THEMES AND CAPSTONE UNITS
17: History, instability, and growth
18: Global economy
21: Innovation
22: Politics and policy
UNIT 3
SCARCITY, WORK, AND
CHOICE
HOW INDIVIDUALS DO THE BEST THEY CAN, AND
HOW THEY RESOLVE THE TRADE-OFF BETWEEN
EARNINGS AND FREE TIME
• Decision making under scarcity is a common problem because we
usually have limited means available to meet our objectives.
• Economists model these situations, first by defining all of the feas-
ible actions, then evaluating which of these actions is best, given the
objectives.
• Opportunity costs describe the unavoidable trade-offs in the presence of
scarcity: satisfying one objective more means satisfying other objectives
less.
• A model of decision making under scarcity can be applied to the
question of how much time to spend working, when facing a trade-off
between more free time and more income.
• This model also helps to explain differences in the hours that people
work in different countries, and the changes in our hours of work
throughout history.
Imagine that you are working in New York, in a job that is paying you $15
an hour for a 40-hour working week, which gives you earnings of $600 per
week. There are 168 hours in a week, so after 40 hours of work, you are left
with 128 hours of free time for all your non-work activities, including
leisure and sleep.
Suppose, by some happy stroke of luck, you are offered a job at a much
higher wage—six times higher. Your new hourly wage is $90. Not only that,
your prospective employer lets you choose how many hours you work each
week.
Will you carry on working 40 hours per week? If you do, your weekly
pay will be six times higher than before: $3,600. Or will you decide that you
are satisfied with the goods you can buy with your weekly earnings of
$600? You can now earn this by cutting your weekly hours to just 6 hours
Clock mechanisms
87
and 40 minutes (a six-day weekend!), and enjoy about 26% more free time
than before. Or would you use this higher hourly wage rate to raise both
your weekly earnings and your free time by some intermediate amount?
The idea of suddenly receiving a six-fold increase in your hourly wage
and being able to choose your own hours of work might not seem very
realistic. But we know from Unit 2 that technological progress since the
Industrial Revolution has been accompanied by a dramatic rise in wages. In
fact, the average real hourly earnings of American workers did increase
more than six-fold during the twentieth century. And while employees
ordinarily cannot just tell their employer how many hours they want to
work, over long time periods the typical hours that we work do change. In
part, this is a response to how much we prefer to work. As individuals, we
can choose part-time work, although this may restrict our job options.
Political parties also respond to the preferences of voters, so changes in
typical working hours have occurred in many countries as a result of
legislation that imposes maximum working hours.
So have people used economic progress as a way to consume more
goods, enjoy more free time, or both? The answer is both, but in different
proportions in different countries. While hourly earnings increased by
more than six-fold for twentieth century Americans, their average annual
work time fell by a little more than one-third. So people at the end of this
century enjoyed a four-fold increase in annual earnings with which they
could buy goods and services, but a much smaller increase of slightly less
than one-fifth in their free time. (The percentage increase in free time
would be higher if you did not count time spent asleep as free time, but it is
still small relative to the increase in earnings.) How does this compare with
the choice you made when our hypothetical employer offered you a six-fold
increase in your wage?
Figure 3.1 shows trends in income and working hours since 1870 in
three countries.
As in Unit 1, income is measured as per-capita GDP in US dollars. This
is not the same as average earnings, but gives us a useful indication of
average income for the purposes of comparison across countries and
through time. In the late nineteenth and early twentieth century, average
income approximately trebled, and hours of work fell substantially. During
the rest of the twentieth century, income per head rose four-fold.
Hours of work continued to fall in the Netherlands and France (albeit
more slowly) but levelled off in the US, where there has been little change
since 1960.
While many countries have experienced similar trends, there are still
differences in outcomes. Figure 3.2 illustrates the wide disparities in free
time and income between countries in 2013. Here we have calculated free
time by subtracting average annual working hours from the number of
hours in a year. You can see that the higher-income countries seem to have
lower working hours and more free time, but there are also some striking
differences between them. For example, the Netherlands and the US have
similar levels of income, but Dutch workers have much more free time. And
the US and Turkey have similar amounts of free time but a large difference
in income.
UNIT 3 SCARCITY, WORK, AND CHOICE
88
In many countries there has been a huge increase in living standards
since 1870. But in some places people have carried on working just as hard
as before but consumed more, while in other countries people now have
much more free time. Why has this happened? We will provide some
answers to this question by studying a basic problem of economics—
scarcity—and how we make choices when we cannot have all of everything
that we want, such as goods and free time.
Study the model of decision making that we use carefully! It will be used
repeatedly throughout the course, because it provides insight into a wide
range of economic problems.
1929
1973
1980
1990 2000 2010 2018
1870
1890
1973
1980
1990 2000 2010 2018
1900 1913
1929
1938
1950 1960
1973
1980 1990 2000 2010 2018
France
Netherlands
US
1,000
1,600
2,200
2,800
3,400
1,000 9,000 17,000 25,000 33,000 41,000 49,000 57,000
GDP per capita
An
nu
al
ho
ur
s
w
or
ke
d
Figure 3.1 Annual hours of work and income (1870–2018).
View this data at OWiD https://tinyco.re/
0762342
Jutta Bolt and Jan Luiten van Zanden.
2020. ‘Maddison style estimates of the
evolution of the world economy. A new
2020 update’. Maddison Project
Database, version 2020. Michael
Huberman and Chris Minns. 2007. ‘The
times they are not changin’: Days and
hours of work in Old and New Worlds,
1870–2000’. Explorations in Economic
History 44 (4): pp. 538–67; OECD
Statistics. GDP is measured at PPP in
1990 international Geary-Khamis dollars.
Chile
Denmark
France
Germany
Greece
Ireland
Italy
Japan
Mexico
Netherlands
Norway
South Korea
Spain
Turkey
UK
US
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
100,000
6,500 6,600 6,700 6,800 6,900 7,000 7,100 7,200 7,300 7,400 7,500
Average annual hours of free time per worker
G
D
P
pe
rc
ap
ita
($
PP
P)
Figure 3.2 Annual hours of free time per worker and income (2020).
View this data at OWiD https://tinyco.re/
2903745
OECD. Average annual hours actually
worked per worker (https://tinyco.re/
6892498). OECD. Level of GDP per capita
and productivity (https://tinyco.re/
1840501). Accessed July 2022.
UNIT 3 SCARCITY, WORK, AND CHOICE
89
QUESTION 3.1 CHOOSE THE CORRECT ANSWER(S)
Currently you work for 40 hours per week at the wage rate of £20 an
hour. Your free hours are defined as the number of hours not spent in
work per week, which in this case is 24 hours × 7 days − 40 hours = 128
hours per week. Suppose now that your wage rate has increased by
25%. If you are happy to keep your total weekly income constant, then:
Your total number of working hours per week will fall by 25%.
Your total number of working hours per week will be 30 hours.
Your total number of free hours per week will increase by 25%.
Your total number of free hours per week will increase by 6.25%.
QUESTION 3.2 CHOOSE THE CORRECT ANSWER(S)
Look again at Figure 3.1 (page 89), which depicts the annual number of
hours worked against GDP per capita in the US, France and the
Netherlands, between 1870 and 2000. Which of the following is true?
An increase in GDP per capita causes a reduction in the number of
hours worked.
The GDP per capita in the Netherlands is lower than that in the US
because Dutch people work fewer hours.
Between 1870 and 2000, French people have managed to increase
their GDP per capita more than ten-fold while more than halving
the number of hours worked.
On the basis of the evidence in the graph, one day French people
will be able to produce a GDP per capita of over $30,000 with less
than 1,000 hours of work.
3.1 LABOUR AND PRODUCTION
In Unit 2 we saw that labour can be thought of as an input in the produc-
tion of goods and services. Labour is work; for example the welding,
assembling, and testing required to make a car. Work activity is often
difficult to measure, which is an important point in later units because
employers find it difficult to determine the exact amount of work that their
employees are doing. We also cannot measure the effort required by dif-
ferent activities in a comparable way (for example, baking a cake versus
building a car), so economists often measure labour simply as the number
of hours worked by individuals engaged in production, and assume that as
the number of hours worked increases, the amount of goods produced also
increases.
As a student, you make a choice every day: how many hours to spend
studying. There may be many factors influencing your choice: how much
you enjoy your work, how difficult you find it, how much work your
friends do, and so on. Perhaps part of the motivation to devote time to
studying comes from your belief that the more time you spend studying, the
higher the grade you will be able to obtain at the end of the course. In this
unit, we will construct a simple model of a student’s choice of how many
hours to work, based on the assumption that the more time spent working,
the better the final grade will be.
UNIT 3 SCARCITY, WORK, AND CHOICE
90
We assume a positive relationship between hours worked and final
grade, but is there any evidence to back this up? A group of educational
psychologists looked at the study behaviour of 84 students at Florida State
University to identify the factors that affected their performance.
At first sight there seems to be only a weak relationship between the
average number of hours per week the students spent studying and their
Grade Point Average (GPA) at the end of the semester. This is in Figure 3.3.
The 84 students have been split into two groups according to their hours
of study. The average GPA for those with high study time is 3.43—only just
above the GPA of those with low study time.
Looking more closely, we discover this study is an interesting
illustration of why we should be careful when we make ceteris paribus
assumptions (remember from Unit 2 that this means ‘holding other things
constant’). Within each group of 42 students there are many potentially
important differences. The conditions in which they study would be an
obvious difference to consider: an hour working in a busy, noisy room may
not be as useful as an hour spent in the library.
In Figure 3.4, we see that students studying in poor environments are
more likely to study longer hours. Of these 42 students, 31 of them have
high study time, compared with only 11 of the students with good environ-
ments. Perhaps they are distracted by other people around them, so it takes
them longer to complete their assignments than students who work in the
library.
Now look at the average GPAs in the top row: if the environment is
good, students who study longer do better—and you can see in the bottom
row that high study time pays off for those who work in poor environments
too. This relationship was not as clear when we didn’t consider the effect of
the study environment.
So, after taking into account environment and other relevant factors
(including the students’ past GPAs, and the hours they spent in paid work
or partying), the psychologists estimated that an additional hour of study
time per week raised a student’s GPA at the end of the semester by 0.24
points on average. If we take two students who are the same in all respects
except for study time, we predict that the one who studies for longer will
Elizabeth Ashby Plant, Karl Anders
Ericsson, Len Hill, and Kia Asberg.
2005. ‘Why study time does not
predict grade point average across
college students: Implications of
deliberate practice for academic
performance.’ Contemporary
Educational Psychology 30 (1):
pp. 96–116.
High study time (42 students) Low study time (42 students)
Average GPA 3.43 3.36
Figure 3.3 Study time and grades.
Elizabeth Ashby Plant, Karl Anders
Ericsson, Len Hill, and Kia Asberg. 2005.
‘Why study time does not predict grade
point average across college students:
Implications of deliberate practice for
academic performance.’ Contemporary
Educational Psychology 30 (1):
pp. 96–116. Additional calculations were
conducted by Ashby Plant, Florida State
University, in June 2015.
High study time Low study time
Good environment 3.63 (11 students) 3.43 (31 students)
Poor environment 3.36 (31 students) 3.17 (11 students)
Figure 3.4 Average GPA in good and poor study environments.
Plant et al. ‘Why study time does not
predict grade point average across
college students’, ibid.
3.1 LABOUR AND PRODUCTION
91
production function A graphical or
mathematical expression
describing the amount of output
that can be produced by any given
amount or combination of input(s).
The function describes differing
technologies capable of producing
the same thing.
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).
marginal product The additional amount of output that is
produced if a particular input was increased by one unit, while
holding all other inputs constant.
have a GPA that is 0.24 points higher for each extra hour: study time raises
GPA by 0.24 per hour, ceteris paribus.
