living standards were trapped
Malthusian trap
Smith Malthus
Escape
0
200
400
600
800
0
15
30
45
60
1260 1300 1400 1500 1600 1700 1800 1900 2000
Year
Re
al
w
ag
e
in
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(1
85
0
=
10
0)
Po
pu
la
tio
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(m
ill
io
ns
)
Population in Britain
Real wage
Figure 2.1 Real wages over seven centuries: Wages of craftsmen (skilled workers) in
London (1264–2001), and the population of Britain.
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; Stephen
Broadberry, Bruce Campbell, Alexander
Klein, Mark Overton and Bas van
Leeuwen. 2015. British Economic
Growth, 1270–1870, Cambridge Univer-
sity Press.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
45
INDEX OF REAL WAGES
The term ‘index’ means the value of
some quantitative amount relative
to its value at some other time (the
reference period) which is usually
normalized to 100.
The term ‘real’ means that the
money wage (say, six shillings per
hour at the time) in each year has
been adjusted to take account of
changes in prices over time. The
result represents the real buying
power of the money the workers
earned.
The reference year is 1850 in this
case, but the curve would have the
same shape if any other year had
been selected. It would be
positioned higher or lower, but
would still look like our familiar
hockey stick.
according to Malthusian logic, followed by a dramatic increase after 1830.
You can see that at the time both were increasing.
QUESTION 2.1 CHOOSE THE CORRECT ANSWER(S)
Figure 2.1 (page 45) shows an index of average real wages of skilled
workers in London between 1264 and 2001. What can we conclude
from this graph?
Skilled workers were paid about £100 in 1408.
The average wage in 1850 was about the same as that in 1408 in
nominal terms (pounds).
The average real wage was more or less constant between 1264
and 1850.
The average real wage increased by around 600% between 1850
and 2001.
Why did the spinning jenny, the steam engine, and a cluster of other
inventions emerge and spread across the economy in Britain at this time?
This is one of the most important questions in economic history, and
historians continue to argue about it.
In this unit we examine one explanation of how these improvements in
technology came about, and why they first occurred in Britain only, and
during the eighteenth century. We will also explore why the long flat part of
Figure 2.1’s hockey stick proved so hard to escape not only in Britain, but
also throughout the world in the 200 years that followed. We will do this by
building models: simplified representations that help us to understand what
is going on by focusing attention on what is important. Models will help us
understand both the kink in the hockey stick and the long flat handle.
•••2.1 ECONOMISTS, HISTORIANS, AND THE INDUSTRIAL
REVOLUTION
Why did the Industrial Revolution happen first in the eighteenth century,
on an island off the coast of Europe?
The following sections of this unit present one model for the sudden and
dramatic rise in living standards that began in eighteenth century Britain.
Based on arguments from Robert Allen, an economic historian, this model
gives a central role to two features of Britain’s economy at the time. In this
account, the relatively high cost of labour, coupled with the low cost of local
energy sources, drove the structural changes of the Industrial Revolution.
What we call the Industrial Revolution was more than just the breaking
of the Malthusian cycle: it was a complex combination of inter-related
intellectual, technological, social, economic and moral changes. Historians
and economists disagree about the relative importance of each of these
elements, and have wrestled with explanations for the primacy of Britain,
and Europe more generally, ever since their revolutions began. Allen’s
explanation is far from the only one.
Robert C. Allen. 2011. Global Eco-
nomic History: A Very Short
Introduction. New York, NY: Oxford
University Press.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
46
• Joel Mokyr, who has worked extensively on the history of technology,
claims that the real sources of technological change are to be found in
Europe’s scientific revolution and its Enlightenment of the century
before. For Mokyr, this period brought the development of new ways to
transfer and transform elite scientific knowledge into practical advice
and tools for the engineers and skilled artisans, who used it to build the
machines of that time. He claims that, while wages and energy prices
might tilt the direction of invention in one direction or another, they are
more like a steering wheel than the motor of technological progress.
• David Landes, a historian, emphasizes the political and cultural
characteristics of nations as a whole (Mokyr, in contrast, focuses on
artisans and entrepreneurs). He suggests European countries pulled
ahead of China because the Chinese state was too powerful and stifled
innovation, and because Chinese culture at the time favoured stability
over change.
• Gregory Clark, an economic historian, also attributes Britain’s take-off
to culture. But for Clark, the keys to success were cultural attributes
such as hard work and savings, which were passed on to future
generations. Clark’s argument follows a long tradition that includes the
sociologist Max Weber, who saw the Protestant countries of northern
Europe, where the Industrial Revolution began, as the particular home
of virtues associated with the ‘spirit of capitalism’.
• Kenneth Pomeranz, a historian, claims that superior European growth
after 1800 was more due to the abundance of coal in Britain than to any
cultural or institutional differences with other countries. Pomeranz also
argues that Britain’s access to agricultural production in its New World
colonies (especially sugar and its by-products) fed the expanding class of
industrial workers, thus helping them to escape the Malthusian trap.
Scholars will probably never completely agree about what caused the
Industrial Revolution. One problem is that this change happened only once,
which makes it more difficult for social scientists to explain. Also, the
European take-off was probably the result of a combination of scientific,
demographic, political, geographic and military factors. Several scholars
argue that it was partly due to interactions between Europe and the rest of
the world too, not just due to changes within Europe.
Historians like Pomeranz tend to focus on peculiarities of time and
place. They are more likely to conclude that the Industrial Revolution
happened because of a unique combination of favourable circumstances
(they may disagree about which ones).
Economists like Allen are more likely to look for general mechanisms
that can explain success or failure across both time and space.
Economists have much to learn from historians, but often a historian’s
argument is not precise enough to be testable using a model (the approach
we will use in this unit). On the other hand, historians may regard eco-
nomists’ models as simplistic, ignoring important historical facts. This
creative tension is what makes economic history so fascinating.
Recently, economic historians have made progress in quantifying eco-
nomic growth over the very long run. Their work helps clarify what
happened, which makes it easier for us to think about why it happened.
Some of their work involves comparing real wages in countries over the
long run. This has involved collecting both wages and the prices of goods
Joel Mokyr. 2004. The gifts of
Athena: Historical origins of the
knowledge economy, 5th ed.
Princeton, NJ: Princeton University
Press.
David S. Landes. 2006. ‘Why Europe
and the west? Why not China?’
Journal of Economic Perspectives
20 (2) (June): pp. 3–22.
Gregory Clark. 2007. A farewell to
alms: A brief economic history of
the world. Princeton, NJ: Princeton
University Press.
Kenneth L. Pomeranz. 2000. The
great divergence: Europe, China,
and the making of the modern
world economy. Princeton, NJ:
Princeton University Press.
If you want to know what these
researchers think of each other’s
work, try searching for ‘Gregory
Clark review Joel Mokyr’ or ‘Robert
Allen review Gregory Clark’.
2.1 ECONOMISTS, HISTORIANS, AND THE INDUSTRIAL REVOLUTION
47
that workers consumed. An even more ambitious series of projects has
calculated GDP per capita back to the Middle Ages.
We will focus on the economic conditions that contributed to Britain’s
take-off, but each economy that broke out of the Malthusian trap took a
different escape route. The national trajectories of the early followers were
influenced in part by the dominant role that Britain had come to play in the
world economy. Germany, for example, could not compete with Britain in
textiles, but the government and large banks played a major role in building
steel and other heavy industries. Japan outcompeted even Britain in some
Asian textile markets, benefiting from the isolation it enjoyed by the sheer
distance from the earlier starters (which in those days was weeks of travel).
