Economics for the IB Diploma

Development of dual economies some countries faring better than others. According
A dual economy (or dualism) was explained in to the evidence, the countries that are better able
Chapter 16, page 444. Dual economies may persist even to take advantage of opportunities offered by trade
as a country grows and develops. They are the outcome and market liberalisation are those that have already
of market forces that do not work to the benefit of all developed an industrial base, and are therefore better
or most people in a country because of the presence able to withstand the competition arising from the
of market failures such as weak market institutions elimination or reduction of trade barriers. Low-income
or co-ordination failures, because of the geographical countries tend to perform the worst, because they
isolation of many groups of people, the persistence can least withstand the competition with larger, more
or growth of great income inequalities and extreme ‘mature’ foreign firms, and this sometimes leads to a
poverty, or government policies that support one sector weakening of their industry together with increased
of the economy at the expense of another. Like all unemployment, poverty and growth of the urban
kinds of market failures that require some government informal sector (see page 485).
intervention for their correction, so dual economies also
require government policies that attempt to eliminate Capital liberalisation, if undertaken before countries
the dualism. The appropriate policy depends on the have developed the necessary institutions, may lead
nature of the dual economy, i.e. whether it involves an to capital flight, reduced ability to conduct monetary
advanced agricultural sector together with traditional, policy in accordance with domestic priorities, and
subsistence agriculture, or an advanced capital-intensive even financial crisis (see page 496).
industrial sector together with a traditional labour-
intensive urban informal sector. The withdrawal of government from provision
of merit goods that often comes with market
Income inequalities liberalisation has negative effects on economic and
We have studied the effects of market-oriented human development.
policies on income distribution in Chapter 12, in
connection with market-based supply-side policies, These processes have the effect of increasing
and in Chapter 17 in connection with the effects of inequalities between rich and poor countries, as well
trade and market liberalisation. The loss of protection as between higher income and lower income groups
of workers resulting from labour-market reforms, within countries.
and increases in unemployment resulting from some
policies to increase competition, including trade Strengths and weaknesses of
liberalisation which often involves the closure of interventionist policies
firms, often result in increases in income inequalities.
In addition, the inability of certain groups of people Strengths
to take advantage of opportunities opened by trade
and market liberalisation can also lead to increasing Discuss the strengths of interventionist policies,
income inequalities (page 486). including the provision of infrastructure, investment in
human capital, the provision of a stable macroeconomic
Insufficient credit for poor people economy and the provision of a social safety net.
As discussed in Chapter 17, page 467, poor people do
not have access to credit, as the market working on Interventionist policies are based on government
its own does not allow poor people with no collateral intervention in markets intended to correct market
and seeking very small loans to acquire the credit they deficiencies and create an environment in which
need. This results in lower investment possibilities, markets can work more effectively. The strengths
greater poverty and poorer income distribution, as of interventionist policies include their potential to
well as the inability to escape the poverty cycle. contribute to the following.

Questionable effects on economic Correcting market failures
growth and development Governments have a major role to play in the
Contrary to expectations, trade and market correction of market failures. This includes policies
liberalisation may not lead to improved export that try to:
performance and greater economic growth and
development in some countries. Experiences have • correct negative environmental externalities of
shown performance to be highly variable, with production and consumption and overuse of
common access resources (Chapter 5)

• provide public goods as well as merit goods that
are underprovided by the market due to positive

Chapter 19 Consequences of economic growth and the balance between markets and intervention 533

consumption externalities – as we know this involves and requires government intervention through the use
investments in human capital (health and education) of appropriate policies in pursuit of these objectives.
and investments in infrastructure (Chapter 5) We studied these policies in Chapters 12 and 14. A
stable macroeconomic environment is important for
• assist in the correction of co-ordination failures ensuring that economic decision-makers (consumers,
(see page 532 above) – government intervention is firms and resource owners) can plan their future
needed to help people escape underdevelopment economic activities (such as consumption investment,
traps by allowing the simultaneous occurrence of imports, exports, etc.). It is a key condition for
necessary activities investment, in particular, leading to the formation of
physical and human capital, which are fundamental
• contribute to the development of market prerequisites for economic growth.
institutions that enable markets to operate more
effectively (see page 532 above). Provision of a social safety net
In Chapter 11, we saw that the market cannot
Investment in human capital ensure that everyone in a society can secure enough
Investment in human capital (education and health) income to satisfy basic needs (food, shelter, etc.). The
was noted above in connection with government government must therefore step in with the provision
policies to correct market failures. Education and of a social safety net to ensure that people falling
health have significant external benefits, thus below a minimum income level will be able to secure
calling for government intervention (such as direct their basic needs. A social safety net is a system of
provision) that increases the consumption of both. government transfers of cash or goods to vulnerable
Education and health are major factors behind groups, undertaken to ensure that these groups do not
increases in productivity that contribute to economic fall below a socially acceptable minimum standard
growth, and they also directly lead to greater of living (see page 309 on transfer payments). The
economic and human development. Investment in provision of a social safety net by the government is
human capital also forms a part of industrial policies, very important in a market-based economy, where
discussed below. (See also page 463.) there are risks of becoming unemployed or falling into
poverty.
Provision of infrastructure
The provision of infrastructure also forms part of Redistributing income
policies to correct market failures (noted above). Another method to deal with the market’s inability
Infrastructure includes a broad range of goods and to secure everyone a minimum income involves
services, also with significant positive externalities. As government’s policy of income redistribution,
a type of physical capital, it includes water supplies, discussed in Chapter 11.
sanitation and sewerage, power, communication,
transportation, roads, irrigation, and many Industrial policies
others. All of these play a very important role in Industrial policies are interventionist supply-side
encouraging economic growth, as well as making policies that include support for small and medium-
possible economic and human development (see sized businesses as well as protection of infant
page 475). They increase productivity, and make a industries (such as through tariffs or subsidies) in order
direct contribution to improved standards of living. to help developing countries in the early stages of
Therefore, there is a strong role for governments in their industrialisation (page 339).
order to ensure the provision of the appropriate kinds
of infrastructure, with the appropriate access by the In addition, industrial policies include government
population. support of appropriate technology transfer from
developed countries and the establishment of a
Provision of a stable macroeconomic research and development capability, as well as the
environment investments in human capital.
A stable macroeconomic environment includes price
stability (the general price level should rise only Industrial policies were a key factor behind the
gradually); full employment (people willing and able to success of the Asian Tigers (page 484). Whereas
work should be able to find a job); a reasonable budget these policies were discouraged by the Washington
deficit; and a reasonable balance of trade (avoidance Consensus, according to New Development Consensus
of large trade or current account deficits). The market they can play an important role in helping developing
mechanism cannot accomplish these tasks on its own, countries develop their industries and higher value-
added activities (page 487).