EXERCISE 3.1 CETERIS PARIBUS ASSUMPTIONS
You have been asked to conduct a research study at your university, just
like the one at Florida State University.
1. In addition to study environment, which factors do you think should
ideally be held constant in a model of the relationship between study
hours and final grade?
2. What information about the students would you want to collect beyond
GPA, hours of study, and study environment?
Now imagine a student, whom we will call Alexei. He can vary the number
of hours he spends studying. We will assume that, as in the Florida study,
the hours he spends studying over the semester will increase the percentage
grade that he will receive at the end, ceteris paribus. This relationship
between study time and final grade is represented in the table in Figure 3.5.
In this model, study time refers to all of the time that Alexei spends
learning, whether in class or individually, measured per day (not per week,
as for the Florida students). The table shows how his grade will vary if he
changes his study hours, if all other factors—his social life, for example—
are held constant.
This is Alexei’s production function: it translates the number of hours
per day spent studying (his input of labour) into a percentage grade (his
output). In reality, the final grade might also be affected by unpredictable
events (in everyday life, we normally lump the effect of these things
together and call it ‘luck’). You can think of the production function as
telling us what Alexei will get under normal conditions (if he is neither
lucky nor unlucky).
If we plot this relationship on a graph, we get the curve in Figure 3.5.
Alexei can achieve a higher grade by studying more, so the curve slopes
upward. At 15 hours of work per day he gets the highest grade he is capable
of, which is 90%. Any time spent studying beyond that does not affect his
exam result (he will be so tired that studying more each day will not achieve
anything), and the curve becomes flat.
We can calculate Alexei’s average product of
labour, as we did for the farmers in Unit 2. If he
works for 4 hours per day, he achieves a grade of
50. The average product—the average number of
percentage points per hour of study—is 50 / 4
= 12.5. In Figure 3.5 it is the slope of a ray from
the origin to the curve at 4 hours per day:
Alexei’s marginal product is the increase in his
grade from increasing study time by one hour.
Follow the steps in Figure 3.5 to see how to
calculate the marginal product, and compare it
with the average product.
UNIT 3 SCARCITY, WORK, AND CHOICE
92
At each point on the production function, the marginal product is the
increase in the grade from studying one more hour. The marginal product
corresponds to the slope of the production function.
0
90
100
80
70
60
Hours of study per day
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
50
40
30
20
10
Fi
na
l g
ra
de
Study hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 or more
Grade 0 20 33 42 50 57 63 69 74 78 81 84 86 88 89 90
Figure 3.5 How does the amount of time spent studying affect Alexei’s grade?
1. Alexei’s production function
The curve is Alexei’s production func-
tion. It shows how an input of study
hours produces an output, the final
grade.
2. Four hours of study per day
If Alexei studies for four hours his grade
will be 50.
3. Ten hours of study per day
… and if he studies for 10 hours he will
achieve a grade of 81.
4. Alexei’s maximum grade
At 15 hours of study per day Alexei
achieves his maximum possible grade,
90. After that, further hours will make
no difference to his result: the curve is
flat.
5. Increasing study time from 4 to 5
hours
Increasing study time from 4 to 5 hours
raises Alexei’s grade from 50 to 57.
Therefore, at 4 hours of study, the mar-
ginal product of an additional hour is 7.
6. Increasing study time from 10 to 11
hours
Increasing study time from 10 to 11
hours raises Alexei’s grade from 81 to
84. At 10 hours of study, the marginal
product of an additional hour is 3. As
we move along the curve, the slope of
the curve falls, so the marginal product
of an extra hour falls. The marginal
product is diminishing.
7. The average product of an hour
spent studying
When Alexei studies for four hours per
day his average product is 50/4 = 12.5
percentage points, which is the slope of
the ray from that point to the origin.
8. The marginal product is lower than
the average product
At 4 hours per day the average product
is 12.5. At 10 hours per day it is lower
(81/10 = 8.1). The average product falls
as we move along the curve. At each
point the marginal product (the slope
of the curve) is lower than the average
product (the slope of the ray).
9. The marginal product is the slope of
the tangent
The marginal product at four hours of
study is approximately 7, which is the
increase in the grade from one more
hour of study. More precisely, the mar-
ginal product is the slope of the
tangent at that point, which is slightly
higher than 7.
3.1 LABOUR AND PRODUCTION
93
diminishing returns A situation in
which the use of an additional unit
of a factor of production results in
a smaller increase in output than
the previous increase. Also known
as: diminishing marginal returns in
production
concave function A function of two
variables for which the line
segment between any two points
on the function lies entirely below
the curve representing the function
(the function is convex when the
line segment lies above the func-
tion).
tangency When two curves share
one point in common but do not
cross. The tangent to a curve at a
given point is a straight line that
touches the curve at that point but
does not cross it.
Alexei’s production function in Figure 3.5 gets flatter the more hours he
studies, so the marginal product of an additional hour falls as we move
along the curve. The marginal product is diminishing. The model captures
the idea that an extra hour of study helps a lot if you are not studying much,
but if you are already studying a lot, then studying even more does not help
very much.
In Figure 3.5, output increases as the input increases, but the marginal
product falls—the function becomes gradually flatter. A production func-
tion with this shape is described as concave.
If we compare the marginal and average products at any point on
Alexei’s production function, we find that the marginal product is below the
average product. For example, when he works for four hours his average
product is 50/4 = 12.5 points per hour, but an extra hour’s work raises his
grade from 50 to 57, so the marginal product is 7. This happens because the
marginal product is diminishing: each hour is less productive than the ones
that came before. And it implies that the average product is also
diminishing: each additional hour of study per day lowers the average
product of all his study time, taken as a whole.
This is another example of the diminishing average product of labour
that we saw in Unit 2. In that case, the average product of labour in food
production (the food produced per worker) fell as more workers cultivated
a fixed area of land.
Lastly, notice that if Alexei was already studying for 15 hours a day, the
marginal product of an additional hour would be zero. Studying more
would not improve his grade. As you might know from experience, a lack of
either sleep or time to relax could even lower Alexei’s grade if he worked
more than 15 hours a day. If this were the case, then his production func-
tion would start to slope downward, and Alexei’s marginal product would
become negative.
Marginal change is an important and common concept in economics.
You will often see it marked as a slope on a diagram. With a production
function like the one in Figure 3.5, the slope changes continuously as we
move along the curve. We have said that when Alexei studies for 4 hours a
day the marginal product is 7, the increase in the grade from one more hour
of study. Because the slope of the curve changes between 4 and 5 hours on
the horizontal axis, this is only an approximation to the actual marginal
product. More precisely, the marginal product is the rate at which the grade
increases, per hour of additional study. In Figure 3.5 the true marginal
product is the slope of the tangent to the curve at 4 hours. In this unit, we
will use approximations so that we can work in whole numbers, but you
may notice that sometimes these numbers are not quite the same as the
slopes.
EXERCISE 3.2 PRODUCTION FUNCTIONS
1. Draw a graph to show a production function that, unlike Alexei’s,
becomes steeper as the input increases.
2. Can you think of an example of a production process that might have
this shape? Why would the slope get steeper?
3. What can you say about the marginal and average products in this
case?
Leibniz: Average and marginal pro-
ductivity (https://tinyco.re/
L030101)
Leibniz: Diminishing marginal pro-
ductivity (https://tinyco.re/
L030102)
Leibniz: Concave and convex func-
tions (https://tinyco.re/L030103)
UNIT 3 SCARCITY, WORK, AND CHOICE
94
MARGINAL PRODUCT
The marginal product is the rate of
change of the grade at 4 hours of
study. Suppose Alexei has been
studying for 4 hours a day, and
studies for 1 minute longer each
day (a total of 4.016667 hours).
Then, according to the graph, his
grade will rise by a very small
amount—about 0.124. A more
precise estimate of the marginal
product (the rate of change) would
be:
If we looked at smaller changes in
study time even further (the rise in
grade for each additional second of
study per day, for example) we
would get closer to the true mar-
ginal product, which is the slope of
the tangent to the curve at 4 hours
of study.
preferences A description of the
benefit or cost we associate with
each possible outcome.
utility A numerical indicator of the
value that one places on an out-
come, such that higher valued
outcomes will be chosen over
lower valued ones when both are
feasible.
QUESTION 3.3 CHOOSE THE CORRECT ANSWER(S)
Figure 3.5 (page 93) shows Alexei’s production function, with the final
grade (the output) related to the number of hours spent studying (the
input).
Which of the following is true?
The marginal product and average product are approximately the
same for the initial hour.
The marginal product and the average product are both constant
beyond 15 hours.
The horizontal production function beyond 15 hours means that
studying for more than 15 hours is detrimental to Alexei’s
performance.
The marginal product and the average product at 20 hours are both
4.5.
3.2 PREFERENCES
If Alexei has the production function shown in Figure 3.5, how many hours
per day will he choose to study? The decision depends on his prefer-
ences—the things that he cares about. If he cared only about grades, he
should study for 15 hours a day. But, like other people, Alexei also cares
about his free time—he likes to sleep, go out or watch TV. So he faces a
trade-off: how many percentage points is he willing to give up in order to
spend time on things other than study?
We illustrate his preferences using Figure 3.6, with free time on the hori-
zontal axis and final grade on the vertical axis. Free time is defined as all the
time that he does not spend studying. Every point in the diagram represents
a different combination of free time and final grade. Given his production
function, not every combination that Alexei would want will be possible,
but for the moment we will only consider the combinations that he would
prefer.
We can assume:
• For a given grade, he prefers a combination with more free time to one
with less free time. Therefore, even though both A and B in Figure 3.6
correspond to a grade of 84, Alexei prefers A because it gives him more
free time.
• Similarly, if two combinations both have 20 hours of free time, he
prefers the one with a higher grade.
• But compare points A and D in the table. Would Alexei prefer D (low
grade, plenty of time) or A (higher grade, less time)? One way to find out
would be to ask him.
Suppose he says he is indifferent between A and D, meaning he would feel
equally satisfied with either outcome. We say that these two outcomes
would give Alexei the same utility. And we know that he prefers A to B, so
B provides lower utility than A or D.
A systematic way to graph Alexei’s preferences would be to start by
looking for all of the combinations that give him the same utility as A and
D. We could ask Alexei another question: ‘Imagine that you could have the
combination at A (15 hours of free time, 84 points). How many points
3.2 PREFERENCES
95
indifference curve A curve of the
points which indicate the combina-
tions of goods that provide a given
level of utility to the individual.
would you be willing to sacrifice for an extra hour of free time?’ Suppose
that after due consideration, he answers ‘nine’. Then we know that he is
indifferent between A and E (16 hours, 75 points). Then we could ask the
same question about combination E, and so on until point D. Eventually we
could draw up a table like the one in Figure 3.6. Alexei is indifferent
between A and E, between E and F, and so on, which means he is indifferent
between all of the combinations from A to D.
The combinations in the table are plotted in Figure 3.6, and joined
together to form a downward-sloping curve, called an indifference curve,
which joins together all of the combinations that provide equal utility or
‘satisfaction’.
Fi
na
l g
ra
de
0
84
75
50
Hours of free time per day
0 242015 16
100
AB
C
D
F
E
G
H
A E F G H D
Hours of free time 15 16 17 18 19 20
Final grade 84 75 67 60 54 50
Figure 3.6 Mapping Alexei’s preferences.
1. Alexei prefers more free time to less
free time
Combinations A and B both deliver a
grade of 84, but Alexei will prefer A
because it has more free time.
2. Alexei prefers a high grade to a low
grade
At combinations C and D Alexei has 20
hours of free time per day, but he
prefers D because it gives him a higher
grade.
3. Indifference
… but we don’t know whether Alexei
prefers A or E, so we ask him: he says
he is indifferent.
4. More combinations giving the same
utility
Alexei says that F is another combina-
tion that would give him the same
utility as A and E.