Japan selectively copied both technology and institutions, introducing
the capitalist economic system while retaining many traditional Japanese
institutions including rule by an emperor, which would last until the
Japanese defeat in the Second World War.
India and China provide even greater contrasts. China experienced the
capitalist revolution when the Communist Party led a transition away from
the centrally planned economy, the antithesis of capitalism that the Party
itself had implemented. India, by contrast, is the first major economy in
history to have adopted democracy, including universal voting rights, prior
to its capitalist revolution.
As we saw in Unit 1, the Industrial Revolution did not lead to economic
growth everywhere. Because it originated in Britain, and spread only slowly
to the rest of the world, it also implied a huge increase in income inequality
between countries. Looking at economic growth around the world in the
nineteenth and twentieth centuries, David Landes once asked: ‘Why are we
so rich and they so poor?’
By ‘we’, he meant the rich societies of Europe and North America. By
‘they’ he meant the poorer societies of Africa, Asia and Latin America.
Landes suggested, a little mischievously, that there were basically two
answers to this question:
One says that we are so rich and they so poor because we are so good
and they so bad; that is, we are hardworking, knowledgeable,
educated, well governed, efficacious, and productive, and they are the
reverse. The other says that we are so rich and they so poor because
we are so bad and they so good: we are greedy, ruthless, exploitative,
aggressive, while they are weak, innocent, virtuous, abused, and
vulnerable.
If you think that the Industrial Revolution happened in Europe because of
the Protestant Reformation, or the Renaissance, or the scientific revolution,
or the development of superior private property rights, or favourable gov-
ernment policies, then you are in the first camp. If you think that it
happened because of colonialism, or slavery, or the demands of constant
warfare, then you are in the second.
You will notice that these are all non-economic forces that, according to
some scholars, had important economic consequences. You can probably
also see how the question of which of Landes’s two answers is right might
become ideologically charged although, as Landes points out, ‘It is not
clear … that one line of argument necessarily precludes the other.’
David S. Landes. 1990. ‘Why are We
So Rich and They So Poor?’. The
American Economic Review 80
(May): pp. 1–13.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
48
Economy
Society
Biosphere
P
hysic
al Environment
Capitalist economic
system
Self-sufficient
family-based
production
Market economy
with family-based
production
and firmsand marketsAn economic system with
private property
Biosphere and
physical environment
Firms Households
Pollution,
waste
Goods, services
Labour force
Land, raw materials, energy, water
Machinery,
equipment
Parents, caring
labour
Pollution,
waste
Models come in many forms. You
have seen three of them already in
Figures 1.5, 1.8 and 1.12 in Unit 1.
flow A quantity measured per unit
of time, such as annual income or
hourly wage.
2.2 ECONOMIC MODELS: HOW TO SEE MORE BY
LOOKING AT LESS
What happens in the economy depends on what millions of people do, and
how their decisions affect the behaviour of others. It would be impossible to
understand the economy by describing every detail of how they act and
interact. We need to be able to stand back and look at the big picture. To do
this, we use models.
To create an effective model we need to distinguish between the
essential features of the economy that are relevant to the question we want
to answer, which should be included in the model, and unimportant details
that can be ignored.
Models come in many forms—and you have seen three of them already
in Figures 1.5, 1.8 and 1.12 in Unit 1. For example, Figure 1.12 illustrated
that economic interactions involve flows of goods (for example when you
buy a washing machine), services (when you purchase haircuts or bus rides),
and also people (when you spend a day working for an employer).
Figure 1.12 was a diagrammatic model illustrating the flows that occur
within the economy, and between the economy and the biosphere. The
model is not ‘realistic’—the economy and the biosphere don’t look anything
like it—but it nevertheless illustrates the relationships among them. The
fact that the model omits many details—and in this sense is unrealistic—is a
feature of the model, not a bug.
Malthus’ explanation of why improvements in technology could not
raise living standards was also based on a model: a simple description of the
relationships between income and population.
Some economists have used physical models to illustrate and explore
how the economy works. For his 1891 PhD thesis at Yale University, Irving
Fisher designed a hydraulic apparatus (Figure 2.2) to represent flows in the
economy. It consisted of interlinked levers and floating cisterns of water to
show how the prices of goods depend on the amount of each good
supplied, the incomes of consumers, and how much they value each good.
The whole apparatus stops moving when the water levels in the cisterns are
the same as the level in the surrounding tank. When it comes to rest, the
position of a partition in each cistern corresponds to the price of each good.
For the next 25 years he would use the contraption to teach students how
markets work.
How models are used in economics
Fisher’s study of the economy illustrates how all models are used:
1. First he built a model to capture the elements of the economy that he
thought mattered for the determination of prices.
2. Then he used the model to show how interactions between these
elements could result in a set of prices that did not change.
3. Finally he conducted experiments with the model to discover the effects
of changes in economic conditions: for example, if the supply of one of
the goods increased, what would happen to its price? What would
happen to the prices of all of the other goods?
Irving Fisher’s doctoral dissertation represented the economy as a big tank
of water, but he wasn’t an eccentric inventor. On the contrary, his machine
was described by Paul Samuelson, himself one of the greatest economists of
the twentieth century, as the ‘greatest doctoral dissertation in economics
2.2 ECONOMIC MODELS: HOW TO SEE MORE BY LOOKING AT LESS
49
equilibrium A model outcome that
is self-perpetuating. In this case,
something of interest does not
change unless an outside or
external force is introduced that
alters the model’s description of
the situation.
subsistence level The level of
living standards (measured by con-
sumption or income) such that the
population will not grow or decline.
ever written’. Fisher went on to become one of the most highly regarded
economists of the twentieth century, and his contributions formed the basis
of modern theories of borrowing and lending that we will describe in
Unit 10.
Fisher’s machine illustrates an important concept in economics. An
equilibrium is a situation that is self-perpetuating, meaning that
something of interest does not change unless an outside or external force
for change is introduced that alters the model’s description of the situation.
Fisher’s hydraulic apparatus represented equilibrium in his model economy
by equalizing water levels, which represented constant prices.
We will use the concept of equilibrium to explain prices in later units,
but we will also apply it to the Malthusian model. An income at
subsistence level is an equilibrium because, just like differences in the
water levels in the various cisterns in Fisher’s machine, movements away
from subsistence income are self-correcting: they automatically lead back
to subsistence income as population rises.
Note that equilibrium means that one or more things in the model are
constant. It does not need to mean that nothing changes. For example, we
might see an equilibrium in which GDP or prices are increasing, but at a
constant rate.
Although it is unlikely that you will build a hydraulic model for yourself,
you will work with many existing models on paper or on a screen, and
sometimes create your own models of the economy.
When we build a model, the process follows these steps:
1. We construct a simplified description of the conditions under which
people take actions.
2. Then we describe in simple terms what determines the actions that
people take.
5
4
3
2
1
0
1
2
3
4
0
P Aa
IA
IIA
IIIA
IIIB
IIB
IB
IC
IIC
5
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2
1
0
UIIIIII0
1
2
3
4
5
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2
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P Bb
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UIIII0
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IIIC
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Figure 2.2 Irving Fisher’s sketch of his hydraulic model of economic equilibrium
(1891).
William C. Brainard and Herbert E. Scarf.
2005. ‘How to Compute Equilibrium
Prices in 1891’. American Journal of Eco-
nomics and Sociology 64 (1): pp. 57–83
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
50
ECONOMIC MODELS
A good model has four attributes:
• It is clear: It helps us better
understand something import-
ant.