534 Section 4 Development economics

Weaknesses mass media and the system of public administration
are weak. It should be noted that multinational
Discuss the limitations of interventionist policies, corporations in their dealings with governments play
including excessive bureaucracy, poor planning and an important role with respect to bribes.
corruption.
Corruption is often associated with lower growth
Government activities are subject to several and poorer development prospects. When it takes the
weaknesses that limit the effectiveness of their form of a payment for something, it works like a tax
interventions in the market. that makes private investments more costly, reducing
the overall level of investment. If it involves bribes to
Excessive bureaucracy receive basic services like education or health care it
A bureaucracy is an administrative structure of an works like a regressive tax, because the bribe is a higher
organisation involving rules that determine how fraction of the income of lower income earners. Unlike
the organisation functions and carries out its tasks. taxes paid to the government that become available
Governments often run into the problem of excessive for use in socially desirable activities, bribes go into the
bureaucracy, meaning there are too many rules pockets of public servants and politicians, depriving
governing procedures, red-tape, unproductive workers, society of resources that could have been used to pay for
high administrative costs and inefficiency. This is a the provision of important merit goods. Bribes for tax
key argument often used in favour of reducing the evasion result in further reducing government revenues.
size of the government sector through privatisation Corruption can also result in a misallocation of
of government-owned enterprises, contracting-out of resources as government officials accept bribes to pursue
government activities, and private financing of public uneconomic projects (such as dams and power plants)
sector projects (see page 340) to reduce bureaucratic instead of socially necessary services like education,
procedures and improve efficiency. health care, sanitation, etc. Corruption can also weaken
sustainable development as government officials may
Poor planning accept bribes to bypass environmental regulations.
Government planning involves making decisions on Finally, corruption damages the people’s trust in the
what and how much of certain goods and services it will state and encourages contempt for the rule of law.
produce, how these will be produced (by use of what
resources), how much they will cost and what revenues Market with government intervention
they might be expected to provide. Planning plays a
major role in government provision of merit goods and Why good governance is important
public goods, as well as numerous government policies
such as taxes, subsidies, transfer payments as well as Explain the importance of good governance in the
virtually all of its economic activities. development process.

Planning may run into difficulties because it According to the World Bank, governance is
requires technical knowledge and expertise on the ‘the manner in which power is exercised in the
part of planners, which they may not possess, as well management of a country’s economic and social
as a tremendous amount of detailed information, resources for development. Good governance . . . is
much of which is often not available. The result is synonymous with sound development management.’9
that planning can become highly bureaucratic and
inefficient, resulting in a waste of resources. Governance is not about what is done for economic
growth and development, but rather how it is done.
Corruption It is about the effectiveness of government, but also
Corruption is defined by the World Bank as ‘the it involves the relations between government and
abuse of public office for private gain’. It can society, and how they interact to make decisions.
take many forms including bribery, construction According to researchers on this topic, good
kickbacks, procurement fraud, extortion, false governance consists of six principles:10
certification, nepotism, embezzlement, and more.
It occurs everywhere in the world, but tends to be • Participation – the extent to which the stakeholders
more important in countries where the legal system, affected by policies are involved in making decisions
and in the implementation of decisions.

9 The World Bank (1992) Governance and Development. sense of governance: empirical evidence from 16 developing
10 Goran Hyden, Julius Court and Kenneth Mease (2004) ‘Making countries’, Overseas Development Institute.

Chapter 19 Consequences of economic growth and the balance between markets and intervention 535

• Fairness – the extent to which rules apply to Bank lending (structural adjustment loans) and
everyone in society equally. lending by the International Monetary Fund (and its
stabilisation policies). At the same time, there was
• Decency – the extent to which the formation and a growing recognition of the limitations of central
implementation of rules does not harm or humiliate planning in communist states. In China and former
anyone. communist countries, a deliberate choice was made
to move toward a stronger market orientation; these
• Accountability – the extent to which political economies are called ‘economies in transition’.12
figures and decision-makers are responsible to
society for the actions and their statements. By the early 2000s, it had become apparent that
neither the extreme of very strong government
• Transparency – the extent to which decisions intervention, nor the extreme of a highly free market
made by government are clear and open. orientation, is appropriate for the conditions of
developing countries (page 487). Attention of policy-
• Efficiency – the extent to which scarce resources makers therefore turned toward finding an appropriate
are used without waste, delays or corruption. mix of market-based and interventionist policies.

Good governance is important because according to Based on the experiences of developing countries
studies making cross-country comparisons, better accumulated over a 60-year period and the evolution
governance is related to more investment and greater of economists’ thinking on this subject, we can arrive
economic growth. The effectiveness of government, at the following broad conclusions:
the efficiency of bureaucracy and rule of law are
positively related to economic performance and adult • Very strong government intervention in the
literacy, and negatively related to infant mortality.11 market, such as that pursued during the
1950s and 1960s, has been mostly discredited
Achieving a balance between markets as a strategy for economic growth and
and intervention development, and international trade. It is
now well understood that very strong government
Discuss the view that economic development may best be intervention leads to misallocation of resources and
achieved through a complementary approach, involving inefficiencies in production, and may result in lower
a balance of market-oriented policies and government rates of growth. As of the early 2000s, there tends
intervention. to be a convergence on the idea that market forces
should be allowed to play an important role, and
During much of the 20th century, many countries that trade, growth and development strategies should
around the world saw significant increases in be for the most part market-led, though with varying
government intervention. In developing countries, degrees and forms of government intervention.
intervention took the form of import-substituting
industrialisation during the 1950s and 1960s, • A market-led economic development
followed later by export promotion (pages 482–84). strategy with a minimum amount of
In communist countries there was a very strong government intervention, such as is
government presence that largely replaced the represented by the Washington Consensus,
market system and took the form of central planning does not take into account the special
(government planning of most economic activities). set of circumstances faced by developing
countries. If such a policy is pursued over an
From the 1980s, there was a shift in most countries extended period, it is likely to lead to only limited
in the direction of less government intervention progress in economic growth and economic and
and a stronger emphasis on markets. This shift was human development, as a result of persisting
influenced by the weaknesses of import-substituting and possibly increasing poverty, a likely increase
industrialisation policies, as well as by market-based in unemployment and underemployment,
supply-side thinking that emerged in the United persisting and probably increasing inequalities in
Kingdom and the United States at that time. It income distribution, insufficient investments in
was also strongly encouraged by the Washington education and health (human capital) as well as
Consensus (page 485), part of which involved World

11 Julius Court (2006) ‘Governance, development and aid that emerged after the break-up of the Soviet Union (15)
effectiveness: a quick guide to complex relationships’, Overseas and Yugoslavia (7), plus the countries of eastern Europe that
Development Institute. experienced a transition to democratic regimes. China, also a
12 Most economies in transition appeared after the collapse of transition economy, has taken a different route by choosing to
communist regimes in eastern Europe and the former Soviet introduce market reforms gradually under the direction of its
Union in 1989–90. The countries in this group include the ones Communist Party.

536 Section 4 Development economics

in infrastructure, unsustainable development, the withdraw and give greater reign to market
continued use of inappropriate technologies, and forces as the country grows and develops.
limited opportunities to expand exports. Countries at lower levels of development are more
likely to be lacking in the necessary institutions
• The New Development Consensus outlines a and regulatory and legal mechanisms required for
number of areas in which governments of markets to work well, thus needing a relatively
developing countries should intervene in greater degree of government intervention.
order to promote growth and development. With growth and development, and the gradual
As of the early 2000s, there is broad agreement establishment of more effective institutions, the
among development economists that there should government can increasingly withdraw, allowing
be government intervention in areas including: market forces to take a stronger hold.
poverty alleviation; reductions in income inequalities
and inequalities in economic opportunities; Test your understanding 19.2
investments in health, education, infrastructure,
technology transfer and the establishment of a 1 Explain some of the main strengths and
research and development capability; some support weaknesses of market-oriented policies.
for small and medium-sized businesses; protection
of the environment and sustainable development. 2 Explain some of the main strengths and
In addition, many economists support the idea weaknesses of interventionist policies.
that developing countries, especially the very
poor ones, may require some protection for their 3 (a) Explain the meaning of good governance.
domestic industries in the initial phases of their (b) Why is good governance important in
industrialisation in the form of industrial policies, economic development?
including protection of infant industries.
4 Why would it be inappropriate to take
• It would be a mistake to take a blanket (or a uniform approach to making policy
uniform) approach to all developing (or any recommendations on the roles of the market
other) countries with regard to proposals and government intervention in developing
for market-led or interventionist strategies countries?
(or any other type of strategies for that
matter). Each country is unique, and should be 5 Explain whether you agree with the
able to tailor its strategies to its own particular propositions that (a) markets and government
needs and conditions, in consultation with aid and intervention should complement each other
development assistance agencies. in developing countries, and (b) governments
should intervene more strongly in countries
• It is likely that countries at lower levels that are at a relatively lower level of economic
of economic development can benefit development, and less strongly as countries
from strategies that are more strongly grow and develop.
interventionist; government can gradually