5. Constructing the indifference curve
By asking more questions, we discover
that Alexei is indifferent between all of
the combinations between A and D.
6. Constructing the indifference curve
These points are joined together to
form an indifference curve.
7. Other indifference curves
Indifference curves can be drawn
through any point in the diagram, to
show other points giving the same
utility. We can construct other curves
starting from B or C in the same way as
before, by finding out which combina-
tions give the same amount of utility.
UNIT 3 SCARCITY, WORK, AND CHOICE
96
consumption good A good or
service that satisfies the needs of
consumers over a short period.
marginal rate of substitution (MRS)
The trade-off that a person is
willing to make between two
goods. At any point, this is the slope
of the indifference curve. See also:
marginal rate of transformation.
If you look at the three curves drawn in Figure 3.6, you can see that the
one through A gives higher utility than the one through B. The curve
through C gives the lowest utility of the three. To describe preferences we
don’t need to know the exact utility of each option; we only need to know
which combinations provide more or less utility than others.
The curves we have drawn capture our typical assumptions about
people’s preferences between two goods. In other models, these will often
be consumption goods such as food or clothing, and we refer to the
person as a consumer. In our model of a student’s preferences, the goods
are ‘final grade’ and ‘free time’. Notice that:
• Indifference curves slope downward due to trade-offs: If you are indifferent
between two combinations, the combination that has more of one good
must have less of the other good.
• Higher indifference curves correspond to higher utility levels: As we move up
and to the right in the diagram, further away from the origin, we move
to combinations with more of both goods.
• Indifference curves are usually smooth: Small changes in the amounts of
goods don’t cause big jumps in utility.
• Indifference curves do not cross: Why? See Exercise 3.3.
• As you move to the right along an indifference curve, it becomes flatter.
To understand the last property in the list, look at Alexei’s indifference
curves, which are plotted again in Figure 3.7. If he is at A, with 15 hours of
free time and a grade of 84, he would be willing to sacrifice 9 percentage
points for an extra hour of free time, taking him to E (remember that he is
indifferent between A and E). We say that his marginal rate of substitu-
tion (MRS) between grade points and free time at A is nine; it is the
reduction in his grade that would keep Alexei’s utility constant following a
one-hour increase of free time.
We have drawn the indifference curves as becoming gradually flatter
because it seems reasonable to assume that the more free time and the
lower the grade he has, the less willing he will be to sacrifice further
percentage points in return for free time, so his MRS will be lower.
In Figure 3.7 we have calculated the MRS at each combination along the
indifference curve. You can see that, when Alexei has more free time and a
lower grade, the MRS—the number of percentage points he would give up
to get an extra hour of free time—gradually falls.
The MRS is just the slope of the indifference curve, and it falls as we
move to the right along the curve. If you think about moving from one
point to another in Figure 3.7, you can see that the indifference curves get
flatter if you increase the amount of free time, and steeper if you increase
the grade. When free time is scarce relative to grade points, Alexei is less
willing to sacrifice an hour for a higher grade: his MRS is high and his
indifference curve is steep.
As the analysis in Figure 3.7 shows, if you move up the vertical line
through 15 hours, the indifference curves get steeper: the MRS increases.
For a given amount of free time, Alexei is willing to give up more grade
points for an additional hour when he has a lot of points compared to when
he has few (for example, if he was in danger of failing the course). By the
time you reach A, where his grade is 84, the MRS is high; grade points are
so plentiful here that he is willing to give up 9 percentage points for an
extra hour of free time.
3.2 PREFERENCES
97
You can see the same effect if you fix the grade and vary the amount of
free time. If you move to the right along the horizontal line for a grade of
54, the MRS becomes lower at each indifference curve. As free time
becomes more plentiful, Alexei becomes less and less willing to give up
grade points for more time.
Leibniz: Indifference curves and
the marginal rate of substitution
(https://tinyco.re/L030201)
Fi
na
l g
ra
de
0
84
75
50
54
Hours of free time per day
0 2415 16
100
2019
A
E
D
H
A E F G H D
Hours of free time 15 16 17 18 19 20
Final grade 84 75 67 60 54 50
Marginal rate of substitution between grade and free
time
9 8 7 6 4
Figure 3.7 The marginal rate of substitution.
1. Alexei’s indifference curves
The diagram shows three indifference
curves for Alexei. The curve furthest to
the left offers the lowest satisfaction.
2. Point A
At A, he has 15 hours of free time and
his grade is 84.
3. Alexei is indifferent between A and E
He would be willing to move from A to
E, giving up 9 percentage points for an
extra hour of free time. His marginal
rate of substitution is 9. The indiffer-
ence curve is steep at A.
4. Alexei is indifferent between H and D
At H he is only willing to give up 4
points for an extra hour of free time.
His MRS is 4. As we move down the
indifference curve, the MRS diminishes,
because points become scarce relative
to free time. The indifference curve
becomes flatter.
5. All combinations with 15 hours of
free time
Look at the combinations with 15 hours
of free time. On the lowest curve the
grade is low, and the MRS is small.
Alexei would be willing to give up only
a few points for an hour of free time. As
we move up the vertical line the
indifference curves are steeper: the
MRS increases.
6. All combinations with a grade of 54
Now look at all the combinations with
a grade of 54. On the curve furthest to
the left, free time is scarce, and the
MRS is high. As we move to the right
along the red line he is less willing to
give up points for free time. The MRS
decreases–the indifference curves get
flatter.
UNIT 3 SCARCITY, WORK, AND CHOICE
98
EXERCISE 3.3 WHY INDIFFERENCE CURVES NEVER
CROSS
In the diagram below, IC1 is an indifference curve
joining all the combinations that give the same level of
utility as A. Combination B is not on IC1.
G
ra
de
Hours of free time per day
IC1
B
A
1. Does combination B give higher or lower utility than
combination A? How do you know?
2. Draw a sketch of the diagram, and add another
indifference curve, IC2, that goes through B and
crosses IC1. Label the point at which they cross as C.
3. Combinations B and C are both on IC2. What does
that imply about their levels of utility?
4. Combinations C and A are both on IC1. What does
that imply about their levels of utility?
5. According to your answers to (3) and (4), how do the
levels of utility at combinations A and B compare?
6. Now compare your answers to (1) and (5), and
explain how you know that indifference curves can
never cross.
EXERCISE 3.4 YOUR MARGINAL RATE OF
SUBSTITUTION
Imagine that you are offered a job at the end of your
university course with a salary per hour (after taxes) of
£12.50. Your future employer then says that you will
work for 40 hours per week leaving you with 128 hours
of free time per week. You tell a friend: ‘at that wage, 40
hours is exactly what I would like.’
1. Draw a diagram with free time on the horizontal axis
and weekly pay on the vertical axis, and plot the
combination of hours and the wage corresponding
to your job offer, calling it A. Assume you need about
10 hours a day for sleeping and eating, so you may
want to draw the horizontal axis with 70 hours at the
origin.
2. Now draw an indifference curve so that A represents
the hours you would have chosen yourself.
3. Now imagine you were offered another job requiring
45 hours of work per week. Use the indifference
curve you have drawn to estimate the level of
weekly pay that would make you indifferent
between this and the original offer.
4. Do the same for another job requiring 35 hours of
work per week. What level of weekly pay would
make you indifferent between this and the original
offer?
5. Use your diagram to estimate your marginal rate of
substitution between pay and free time at A.
3.2 PREFERENCES
99
opportunity cost When taking an
action implies forgoing the next
best alternative action, this is the
net benefit of the foregone
alternative.
AccountAnt:
Economist:
QUESTION 3.4 CHOOSE THE CORRECT ANSWER(S)
Figure 3.6 (page 96) shows Alexei’s indifference curves for free time
and final grade. Which of the following is true?
Alexei prefers C to B because at C he has more free time.
Alexei is indifferent between the grade of 84 with 15 hours of free
time, and the grade of 50 with 20 hours of free time.
Alexei prefers D to C, because at D he has the same grade and more
free time.
At G, Alexei is willing to give up 2 hours of free time for 10 extra
grade points.
QUESTION 3.5 CHOOSE THE CORRECT ANSWER(S)
What is the marginal rate of substitution (MRS)?
The ratio of the amounts of the two goods at a point on the indiffer-
ence curve.
The amount of one good that the consumer is willing to trade for
one unit of the other.
The change in the consumer’s utility when one good is substituted
for another.
The slope of the indifference curve.
3.3 OPPORTUNITY COSTS
Alexei faces a dilemma: we know from looking at his preferences that he
wants both his grade and his free time to be as high as possible. But given
his production function, he cannot increase his free time without getting a
lower grade in the exam. Another way of expressing this is to say that free
time has an opportunity cost: to get more free time, Alexei has to forgo the
opportunity of getting a higher grade.
In economics, opportunity costs are relevant whenever we study indi-
viduals choosing between alternative and mutually exclusive courses of
action. When we consider the cost of taking action A we include the fact
that if we do A, we cannot do B. So ‘not doing B’ becomes part of the cost of
doing A. This is called an opportunity cost because doing A means forgoing
the opportunity to do B.
Imagine that an accountant and an economist have been asked to report
the cost of going to a concert, A, in a theatre, which has a $25 admission
cost. In a nearby park there is concert B, which is free but happens at the
same time.
The cost of concert A is your ‘out-of-pocket’ cost: you paid
$25 for a ticket, so the cost is $25.
But what do you have to give up to go to concert A? You give
up $25, plus the enjoyment of the free concert in the park. So the
cost of concert A for you is the out-of-pocket cost plus the oppor-
tunity cost.
Suppose that the most you would have been willing to pay to attend the free
concert in the park (if it wasn’t free) was $15. The benefit of your next best
UNIT 3 SCARCITY, WORK, AND CHOICE
100
economic cost The out-of-pocket
cost of an action, plus the oppor-
tunity cost.
AccountAnt:
Economist:
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.
alternative to concert A would be $15 of enjoyment in the park. This is the
opportunity cost of going to concert A.
So the total economic cost of concert A is $25 + $15 = $40. If the
pleasure you anticipate from being at concert A is greater than the eco-
nomic cost, say $50, then you will forego concert B and buy a ticket to the
theatre. On the other hand, if you anticipate $35 worth of pleasure from
concert A, then the economic cost of $40 means you will not choose to go
to the theatre. In simple terms, given that you have to pay $25 for the ticket,
you will instead opt for concert B, pocketing the $25 to spend on other
things and enjoying $15 worth of benefit from the free park concert.
Why don’t accountants think this way? Because it is not their job.
Accountants are paid to keep track of money, not to provide decision rules
on how to choose among alternatives, some of which do not have a stated
price. But making sensible decisions and predicting how sensible people
will make decisions involve more than keeping track of money. An
accountant might argue that the park concert is irrelevant:
Whether or not there is a free park concert does not affect
the cost of going to the concert A. The cost to you is always $25.
But whether or not there is a free park concert can affect
whether you go to concert A or not, because it changes your avail-
able options. If your enjoyment from A is $35 and your next best
alternative is staying at home, with enjoyment of $0, you will choose
concert A. However, if concert B is available, you will choose it
over A.
In Unit 2, we said that if an action brings greater net benefits than the next
best alternative, it yields an economic rent and you will do it. Another way
of saying this is that you receive an economic rent from taking an action
when it results in a benefit greater than its economic cost (the sum of out-
of-pocket and opportunity costs).
The table in Figure 3.8 summarizes the example of your choice of which
concert to attend.
A high value on
the theatre choice (A)
A low value on
the theatre choice (A)
Out-of-pocket cost (price of ticket for A) $25 $25
Opportunity cost (foregone pleasure of B, park
concert)
$15 $15
Economic cost (sum of out-of-pocket and opportunity
cost)
$40 $40
Enjoyment of theatre concert (A) $50 $35
Economic rent (enjoyment minus economic cost) $10 −$5
Decision A: Go to the theatre concert. B: Go to the park concert.