• It predicts accurately: Its
predictions are consistent with
evidence.
• It improves communication: It
helps us to understand what we
agree (and disagree) about.
• It is useful: We can use it to find
ways to improve how the eco-
nomy works.
3. We determine how each of their actions affects each other.
4. We determine the outcome of these actions. This is often an equilibrium
(something is constant).
5. Finally, we try to get more insight by studying what happens to certain
variables when conditions change.
Economic models often use mathematical equations and graphs as well as
words and pictures.
Mathematics is part of the language of economics, and can help us to
communicate our statements about models precisely to others. Much of the
knowledge of economics, however, cannot be expressed by using
mathematics alone. It requires clear descriptions, using standard definitions
of terms.
We will use mathematics as well as words to describe models, usually in
the form of graphs. If you want, you will also be able to look at some of the
equations behind the graphs. Just look for the references to our Leibniz
features in the margins.
A model starts with some assumptions or hypotheses about how people
behave, and often gives us predictions about what we will observe in the
economy. Gathering data on the economy, and comparing it with what a
model predicts, helps us to decide whether the assumptions we made when
we built the model—what to include, and what to leave out—were justified.
Governments, central banks, corporations, trade unions, and anyone
else who makes policies or forecasts use some type of simplified model.
Bad models can result in disastrous policies, as we will see later. To have
confidence in a model, we need to see whether it is consistent with
evidence.
We will see that our economic models of the vicious circle of Malthusian
subsistence living standards and the permanent technological revolution
pass this test—even though they leave many questions unanswered.
EXERCISE 2.1 DESIGNING A MODEL
For a country (or city) of your choice, look up a map of the railway or
public transport network.
Much like economic models, maps are simplified representations of
reality. They include relevant information, while abstracting from
irrelevant details.
1. How do you think the designer selected which features of reality to
include in the map you have selected?
2. In what way is a map not like an economic model?
Introducing the Leibnizes
(https://tinyco.re/L020201)
2.2 ECONOMIC MODELS: HOW TO SEE MORE BY LOOKING AT LESS
51
ceteris paribus Economists often
simplify analysis by setting aside
things that are thought to be of less
importance to the question of
interest. The literal meaning of the
expression is ‘other things equal’. In
an economic model it means an
analysis ‘holds other things con-
stant’.
incentive Economic reward or
punishment, which influences the
benefits and costs of alternative
courses of action.
relative price The price of one
good or service compared to
another (usually expressed as a
ratio).
economic rent A payment or other
benefit received above and beyond
what the individual would have
received in his or her next best
alternative (or reservation option).
See also: reservation option.
•2.3 BASIC CONCEPTS: PRICES, COSTS, AND
INNOVATION RENTS
In this unit, we are going to build an economic model to help explain the
circumstances under which new technologies are chosen, both in the past
and in contemporary economies. We use four key ideas of economic
modelling:
• Ceteris paribus and other simplifications help us focus on the variables
of interest. We see more by looking at less.
• Incentives matter, because they affect the benefits and costs of taking
one action as opposed to another.
• Relative prices help us compare alternatives.
• Economic rent is the basis of how people make choices.
Part of the process of learning to do economics involves learning a new
language. The terms below will recur frequently in the units that follow,
and it is important to learn how to use them precisely and with confidence.
Ceteris paribus and simplification
As is common in scientific inquiry, economists often simplify an analysis by
setting aside things that are thought to be of less importance to the question
of interest, by using the phrase ‘holding other things constant’ or, more
often, the Latin expression ceteris paribus, meaning ‘other things equal’. For
example, later in the course we simplify an analysis of what people would
choose to buy by looking at the effect of changing a price—ignoring other
influences on our behaviour like brand loyalty, or what others would think
of our choices. We ask: what would happen if the price changed, but
everything else that might influence the decision was the same. These ceteris
paribus assumptions, when used well, can clarify the picture without
distorting the key facts.
When we study the way that a capitalist economic system promotes
technological improvements, we will look at how changes in wages affect
firms’ choice of technology. For the simplest possible model we ‘hold con-
stant’ other factors affecting firms. So we assume:
• Prices of all inputs are the same for all firms.
• All firms know the technologies used by other firms.
• Attitudes towards risk are similar among firm owners.
EXERCISE 2.2 USING CETERIS PARIBUS
Suppose you build a model of the market for umbrellas,
in which the predicted number of umbrellas sold by a
shop depends on their colour and price, ceteris paribus.
1. The colour and the price are variables used to
predict sales. Which other variables are being held
constant?
Which of the following questions do you think this
model might be able to answer? In each case, suggest
improvements to the model that might help you to
answer the question.
2. Why are annual umbrella sales higher in the capital
city than in other towns?
3. Why are annual umbrella sales higher in some shops
in the capital city than others?
4. Why have weekly umbrella sales in the capital city
risen over the last six months?
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
52
Incentives matter
Why did the water in Fisher’s hydraulic economy machine move when he
changed the quantity of ‘supply’ or ‘demand’ for one or more of the goods,
so that the prices were no longer in equilibrium?
• Gravity acts on the water so it finds the lowest level.
• Channels allow the water to seek out the lowest level, but restrict the
ways in which it can flow.
All economic models have something equivalent to gravity, and a
description of the kinds of movements that are possible. The equivalent of
gravity is the assumption that, by taking one course of action over another,
people are attempting to do as well as they can (according to some
standard).
The analogy to the free movement of water in Fisher’s machine is that
people are free to select different courses of action, rather than simply
being told what to do. This is where economic incentives affect the choices
we make. But we can’t do everything we want to do: not every channel is
open to us.
Like many economic models, the one we use to explain the permanent
technological revolution is based on the idea that people or firms respond
to economic incentives. As we will see in Unit 4, people are motivated not
only by the desire for material gain but also by love, hate, sense of duty, and
desire for approval. But material comfort is an important motive, and eco-
nomic incentives appeal to this motive.
When owners or managers of firms decide how many workers to hire,
or when shoppers decide what and how much to buy, prices are going to be
an important factor determining their decision. If prices are a lot lower in
the discount supermarket than in the corner shop, and it is not too far away,
then this will be a good argument for shopping in the supermarket rather
than in the shop.
Relative prices
A third characteristic of many economic models is that we are often
interested in ratios of things, rather than their absolute level. Economics
focuses attention on alternatives and choices. If you are deciding where to
shop, it is not the corner shop prices alone that matter, but rather the prices
relative to those in the supermarket and relative to the costs of reaching the
supermarket. If all of these were to rise by 5%, your decision probably
wouldn’t change.
Relative prices are simply the price of one option relative to another. We
often express relative price as the ratio of two prices. We will see that they
matter a lot in explaining not just what shoppers (or consumers, as we
usually call them) decide to buy, but why firms make the choices that they
do. When we study the Industrial Revolution, you will see that the ratio of
energy prices (the price of coal, for example, to power a steam engine), to
the wage rate (the price of an hour of a worker’s time) plays an important
part in the story.
Reservation positions and rents
Imagine that you have figured out a new way of reproducing sound in high
quality. Your invention is much cheaper to use than anyone else’s method.
Your competitors cannot copy you, either because they cannot figure out
2.3 BASIC CONCEPTS: PRICES, COSTS, AND INNOVATION RENTS
53
reservation option A person’s next
best alternative among all options
in a particular transaction. Also
known as: fallback option. See also:
reservation price.
how to do it or because you have a patent on the process (making it illegal
for them to copy you). So they continue offering their services at a price
that is much higher than your costs.