Real world focus

Economic growth and development in Peru

During the 1990s, Peru reoriented its economy toward the about two decades. By 2005–6, real GDP per capita just
market to achieve economic growth and development. This managed to reach the same levels of the 1970s.
involved abandoning its policies of import substitution,
including elimination of price controls, lowering trade An important factor behind the collapse involved massive
protection barriers, lowering restrictions on foreign direct declines in export revenues, due to excessive specialisation
investment, and reducing state ownership of firms. Since in the export of only a few primary commodities: minerals
2002, it has experienced high rates of growth, and has been (mining of copper, gold and zinc) and agriculture (coffee,
the fastest growing economy in Latin America. sugar, potatoes). Terms of trade shocks caused by declines
in global commodity prices reduced the value of exports
Peru’s economic performance was not always so by more than 80% in 1979–93, resulting in declining
favourable. In the late 1970s the economy had suffered incomes, increasing unemployment and poverty, a balance
a serious collapse, and remained mostly depressed for
(continued over)

Chapter 19 Consequences of economic growth and the balance between markets and intervention 537

of payments crisis, extremely high rates of inflation no social protection. The export sectors driving Peru’s
(hyperinflation), a debt crisis and even violence. high growth rates have not helped increase employment.
Mining involves highly capital-intensive production
In the decade of the 2000s, a global commodity boom methods and technologies. Whereas mining accounts for
led to record high prices of minerals and other commodity about 60% of Peru’s exports, it is responsible for less than
exports, resulting in a dramatic increase in Peru’s export 0.5% of employment. Unemployment stands at 10%, while
revenues, and contributing to the achievement of very high underemployment affects 50% of the labour force.
rates of growth.
Much of mining is carried out by multinational
High growth rates have also been attributed to a stable corporations (MNCs), and profits go to the foreign owners
macroeconomic environment and market-oriented reforms. of capital. Since 2001, GDP per capita has been growing
Both these factors contribute to high levels of foreign direct much more rapidly than GNI per capita, and the gap
investment, as well as private domestic investment. Market between the two growth rates is increasing. MNCs are
reforms have led to a strong export orientation in foreign also major polluters of the environment. Yet they have
trade, increased competition, and greater efficiencies in threatened to move to other countries if environmental
production. regulations are enforced. In addition, MNCs have been
accused of diverting water from agricultural production as
Yet Peru has been diversifying slowly into new well causing the relocation of local populations.
products for export. Continued lack of diversification into
new export products with higher value added may become Yet it is argued by some economists that MNCs
an obstacle to growth in the future. Economists argue that are responsible for important benefits to the Peruvian
the government should work closely with the private sector economy, including high economic growth and the transfer
to find new areas for production and export, and should of technology.
pursue industrial policies to provide support in the form of
education and training, research and development (R&D) The government has responded to growing income
and new technology development that is labour intensive inequalities with an anti-poverty programme providing
and appropriate to local needs. cash transfers to low-income families on condition that
they send their children to school regularly. However,
Another problem concerns growing income inequalities this programme tends to target the urban rather than the
that threaten social unrest. These are especially apparent in the rural poor. Also, some money allocated to this programme
contrast between coastal regions concentrating most growth remains unspent to avoid the possibility of corruption.
in economic activity, and the rural highlands of the Andes.
Nearly 45% of Peruvians have incomes under the poverty At the same time, the country’s public administration
line, and about 16% live in extreme poverty. In the Andean institutions must be strengthened. While governance
region, nearly 70% of the population live in poverty. has improved, there is room for more improvement. The
country’s primary education and health care systems
Part of the problem involves the geographical need to be strengthened. Reform of the education and
isolation of groups who have no contact with the market health ministries, and the public administration system
economy. For people who are cut off, social services and are important for the success of anti-poverty efforts. Also,
infrastructure are highly inadequate: 39% of the Peruvian major investments in infrastructure and human capital
population do not have access to electricity, while 69% are needed to support Peru’s ability to achieve economic
live with unacceptable sanitation services. Rural poverty development.
is threatening Peru’s tropical forests, the fourth largest
in the world, due to shifting populations that cut down Source: Adapted from Ricardo Hausman and Bailey Klinger (2008)
forests to open up land for habitation and agriculture, and ‘Growth diagnostics in Peru’, CID Working Paper No. 181, Center
unsustainable, illegal logging. for International Development, Harvard University; ‘Poverty amid
progress,’ in The Economist, 8 May 2008; ‘USAID budget: Peru’, USAID,
Growth of employment in the formal sector is not 2006; Guillermo Cornejo (2008) ‘Peru’s economic model and poverty
high enough to absorb the urban labour force. Over 50% reduction: is it working?’, Council on Hemispheric Affairs; ‘More than
of non-agricultural workers work in the urban informal 40% of Peruvians live in poverty’, EFE News Service, 22 April 2008.
sector, working very long hours for low wages and with
3 Suppose you are a policy adviser to the
Applying your skills Peruvian government. What policy
recommendations would you provide
1 Explain the meaning of good governance. regarding an appropriate balance between
How can Peru improve its governance? market-oriented policies and government
How will this help in its efforts to grow and intervention to promote Peru’s economic
develop? growth and development?

2 Using Peru as an example, discuss strengths
and weaknesses of (a) market-oriented policies,
and (b) interventionist policies.

538 Section 4 Development economics

Assessment Higher level
• Exam practice: Paper 2, Chapter 19
The Student’s CD-ROM at the back of this book
provides practice of examination questions based on SL/HL core topics (Text/data 26 and 27,
the material you have studied in this chapter. questions B.21–B.25)

Standard level
• Exam practice: Paper 2, Chapter 19,

SL/HL core topics (Text/data 26 and 27,
questions B.21–B.25)

Chapter 19 Consequences of economic growth and the balance between markets and intervention 539

Introduction to the CD-ROM

The CD-ROM of the second edition of the textbook objectives (AOs), learning outcomes and command
Economics for the IB Diploma contains the following: terms as they relate to the learning outcomes and
exam questions. In addition, it contains some general
Quantitative techniques chapter guidelines on answering examination questions.