Figure 3.8 Opportunity costs and economic rent: Which concert will you choose?
3.3 OPPORTUNITY COSTS
101
feasible frontier The curve made of
points that defines the maximum
feasible quantity of one good for a
given quantity of the other. See
also: feasible set.
QUESTION 3.6 CHOOSE THE CORRECT ANSWER(S)
You are a taxi driver in Melbourne who earns A$50 for a day’s work.
You have been offered a one-day ticket to the Australian Open for
A$40. As a tennis fan, you value the experience at A$100. With this
information, what can we say?
The opportunity cost of the day at the Open is A$40.
The economic cost of the day at the Open is A$40.
The economic rent of the day at the Open is A$10.
You would have paid up to A$100 for the ticket.
EXERCISE 3.5 OPPORTUNITY COSTS
The British government introduced legislation in 2012 that gave
universities the option to raise their tuition fees. Most chose to increase
annual tuition fees for students from £3,000 to £9,000.
Does this mean that the cost of going to university has tripled? (Think
about how an accountant and an economist might answer this question.
To simplify, assume that the tuition fee is an ‘out of pocket’ cost. Ignore
student loans.)
3.4 THE FEASIBLE SET
Now we return to Alexei’s problem of how to choose between grades and
free time. Free time has an opportunity cost in the form of lost percentage
points in his grade (equivalently, we might say that percentage points have
an opportunity cost in the form of the free time Alexei has to give up to
obtain them). But before we can describe how Alexei resolves his dilemma,
we need to work out precisely which alternatives are available to him.
To answer this question, we look again at the production function. This
time we will show how the final grade depends on the amount of free time,
rather than study time. There are 24 hours in a day. Alexei must divide this
time between studying (all the hours devoted to learning) and free time (all
the rest of his time). Figure 3.9 shows the relationship between his final
grade and hours of free time per day—the mirror image of Figure 3.5. If
Alexei studies solidly for 24 hours, that means zero hours of free time and a
final grade of 90. If he chooses 24 hours of free time per day, we assume he
will get a grade of zero.
In Figure 3.9, the axes are final grade and free time, the two goods that
give Alexei utility. If we think of him choosing to consume a combination
of these two goods, the curved line in Figure 3.9 shows what is feasible. It
represents his feasible frontier: the highest grade he can achieve given the
amount of free time he takes. Follow the steps in Figure 3.9 to see which
combinations of grade and free time are feasible, and which are not, and
how the slope of the frontier represents the opportunity cost of free time.
UNIT 3 SCARCITY, WORK, AND CHOICE
102
D0
90
100
Hours of free time per day
0 24
80
14
E
A
C
70
50
40
30
20
10
Feasible set
13
60
19 20
F
Fi
na
l g
ra
de
B
A E C F
Free time 13 14 19 20
Grade 84 81 57 50
Opportunity cost 3 7
Figure 3.9 How does Alexei’s choice of free time affect his grade?
1. The feasible frontier
This curve is called the feasible
frontier. It shows the highest final
grade Alexei can achieve given the
amount of free time he takes. With 24
hours of free time, his grade would be
zero. By having less free time, Alexei
can achieve a higher grade.
2. A feasible combination
If Alexei chooses 13 hours of free time
per day, he can achieve a grade of 84.
3. Infeasible combinations
Given Alexei’s abilities and conditions
of study, under normal conditions he
cannot take 20 hours of free time and
expect to get a grade of 70 (remember,
we are assuming that luck plays no
part). Therefore B is an infeasible com-
bination of hours of free time and final
grade.
4. A feasible combination
The maximum grade Alexei can
achieve with 19 hours of free time per
day is 57.
5. Inside the frontier
Combination D is feasible, but Alexei is
wasting time or points in the exam. He
could get a higher grade with the same
hours of study per day, or have more
free time and still get a grade of 70.
6. The feasible set
The area inside the frontier, together
with the frontier itself, is called the
feasible set. (A set is a collection of
things–in this case all the feasible com-
binations of free time and grade.)
7. The opportunity cost of free time
At combination A Alexei could get an
extra hour of free time by giving up 3
points in the exam. The opportunity
cost of an hour of free time at A is 3
points.
8. The opportunity cost varies
The more free time he takes, the higher
the marginal product of studying, so
the opportunity cost of free time
increases. At C the opportunity cost of
an hour of free time is higher than at A:
Alexei would have to give up 7 points.
9. The slope of the feasible frontier
The opportunity cost of free time at C is
7 points, corresponding to the slope of
the feasible frontier. At C, Alexei would
have to give up 7 percentage points
(the vertical change is −7) to increase
his free time by 1 hour (the horizontal
change is 1). The slope is −7.
3.4 THE FEASIBLE SET
103
feasible set All of the combinations
of the things under consideration
that a decision-maker could choose
given the economic, physical or
other constraints that he faces. See
also: feasible frontier.
marginal rate of transformation
(MRT) The quantity of some good
that must be sacrificed to acquire
one additional unit of another
good. At any point, it is the slope of
the feasible frontier. See also: mar-
ginal rate of substitution.
Any combination of free time and final grade that is on or inside the
frontier is feasible. Combinations outside the feasible frontier are said to be
infeasible given Alexei’s abilities and conditions of study. On the other
hand, even though a combination lying inside the frontier is feasible,
choosing it would imply Alexei has effectively thrown away something that
he values. If he studied for 14 hours a day, then according to our model, he
could guarantee himself a grade of 89. But he could obtain a lower grade
(70, say), if he just stopped writing before the end of the exam. It would be
foolish to throw away points like this for no reason, but it would be
possible. Another way to obtain a combination inside the frontier might be
to sit in the library doing nothing—Alexei would be taking less free time
than is available to him, which again makes no sense.
By choosing a combination inside the frontier, Alexei would be giving
up something that is freely available—something that has no opportunity
cost. He could obtain a higher grade without sacrificing any free time, or
have more time without reducing his grade.
The feasible frontier is a constraint on Alexei’s choices. It represents the
trade-off he must make between grade and free time. At any point on the
frontier, taking more free time has an opportunity cost in terms of grade
points foregone, corresponding to the slope of the frontier.
Another way to express the same idea is to say that the feasible frontier
shows the marginal rate of transformation: the rate at which Alexei can
transform free time into grade points. Look at the slope of the frontier
between points A and E in Figure 3.9.
• The slope of AE (vertical distance divided by horizontal distance) is −3.
• At point A, Alexei could get one more unit of free time by giving up 3
grade points. The opportunity cost of a unit of free time is 3.
• At point E, Alexei could transform one unit of time into 3 grade points.
The marginal rate at which he can transform free time into grade points
is 3.
Note that the slope of AE is only an approximation to the slope of the
frontier. More precisely, the slope at any point is the slope of the tangent,
and this represents both the MRT and the opportunity cost at that point.
Note that we have now identified two trade-offs:
• The marginal rate of substitution (MRS): In the previous section, we saw
that it measures the trade-off that Alexei is willing to make between final
grade and free time.
• The marginal rate of transformation (MRT): In contrast, this measures the
trade-off that Alexei is constrained to make by the feasible frontier.
As we shall see in the next section, the choice Alexei makes between his
grade and his free time will strike a balance between these two trade-offs.
Leibniz: Marginal rates of
transformation and substitution
(https://tinyco.re/L030401)
UNIT 3 SCARCITY, WORK, AND CHOICE
104
QUESTION 3.7 CHOOSE THE CORRECT ANSWER(S)
Look at Figure 3.5 (page 93) which shows Alexei’s production function:
how the final grade (the output) depends on the number of hours spent
studying (the input).
Free time per day is given by 24 hours minus the hours of study per
day. Consider Alexei’s feasible set of combinations of final grade and
hours of free time per day. What can we conclude?
To find the feasible set one needs to know the number of hours that
Alexei sleeps per day.
The feasible frontier is a mirror image of the production function
above.
The feasible frontier is horizontal between 0 and 10 hours of free
time per day.
The marginal product of labour at 10 hours of study equals the mar-
ginal rate of transformation at 14 hours of free time.
3.5 DECISION MAKING AND SCARCITY
The final step in this decision-making process is to determine the combina-
tion of final grade and free time that Alexei will choose. Figure 3.10a brings
together his feasible frontier (Figure 3.9) and indifference curves (Figure
3.6). Recall that the indifference curves indicate what Alexei prefers, and
their slopes shows the trade-offs that he is willing to make; the feasible
frontier is the constraint on his choice, and its slope shows the trade-off he
is constrained to make.
Figure 3.10a shows four indifference curves, labelled IC1 to IC4. IC4
represents the highest level of utility because it is the furthest away from
the origin. No combination of grade and free time on IC4 is feasible, how-
ever, because the whole indifference curve lies outside the feasible set.
Suppose that Alexei considers choosing a combination somewhere in the
feasible set, on IC1. By working through the steps in Figure 3.10a, you will
see that he can increase his utility by moving to points on higher indiffer-
ence curves until he reaches a feasible choice that maximizes his utility.
Alexei maximizes his utility at point E, at which his indifference curve is
tangent to the feasible frontier. The model predicts that Alexei will:
• choose to spend 5 hours each day studying, and 19 hours on other
activities
• obtain a grade of 57 as a result
We can see from Figure 3.10a that at E, the feasible frontier and the highest
attainable indifference curve IC3 are tangent to each other (they touch but
do not cross). At E, the slope of the indifference curve is the same as the
slope of the feasible frontier. Now, remember that the slopes represent the
two trade-offs facing Alexei:
• The slope of the indifference curve is the MRS: It is the trade-off he is
willing to make between free time and percentage points.
• The slope of the frontier is the MRT: It is the trade-off that he is
constrained to make between free time and percentage points because it
is not possible to go beyond the feasible frontier.
3.5 DECISION MAKING AND SCARCITY
105
Alexei achieves the highest possible utility where the two trade-offs just
balance (E). His optimal combination of grade and free time is at the point
where the marginal rate of transformation is equal to the marginal rate of
substitution.
Figure 3.10b shows the MRS (slope of indifference curve) and MRT
(slope of feasible frontier) at the points shown in Figure 3.10a. At B and D,
the number of points Alexei is willing to trade for an hour of free time
(MRS) is greater than the opportunity cost of that hour (MRT), so he
Leibniz: Optimal allocation of free
time: MRT meets MRS
(https://tinyco.re/L030501)
Fi
na
l g
ra
de
0
90
Hours of free time per day
0 24
57
100
Feasible frontier
IC1
IC2
IC3
IC4
B
A
C
D
E
19
MRS = MRT
Figure 3.10a How many hours does Alexei decide to study?
1. Which point will Alexei choose?
The diagram brings together Alexei’s
indifference curves and his feasible
frontier.
2. Feasible combinations
On the indifference curve IC1, all com-
binations between A and B are feasible
because they lie in the feasible set.
Suppose Alexei chooses one of these
points.
3. Could do better
All combinations in the lens-shaped
area between IC1 and the feasible
frontier are feasible, and give higher
utility than combinations on IC1. For
example, a movement to C would
increase Alexei’s utility.
4. Could do better
Moving from IC1 to point C on IC2
increases Alexei’s utility. Switching
from B to D would raise his utility by an
equivalent amount.
5. The best feasible trade-off
But again, Alexei can raise his utility by
moving into the lens-shaped area
above IC2. He can continue to find feas-
ible combinations on higher
indifference curves, until he reaches E.
6. The best feasible trade-off
At E, he has 19 hours of free time per
day and a grade of 57. Alexei
maximizes his utility: he is on the high-
est indifference curve obtainable, given
the feasible frontier.
7. MRS = MRT
At E the indifference curve is tangent to
the feasible frontier. The marginal rate
of substitution (the slope of the
indifference curve) is equal to the mar-
ginal rate of transformation (the slope
of the frontier).