If you match their price, or undercut them by just a bit, you will be able
to sell as much as you can produce, so you can charge the same price but
make profits that greatly exceed those of your competitors. In this case, we
say that you are making an innovation rent. Innovation rents are a form of
economic rent—and economic rents occur throughout the economy. They
are one of the reasons why capitalism can be such a dynamic system.
We will use the idea of innovation rents to explain some of the factors
contributing to the Industrial Revolution. But economic rent is a general
concept that will help explain many other features of the economy.
When taking some action (call it action A) results in a greater benefit to
yourself than the next best action, we say that you have received an eco-
nomic rent.
The term is easily confused with everyday uses of the word, such as the rent
for temporary use of a car, apartment, or piece of land. To avoid this
confusion, when we mean economic rent, we emphasize the word ‘eco-
nomic’. Remember, an economic rent is something you would like to get,
not something you have to pay.
The alternative action with the next greatest net benefit (action B), is
often called the ‘next best alternative’, your ‘reservation position’, or the
term we use: reservation option. It is ‘in reserve’ in case you do not choose
A. Or, if you are enjoying A but then someone excludes you from doing it,
your reservation option is your Plan B. This is why it is also called a
‘fallback option’.
Economic rent gives us a simple decision rule:
• If action A would give you an economic rent (and nobody else would suffer):
Do it!
• If you are already doing action A, and it earns you an economic rent: Carry
on doing it!
This decision rule motivates our explanation of why a firm may innovate by
switching from one technology to another. We start in the next section by
comparing technologies.
QUESTION 2.2 CHOOSE THE CORRECT ANSWER(S)
Which of the following is an economic rent?
The amount you pay your landlord for the use of an apartment.
The amount you pay to hire a car for a weekend.
The extra profit that a successful innovator makes on bringing a
new product to the market before its competitors.
The extra profit that a firm makes when it doubles in size and there
are no changes to costs or the price for each unit of its output.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
54
dominated We describe an out-
come in this way if more of
something that is positively valued
can be attained without less of
anything else that is positively
valued. In short: an outcome is
dominated if there is a win-win
alternative.
•2.4 MODELLING A DYNAMIC ECONOMY: TECHNOLOGY
AND COSTS
We now apply these modelling ideas to explain technological progress. In
this section we consider:
• What is a technology?
• How does a firm evaluate the cost of different technologies?
What is a technology?
Suppose we ask an engineer to report on the technologies that are available
to produce 100 metres of cloth, where the inputs are labour (number of
workers, each working for a standard eight-hour day) and energy (tonnes of
coal). The answer is represented in the diagram and table in Figure 2.3. The
five points in the table represent five different technologies. For example,
technology E uses 10 workers and 1 tonne of coal to produce 100 metres of
cloth.
Follow the steps in Figure 2.3 (page 56) so you can understand the five
technologies.
We describe the E-technology as relatively labour-intensive and the A-
technology as relatively energy-intensive. If an economy were using
technology E and shifted to using technology A or B we would say that they
had adopted a labour-saving technology, because the amount of labour used
to produce 100 metres of cloth with these two technologies is less than with
technology E. This is what happened during the Industrial Revolution.
Which technology will the firm choose? The first step is to rule out tech-
nologies that are obviously inferior. We begin in Figure 2.4 with the A-
technology and look to see whether any of the alternative technologies use
at least as much labour and coal. The C-technology is inferior to A: to
produce 100 metres of cloth, it uses more workers (three rather than one)
and more coal (7 tonnes rather than 6 tonnes). We say the C-technology is
dominated by the A-technology: assuming all inputs must be paid for, no
firm will use technology C when A is available. The steps in Figure 2.4 show
you how to see which of the technologies are dominated, and which tech-
nologies dominate.
Using only the engineering information about inputs, we have narrowed
down the choices: the C- and D-technologies would never be chosen. But
how does the firm choose between A, B and E? This requires an assumption
about what the firm is trying to do. We assume its goal is to make as much
profit as possible, which means producing cloth at the least possible cost.
Making a decision about technology also requires economic information
about relative prices—the cost of hiring a worker relative to that of
purchasing a tonne of coal. Intuitively, the labour-intensive E-technology
would be chosen if labour was very cheap relative to the cost of coal; the
energy-intensive A-technology would be preferable in a situation where
coal is relatively cheap. An economic model helps us be more precise than
this.
How does a firm evaluate the cost of production using different
technologies?
The firm can calculate the cost of any combination of inputs that it might
use by multiplying the number of workers by the wage and the tonnes of
2.4 MODELLING A DYNAMIC ECONOMY: TECHNOLOGY AND COSTS
55
isocost line A line that represents
all combinations that cost a given
total amount.
coal by the price of coal. We use the symbol w for the wage, L for the
number of workers, p for the price of coal and R for the tonnes of coal:
Suppose that the wage is £10 and the price of coal is £20 per tonne. In the
table in Figure 2.5, we have calculated the cost of employing two workers
and three tonnes of coal, which is £80. This corresponds to combination P1
in the diagram. If the firm were to employ more workers—say, six—but
reduce the input of coal to one tonne (point P2), that would also cost £80.
A
B
C
D
E
1 2 3 4 5 6 7 8 9 10
To
nn
es
o
f c
oa
l
Number of workers
1
2
3
4
5
6
7
8
9
10
Technology Number of workers Coal required (tonnes)
A 1 6
B 4 2
C 3 7
D 5 5
E 10 1
Figure 2.3 Different technologies for producing 100 metres of cloth.
1. Five technologies for producing
100 metres of cloth compared
The table describes five different tech-
nologies that we refer to in the rest of
this section. They use different
quantities of labour and coal as inputs
for producing 100 metres of cloth.
2. Technology A: energy-intensive
The A-technology is the most energy-
intensive, using 1 worker and 6 tonnes
of coal.
3. Technology B
The B-technology uses 4 workers and
2 tonnes of coal: it is a more labour-
intensive technology than A.
4. Technology C
The C-technology uses 3 workers and
7 tonnes of coal.
5. Technology D
The D-technology uses 5 workers and
5 tonnes of coal.
6. Technology E: Labour-intensive
Finally, the E-technology uses 10
workers and 1 tonne of coal. This is the
most labour-intensive of the five tech-
nologies.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
56
Follow the steps in Figure 2.5 to see how we construct isocost lines to
compare the costs of all combinations of inputs.
Isocost lines join all the combinations of workers and coal that cost the
same amount. We can use them to help us compare the costs of the three
technologies A, B, and E that remain in play (that is, are not dominated).
The table in Figure 2.6 shows the cost of producing 100 metres of cloth
with each technology when the wage is £10 and the price of coal is £20.
Clearly the B-technology allows the firm to produce cloth at lower cost.
In the diagram, we have drawn the isocost line through the point
representing technology B. This shows immediately that, at these input
prices (remember that the wage is the ‘price’ of labour), the other two tech-
nologies are more costly.
We can see from Figure 2.6 that B is the least-cost technology when
w = 10 and p = 20. The other available technologies will not be chosen at
these input prices. Notice that it is the relative price that matters and not
the absolute price: if both prices doubled, the diagram would look almost
A
B
C
D
E
1 2 3 4 5 6 7 8 9 10
To
nn
es
o
f c
oa
l
Number of workers
1
2
3
4
5
6
7
8
9
10
Figure 2.4 Technology A dominates C; technology B dominates D.