This is a detailed chapter containing all the Paper 1
quantitative techniques you need to understand in
order to excel in your IB economics course. It enables Paper 1 questions are organised by section, i.e. Section
you to review everything from percentages and A on microeconomics followed by Section B on
percentage changes to understanding the essentials of macroeconomics, and by chapter within each section.
relationships between variables, and interpreting and They are conveniently separated into part (a) and part
constructing diagrams and graphs. For students taking (b) questions, and are also divided into ‘SL/HL core’
the course at higher level, it explains everything questions, which should be attempted by all students
you need to know about linear demand and supply at both SL and HL, and ‘HL’ questions which should
functions, solving linear equations, and performing be attempted by HL students.
all necessary calculations and constructing graphs.
You will also find a detailed section on how to use a Paper 2
graphic display calculator (GDC) as an aid to graphing.
There are numerous cross-references between the Paper 2 questions are organised by section, i.e.
book and this CD-ROM chapter; as you read the Section A on international economics followed
textbook, you will be referred to the relevant sections by Section B on development economics, and by
of this chapter where you can easily find important chapter within each section. Most texts/data are
background material. This CD-ROM chapter follows used as the basis of both SL/HL core questions as
the style of the book, and has numerous ‘Test your well as HL questions. HL material is examined by HL
understanding’ questions containing exercises of the question parts that are marked as ‘higher level’. Each
type that will appear in your exams. You will find the HL question part is accompanied by an alternative
answers to all these questions on the teacher support question part taken from SL/HL core topics that are
website at ibdiploma.cambridge.org. marked as ‘core’. This way all students, at both SL
and HL, can have the benefit of completing full 20-
Examination practice mark paper 2 questions.

This is an extensive section of the CD-ROM where you Paper 3
will find a very large number of examination questions
for each of the exam papers 1, 2, and 3. The questions Paper 3 is for HL only. Questions are organised by
cover each and every learning outcome in the entire syllabus section and by chapter within each section.
economics guide, with the appropriate command They cover mainly higher-level material, including all
terms at the appropriate level of assessment objectives. the quantitative items in the syllabus.
This section is divided into four parts. You will find
markschemes for many of these questions on the Important diagrams
teacher support website at ibdiploma.cambridge.org.
This section of the CD-ROM, entitled ‘Important
Introduction to IB economics examination diagrams to remember’ reproduces all the important
papers diagrams of the textbook, organised according to
chapter, and topic within each chapter. This section
This introduction provides background information on enables you to do a quick review of diagrams that you
examinations, including an explanation of assessment should ensure you understand and can draw yourself
in connection with possible questions that are likely to
appear on exams.

© Cambridge University Press 2012 Economics for the IB Diploma 1

Supplementary material for Chapter 9 Introduction to the CD-ROM

This chapter is an extension of Chapter 9 and is useful (though very rough and approximate) guide
not part of required material (it is ‘supplementary to classifying countries as economically more or less
material’). It is concerned with the famous developed.
model attributed to John Maynard Keynes, and is
recommended for students who are interested in List of Nobel Prize winners
gaining a deeper understanding of macroeconomics.
For the interested student, there is also a list of
List of countries according to the all Nobel Prize winners in Economics and a brief
World Bank’s classification system description of their work, beginning in 1969 when this
prize was first awarded.
The World Bank classifies countries around the world
according to their income levels, and this serves as a

© Cambridge University Press 2012 Economics for the IB Diploma 2

Quantitative techniques

The material contained in this chapter has been and express the first score as 119 and the second as
compiled to provide you with the mathematical 140
background you will need to answer questions in your 116 . This shows you scored better in the first test.
IB Economics exams involving the use of diagrams and
graphs, as well as the use of mathematical techniques. 140

Sections 1 and 2 of this chapter are intended for A much simpler way, however, is to express the two
students studying economics at both standard and
higher levels. Section 3 is intended for students scores as percentages, which are 85% for the first
taking the course at higher level only, and focuses
on the quantitative methods you will need to answer and 82.8% for the second. The use of percentages
questions in higher level paper 3.
is not only a much easier method, but it also allows
Students sometimes come to the study of
economics concerned that the course may be based you to compare all your other test scores with
on mathematical techniques they might be unable to
handle. However, as you will discover in the pages that each other.
follow, the mathematics you need to do well in your
IB course is quite limited. The few simple techniques Percentages in relation to fractions
you will find here repeat themselves in a variety of and decimals
applications in your IB course. Most if not all of these
techniques involve mathematical ideas or methods Changing a fraction and a decimal
you have very likely already encountered in your
earlier years as a student or as part of your IB studies. into a percentage
Therefore, most of what is included in this chapter will
be simply a review for you. Let’s say we would like to express a fraction, such as

Note that you will find answers to all the ‘Test 34 , as a percentage:
your understanding’ questions in this chapter on the 75
teacher support website at ibdiploma.cambridge.org.
(i) We divide the numerator by the denominator,
1 Percentages and percentage changes which converts the fraction into a decimal.

Percentages (ii) We multiply by 100%:

Why percentages are important 34 = 0.4533; 0.4533 × 100% = 45.33%
‘Per cent’ means ‘out of 100’. It is simply another way 75
of expressing a fraction or a decimal (which is also a
kind of fraction) as a number in relation to 100. Changing a percentage into a fraction
To change a percentage into a fraction, we do the
Percentages allow us easily to make comparisons following:
between fractions that cannot otherwise be easily (i) divide the percentage by 100 and remove the % sign
compared. Suppose you take two tests, and you score (ii) simplify the resulting fraction.
17 in one and 29 in the other. In which test did
20 35 For example:
you get the higher score? There are only two ways to
answer this question. One is to the find the lowest 50% 50 1 78% = 78 = 39
common denominator of the fractions, which is 140, 100 2 100 50

175% = 175 = 7
100 4

Changing a percentage into a decimal
We divide the percentage by 100 (move the
decimal point two places to the left) and remove
the % sign:

50% = 0.50 78% = 0.78 175% = 1.75

© Cambridge University Press 2012 Economics for the IB Diploma 1

Quantitative techniques

Using percentages: examples noted earlier, 17 Test your understanding 1
Example 1: Convert the test scores
20
and 29 , into percentages.
35 1 Change the following decimals into percentages:

17 × 100% = 0.850 × 100% = 85.0% (a) 0.573 (b) 0.628 (c) 1.247 (d) 0.645.
20
2 Change the following fractions into percentages:

29 × 100% = 0.829 × 100% = 82.9% (a) 3 (b) 271 (c) 175 (d) 5 .
35 9 977 65 178

3 Change the following percentages into decimals:

(Note that when we multiply by 100%, we simply (a) 24.5% (b) 25% (c) 99% (d) 125%.
move the decimal point two places to the right and
add the % sign.) 4 In a class of 25 students, 15 came to school by
bus, and the rest walked to school. (a) What
Example 2: In 2009, the total population of a country percentage of students came by bus? (b) What
called Mountainland was 46.3 million. The rural percentage of students walked?
population (living outside of cities) of Mountainland
in the same year was 17.7 million. What percentage of 5 A business makes a profit of 25% of its sales of
Mountainland’s population was rural? $17 000. How much profit does it make?

We express the rural population as a fraction of 6 In 2009, 14% of Mountainland’s population
the total population, and convert this fraction into a (of 46.3 million) were university graduates.
percentage: How many people does this correspond to?