UNIT 3 SCARCITY, WORK, AND CHOICE
106
constrained choice problem This
problem is about how we can do
the best for ourselves, given our
preferences and constraints, and
when the things we value are
scarce. See also: constrained
optimization problem.
prefers to increase his free time. At A, the MRT is greater than the MRS so
he prefers to decrease his free time. And, as expected, at E the MRS and
MRT are equal.
We have modelled the student’s decision on study hours as what we call
a constrained choice problem: a decision-maker (Alexei) pursues an
objective (utility maximization in this case) subject to a constraint (his feas-
ible frontier).
In our example, both free time and points in the exam are scarce for
Alexei because:
• Free time and grades are goods: Alexei values both of them.
• Each has an opportunity cost: More of one good means less of the other.
In constrained choice problems, the solution is the individual’s optimal
choice. If we assume that utility maximization is Alexei’s goal, the optimal
combination of grade and free time is a point on the feasible frontier at
which:
The table in Figure 3.11 summarizes Alexei’s trade-offs.
EXERCISE 3.6 EXPLORING SCARCITY
Describe a situation in which Alexei’s grade points and free time would not
be scarce. Remember, scarcity depends on both his preferences and the
production function.
B D E A
Free time 13 15 19 22
Grade 84 78 57 33
MRT 2 4 7 9
MRS 20 15 7 3
Figure 3.10b How many hours does Alexei decide to study?
The trade-off Where it is on the
diagram
It is equal to …
MRS Marginal rate of substitution: The number of
percentage points Alexei is willing to trade for an
hour of free time
The slope of the
indifference curve
MRT, or opportunity
cost of free time
Marginal rate of transformation: The number of
percentage points Alexei would gain (or lose) by
giving up (or taking) another hour of free time
The slope of the
feasible frontier
The marginal product
of labour
Figure 3.11 Alexei’s trade-offs.
3.5 DECISION MAKING AND SCARCITY
107
QUESTION 3.8 CHOOSE THE CORRECT ANSWER(S)
Figure 3.10a (page 106) shows Alexei’s feasible frontier and his indiffer-
ence curves for final grade and hours of free time per day. Suppose
that all students have the same feasible frontier, but their indifference
curves may differ in shape and slope depending on their preferences.
Use the diagram to decide which of the following is (are) correct.
Alexei will choose a point where the marginal rate of substitution
equals the marginal rate of transformation.
C is below the feasible frontier but D is on the feasible frontier.
Therefore, Alexei may select point D as his optimal choice.
All students with downward-sloping indifference curves, whatever
the slope, would choose point E.
At E, Alexei has the highest ratio of final grade per hour of free time
per day.
••3.6 HOURS OF WORK AND ECONOMIC GROWTH
In 1930, John Maynard Keynes, a British economist, published an essay
entitled ‘Economic Possibilities for our Grandchildren’, in which he
suggested that in the 100 years that would follow, technological
improvement would make us, on average, about eight times better off. What
he called ‘the economic problem, the struggle for subsistence’ would be
solved, and we would not have to work more than, say, 15 hours per week
to satisfy our economic needs. The question he raised was: how would we
cope with all of the additional leisure time?
Keynes’ prediction for the rate of technological progress in countries
such as the UK and the US has been approximately right, and working
hours have indeed fallen, although much less than he expected—it seems
unlikely that average working hours will be 15 hours per week by 2030. An
article by Tim Harford in the Undercover Economist column of the Finan-
cial Times examines why Keynes’ prediction was wrong.
As we saw in Unit 2, new technologies raise the productivity of labour.
We now have the tools to analyse the effects of increased productivity on
living standards, specifically on incomes and the free time of workers.
So far, we have considered Alexei’s choice between studying and free
time. We now apply our model of constrained choice to Angela, a self-
sufficient farmer who chooses how many hours to work. We assume that
Angela produces grain to eat and does not sell it to anyone else. If she
produces too little grain, she will starve.
What is stopping her producing the most grain possible? Like the
student, Angela also values free time—she gets utility from both free time
and consuming grain.
But her choice is constrained: producing grain takes labour time, and
each hour of labour means Angela foregoes an hour of free time. The hour
of free time sacrificed is the opportunity cost of the grain produced. Like
Alexei, Angela faces a problem of scarcity: she has to make a choice between
her consumption of grain and her consumption of free time.
To understand her choice, and how it is affected by technological
change, we need to model her production function, and her preferences.
John Maynard Keynes. 1963. ‘Eco-
nomic Possibilities for our
Grandchildren’. In Essays in
Persuasion, New York, NY:
W. W. Norton & Co.
Tim Harford. 2015. ‘The rewards
for working hard are too big for
Keynes’s vision’. The Undercover
Economist. First published by The
Financial Times. Updated 3 August
2015.
UNIT 3 SCARCITY, WORK, AND CHOICE
108
Figure 3.12 shows the initial production function before the change
occurs: the relationship between the number of hours worked and the
amount of grain produced. Notice that the graph has a similar concave
shape to Alexei’s production function: the marginal product of an addi-
tional hour’s work, shown by the slope, diminishes as the number of hours
increases.
A technological improvement such as seeds with a higher yield, or better
equipment that makes harvesting quicker, will increase the amount of grain
produced in a given number of hours. The analysis in Figure 3.12
demonstrates the effect on the production function.
Notice that the new production function is steeper than the original one
for every given number of hours. The new technology has increased
Angela’s marginal product of labour: at every point, an additional hour of
work produces more grain than under the old technology.
Q
ua
nt
ity
o
f g
ra
in
p
ro
du
ce
d
0
74
64
100
Hours of work per day
0 8 12 24
C
PFnew
PF
D
B
Working
hours
0 1 2 3 4 5 6 7 8 9 10 11 12 13 18 24
Grain 0 9 18 26 33 40 46 51 55 58 60 62 64 66 69 72
Figure 3.12 How technological change affects the production function.
1. The initial technology
The table shows how the amount of
grain produced depends on the number
of hours worked per day. For example,
if Angela works for 12 hours a day she
will produce 64 units of grain. This is
point B on the graph.
2. A technological improvement
An improvement in technology means
that more grain is produced for a given
number of working hours. The produc-
tion function shifts upward, from PF to
PFnew.
3. More grain for the same amount of
work
Now if Angela works for 12 hours per
day, she can produce 74 units of grain
(point C).
4. Or same grain, less work
Alternatively, by working 8 hours a day
she can produce 64 units of grain (point
D), which previously took 12 hours.
3.6 HOURS OF WORK AND ECONOMIC GROWTH
109
Figure 3.13 shows Angela’s feasible frontier, which is just the mirror
image of the production function, for the original technology (FF), and the
new one (FFnew).
As before, what we call free time is all of the time that is not spent
working to produce grain—it includes time for eating, sleeping, and
everything else that we don’t count as farm work, as well as her leisure time.
The feasible frontier shows how much grain can be produced and con-
sumed for each possible amount of free time. Points B, C, and D represent
the same combinations of free time and grain as in Figure 3.12. The slope of
the frontier represents the MRT (the marginal rate at which free time can
be transformed into grain) or equivalently the opportunity cost of free time.
You can see that technological progress expands the feasible set: it gives her
a wider choice of combinations of grain and free time.
Now we add Angela’s indifference curves to the diagram, representing
her preferences for free time and grain consumption, to find which com-
bination in the feasible set is best for her. Figure 3.14 shows that her
optimal choice under the original technology is to work for 8 hours a day,
giving her 16 hours of free time and 55 units of grain. This is the point of
tangency, where her two trade-offs balance out: her marginal rate of substi-
tution (MRS) between grain and free time (the slope of the indifference
curve) is equal to the MRT (the slope of the feasible frontier). We can think
of the combination of free time and grain at point A as a measure of her
standard of living.
Follow the steps in Figure 3.14 to see how her choice changes as a result
of technological progress.
Technological change raises Angela’s standard of living: it enables her to
achieve higher utility. Note that in Figure 3.14 she increases both her con-
sumption of grain and her free time.
It is important to realize that this is just one possible result. Had we
drawn the indifference curves or the frontier differently, the trade-offs
Angela faces would have been different. We can say that the improvement
in technology definitely makes it feasible to both consume more grain and
Leibniz: Modelling technological
change (https://tinyco.re/L030601)
Q
ua
nt
ity
o
f g
ra
in
p
ro
du
ce
d
0
74
64
100
Hours of free time per day
0 1612 24
CFF
DB
FFnew
Figure 3.13 An improvement in technology expands Angela’s feasible set.
UNIT 3 SCARCITY, WORK, AND CHOICE
110
have more free time, but whether Angela will choose to have more of both
depends on her preferences between these two goods, and her willingness
to substitute one for the other.
To understand why, remember that technological change makes the pro-
duction function steeper: it increases Angela’s marginal product of labour.
This means that the opportunity cost of free time is higher, giving her a
greater incentive to work. But also, now that she can have more grain for
each amount of free time, she may be more willing to give up some grain
for more free time: that is, reduce her hours of work.
These two effects of technological progress work in opposite directions.
In Figure 3.14, the second effect dominates and she chooses point E, with
more free time as well as more grain. In the next section, we look more
carefully at these two opposing effects, using a different example to
disentangle them.
FFnew
Q
ua
nt
ity
o
f g
ra
in
p
ro
du
ce
d
0
61
55
100
0 16 17 24
FF
A
E
IC1
IC2
IC3
IC4
MRS = MRT
Hours of free time per day
Figure 3.14 Angela’s choice between free time and grain.
1. Maximizing utility with the original
technology
The diagram shows the feasible set
with the original production function,
and Angela’s indifference curves for
combinations of grain and free time.
The highest indifference curve she can
attain is IC3, at point A.
2. MRS = MRT for maximum utility
Her optimal choice is point A on the
feasible frontier. She enjoys 16 hours of
free time per day and consumes 55
units of grain. At A, her MRS is equal to
the MRT.
3. Technological progress
An improvement in technology
expands the feasible set. Now she can
do better than at A.
4. Angela’s new optimal choice
When the technology of farming has
improved, Angela’s optimal choice is
point E, where FFnew is tangent to
indifference curve IC4. She has more
free time and more grain than before.
3.6 HOURS OF WORK AND ECONOMIC GROWTH
111
025
50
75
100
Hours of study per day
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Fi
na
l g
ra
de
Fi
na
l g
ra
de
0
25
50
75
100
Hours of free time per day
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
QUESTION 3.9 CHOOSE THE CORRECT ANSWER(S)
The figures show Alexei’s production function and his
corresponding feasible frontier for final grade and
hours of work or free time per day. They show the
effect of an improvement in his studying technique,
represented by the tilting up of the two curves.
Consider now two cases of further changes in Alexei’s
study environment:
Case A. He suddenly finds himself needing to spend 4
hours a day caring for a family member. (You may
assume that his marginal product of labour is
unaffected for the hours that he studies.)
Case B. For health reasons his marginal product of
labour for all hours is reduced by 10%.
Then:
For case A, Alexei’s production function shifts to
the right.
For case A, Alexei’s feasible frontier shifts to the
left.
For case B, Alexei’s production function shifts
down in a parallel manner.
For case B, Alexei’s feasible frontier rotates down-
wards, pivoted at the intercept with the horizontal
axis.
EXERCISE 3.7 YOUR PRODUCTION FUNCTION
1. What could bring about a technological improvement in your produc-
tion function and those of your fellow students?
2. Draw a diagram to illustrate how this improvement would affect your
feasible set of grades and study hours.
3. Analyse what might happen to your choice of study hours, and the
choices that your peers might make.
3.7 INCOME AND SUBSTITUTION EFFECTS ON HOURS
OF WORK AND FREE TIME
Imagine that you are looking for a job after you leave college. You expect to
be able to earn a wage of $15 per hour. Jobs differ according to the number
of hours you have to work—so what would be your ideal number of hours?