1. Which technologies dominate
others?
The five technologies for producing 100
metres of cloth are represented by the
points A to E. We can use this figure to
show which technologies dominate
others.
2. A dominates C
Clearly, technology A dominates the C-
technology: the same amount of cloth
can be produced using A with fewer
inputs of labour and energy. This
means that, whenever A is available,
you would never use C.
3. B dominates D
Technology B dominates the D-techno-
logy: the same amount of cloth can be
produced using B with fewer inputs of
labour and energy. Note that B would
dominate any other technology that is
in the shaded area above and to the
right of point B.
4. E does not dominate
Technology A dominates C; technology
B dominates D. The E-technology does
not dominate any of the other avail-
able technologies. We know this
because none of the other four techno-
logies are in the area above and to the
right of E.
2.4 MODELLING A DYNAMIC ECONOMY: TECHNOLOGY AND COSTS
57
the same: the isocost line through B would have the same slope, although
the cost would be £160.
We can now represent the isocost lines for any wage w and coal price p
as equations. To do this, we write c for the cost of production. We begin
with the cost of production equation:
that is:
This is one way to write the equation of the isocost line for any value of c.
Cost above £80
Cost = £150
Q1
Q2
P1
P2
Cost = £80 Cost = £120
J
Cost = £40
H
1
2
3
4
5
6
7
8
9
10
To
nn
es
o
f c
oa
l
Number of workers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Figure 2.5 Isocost lines when the wage is £10 and the price of coal is £20.
1. The total cost at P1
The total cost of employing 2 workers
with 3 tonnes of coal is (2 × 10) + (3 ×
20) = £80.
2. P2 also costs £80
If the number of workers is increased to
6, costing £60, and the input of coal is
reduced to 1 tonne, the total cost will
still be £80.
3. The isocost line for £80
The straight line through P1 and P2
joins together all the points where the
total cost is £80. We call this an isocost
line: iso is the Greek for ‘same’. When
drawing the line, we simplify by
assuming that fractions of workers and
of coal can be purchased.
4. A higher isocost line
At point Q1 (3 workers, 6 tonnes of
coal) the total cost is £150. To find the
£150 isocost line, look for another point
costing £150: if 2 more workers are
employed, the input of coal should be
reduced by 1 tonne to keep the cost at
£150. This is point Q2.
5. More isocost lines
We could draw isocost lines through
any other set of points in the diagram.
If prices of inputs are fixed, the isocost
lines are parallel. A simple way to draw
any line is to find the end points: for
example, the £80 line joins the points J
(4 tonnes of coal and no workers) and
H (8 workers, no coal).
6. The slope of every isocost line is:
−(w/p)
The slope of the isocost lines is neg-
ative (they slope downward). In this
case the slope is −0.5, because at each
point, if you hired one more worker,
costing £10, and reduced the amount of
coal by 0.5 tonnes, saving £10, the total
cost would remain unchanged. The
slope is equal to −(w/p), the wage
divided by the price of coal.
7. Points above an isocost line cost
more
If we look at one isocost line—the £80
one—we can see that all points above
the line cost more than £80, and all
points below cost less.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
58
To draw an isocost line, it can help to express it in the form:
where a, which is a constant, is the vertical axis intercept and b is the slope
of the line. In our model, tonnes of coal, R, are on the vertical axis, the
number of workers, L, is on the horizontal axis and we shall see that the
slope of the line is the wage relative to the price of coal, −(w/p). The isocost
line slopes downward so the slope term in the equation −(w/p) is negative.
The equation:
can be rewritten as:
and further rearranged as:
So when w = 10 and p = 20, the isocost line for c = 80 has a vertical axis
intercept of 80/20 = 4 and a negative slope equal to −(w/p) = −1/2. The
slope is the relative price of labour.
Cost = £80
E
B
A
Cost above £80
H
J
1
1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7
To
nn
es
o
f c
oa
l
Number of workers
Technology Number of workers Coal required (tonnes) Total cost (£)
B 4 2 80
A 1 6 130
E 10 1 120
Wage £10, cost of coal £20 per tonne
Figure 2.6 The cost of using different technologies to produce 100 metres of cloth:
Low relative cost of labour.
2.4 MODELLING A DYNAMIC ECONOMY: TECHNOLOGY AND COSTS
59
EXERCISE 2.3 ISOCOST LINES
Suppose the wage is £10 but the
price of coal is only £5.
1. What is the relative price of
labour?
2. Using the method in the text,
write down the equation of the
isocost line for c = £60, and
rewrite it in the standard form y
= a + bx.
3. Write the equations for the £30
and £90 isocost lines in the
standard form too, and draw all
three lines on a diagram. How
does the set of isocost lines for
these input prices compare to
the ones for w = 10 and p = 20?
•2.5 MODELLING A DYNAMIC ECONOMY: INNOVATION
AND PROFIT
We have seen that when the wage is £10 and the price of coal is £20, B is the
least-cost technology.
Any change in the relative price of these two inputs will change the slope
of the isocost lines. Looking at the positions of the three technologies in
Figure 2.7, we can imagine that if the isocost line becomes sufficiently steep
(with the wage rising relative to the cost of coal), B will no longer be the
least-cost technology: the firm will switch to A. This is what happened in
England in the eighteenth century.
Let’s look at how a change in relative prices could cause this to happen.
Suppose that the price of coal falls to £5 while the wage remains at £10.
Looking at the table in Figure 2.7, with the new prices, the A-technology
allows the firm to produce 100 metres of cloth at least cost. Cheaper coal
makes each method of production cheaper, but the energy-intensive tech-
nology is now cheapest.
Remember that to draw the isocost line through any point, such as A, we
calculate the cost at A (£40) then look for another point with the same cost.
The easiest way is to find one of the end points F or G. For example, if no
coal was used, four workers could be hired for £40. This is point F.
You can see from Figure 2.7 that with the new relative price the A-tech-
nology lies on the £40 isocost line, and the other two available technologies
lie above it. They will not be chosen if the A-technology is available.
How does a cost-reducing innovation raise the profits of the firm?
The next step is to calculate the gains to the first firm to adopt the least-cost
technology (A) when the relative price of labour to coal rises. Like all its
competitors, the firm is initially using the B-technology and minimizing its
costs: this is shown in Figure 2.8 by the dashed isocost line through B (with
end points H and J).
Once the relative prices change, the new isocost line through the B-tech-
nology is steeper and the cost of production is £50. Switching to the A-
technology (which is more energy-intensive and less labour-intensive) to
produce 100 metres of cloth reduces costs to £40. Follow the steps in
Figure 2.8 to see how isocost lines change with the new relative prices.
The firm’s profits are equal to the revenue it gets from selling output
minus its costs.
Whether the new or old technology is used, the same prices have to be
paid for labour and coal, and the same price is received for selling
100 metres of cloth. The change in profit is thus equal to the fall in costs
associated with adopting the new technology, and profits rise by £10 per
100 metres of cloth:
In this case, the economic rent for a firm switching from B to A is £10 per
100 metres of cloth, which is the cost reduction made possible by the new
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
60
entrepreneur A person who creates
or is an early adopter of new tech-
nologies, organizational forms, and
other opportunities.
technology. The decision rule (if the economic rent is positive, do it!) tells
the firm to innovate.
In our example, the A-technology was available, but not in use until a
first-adopter firm responded to the incentive created by the increase in the
relative price of labour. The first adopter is called an entrepreneur. When
we describe a person or firm as entrepreneurial, it refers to a willingness to
try out new technologies and to start new businesses.