% of population that is rural = 17.7 million × 100% Percentage changes
46.3 million
Students studying economics at standard level should
= 0.3823 × 100% = 38.23% be able to understand and interpret percentage
changes, but will not have to perform calculations
Example 3: In a country called Flatland, 22 million in exams. Students taking the course at higher level
people live in cities and 38 million live in the should be able to calculate percentage changes.
countryside. What percentage of Flatland’s population
lives in cities? Given two numbers, how to calculate
a percentage change
The total population is: To calculate a percentage change, we must have an
initial number and a final number. The percentage
22 million + 38 million = 60 million change expresses the change (an increase or a decrease)
as a percentage of the initial number. Suppose we
Therefore, the percentage of people in cities is: want to find the percentage change from 50 to 75. We
express the change as a fraction of the initial number
22 × 100% = 36.7% and then convert this into a percentage. The change is
60 25 (= 75 − 50), and the initial number is 50. Therefore,
we have 25 = 0.50, which is equivalent to 50%.
Example 4: 12% of a graduating class of 150 students
plan to study economics at university. How many 50
students plan to study economics? More generally, we can calculate a percentage
change in a variable, A, by using the following formula:
When we want to find a number that corresponds
to a percentage of another given number, we % change in A
multiply the given number by the percentage in
decimal form: = final value of A initial value of A × 100%
initial value of A
12% = 0.12; 0.12 × 150 = 18 students
A percentage increase or percentage decrease is shown by
Example 5: 70% of 140 students are actively whether the percentage change that is calculated by
involved in sports. How many students are involved in use of this formula is a positive or negative number.
sports?
Example 6: Suppose the population of Mountainland
70% = 0.70; 0.70 × 140 = 98 students was 45.7 million in 2008 and 46.3 million in 2009.
What was the percentage change in population from
2008 to 2009?

© Cambridge University Press 2012 Economics for the IB Diploma 2

Applying the formula, we have Quantitative techniques

% change in population In practice, when multiplying a decimal by 100%
to convert it into a percentage, we drop the ‘%’ so
= 46.3 illi 45.7million × 100 = 0.6 million × 100% it looks like we are multiplying the decimal by ‘100’.
45 7million 45.7million
Given a number and its percentage
= 0.013 × 100% = 1.3% change, how to calculate the change
and the final number
The population of Mountainland thus increased by Example 9: Due to a combination of a higher birth rate
1.3% (1.3 is a positive number). 1.3% is a percentage and a large influx of immigrants into Mountainland,
increase. the population increased by 4.8% in the period 2009–
10. The size of the population was 46.3 million in 2009.
Example 7: Now suppose that the rural population of (a) How many people were added to Mountainland’s
Mountainland was 18.3 million in 2008 and 17.7 million population in 2009–10? (b) What was the size of the
in 2009. What was the percentage change? population in 2010 as a result of the 4.8% increase?
(a) The number of people added is 4.8% of the whole
% change in rural population
population in 2009 (46.3 million). Therefore:
= 17.7 illi 18 3 million × 100% = −0 6 million× 100%
1 3 million 18.3 million 4.8% × 46.3 million = 0.048 × 46.3 million
= 2.2 million people
= −0.033 × 100% = −3.3%
(b) We can find the 2010 population in two ways:
The rural population of Mountainland therefore (i) Add the increase of 2.2 million to the initial
decreased by 3.3% (−3.3 is a negative number). population of 46.3 million:

Example 8: The data in the table below show 2.2 million + 46.3 million = 48.5 million in 2010
Mountainland’s real GDP (real output produced) for (ii) A more direct way is to begin with the initial
the period 2008−10. Calculate the rate of growth in real
GDP in (a) 2008–9, and (b) 2009–10. population of 46.3 million, and multiply this
by 1 plus the percentage change in decimal
Year Real GDP (in trillion Mnl, the national currency) form, or 1 + 0.048 = 1.048:
2008 5.6
2009 5.7 population in 2010 = 46.3 million × 1.048
2010 5.5 = 48.5 million people in 2010

A percentage change may sometimes be referred to as Note that the answers obtained in the two ways are
‘rate of growth’, which may be positive or negative. identical.

(a) Rate of growth in real GDP, 2008–9: Example 10: The rural population in Mountainland,
which was 17.7 million in 2009, fell by 3.8% in 2009–
% growth in real GDP (2008–2009) 10. What was the size of the rural population in 2010?

= 5.7 trillion 5.6 trillion × 100% = 0 1 trillion × 100% Again, we can do this in two ways:
5 6 trillion 5 6 trillion (i) Find by how much the rural population fell, and

= 0.018 × 100% = 1.8% subtract this from the rural population in 2009:
Mountainland experienced a positive rate of growth
in real GDP of 8% in 2008–9. rural population decrease 2009–10 = 3.8% × 17.7
million = 0.038 × 17.7 million = 0.7 million people
(b) Rate of growth in real GDP, 2009–10:
rural population in 2010 = 17.7 million − 0.7 million
% growth in real GDP (2009–2010) = 17.0 million people

= 5.5 trillion 5.7 trillion × 100% = −0 2 trillion × 100% (ii) In a more direct way, we take the initial population
5 7 trillion 5 7 trillion of 17.7 million, and multiply this by 1 minus the
percentage change in decimal form, or 1 − 0.038
= −0.035 × 100% = −3.5% = 0.962:
rural population in 2010 = 17.7 million × 0.962
Mountainland experienced a negative rate of growth = 17.0 million people
in real GDP of −3.5% in 2009–10.
Note that the answers obtained in the two ways are
© Cambridge University Press 2012 identical.

Economics for the IB Diploma 3

Test your understanding 2 Quantitative techniques

1 You are interested in buying a book that cost 30 between the countries in the world according to
Mnl, but discover that its price has increased by income levels. The variable is population, which varies
20%. What is the book’s new price? according to group of countries. The last column
shows the percentage of the world’s population that
2 Riverland’s GDP of 259 Rvl billion in 2009 grew was in each income group. ‘High income’ countries are
to 272 Rvl billion in 2010 but then fell to 267 those considered to be economically more developed,
Rvl billion in 2011. Calculate the rate of growth while ‘upper middle income’, ‘lower middle income’
in Riverland’s GDP in the period (a) 2009–10, and ‘low income’ countries are considered to be
and (b) 2010–11. economically less developed.

3 In 2005, Riverland had a population of This information is presented as a pie chart in
32.9 million people. In the period 2005–10, Figure 1. The pie chart is derived by multiplying the
its population grew by 7.2%. What was its 360° of a circle by the same percentage that appears
population in 2010? for each income level in the table, thus obtaining the
‘slice’ of the ‘pie’ that corresponds to each income
4 It is estimated that Flatland’s unemployed level. We can see straightaway that a far larger
workers were 1.2 million in 2009. By 2010, the percentage of the world’s population, or 84% (=14.2%
number of unemployed had fallen to 1 million. + 55.3% + 14.5%) lives in economically less developed
What was the percentage change in unemployed countries, compared to only 16% who live in more
workers over this period? developed ones. Note that Table 1 and Figure 1
display exactly the same information, yet it is much
5 A company had profits of $2.5 million in 2009. easier to ‘read’ it in the pie chart.
It insists on an 8.0% increase in profits per year.
What will its profits be in 2010 if it meets its goal? Table 1 World population (in millions) and distribution among countries
grouped by income levels, 2008
2 Understanding and interpreting
graphs and diagrams Income level Population % of total
(millions)
Graphs and diagrams are simply ‘pictures’ showing
how variables change and how they are related to each High income 1068.5 16.0
other. Sometimes, the information contained in graphs Upper middle income 948.5 14.2
and diagrams can be described in words; however, Lower middle income 3702.2 55.3
‘pictures’ allow us to see and understand information Low income 972.8 14.5
far more quickly and effectively. Therefore, graphs and Total 6692.0 100.0
diagrams are very important in presenting real-world
information as well as in building and presenting Source: The World Bank, Data Catalog (http://data.worldbank.org/
economic theories and models. data-catalog).