Together, the wage and the hours of work will determine how much free
time you will have, and your total earnings.
We will work in terms of daily average free time and consumption, as we
did for Angela. We will assume that your spending—that is, your average
consumption of food, accommodation, and other goods and services—
cannot exceed your earnings (for example, you cannot borrow to increase
your consumption). If we write w for the wage, and you have t hours of free
UNIT 3 SCARCITY, WORK, AND CHOICE
112
budget constraint An equation that
represents all combinations of
goods and services that one could
acquire that exactly exhaust one’s
budgetary resources.
time per day, then you work for (24 − t) hours, and your maximum level of
consumption, c, is given by:
We will call this your budget constraint, because it shows what you can
afford to buy.
In the table in Figure 3.15 we have calculated your free time for hours
of work varying between 0 and 16 hours per day, and your maximum con-
sumption, when your wage is w = $15.
Figure 3.15 shows the two goods in this problem: hours of free time (t)
on the horizontal axis, and consumption (c) on the vertical axis. When we
plot the points shown in the table, we get a downward-sloping straight line:
this is the graph of the budget constraint. The equation of the budget con-
straint is:
The slope of the budget constraint corresponds to the wage: for each addi-
tional hour of free time, consumption must decrease by $15. The area
under the budget constraint is your feasible set. Your problem is quite
similar to Angela’s problem, except that your feasible frontier is a straight
line. Remember that for Angela the slope of the feasible frontier is both the
MRT (the rate at which free time could be transformed into grain) and the
opportunity cost of an hour of free time (the grain foregone). These vary
because Angela’s marginal product changes with her hours of work. For
you, the marginal rate at which you can transform free time into consump-
tion, and the opportunity cost of free time, is constant and is equal to your
wage (in absolute value): it is $15 for your first hour of work, and still $15
for every hour after that.
What would be your ideal job? Your preferred choice of free time and
consumption will be the combination on the feasible frontier that is on the
highest possible indifference curve. Work through Figure 3.15 to find the
optimal choice.
If your indifference curves look like the ones in Figure 3.15, then you
would choose point A, with 18 hours of free time. At this point your MRS—
the rate at which you are willing to swap consumption for time—is equal to
the wage ($15, the opportunity cost of time). You would like to find a job in
which you can work for 6 hours per day, and your daily earnings would be
$90.
Like the student, you are balancing two trade-offs:
Your optimal combination of consumption and free time is the point on
the budget constraint where:
3.7 INCOME AND SUBSTITUTION EFFECTS ON HOURS OF WORK AND FREE TIME
113
While considering this decision, you receive an email. A mysterious
benefactor would like to give you an income of $50 a day—for life (all you
have to do is provide your banking details.) You realize at once that this will
affect your choice of job. The new situation is shown in Figure 3.17: for
each level of free time, your total income (earnings plus the mystery gift) is
$50 higher than before. So the budget constraint is shifted upwards by
$50—the feasible set has expanded. Your budget constraint is now:
Co
ns
um
pt
io
n
($
)
0
75
225
150
300
Hours of free time
8 10 12 14 16 18 20 22 24
IC1
IC2
A
Hours of work 0 2 4 6 8 10 12 14 16
Free time, t 24 22 20 18 16 14 12 10 8
Consumption, c 0 $30 $60 $90 $120 $150 $180 $210 $240
The equation of the budget constraint is c = w(24 − t)
The wage is w = $15, so the budget constraint is c = 15(24 − t)
Figure 3.15 Your preferred choice of free time and consumption.
1. The budget constraint
The straight line is your budget con-
straint: it shows the maximum amount
of consumption you can have for each
level of free time.
2. The slope of the budget constraint
The slope of the budget constraint is
equal to the wage, $15 (in absolute
value). This is your MRT (the rate at
which you can transform time into con-
sumption), and it is also the opportunity
cost of free time.
3. The feasible set
The budget constraint is your feasible
frontier, and the area below it is the
feasible set.
4. Your ideal job
Your indifference curves show that your
ideal job would be at point A, with 18
hours of free time and daily earnings of
$90. At this point your MRS is equal to
the slope of the budget constraint,
which is the wage ($15).
UNIT 3 SCARCITY, WORK, AND CHOICE
114
income effect The effect that the
additional income would have if
there were no change in the price
or opportunity cost.
Notice that the extra income of $50 does not change your opportunity cost
of time: each hour of free time still reduces your consumption by $15 (the
wage). Your new ideal job is at B, with 19.5 hours of free time. B is the point
on IC3 where the MRS is equal to $15. With the indifference curves shown
in this diagram, your response to the extra income is not simply to spend
$50 more; you increase consumption by less than $50, and you take some
extra free time. Someone with different preferences might not choose to
increase their free time: Figure 3.18 shows a case in which the MRS at each
value of free time is the same on both IC2 and the higher indifference curve
IC3. This person chooses to keep their free time the same, and consume $50
more.
The effect of additional (unearned) income on the choice of free time is
called the income effect. Your income effect, shown in Figure 3.17, is pos-
itive—extra income raises your choice of free time. For the person in Figure
3.18, the income effect is zero. We assume that for most goods the income
effect will be either positive or zero, but not negative: if your income
increased, you would not choose to have less of something that you valued.
The trade-off Where it is on the diagram
MRS Marginal rate of substitution: The amount of
consumption you are willing to trade for an
hour of free time.
The slope of the
indifference curve.
MRT Marginal rate of transformation: The amount
of consumption you can gain from giving up an
hour of free time, which is equal to the wage,
w.
The slope of the budget
constraint (the feasible
frontier) which is equal to
the wage.
Figure 3.16 Your two trade-offs.
Co
ns
um
pt
io
n
($
)
0
75
225
150
300
Hours of free time
8 10 12 14 16 18 20 22 24
IC1
IC2
IC3
A
B
Figure 3.17 The effect of additional income on your choice of free time and
consumption.
3.7 INCOME AND SUBSTITUTION EFFECTS ON HOURS OF WORK AND FREE TIME
115
You suddenly realize that it might not be wise to give the mysterious
stranger your bank account details (perhaps it is a hoax). With regret you
return to the original plan, and find a job requiring 6 hours of work per day.
A year later, your fortunes improve: your employer offers you a pay rise of
$10 per hour and the chance to renegotiate your hours. Now your budget
constraint is:
In Figure 3.19a you can see how the budget constraint changes when the
wage rises. With 24 hours of free time (and no work), your consumption
would be 0 whatever the wage. But for each hour of free time you give up,
your consumption can now rise by $25 rather than $15. So your new
budget constraint is a steeper straight line through (24, 0), with a slope
equal to $25. Your feasible set has expanded. And now you achieve the
highest possible utility at point D, with only 17 hours of free time. So you
ask your employer if you can work longer hours—a 7-hour day.
Compare the outcomes in Figure 3.17 and 3.19a. With an increase in
unearned income you want to work fewer hours, while the wage increase in
Figure 3.19a makes you decide to increase your working hours. Why does
this happen? Because there are two effects of a wage increase:
• More income for every hour worked: For each level of free time you can
have more consumption, and your MRS is higher: you are now more
willing to sacrifice consumption for extra free time. This is the income
effect we saw in Figure 3.17—you respond to additional income by
taking more free time as well as increasing consumption.
Co
ns
um
pt
io
n
($
)
0
75
225
150
300
Hours of free time
8 10 12 14 16 18 20 22 24
IC2
IC3
A
B
Figure 3.18 The effect of additional income for someone whose MRS doesn’t
change when consumption rises.
UNIT 3 SCARCITY, WORK, AND CHOICE
116
substitution effect The effect that
is only due to changes in the price
or opportunity cost, given the new
level of utility.
INCOME AND SUBSTITUTION EFFECTS
A wage rise:
• raises your income for each level of free time, increasing
the level of utility you can achieve
• increases the opportunity cost of free time
So it has two effects on your choice of free time:
• The income effect (because the budget constraint shifts
outwards): the effect that the additional income would have
if there were no change in the opportunity cost.
• The substitution effect (because the slope of the budget
constraint, the MRT, rises): the effect of the change in the
opportunity cost, given the new level of utility.
• The budget constraint is steeper: The opportunity cost of free time is now
higher. In other words, the marginal rate at which you can transform
time into income (the MRT) has increased. And that means you have an
incentive to work more—to decrease your free time. This is called the
substitution effect.
The substitution effect captures the idea that when a good becomes more
expensive relative to another good, you choose to substitute away from the
relatively more expensive good toward the relatively cheaper good. It is the
effect that a change in the opportunity cost would have on its own, for a
given utility level.
We can show both of these effects in the diagram. Before the wage rise
you are at A on IC2. The higher wage enables you to reach point D on IC4.
Figure 3.19b shows how we can decompose the change from A to D into
two parts that correspond to these two effects.
You can see in Figure 3.19b that with indiffer-
ence curves of this typical shape a substitution
effect will always be negative: with a higher
opportunity cost of free time you choose a point
on the indifference curve with a higher MRS,
which is a point with less free time (and more
consumption). The overall effect of a wage rise
depends on the sum of the income and substitu-
tion effects. In Figure 3.19b the negative
substitution effect is bigger than the positive
income effect, so free time falls.
Leibniz: Mathematics of income
and substitution effects
(https://tinyco.re/L030701)
Co
ns
um
pt
io
n
($
)
0
75
225
150
300
Hours of free time
8 10 12 14 16 18 20 22 24
IC2
IC4
A
D
Figure 3.19a The effect of a wage rise on your choice of free time and consumption.
3.7 INCOME AND SUBSTITUTION EFFECTS ON HOURS OF WORK AND FREE TIME
117
AC
Substitution
effect
Overall
effect
Income
effect
Co
ns
um
pt
io
n
($
)
Hours of free time
8 10 12 14 16 18 20 22 24
IC2
IC4
D
0
75
225
150
300
Figure 3.19b The effect of a wage rise on your choice of free time and consumption.
1. A rise in wages
When the wage is $15 your best choice
of hours and consumption is at point A.
The steeper line shows your new
budget constraint when the wage rises
to $25. Your feasible set has expanded.
2. Now you can reach a higher
indifference curve
Point D on IC4 gives you the highest
utility. At point D, your MRS is equal to
the new wage, $25. You have only 17
hours of free time, but your consump-
tion has risen to $175.
3. If there was no change in opportunity
cost of free time
The dotted line shows what would
happen if you had enough income to
reach IC4 without a change in the
opportunity cost of free time. You
would choose C, with more free time.
4. The income effect
The shift from A to C is called the
income effect of the wage rise; on its
own it would cause you to take more
free time.
5. The substitution effect
The rise in the opportunity cost of free
time makes the budget constraint
steeper. This causes you to choose D
rather than C, with less free time. This is
called the substitution effect of the
wage rise.
6. The sum of the income and
substitution effects
The overall effect of the wage rise
depends on the sum of the income and
substitution effects. In this case the
substitution effect is bigger, so with the
higher wage you take less free time.
UNIT 3 SCARCITY, WORK, AND CHOICE
118
Technological progress
If you look back at Section 3.6, you will see that Angela’s response to a rise
in productivity was also determined by these two opposing effects: an
increased incentive to work produced by the rise in the opportunity cost of
free time, and an increased desire for free time when her income rises.
We used the model of the self-sufficient farmer to see how technological
change can affect working hours. Angela can respond directly to the
increase in her productivity brought about by the introduction of a new
technology. Employees also become more productive as a result of techno-
logical change, and if they have sufficient bargaining power, their wages
will rise. The model in this section suggests that, if that happens, technolo-
gical progress will also bring about a change in the amount of time
employees wish to spend working.
The income effect of a higher wage makes workers want more free time,
while the substitution effect provides an incentive to work longer hours. If
the income effect dominates the substitution effect, workers will prefer
fewer hours of work.