The economist Joseph Schumpeter (see below) made the adoption of
technological improvements by entrepreneurs a key part of his explanation
for the dynamism of capitalism. This is why innovation rents are often
called Schumpeterian rents.
Innovation rents will not last forever. Other firms, noticing that
entrepreneurs are making economic rents, will eventually adopt the new
technology. They will also reduce their costs and their profits will increase.
Cost = £40
B
E
A
G
F
1
1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7
8
9
10
To
nn
es
o
f c
oa
l
Number of workers
Technology Number of workers Coal required (tonnes) Total cost (£)
B 4 2 50
A 1 6 40
E 10 1 105
Wage £10, cost of coal £5 per tonne
Figure 2.7 The cost of using different technologies to produce 100 metres of cloth:
high relative cost of labour.
1. Technology A costs the least when
coal is relatively cheap
When the wage is £10 and the price of
coal is £5, the table shows that the A-
technology, which is more energy-
intensive than the others, can produce
100 metres of cloth at a lower cost than
B or E.
2. The £40 isocost curve when w = 10
and p = 5
The A-technology is on the isocost line
FG. At any point on this line, the total
cost of inputs is £40. Technologies B
and E are above this line, with higher
costs.
3. The slope of the isocost line
The slope of the isocost line can be
found by calculating the relative price
of labour. It is equal to −(10/5) = −2. If
you spent £10 on labour by hiring an
extra worker, you could reduce coal by
2 tonnes and keep the total cost at £40.
2.5 MODELLING A DYNAMIC ECONOMY: INNOVATION AND PROFIT
61
creative destruction Joseph
Schumpeter’s name for the process
by which old technologies and the
firms that do not adapt are swept
away by the new, because they
cannot compete in the market. In
his view, the failure of unprofitable
firms is creative because it releases
labour and capital goods for use in
new combinations.
In this case, with higher profits per 100 metres of cloth, the lower-cost
firms will thrive. They will increase their output of cloth. As more firms
introduce the new technology, the supply of cloth to the market increases
and the price will start to fall. This process will continue until everyone is
using the new technology, at which stage prices will have declined to the
point where no one is earning innovation rents. The firms that stuck to the
old B-technology will be unable to cover their costs at the new lower price
for cloth, and they will go bankrupt. Joseph Schumpeter called this creative
destruction.
Cost = £50
Cost = £80
B
A
G
J
N
MF H
Cost = £401
1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7
8
9
10
To
nn
es
o
f c
oa
l
Number of workers
Technology Number of workers Coal required (tonnes) Total cost (£)
Wage £10, Cost of coal £20 per tonne
B 4 2 80
Wage £10, Cost of coal £5 per tonne
B 4 2 50
A 1 6 40
Figure 2.8 The cost of using different technologies to produce 100 metres of cloth.
1. At the original relative price, B is the
lower cost technology
When the wage is £10 and the price of
coal is relatively high at £20, the cost of
producing 100 metres of cloth using
technology B is £80: choosing the B-
technology puts the firm on the HJ
isocost curve.
2. The price of coal falls to £5
If the price of coal falls relative to the
wage as shown by the isocost curve FG,
then using the A-technology, which is
more energy-intensive than B, costs
£40. From the table, we see that with
these relative prices, A is now the least-
cost technology.
3. B now costs more than A
At the new relative prices, the B-tech-
nology is on the isocost line MN, where
the cost is £50. Switching to technology
A will be cheaper.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
62
Lynne Kiesling, a historian of eco-
nomic thought, discusses Joseph
Schumpeter. https://tinyco.re/
0912366
evolutionary economics An
approach that studies the process
of economic change, including
technological innovation, the
diffusion of new social norms, and
the development of novel institu-
tions.
QUESTION 2.3 CHOOSE THE CORRECT ANSWER(S)
Figure 2.3 (page 56) shows different technologies for producing
100 metres of cloth.
From the graph, what can we conclude?
Technology D is more energy-intensive than technology C.
Technology B dominates technology D.
Technology A is the cost-minimizing technology at all prices of coal
and wages.
Technology C can sometimes be a cheaper technology than A.
QUESTION 2.4 CHOOSE THE CORRECT ANSWER(S)
Look at the three isocost lines in Figure 2.8 (page 62).
Based on this information, what can we conclude?
When the wage is £10 and the price of coal is £5, the combination of
inputs at point N is more costly than the inputs at point B.
Isocosts MN and FG represent the same price ratio (wage/price of
coal) but different total costs of production.
Isocost HJ represents a higher (wage/price of coal) ratio than iso-
cost FG.
Isocost HJ represents all points that can produce 100 metres of
cloth at a particular price ratio.
GREAT ECONOMISTS
Joseph Schumpeter
Joseph Schumpeter (1883–1950)
developed one of the most import-
ant concepts of modern
economics: creative destruction.
Schumpeter brought to eco-
nomics 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 produc-
tion, and opens up new markets.
Imitators follow, and the innova-
tion 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 com-
binations.
2.5 MODELLING A DYNAMIC ECONOMY: INNOVATION AND PROFIT
63
Joseph A. Schumpeter. 1949.
‘Science and Ideology’
(https://tinyco.re/4561610). The
American Economic Review 39
(March): pp. 345–59.
Joseph A. Schumpeter. 1997. Ten
Great Economists. London:
Routledge.
Joseph A. Schumpeter. 1962.
Capitalism, Socialism, and
Democracy. New York: Harper &
Brothers.
•••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.
What did inventions such as the spinning jenny do? The first spinning
jennies had eight spindles. One machine operated by just one adult there-
fore 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.
This decentralized process generates a continued improvement in
productivity, which leads to growth, so Schumpeter argued it is virtuous.
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 (https://tinyco.re/0746014)) 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.
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.
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.
Old technology New technology
Lots of workers Few workers
Little machinery (spinning wheels) Lots of capital goods (spinning mules, factory
buildings, water wheels or steam engines)
… requiring only human energy … requiring energy (coal)
Labour-intensive Labour-saving
Capital-saving Capital-intensive
Energy-saving Energy-intensive
Figure 2.9 The change in spinning technology during the Industrial Revolution.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
64
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.
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.
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
0
1
2
3
4
5
Newcastle,
England
London Amsterdam Strasbourg,
France
Paris Beijing
La
bo
ur
er
's
da
ily
w
ag
e/
pr
ic
e
of
1
m
ill
io
n
BT
U
s
Figure 2.10 Wages relative to the price of energy (early 1700s).
View this data at OWiD https://tinyco.re/
2761827
Page 140 of Robert C. Allen. 2008. The
British Industrial Revolution in Global
Perspective. Cambridge: Cambridge Uni-
versity Press.
2.6 THE BRITISH INDUSTRIAL REVOLUTION
65
Economic historian Bob Allen
addresses the question of why
Britain industrialized when others
did not. https://tinyco.re/7532008
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.
EXERCISE 2.4 BRITAIN BUT NOT FRANCE
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?
0
0.5
0.9
1.4
1.8
1580 1600 1620 1640 1660 1680 1700 1720 1740 1760 1780 1800 1820
Year
W
ag
es
re
la
tiv
e
to
th
e
co
st
of
ca
pi
ta
l
England
France
Figure 2.11 Wages relative to the cost of capital goods (late sixteenth to the early
nineteenth century).