Graphs that display information about 14.5%
a single variable low income

A variable is a measure of something that can take 55.3% 16.0%
on different values; it is something that ‘varies’ or lower middle high income
‘changes’. Very often, we are interested in studying
changes in a single variable. We can do this by using income 14.2%
three types of graph: pie charts, bar graphs and line upper middle
graphs. Each one serves different purposes (though
there are also some overlaps). income

Pie charts Figure 1 Pie chart: world population (millions) and distribution among
Pie charts are convenient to use when we want to countries grouped by income levels, 2008
show how a whole is divided up between different
parts. The ‘raw data’ appearing in Table 1 present how Source: The World Bank, Data Catalog (http://data.worldbank.org/
the total population in the world in 2008 was divided data-catalog).

© Cambridge University Press 2012 Economics for the IB Diploma 4

Quantitative techniques

Bar graphs Bar graphs, on the other hand, are very useful in
The information in Table 1, presented in a pie chart providing a visual representation of other kinds of
in Figure 1, can also be presented as a bar graph, information and data that cannot be shown in a
as shown in Figure 2. In Figure 2(a), percentages pie chart. They are very convenient for illustrating
of the world’s population are measured along the cross-section data, which are the values taken
vertical axis, and the income groups appear along by a single variable at a particular time (such as a
the horizontal axis. Figure 2(b) is the same as year) for different groups in a population. The bar
Figure 2(a) except that the axes have been reversed. graph in Figure 3(a) measures on its vertical axis
Both presentations are used equally effectively. the percentage of children of primary school age
who are enrolled in school, against the countries
However, comparing the pie chart in Figure 1 with of the four income groups, which appear on the
the two bar graphs in Figure 2, we can see that the pie horizontal axis, in 2007. This graph tells us that
chart provides a more effective representation of the 95% of children in high-income countries attend
different shares of the world’s population, because it primary school, compared to 77.6% in low-income
allows the viewer to see more clearly the relative size ones, and so on for the other two groups and the
of each share of the whole. world as a whole.

(a) Presentation 1% of population 55.3% 14.5% Bar graphs need not measure percentages on the
60 14.2% vertical axis. The bar graph in Figure 3(b) shows the
50 low number of tourist arrivals per 1000 people in a given
40 income year for selected countries. For example, in Cyprus,
30 there are 2676 tourists per year for every 1000 local
20 16% residents, in Saint Kitts and Nevis there are 2259, and
10 so on for the other countries shown.

0 high upper lower Bar graphs are also useful in presenting how a
income variable changes for each group from one time period
middle middle to another. This can be seen in Figure 3(c), which
shows the rate of growth of GDP for three years and
income income for seven country groups. This kind of graph allows
us to see not only how the variable, in this case the
country group rate of growth in GDP, varies from region to region
(highest in countries of East Asia and Pacific and
(b) Presentation 2 lowest in high income countries), but also, we can see
that for all country groups, the rate of growth of GDP
country 14.5% was lower in 2008 compared to 2007, and was in some
group cases lower than in 2006.

low Some variables illustrated in bar graphs may
income sometimes take on negative values, that is, the bars
can fall below the horizontal axis. Whether or not
lower 55.3% this can happen depends of course on the nature
middle of the variable (it could not happen in Figure 3(b)
income 14.2% because there cannot be a negative number of
tourists). Figure 3(d) shows the current account
upper balance as a percentage of GDP in selected countries
middle (we will study the current account balance in
income Chapter 14 of the textbook). Very briefly and simply
(for the time being), the current account balance
high 16% is a measure of inflows and outflows of money in
income a country for particular purposes. If inflows are
10 20 30 40 50 60 greater than outflows, there is a positive balance,
0 % of population which appears as a bar above the horizontal axis.
If inflows are smaller than outflows, there is a
Figure 2 Bar graphs based on the information in Table 1 negative balance and this appears as a bar below the
horizontal axis.

© Cambridge University Press 2012 Economics for the IB Diploma 5

Quantitative techniques

(a) Primary school enrolment (% of primary school-age children), (c) GDP growth, by region, %
2007
GDP growth, by region (%)
% of children of primary school 100 93% 12
age enrolled in school 95% 2006 2007 2008

90 87% 86.9% 9

80 77.6% 6

3

70

0 East Europe & Latin Middle South Sub- high
Central America East & Asia Saharan income
Asia & Africa
0 high upper lower low world Pacific Asia & Caribbean North
income middle middle income Africa
income income
Source: The World Bank, World Development Indicators 2009.
country groups

Source: The World Bank, Data Catalog (http://data.worldbank.org/ (d) Current account balance in selected countries, 2006
data-catalog). 10 China 9.4%

(b) Tourist arrivals per 1000 people in selected countries current account balance as % of GDP 8

6
4 Japan 9.4%
2 Thailand 1.5%

number of arrivals per 1000 people 3000 0
2676
2259 -2
2000
-4

1601 -6
United States -6.1%
1000 941
680 -8

-10 New Zealand -8.9%

0 Cyprus Seychelles Dominica Iceland Saint Kitts -12
and Nevis Greece -12.1%

Source: NationMaster.com. -14

Figure 3 Bar graphs (cross-section data) Source: NationMaster.com.

Line graphs (EU) as well as in two EU countries. The graph covers a
Line graphs are a convenient way to represent a period of 28 years, and is very effective in illustrating
variable that takes on different values over time. We the fluctuations in the rate of unemployment.
have seen that this can to some extent also be shown In addition, it allows us to make comparisons in
in a bar graph, as in Figure 3(c). However, if we are unemployment rates of individual countries and the
interested in seeing how a variable changes over EU, whose unemployment rate is an average over all
an extended period, and also want to easily make its members. As we can see, Cyprus’s unemployment
comparisons, a line graph is more appropriate. A line rate has been lower and Belgium’s higher (until about
graph typically measures time (in months, years, etc.) 2003–4) than the average over the EU.
on the horizontal axis, while the variable that is being
examined appears on the vertical axis. Line graphs The variables illustrated in line graphs can also
showing change over time use time-series data, sometimes take on negative values, as in the case
which are data for a variable that changes over time. of bar graphs. Figure 4(b) shows the annual rate of
growth of agricultural output (per person) in Sub-
Figure 4(a) shows how the unemployment rate (the Saharan Africa for the period 1968–2004. In some
percentage of unemployed people out of the total years this has been positive (above the horizontal
labour force) varies over time in the European Union axis) while in others it has been negative (below the

© Cambridge University Press 2012 Economics for the IB Diploma 6

(a) Unemployment rate in the EU and selected EU countriesunemployment rate (%) Quantitative techniques
16
annual growth rate (%) easily make sense of the information and if possible,
14 detect patterns that increase our understanding of
Belgium the complicated world around us. Yet very often we
want to go beyond a description of the world offered
12 by these graphs in order to discover how variables are
related to each other. To do this, we must use graphs
10 that focus on two interrelated variables. These kinds
8 EU of graphs are very important in illustrating economic
theories and building economic models.
6
Constructing and interpreting graphs
4 that relate two variables to each other
2 Cyprus Graphs that illustrate how variables are related to
each other measure a different variable on each axis.
1980 1985 1990 1995 2000 2005 2010 2015 Each axis on the graph represents a number line,
Source: World Health Organization/Europe, Health for all database, which measures units of the variable. Figure 5(a)
January 2010. presents a vertical and a horizontal number line.
(b) Agricultural output growth per person in sub-Saharan Africa The vertical number line begins with negative
numbers at the bottom end, which increase as we
4.0 move upward until they reach 0, and then become
positive. The horizontal number line begins with
2.0 negative numbers at the left, which increase as
we move rightward until they reach zero, and
0.0 then become positive. In both number lines, the
number 0 is called the origin. In each number line,
-2.0 the numbers represent units of the variable that is
being measured. Therefore, the value of the variable
-4.0 measured on the vertical number line increases in
1968 1972 1976 1980 1984 1988 1992 1996 2000 2004 the upward direction, and the value of the variable
measured on the horizontal number line increases in
Source: The World Bank, World Development Report, 2008. the rightward direction.