QUESTION 3.10 CHOOSE THE CORRECT ANSWER(S)
Figure 3.15 (page 114) depicts your budget constraint when the hourly
wage is $15.
Which of the following is (are) true?
The slope of the budget constraint is the negative of the wage rate
(–15).
The budget constraint is a feasible frontier with a constant marginal
rate of transformation.
An increase in the wage rate would cause a parallel upward shift in
the budget constraint.
A gift of $60 would make the budget constraint steeper, with the
intercept on the vertical axis increasing to $300.
3.8 IS THIS A GOOD MODEL?
We have looked at three different contexts in which people decide how long
to spend working—a student (Alexei), a farmer (Angela), and a wage earner.
In each case we have modelled their preferences and feasible set, and the
model tells us that their best (utility-maximizing) choice is the level of
working hours at which the slope of the feasible frontier is equal to the
slope of the indifference curve.
You may have been thinking: this is not what people do!
Billions of people organize their working lives without knowing
anything about MRS and MRT (if they did make decisions that way,
perhaps we would have to subtract the hours they would spend making
calculations). And even if they did make their choice using mathematics,
most of us can’t just leave work whenever we want. So how can this model
be useful?
Remember from Unit 2 that models help us ‘see more by looking at less’.
Lack of realism is an intentional feature of this model, not a shortcoming.
3.8 IS THIS A GOOD MODEL?
119
Trial and error replaces calculations
Can a model that ignores how we think possibly be a good model of how
we choose?
Milton Friedman, an economist, explained that when economists use
models in this way they do not claim that we actually think through these
calculations (such as equating MRS to MRT) each time we make a decision.
Instead we each try various choices (sometimes not even intentionally) and
we tend to adopt habits, or rules of thumb that make us feel satisfied and
not regret our decisions.
In his book Essays in positive economics, he described it as similar to
playing billiards (pool):
Similarly, if we see a person regularly choosing to go to the library after
lectures instead of going out, or not putting in much work on their farm, or
asking for longer shifts after a pay rise, we do not need to suppose that this
person has done the calculations we set out. If that person later regretted
the choice, next time they might go out a bit more, work harder on the
farm, or cut their hours back. Eventually we could speculate they might end
up with a decision on work time that is close to the result of our
calculations.
That is why economic theory can help to explain, and sometimes even
predict, what people do—even though those people are not performing the
mathematical calculations that economists make in their models.
The influence of culture and politics
A second unrealistic aspect of the model: employers typically choose
working hours, not individual workers, and employers often impose a
longer working day than workers prefer. As a result, the hours that many
people work are regulated by law, so that beyond some maximum amount
neither the employee nor the employer can choose to work. In this case the
government has limited the feasible set of hours and goods.
Although individual workers often have little freedom to choose their
hours, it may nevertheless be the case that changes in working hours over
time, and differences between countries, partly reflect the preferences of
workers. If many individual workers in a democracy wish to lower their
hours, they may ‘choose’ this indirectly as voters, if not individually as
workers. Or they may bargain as members of a trade union for contracts
requiring employers to pay higher overtime rates for longer hours.
Consider the problem of predicting the shots made by an expert
billiard player. It seems not at all unreasonable that excellent
predictions would be yielded by the hypothesis that the billiard player
made his shots as if he knew the complicated mathematical formulas
that would give the optimum directions of travel, could estimate
accurately by eye the angles, etc., describing the location of the balls,
could make lightning calculations from the formulas, and could then
make the balls travel in the direction indicated by the formulas.
Milton Friedman. 1953. Essays in
positive economics, 7th ed.
Chicago: University of Chicago
Press.
Our confidence in this hypothesis is not based on the belief that
billiard players, even expert ones, can or do go through the process
described. It derives rather from the belief that, unless in some way
or other they were capable of reaching essentially the same result,
they would not in fact be expert billiard players.
UNIT 3 SCARCITY, WORK, AND CHOICE
120
This explanation stresses culture (meaning changes in preferences or
differences in preferences among countries) and politics (meaning differ-
ences in laws, or trade union strength and objectives). They certainly help
to explain differences in working hours between countries:
Cultures seem to differ. Some northern European cultures highly value
their vacation times, while South Korea is famous for the long hours that
employees put in. Legal limits on working time differ. In Belgium and
France the normal work week is limited to 35–39 hours, while in Mexico
the limit is 48 hours and in Kenya even longer.
But, even on an individual level, we may influence the hours we work.
For example, employers who advertise jobs with the working hours that
most people prefer may find they have more applicants than other
employers offering too many (or too few) hours.
Remember, we also judge the quality of a model by whether it provides
insight into something that we want to understand. In the next section, we
will look at whether our model of the choice of hours of work can help us
understand why working hours differ so much between countries and why,
as we saw in the introduction, they have changed over time.
EXERCISE 3.8 ANOTHER DEFINITION OF ECONOMICS
Lionel Robbins, an economist, wrote in 1932 that: ‘Economics is the science
that studies human behaviour as a relationship between given ends and
scarce means which have alternative uses.’
1. Give an example from this unit to illustrate the way that economics
studies human behaviour as a relationship between ‘given ends and
scarce means with alternative uses’.
2. Are the ‘ends’ of economic activity, that is, the things we desire, fixed?
Use examples from this unit (study time and grades, or working time
and consumption) to illustrate your answer.
3. The subject matter that Robbins refers to—doing the best you can in a
given situation—is an essential part of economics. But is economics
limited to the study of ‘scarce means which have alternative uses’? In
answering this question, include a contrast between Robbins’ definition
and the one given in Unit 1, and note that Robbins wrote this passage
at a time when 15% of the British workforce was unemployed.
••3.9 EXPLAINING OUR WORKING HOURS: CHANGES
OVER TIME
During the year 1600, the average British worker was at work for 266 days.
This statistic did not change much until the Industrial Revolution. Then, as
we know from the previous unit, wages began to rise, and working time
rose too: to 318 days in 1870.
Meanwhile, in the US, hours of work increased for many workers who
shifted from farming to industrial jobs. In 1865 the US abolished slavery,
and former slaves used their freedom to work much less. From the late
nineteenth century until the middle of the twentieth century, working time
in many countries gradually fell. Figure 3.1 at the beginning of this unit
showed how annual working hours have fallen since 1870 in the
Netherlands, the US and France.
Lionel Robbins. 1984. An essay on
the nature and significance of eco-
nomic science, 3rd ed. New York:
New York University Press.
Robert Whaples. 2001. ‘Hours of
work in U.S. History’ EH.Net
Encyclopedia.
3.9 EXPLAINING OUR WORKING HOURS: CHANGES OVER TIME
121
The simple models we have constructed cannot tell the whole story.
Remember that the ceteris paribus assumption can omit important details:
things that we have held constant in models may vary in real life.
As we explained in the previous section, our model omitted two import-
ant explanations, which we called culture and politics. Our model provides
another explanation: economics.
Look at the two points in Figure 3.20, giving estimates of average
amounts of daily free time and goods per day for employees in the US in
1900 and in 2020. The slopes of the budget constraints through points A
and D are the real wage (goods per hour) in 1900 and in 2020. This shows
us the feasible sets of free time and goods that would have made these
points possible. Then we consider the indifference curves of workers that
would have led workers to choose the hours they did. We cannot measure
indifference curves directly: we must use our best guess of what the prefer-
ences of workers would have been, given the actions that they took.
How does our model explain how we got from point A to point D? You
know from Figure 3.19b that the increase in wages would lead to both an
income effect and a substitution effect. In this case, the income effect
outweighs the substitution effect, so both free time and goods consumed
per day go up. Figure 3.20 is thus simply an application to history of the
model illustrated in Figure 3.19b. Work through the steps to see the income
and substitution effects.
How could reasoning in this way explain the other historical data that
we have?
First, consider the period before 1870 in Britain, when both working
hours and wages rose:
• Income effect: At the relatively low level of consumption in the period
before 1870, workers’ willingness to substitute free time for goods did
not increase much when rising wages made higher consumption
possible.
• Substitution effect: But they were more productive and paid more, so each
hour of work brought more rewards than before in the form of goods,
increasing the incentive to work longer hours.
• Substitution effect dominated: Therefore before 1870 the negative substi-
tution effect (free time falls) was bigger than the positive income effect
(free time rises), so work hours rose.
During the twentieth century we saw rising wages and falling working
hours. Our model accounts for this change as follows:
• Income effect: By the late nineteenth century workers had a higher level
of consumption and valued free time relatively more—their marginal
rate of substitution was higher—so the income effect of a wage rise was
larger.
• Substitution effect: This was consistent with the period before 1870.
• Income effect now dominates: When the income effect began to outweigh
the substitution effect, working time fell.
We should also consider the possibility that preferences change over time. If
you look carefully at Figure 3.1 you can see that in the last part of the
twentieth century hours of work rose in the US, even though wages hardly
increased. Hours of work also rose in Sweden during this period.
UNIT 3 SCARCITY, WORK, AND CHOICE
122
conspicuous consumption The purchase of goods or services to
publicly display one’s social and economic status.
Why? Perhaps Swedes and Americans came to
value consumption more over these years. In other
words, their preferences changed so that their MRS
fell (they became more like today’s South Korean
workers). This may have occurred because in both
the US and Sweden the share of income gained by
the very rich increased considerably, and the lavish
consumption habits of the rich set a higher
standard for everyone else. As a result, many people
of lesser means tried to mimic the consumption
habits of the rich, a habit known as conspicuous
consumption. According to this explanation,
Swedes and Americans were ‘keeping up with the
Joneses’. The Joneses got richer, leading everyone
else to change their preferences.
The combined political, cultural and economic
influences on our choices may produce some surprising trends. In our
‘Economist in action’ video, Juliet Schor, a sociologist and economist who has
written about the paradox that many of the world’s wealthiest people are
working more despite gains in technology, asks what this means for our
quality of life, and for the environment.
The term ‘conspicuous consumption’ was coined by Thorstein
Veblen (1857–1929), an economist, in his book Theory of the
Leisure Class. At the time, he was describing the habits only of
the upper classes. But increasing disposable income during the
twentieth century means the term is now applied to anyone
who ostentatiously consumes expensive goods and services as
a public display of wealth.
Thorstein Veblen. (1899) 2007. Theory of the Leisure Class.
Oxford: Oxford University Press.
1900
2020
A
D
Income effect
C
Substitution
effect
Overall effect
0
50
100
150
200
14 16 18 20 22 24
Free time per day
G
oo
ds
pe
rd
ay
($
)
Figure 3.20 Applying the model to history: Increased goods and free time in the US
(1900–2020).
OECD. Average annual hours actually
worked per worker (https://tinyco.re/
6892498). Accessed October 2021.
Michael Huberman and Chris Minns.
2007. ‘The times they are not changin’:
Days and hours of work in Old and New
Worlds, 1870–2000’. Explorations in Eco-
nomic History 44 (4): pp. 538–567.
1. Using the model to explain historical
change
We can interpret the change between
1900 and 2020 in daily free time and
goods per day for employees in the US
using our model. The solid lines show
the feasible sets for free time and
goods in 1900 and 2020, where the
slope of each budget constraint is the
real wage.
2. The indifference curves
Assuming that workers chose the hours
they worked, we can infer the
approximate shape of their indiffer-
ence curves.
3. The income effect
The shift from A to C is the income
effect of the wage rise, which on its
own would cause US workers to take
more free time.
4. The substitution effect
The rise in the opportunity cost of free
time caused US workers to choose D
rather than C, with less free time.
5. Income and substitution effects
The overall effect of the wage rise
depends on the sum of the income and
substitution effects. In this case the
income effect is bigger, so with the
higher wage US workers took more free
time as well as more goods.