View this data at OWiD https://tinyco.re/
7417234
Page 138 in Robert C. Allen. 2008. The
British Industrial Revolution in Global
Perspective. Cambridge: Cambridge Uni-
versity Press.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
66
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 coun-
tries 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.
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.
Robert C. Allen. 2009. ‘The indus-
trial revolution in miniature: The
spinning Jenny in Britain, France,
and India’. The Journal of Eco-
nomic History 69 (04) (November):
p. 901.
B
A
F
G
H
J
1700s (isocost FG)
• Steep isocost: relative price of labour to coal is high.
• A-technology now lower cost than the B-technology.
• We know this because B lies outside the line FG.
1600s (isocost HJ)
• Firms use technology B.
• At this relative price, no incentive to develop technology A.
• We know this because A costs more (it lies outside the line HJ).
1
1 2 3 4 5 6 7 8 9 10 11 12 13
2
3
4
5
6
7
8
9
10
To
nn
es
o
f c
oa
l
Number of workers
Figure 2.12 The cost of using different technologies to produce 100 metres of cloth
in Britain in the seventeenth and eighteenth centuries.
1. Technology in the 1600s
In the 1600s, the relative prices are
shown by isocost line HJ. The B-techno-
logy was used. At those relative prices,
there was no incentive to develop a
technology like A, which is outside the
isocost line HJ.
2. 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-techno-
logy lower cost than the B-technology.
3. 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.
2.6 THE BRITISH INDUSTRIAL REVOLUTION
67
Either way, the new technologies spread, and the divergence in techno-
logies and living standards was eventually replaced by convergence—at
least among those countries where the capitalist revolution had taken off.
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′.
David S. Landes. 2003. The
unbound Prometheus: Technolo-
gical change and industrial
development in western Europe
from 1750 to the present.
Cambridge, UK: Cambridge Univer-
sity Press.
B
A
F
G
J
H
Cost = £40
Cost = £80
A′
1
1 2 3 4 5 6 7 8 9 10
2
3
4
5
6
7
8
9
10
To
nn
es
o
f c
oa
l
Number of workers
Figure 2.13 The cost of using different technologies to produce 100 metres of cloth.
1. 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 tech-
nology, B, is chosen.
2. An improvement in technology
Improvements in cloth-making techno-
logy occur, resulting in a new
technology, labelled A′. This techno-
logy uses only half as much energy per
worker to produce 100 metres of cloth.
The new technology dominates the A-
technology.
3. 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 eco-
nomies (isocost line HJ). The new
labour- and energy-saving technology,
A′, is inside FG and HJ, so it will be
adopted in both economies.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
68
factors of production The labour, machinery and equipment
(usually referred to as capital), land, and other inputs to a pro-
duction process.
QUESTION 2.5 CHOOSE THE CORRECT ANSWER(S)
Look again at Figure 2.12 (page 67) which depicts iso-
cost 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 iso-
cost 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.
EXERCISE 2.5 WHY DID THE INDUSTRIAL REVOLUTION NOT HAPPEN IN
ASIA?
Read David Landes’ answer to this question (https://tinyco.re/5958995),
and this summary of research on the great divergence (https://tinyco.re/
6223568) 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.
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 dif-
ferent model.
Malthus provided a model of the economy that predicts a pattern of eco-
nomic 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.
Gregory Clark, an economic
historian, argues that the whole
world was Malthusian from
prehistory until the eighteenth
century. Gregory Clark. 2007. A
farewell to alms: A brief economic
history of the world. Princeton, NJ:
Princeton University Press. James
Lee and Wang Feng discuss ways in
which China’s demographic system
differed from Europe’s, and
question the Malthusian
hypothesis that Chinese poverty
was due to population growth.
James Lee 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.
2.7 MALTHUSIAN ECONOMICS: DIMINISHING AVERAGE PRODUCT OF LABOUR
69
average product Total output
divided by a particular input, for
example per worker (divided by the
number of workers) or per worker
per hour (total output divided by
the total number of hours of labour
put in).
PRODUCTION FUNCTION
This describes the relationship
between the amount of output
produced and the amounts of
inputs used to produce it.
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:
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.
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.
Leibniz: Malthusian Economics:
Diminishing Average Product of
Labour (https://tinyco.re/L020701)
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
70
diminishing average product of
labour A situation in which, as
more labour is used in a given pro-
duction process, the average
product of labour typically falls.
EXERCISE 2.6 THE FARMERS’ PRODUCTION FUNCTION
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 produc-
tion. This worried Malthus.
Labour input (number of workers) Grain output (kg) Average product of labour (kg/worker)
200 200,000 1,000
400 330,000 825
600 420,000 700
800 500,000 625
1,000 570,000 570
1,200 630,000 525
1,400 684,000 490
1,600 732,000 458
1,800 774,000 430
2,000 810,000 405
2,200 840,000 382
2,400 864,000 360
2,600 882,000 340
2,800 894,000 319
3,000 900,000 300
Figure 2.14a Recorded values of a farmer’s production function: Diminishing
average product of labour.
2.7 MALTHUSIAN ECONOMICS: DIMINISHING AVERAGE PRODUCT OF LABOUR
71
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.
225
450
675
900
0
Number of farmers
0
Kg
o
f g
ra
in
p
ro
du
ce
d
(t
ho
us
an
ds
)
400 1,200 1,600 2,000 2,400 2,800800
The farmers’ production function:
This shows how the number of
farmers working the land
translates into grain harvested.
Slope = 732,000/1,600 = 458
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.
A
B
500
732
Figure 2.14b The farmers’ production function: Diminishing average product of
labour.
1. 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.
2. Output when there are 800 farmers
Point A on the production function
shows the output of grain produced by
800 farmers.
3. Output when there are 1,600 farmers
Point B on the production function
shows the amount of grain produced by
1,600 farmers.
4. 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.
5. 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.
6. 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.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
72
QUESTION 2.6 CHOOSE THE CORRECT ANSWER(S)
Look again at Figure 2.14b (page 72) 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 produc-
tion function curve will be higher and parallel to the curve above.
A discovery of new high-yielding crop seeds would tilt the produc-
tion function curve higher, pivoted anti-clockwise at the origin.
In a year of bad drought, the production curve can slope down-
wards 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.
••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:
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
Thomas Robert Malthus, 1830. A
Summary View on the Principle of
Population. London: J. Murray.
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.
2.8 MALTHUSIAN ECONOMICS: POPULATION GROWS WHEN LIVING STANDARDS RISE
73
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 pop-
ulation 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.
EXERCISE 2.7 ARE PEOPLE REALLY LIKE OTHER ANIMALS?
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.
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
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
74
Improvement in technology
Equilibrium
Subsistence incomes
prevail
Population constant
Equilibrium
Subsistence incomes
prevail
Population constant at
higher level
Improvement
in technology
Average
output per
farmer rises
Farmers’
incomes
rise
Population
rises
Less land
per farmer
Average
output per
farmer falls
Farmers’
incomes
fall
Figure 2.15 Malthus’ model: The effect of an improvement in technology.
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 tech-
nology.
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 pop-
ulation but not higher wages. This depressing conclusion was once
regarded as so universal and inescapable that it was called Malthus’ Law.
2.8 MALTHUSIAN ECONOMICS: POPULATION GROWS WHEN LIVING STANDARDS RISE
75
Real wage Real wage
Population growth
negativePopulationPopMedium
WageHigh
WageLow
PopLow
Real wage Population
rising
Population
falling
positive0 +–
B
A A′
B′
(subsistence)
Figure 2.16 A Malthusian economy.