Figure 4 Line graphs (time-series data) To construct a graph, we put the vertical and
horizontal number lines together, so that they are
horizontal axis). As you may remember from the perpendicular to each other and intersect at the
discussion above, a positive rate of growth means that origin of each one, as shown in Figure 5(b). Each
output is increasing, while a negative rate of growth number line in the graph is referred to as an axis. By
indicates decreasing output. convention, the horizontal axis is sometimes called
the x-axis and the vertical is called the y-axis. The four
Test your understanding 3 spaces that are carved out by the intersecting axes
are called quadrants, and are numbered from I to IV.
Look through local newspapers and magazines and Quadrant I represents combinations of two positive
find examples of pie charts, bar graphs and line numbers, quadrants II and IV represent combinations
graphs. Which of these display cross-section data; of one positive and one negative number, and
which display time-series data? Explain, in a general quadrant III represents combinations of two negative
way, what each graph illustrates, and describe any numbers.
patterns or trends you detect.
In economics, most of the relationships we
Graphs displaying the relationship between examine involve combinations of two positive
two variables numbers, in which case we simplify the graph
by considering only the first quadrant, ignoring
Pie charts, bar graphs and line graphs that display the remaining three. This is shown in Figure 5(c).
information about a single variable are usually However, sometimes we may want to examine
constructed in order to present real world data in relationships involving one positive and one
an organised and logical way, allowing viewers to negative number, in which case we may consider a
graph such as in Figure 5(d) or (e).

© Cambridge University Press 2012 Economics for the IB Diploma 7

Quantitative techniques

(a) Horizontal and vertical number lines (b) The four quadrants

vertical vertical
number line axis (y axis)

3 3

annual growth rate (%) 2 II 2 I

1 horizontal 1 origin

0 origin number line horizontal
1 2 3 axis (x axis)
-3 -2 -1 0 1 2 3 -3 -2 -1 0
-1 -1 IV

-2 origin III -2

-3 -3

(c) Quadrant I (d) Quadrants I and IV (e) Quadrants I and II

vertical axis vertical axis vertical axis
4 3 3
2I
3 1 II 2 I
0 horizontal
2I -1 1 2 3 axis 1
-2 IV
1 -3 -3 -2 -1 0 1 2 horizontal
3 axis

0 horizontal
1 2 3 4 axis

Figure 5 Number lines and quadrants Each point in a graph can be represented as (h,v),
where h = the value of the variable on the horizontal
Positive (direct) relationships between axis and v = the variable on the vertical axis.
two variables
Each point on a graph is specified by two numbers, Drawing a line through all the points gives a
one from each of the two axes. Suppose we are straight line, which is called a curve. All lines in
examining the relationship between the following two graphs (and diagrams) are referred to as curves,
variables: the number of calories consumed per day regardless whether they are straight or curved.
and the amount of weight (in kilograms, abbreviated
as kg) that will be gained in one month. The data on Note that the horizontal axis contains a squiggly
these two variables are presented in Table 2 on page 9, part close to the vertical axis. The reason is that the
and are graphed (or plotted) in Figure 6(a) where daily numbers on this axis jump from 0 to 1500 in a very
caloric consumption is measured on the horizontal short space, whereas all other points have an identical
axis and monthly weight gain on the vertical axis. distance between them, each space representing 250
Each pair of points in the table corresponds to a point calories. The squiggly line means that some numbers
in the graph. For example, point e corresponds to 2500 of the number line of this axis have been skipped.
calories per day, and to 2 kg of weight gain per month.
On the graph, this point is found by drawing a line Once a line is drawn connecting the points in a
upward from 2500 on the horizontal axis, and also graph, it is possible to read off other combinations
drawing a horizontal line from 2 on the vertical axis; of the two variables. For example, a point exactly in
point e is where the two lines meet. Every other point between points e and f on the curve corresponds to
on the graph is plotted in the same way. the points between the values of the two variables on
each of the axes, which are 2.5 kg and 2625 calories.
Each point in the graph is represented as: (h,v),
where h takes on the value of the variable measured The graph shows that consumption of 2000 calories
on the horizontal axis and v takes on the value of per day results in a steady weight, as weight gain is 0 kg.
the variable measured on the vertical axis. Therefore, If calories consumed rise above 2000 per day, the result
point e is represented as (2500,2); point g as (3000,4). is weight gain, while if they are less, the result is weight
loss (negative ‘weight gain’ is equivalent to weight loss).
© Cambridge University Press 2012
Economics for the IB Diploma 8

Quantitative techniques

Table 2 The relationship between calories consumed daily and weight gain Table 3 The relationship between hours of sleep and mistakes
per month on tests

Daily caloric Monthly weight Point on graph Number of hours Number of Point on graph
consumption gain (kg) (Figure 6(a)) (Figure 6(b))
−2 a of sleep mistakes on tests a
1500 −1 b b
1750 0 c 4 10 c
2000 1 d d
2250 2 e 58 e
2500 3 f f
2750 4 g 66
3000
74

82

90

(a) Calories consumed and weight gain: a positive relationship (b) Hours of sleep and mistakes on tests: a negative relationship

4g 12
10 a
3f 8b
2e 6c
monthly weight gain (kg) 4d
mistakes on tests 2e
1d daily
caloric f
c 0 456789
0
hours of sleep
1500 1750 2000 2250 2500 2750 3000 consumption
-1 b

-2 a

-3

-4

Figure 6 Positive and negative relationships between two variables

The curve of Figure 6(a) shows that the two variables and number of mistakes on tests. Each pair of data
we are examining are related in a particular way: as daily corresponds to a single point in the graph that
consumption of calories increases, weight gain also appears in Figure 6(b). This graph is plotted entirely in
increases. This is called a positive, or direct relationship: quadrant I, with positive values of both variables, as it
is not possible to have a negative number for hours of
A positive (or direct) relationship between two sleep or for mistakes on tests. This graph shows that
variables is illustrated by a curve that moves upward few hours of sleep are associated with a larger number
and to the right, showing that as one variable of mistakes on tests, while more hours of sleep mean
increases, the other also increases. Alternatively, if fewer mistakes on tests. This is called a negative, also
one variable decreases, the other also decreases. In known as an indirect, relationship:
a positive relationship, the two variables change in
the same direction. A negative (or indirect) relationship between
two variables is illustrated by a curve that moves
Negative (or indirect) relationships downward and to the right, showing that as one
between two variables variable increases, the other variable decreases. In a
Let’s now consider a different kind of relationship, negative relationship, the two variables change in
using the information of Table 3, which provides opposite directions.
data on two variables: number of hours of sleep
Economics for the IB Diploma 9
© Cambridge University Press 2012