3.9 EXPLAINING OUR WORKING HOURS: CHANGES OVER TIME
123
Juliet Schor: Why do we work so
hard? https://tinyco.re/9852155
QUESTION 3.11 CHOOSE THE CORRECT ANSWER(S)
Figure 3.20 (page 123) depicts a model of labour supply and consump-
tion for the US in 1900 and 2020. The wage rate is shown to have
increased between the two years.
Which of the following are true?
The substitution effect corresponds to the steepening of the budget
constraint. This is represented by the move from point A to point D.
The income effect corresponds to the parallel shift in the budget
constraint outwards due to the higher income. This is represented
by the move from point A to C.
As shown, the income effect dominates the substitution effect,
leading to a reduction in the hours of work.
If Americans had had different preferences, they might have
responded to this wage rise by reducing their free time.
What about the future? The high-income economies will continue to
experience a major transformation: the declining role of work in the course
of our lifetimes. We go to work at a later age, stop working at an earlier age
of our longer lives, and spend fewer hours at work during our working
years. Robert Fogel, an economic historian, estimated the total working
time, including travel to and from work and housework, in the past. He
made projections for the year 2040, defining what he called discretionary
time as 24 hours a day minus the amount we all need for biological
maintenance (sleeping, eating and personal hygiene). Fogel calculated
leisure time as discretionary time minus working time.
In 1880 he estimated that lifetime leisure time was just a quarter of
lifetime work hours. In 1995 leisure time exceeded working time over a
person’s entire life. He predicted that lifetime leisure would be three times
of lifetime working hours by the year 2040. His estimates are in Figure 3.21.
Robert William Fogel. 2000. The
fourth great awakening and the
future of egalitarianism: The polit-
ical realignment of the 1990s and
the fate of egalitarianism. Chicago:
University of Chicago Press.
0
100,000
200,000
300,000
400,000
1880 1995 2040
Year
Li
fe
tim
e
ho
ur
s
Lifetime discretionary hours
Lifetime work hours
Lifetime leisure hours
Figure 3.21 Estimated lifetime hours of work and leisure (1880, 1995, 2040).
Robert William Fogel. 2000. The Fourth
Great Awakening and the Future of
Egalitarianism. Chicago: University of
Chicago Press.
UNIT 3 SCARCITY, WORK, AND CHOICE
124
We do not yet know if Fogel has overstated the future decline in
working time, as Keynes once did. But he certainly is right that one of the
great changes brought about by the technological revolution is the vastly
reduced role of work in the life of an average person.
EXERCISE 3.9 SCARCITY AND CHOICE
1. Do our models of scarcity and choice provide a plausible explanation
for the observed trends in working hours during the twentieth century?
2. What other factors, not included in the model, might be important in
explaining what has happened?
3. Remember Keynes’ prediction that working hours would fall to 15
hours per week in the century after 1930. Why do you think working
hours have not changed as he expected? Have people’s preferences
changed? The model focuses on the number of hours workers would
choose, so do you think that many employees are now working longer
than they would like?
4. In his essay, Keynes said that people have two types of economic needs
or wants: absolute needs that do not depend on the situation of other
fellow humans, and relative needs—which he called ‘the desire for
superiority’. The phrase ‘keeping up with the Joneses’ captures a similar
idea that our preferences could be affected by observing the consump-
tion of others. Could relative needs help to explain why Keynes was so
wrong about working hours?
••3.10 EXPLAINING OUR WORKING HOURS:
DIFFERENCES BETWEEN COUNTRIES
Figure 3.2 showed that in countries with higher income (GDP per capita)
workers tend to have more free time, but also that there are big differences
in annual hours of free time between countries with similar income levels.
To analyse these differences using our model, we need a different measure
of income that corresponds more closely to earnings from employment.
The table in Figure 3.22 shows working hours for five countries, together
with the disposable income of an average employee (based on the taxes and
benefits for a single person without children).
From these figures we have calculated annual free time, and the average
wage (by dividing annual income by annual hours worked). Finally, free
time per day and daily consumption are calculated by dividing annual free
time and earnings by 365.
Figure 3.23 shows how we might use this data, with the model of Section
3.7, to understand the differences between the countries. From the data in
Figure 3.22, we have plotted daily consumption and free time for a typical
worker in each country, with the corresponding budget constraint
constructed as before, using a line through (24, 0) with slope equal to the
wage. We have no information about the preferences of workers in each
country, and we don’t know whether the combinations in the diagram can
be interpreted as a choice made by the workers (rather than by their
employers, for example, or regulated by law). But, if we assume that their
hours of free time do reflect the workers’ choices, we can consider what the
data tells us about the preferences of workers in different countries.
3.10 EXPLAINING OUR WORKING HOURS: DIFFERENCES BETWEEN COUNTRIES
125
Follow the steps in Figure 3.23 to see some hypothetical indifference
curves that could explain the differences among countries.
Point Q in the last step of the figure is a point of intersection of the two
indifference curves shown for the Netherlands and the US. At that point the
Dutch indifference curve is steeper than the US one. This means that if
consuming the amount of goods and free time indicated by point Q on
average Dutch people would be willing to give up more units of daily goods
for an hour of free time (this is the MRS) than Americans.
This is consistent with the idea that the Dutch value their free time more
than Americans, relative to how much they value goods. If two indifference
curves cross we know that they are based on different preferences; because
it means valuing things differently when experiencing the same situation
(amount of free time and goods).
What are called differences in culture between two countries – whether
it is how much people value free time, or what they like to eat – often can
be expressed as differences in the indifference maps that are common in the
two countries. Given that cultures differ it may be important to take
account of differences in preferences among countries, or among indi-
viduals.
EXERCISE 3.10 PREFERENCES AND CULTURE
Suppose that the points plotted in Figure 3.23 (page 127) reflect the
choices of free time and consumption made by workers in these five coun-
tries according to our model.
1. Is it possible that people in Turkey and the US have the same prefer-
ences? If so, how will a wage rise in Turkey affect consumption and free
time? What does this imply about the income and substitution effects?
2. Suppose that people in Turkey and South Korea have the same prefer-
ences. In that case, what can you say about the income and substitution
effects of a wage increase?
3. If wages in South Korea increased, would you expect consumption
there to be higher or lower than in the Netherlands? Why?
Country Average annual hours
worked per employee
Average annual
disposable income
Average
annual free
time
Wage (disposable
income per hour
worked)
Freetime
per day
Consumption
per day
US 1,767 54,854 6,777 31.04 19.16 150.28
South Korea 1,908 26,799 6,636 14.05 18.77 73.42
Netherlands 1,399 39,001 7,145 27.88 20.17 106.85
Turkey 1,832 21,800 6,712 11.90 18.98 59.73
Mexico 2,124 17,384 6,420 8.18 18.18 47.63
Figure 3.22 Free time and consumption per day across countries (2020).
OECD. Average annual hours actually worked per worker (https://tinyco.re/6892498). Accessed
October 2021. Net income after taxes calculated in US dollars using PPP exchange rates.
UNIT 3 SCARCITY, WORK, AND CHOICE
126
Mexico
Netherlands
South
Korea
Turkey
US
Q
0
50
100
150
200
250
14 17 19 22 24
Free time per day (hours)
G
oo
ds
pe
rd
ay
($
)
Figure 3.23 Using the model to explain free time and consumption per day across
countries (2020).
OECD. Average annual hours actually
worked per worker (https://tinyco.re/
6892498). Accessed October 2021. Net
income after taxes calculated in US
dollars using PPP exchange rates.
1. Differences between countries
We can use our model and data from
Figure 3.22 to understand the differ-
ences between the countries. The solid
lines show the feasible sets of free time
and goods for the five countries in
Figure 3.22.
2. Indifference curves of workers
We have drawn indifference curves
that would explain why workers chose
these points.
3. The US and the Netherlands
Point Q is at the intersection of the
indifference curves for the US and the
Netherlands. At this point Americans
are willing to give up fewer units of
daily goods for an hour of free time
than the Dutch.
3.10 EXPLAINING OUR WORKING HOURS: DIFFERENCES BETWEEN COUNTRIES
127
19
00
19
13
19
29
19
38
19
50
19
60
19
73
19
80
19
90
20
00
1,000
1,500
2,000
2,500
3,000
3,500
An
nu
al
ho
ur
s
of
w
or
k
France
Germany
Netherlands
Sweden
UK
Switzerland
A
19
00
19
13
19
29
19
38
19
50
19
60
19
73
19
80
19
90
20
00
1,000
1,500
2,000
2,500
3,000
3,500
Australia
Canada
Japan
UK
US
B
Year
Michael Huberman and Chris Minns.
2007. ‘The times they are not changin’:
Days and hours of work in Old and New
Worlds, 1870–2000’ (https://tinyco.re/
2758271). Explorations in Economic
History 44 (4): pp. 538–567.
EXERCISE 3.11 WORKING HOURS ACROSS COUNTRIES AND TIME
The figure below illustrates what has happened to working hours in many
countries during the twentieth century (the UK is in both charts to aid
comparison).
1. How would you describe what happened?
2. How are the countries in Panel A of the figure different from those in
Panel B?
3. What possible explanations can you suggest for why the decline in
working hours was greater in some countries than in others?
4. Why do you think that the decline in working hours is faster in most
countries in the first half of the century?
5. In recent years, is there any country in which working hours have
increased? Why do you think this happened?
3.11 CONCLUSION
We have used a model of decision making under scarcity to analyse choices
of hours of work, and understand why working hours have fallen over the
last century. People’s preferences with respect to goods and free time are
described by indifference curves, and their production function (or budget
constraint) determines their feasible set. The choice that maximizes utility
is a point on the feasible frontier where the marginal rate of substitution
(MRS) between goods and free time is equal to the marginal rate of
transformation (MRT).
An increase in productivity or wages alters the MRT, raising the oppor-
tunity cost of free time. This provides an incentive to work longer hours
(the substitution effect). But higher income may increase the desire for free
time (the income effect). The overall change in hours of work depends on
which of these effects is bigger.
UNIT 3 SCARCITY, WORK, AND CHOICE
128
Concepts introduced in Unit 3
Before you move on, review these definitions:
• Constrained choice problem
• Scarcity
• Opportunity cost
• Marginal product
• Indifference curve
• Marginal rate of substitution (MRS)
• Marginal rate of transformation (MRT)
• Feasible set
• Budget constraint
• Income effect
• Substitution effect
3.12 REFERENCES
Consult CORE’s Fact checker for a detailed list of sources.
Fogel, Robert William. 2000. The Fourth Great Awakening and the Future of
Egalitarianism. Chicago: University of Chicago Press.
Friedman, Milton. 1953. Essays in Positive Economics. Chicago: University of
Chicago Press.
Harford, Tim. 2015. ‘The rewards for working hard are too big for Keynes’s
vision’ (https://tinyco.re/5829245). The Undercover Economist. First
published by The Financial Times. Updated 3 August 2015.
Keynes, John Maynard. 1963. ‘Economic Possibilities for our
Grandchildren’. In Essays in Persuasion, New York, NY: W. W. Norton
& Co.
Plant, E. Ashby, K. Anders Ericsson, Len Hill, and Kia Asberg. 2005. ‘Why
study time does not predict grade point average across college
students: Implications of deliberate practice for academic
performance’. Contemporary Educational Psychology 30 (1): pp. 96–116.
Robbins, Lionel. 1984. An Essay on the Nature and Significance of Economic
Science (https://tinyco.re/4002310). New York: New York University
Press.
Schor, Juliet B. 1992. The Overworked American: The Unexpected Decline Of
Leisure. New York, NY: Basic Books.
Veblen, Thorstein. 2007. The Theory of the Leisure Class. Oxford: Oxford
University Press.
Whaples, Robert. 2001. ‘Hours of work in U.S. History’ (https://tinyco.re/
1660378). EH.Net Encyclopedia.
3.12 REFERENCES
129