EINSTEIN
Modelling Malthus
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.
1. 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.
2. 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).
3. 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 popu-
lation growth is equal to zero. So if the
economy is at point A, it is in equilib-
rium: population stays constant and
wages remain at subsistence level.
4. 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.
5. The economy returns to equilibrium
As the population rises, the economy
moves down the line in the left dia-
gram: wages fall until they reach
equilibrium at A.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
76
Real wage Real wage
Population growth
negativePopulationPopMedium
WageHigh
WageLow
Real wage, initial
Real wage: after a new
technology is introduced
Population
rising
Population
falling
positive0 +
A A′
PopHigh
C
C′
D D′
(subsistence)
–
Figure 2.17 The introduction of a new technology in a Malthusian economy.
The two diagrams together explain the Malthusian population trap. Pop-
ulation 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.
1. Initially the economy is in
equilibrium
The economy starts at point A, with a
medium-sized population and wage at
subsistence level.
2. 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 popula-
tion. The real wage line shifts upward.
At the initial population level, the
wage increases and the economy
moves to point D.
3. Population begins to rise
At point D, the wage has risen above
subsistence level and therefore the
population starts to grow (point D′).
4. 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.
5. C is the equilibrium with the new
technology
At C, the wage has reached
subsistence level again. The popula-
tion remains constant (point C′). The
population is higher at equilibrium C
than it was at equilibrium A.
EXERCISE 2.8 LIVING STANDARDS IN THE MALTHUSIAN WORLD
Imagine that the population growth curve in the right panel of Figure
2.16 (page 76) 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.
2.8 MALTHUSIAN ECONOMICS: POPULATION GROWS WHEN LIVING STANDARDS RISE
77
••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. Pop-
ulation 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.
1280s
1290s
1300s
1310s
1320s
1330s
1340s
1350s
1360s
1370s
1420s
1430s
1480s
1490s
1500s
1510s
1530s
1540s
1550s
1570s
1580s
1590s
1600s
40
55
70
85
100
2 3 4 5 6
Population (millions)
Re
al
w
ag
e
in
de
x
(1
86
0
=
10
0)
Figure 2.18 The Malthusian trap: Wages and population (1280s–1600s).
View this data at OWiD https://tinyco.re/
7264218
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.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
78
1347 Black Death
1351 Statute of Labourers
1381 Peasants' Revolt
30
50
70
90
110
1300 1400 1500 1600
Year
Re
al
w
ag
e
in
de
x
(1
85
0
=
10
0)
Black Death
Population and
labour supply fall
More and better
land per farmer
Average output
per farmer rises
Rural income
and wages rise
Bargaining power of farmers and
employees rises
Bargaining power of farmer and
employees falls
Peasants’
Revolt
Population and
labour supply
rise
Less land
per farmer
Average output
per farmer falls
Rural income
and wages fall
Figure 2.19 The Black Death, labour supply, politics, and the wage: A Malthusian
economy.
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.
1. 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.
2. 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.
3. 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.
4. 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.
5. 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.
6. Malthusian stagnation (1350–1600)
By 1600, real wages had fallen to the
level they were 300 years previously.
2.9 THE MALTHUSIAN TRAP AND LONG-TERM ECONOMIC STAGNATION
79
7. 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.
EXERCISE 2.9 WHAT WOULD YOU
ADD?
The cause-and-effect diagram that
we created in Figure 2.19 (page 79)
made use of many ceteris paribus
assumptions.
1. How does this model simplify
reality?
2. What has been left out?
3. Try redrawing the figure to
include other factors that you
think are important.
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.
QUESTION 2.7 CHOOSE THE CORRECT ANSWER(S)
Look again at Figure 2.1 (page 45) and Figure 2.19 (page 79) 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.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
80
EXERCISE 2.10 DEFINING ECONOMIC PROGRESS
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 Con-
stantinople (present-day Istanbul).
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 eco-
nomy 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.
•••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 popula-
tion 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.
William H. McNeill. 1976. Plagues
and peoples. Garden City, NY:
Anchor Press.
2.10 ESCAPING FROM MALTHUSIAN STAGNATION
81
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’.
Figure 2.21 zooms in on this ‘great escape’ portion of the wage data.
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.
1280s
1290s
1330s
1340s
1350s
1370s
1430s
1490s
1570s
1590s
1740s
1770s
1780s
1800s
1810s
1820s
1830s
1840s
1850s 1860sMalthusian traps
Escape
18th century
13th to 16th century
40
55
70
85
100
0 5 10 15 20
Population (millions)
Re
al
w
ag
e
in
de
x
(1
86
0
=
10
0)
Figure 2.20 Escaping the Malthusian trap.
View this data at OWiD https://tinyco.re/
1902874
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.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
82
1764
Hargreaves' spinning jenny
1781 Watt's steam engine
1833 Factory Act (no child
labour under 9 years)
1844 Factory Act (children
work only 6.5 hours day)
1847 Ten Hours Act (limits work
hours for women & children)
1918 Voting rights
for all males
1928 Universal
suffrage
0
100
200
300
400
1760 1810 1860 1910 1930
Year
In
de
x
(1
76
0
=
10
0)
Real wages Labour productivity
More and better capital goods
per worker
Average output
per worker rises
Higher profitsDisplaced
workers
Bargaining
power of
workers falls
Kept wages
from rising
Bargaining power of workers rises
Expansion
of factory
production
Demand for
labour rises
Labour supply
falls
Extension of the
right to vote
Wages rise
Restrictions on employing women
and children, factory hours
The Industrial
Revolution
Figure 2.21 Escaping the Malthusian trap. Note: Labour productivity and real wages
are five-year centred moving averages.
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.
1. 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.
2. The permanent technological
revolution
The story begins with technological
improvements, such as the spinning
jenny and the steam engine, that
increased output per worker. Innova-
tion continued as the technological
revolution became permanent,
displacing thousands of spinsters,
weavers and farmers.
3. 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.
4. 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.
2.10 ESCAPING FROM MALTHUSIAN STAGNATION
83
5. 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.
6. 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 technolo-
gical revolution.
In our ‘Economist in action’ video,
Suresh Naidu, an economic
historian, explains how population
growth, technological development
and political events interacted to
produce the real wage hockey stick.
https://tinyco.re/5555923
QUESTION 2.8 CHOOSE THE CORRECT ANSWER(S)
Look again at Figure 2.20 (page 82), 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 eco-
nomy’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.
EXERCISE 2.11 THE BASIC INSTITUTIONS OF CAPITALISM
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 produc-
tion 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.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH
84
We showed how the Malthusian model of a vicious circle, in which pop-
ulation 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.
Concepts introduced in Unit 2
Before you move on, review these definitions:
• Equilibrium
• Ceteris paribus
• Relative prices
• Incentives
• Diminishing average product of labour
• Reservation option
• Economic rent
• Isocost line
• Innovation rent
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?’
(https://tinyco.re/5958995). 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
(https://tinyco.re/8473883).
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.
2.12 REFERENCES
85
Pomeranz, Kenneth L. 2000. The Great Divergence: Europe, China, and the
Making of the Modern World Economy. Princeton, NJ: Princeton Uni-
versity Press.
Schumpeter, Joseph A. 1949. ‘Science and Ideology’ (https://tinyco.re/
4561610). 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’
(https://tinyco.re/8488199). Updated 1 December 2007.
UNIT 2 TECHNOLOGY, POPULATION, AND GROWTH