Graphs and the cause-and-effect Quantitative techniques
relationship between two variables
One important reason why we construct and study Case 1: We may observe that a society has a large
two-variable graphs is that we are trying to discover number of doctors (per capita or per person in the
causal relationships between variables. A causal population) and it also has high rates of certain
relationship is a ‘cause-and-effect’ relationship, where diseases. We could conclude that the high rate of
changes in one variable are seen as causing changes diseases has given rise to a large number of doctors
in the other variable. The variable that initiates the (though we could also conclude the opposite). But
change is called the independent variable, and would this be a valid argument? It is very possible
the variable that is influenced or affected as a result is (and likely) that each of these (the large number of
called the dependent variable. A causal relationship doctors and the high rate of diseases) has separate,
is called a functional relation, where the independent causes, and the apparent relation
dependent variable is a function of the independent between the two is coincidental.
variable. Two-variable graphs usually (though not
always) display such functional relations. Case 2: A second possible difficulty is illustrated
by the following simple example. Runny noses are
In Figure 6(a), the independent variable (or the observed to appear together with sore throats. We
‘cause’) is the daily consumption of calories, and the therefore conclude that a runny nose causes a sore
dependent variable (or the ‘effect’) is monthly weight throat (or vice versa). But this is clearly nonsense.
gain. Monthly weight gain depends on consumption Both runny noses and sore throats are caused by
of calories, hence is the dependent variable. Figure 6(a) another (third) factor, which is usually a virus. In
shows a positive causal relationship. In Figure 6(b), this case, the association of runny noses and sore
the independent variable is the number of hours of throats is usually not coincidental, but the two are
sleep; in this relationship, mistakes on tests depend not causally related to each other.
on hours of sleep. In Figure 6(b), we see a negative
causal relationship. Case 3: A third difficulty arises in the event that
there may be a causal relationship between two
Two-variable graphs usually represent a causal variables, but we cannot be sure which causes
relationship between the variables, where the which. For example, it is generally observed that
independent variable is the ‘cause’ and the dependent people with more education also have higher
variable is the ‘effect’. Causal relationships are very incomes. It may therefore be supposed that more
important for making hypotheses, constructing education allows people to get better jobs and
theories that try to explain events and as building therefore earn higher incomes. However, the
blocks of models that illustrate theories. opposite is also possible, as people with higher
incomes have greater possibilities to become
Test your understanding 4 educated. So which causes which?

For each of the following pairs of variables, explain In the first two cases, there is an association (in
(i) whether there is likely to be a positive or negative mathematical terms this is called a correlation)
causal relationship between them, and (ii) which is between the two variables, but with no causation. In
the dependent and which is the independent variable: the first case, this is due to coincidence; in the second,
it is due to there being another causal factor which
(a) income and saving affects both variables. In the third case, the association
(or correlation) may well be due to causation, but we
(b) number of DVDs purchased and price of DVDs cannot be sure which is the causal factor.

(c) level of salary and number of years of working The cases of demand and supply
experience
In your study of economics, you will encounter many
(d) the temperature and number of swimmers on kinds of relationships between variables that are
the beach. illustrated as graphs or diagrams. Two very important
relationships you will make great use of are those of
Causation versus association (correlation) demand and supply.
Two variables may sometimes appear to be related
to each other, and yet there may not be a causal Demand
relationship between them. There are three important
cases leading to difficulties. Demand as a relationship between price
and quantity demanded
Demand involves the relationship between the price of
a good and the quantity of the good consumers want

© Cambridge University Press 2012 Economics for the IB Diploma 10

Quantitative techniques

to buy. Table 4 shows the quantity of pizzas that the Shifts of the demand curve and the ceteris
residents of Olemoo want to buy at different possible paribus assumption
prices (in Olemooan $) each week. The data in Table 4 So far, we have studied the relationship between
are graphed (or plotted) in Figure 7, where we see that two variables only. However, in the real world, a
there is a negative (or indirect) relationship between dependent variable usually depends on more than
price and quantity: the higher the price, the fewer the just one independent variable. For example, the
pizzas that Olemooans want to buy. The quantity of amount of pizzas that Olemooans want to buy very
pizzas Olemooans want to buy at each price is called likely depends not only on the price of pizzas but
quantity demanded. also on Olemooans’ income, Olemooans’ tastes (how
much they like pizza), the number of people in the
Note that of the two variables we are considering, Olemooan population, and other factors. Taking
price and quantity demanded, price is the income as an example, it is likely that as Olemooans’
independent variable and quantity demanded is the income increases, they will want to buy more pizzas.
dependent variable. This is because the quantity of Yet this complicates matters. What if income increases,
pizzas Oloemooans want to buy depends on the price and at the same time the price of pizzas also increases?
of pizzas. Therefore, there is a negative causal Will Olemooans want to buy more or fewer pizzas?
relationship between price and quantity demanded.
According to correct mathematical practice, the We now have three variables, but with the
independent variable is plotted on the horizontal axis possibility of showing only two of these at the same
and the dependent variable on the vertical axis (as time in a graph of a demand curve. To resolve this
in the cases of Figures 6 (a) and (b) above). However, problem, we plot the relationship between price and
many economics graphs do not follow the customary quantity demanded on the assumption that income
mathematical practice. In the case of demand, the (plus all other things that can affect demand for pizzas)
independent variable ‘price’ always appears on the vertical is constant or unchanging. This is called the ceteris
paribus assumption (explained also in Chapter 1 of the
axis, while the dependent variable, ‘quantity’, always textbook, page 10), which means that all other things
that can affect a relationship between two variables are
appears on the horizontal axis. assumed to be constant or unchanging.

Table 4 Demand for pizzas by Olemooans To deal with the likely effects of income on pizzas
demanded in a graph, we use the information in
Price per kg Quantity demanded Table 5, which contains data on quantities of pizzas
(Olemooan $) (thousand kg per week) demanded for different levels of income. The data in
the column indicating ‘middle income’, are the same
1 9 as those used to plot the demand curve in Figure 7.
2 7
3 5 Figure 8 graphs the demand curves corresponding
4 3 to each of the three income levels. We can see that
5 1 if Olemooans at first have a middle income (the
middle curve), but then their income increases, the
5price per pizza entire demand curve shifts (or moves) to the right,
4(Olemooan $) to the curve labelled ‘high income’. This curve tells
3 us that for any particular price, Olemooans will buy
2 more pizzas with a higher income, and is called ‘an
1 increase in demand’. If, however, Olemooans’ income
falls, their demand curve will shift to the left to the
0 1 2 3 4 5 6 7 8 9 10 curve labelled ‘low income’; this is called a ‘decrease
quantity in demand’. This means that for a particular price,
Olemooans will buy fewer pizzas.
(thousand pizzas per week)
Leftward/rightward shifts and upward/
Figure 7 Demand curve: price of pizzas and quantity demanded downward shifts of the demand curve
We have referred to the demand curve as shifting
© Cambridge University Press 2012 ‘to the right’ or ‘to the left’, which is the customary
practice. However, if you examine Figure 8, you will
notice that a rightward shift looks the same as an
upward shift, and a leftward shift looks exactly the

Economics for the IB Diploma 11

Table 5 Demand for pizzas by Olemooans at different income levels Quantitative techniques

Price per kg Quantity Quantity Quantity Distinguishing between a movement along
(Olemooan $) bought bought bought the demand curve and a shift of the curve
(thousand (thousand It is very important to make a distinction between a
(thousand pizzas per pizzas per movement along a demand curve, and a shift
pizzas per week) week) of a demand curve. In a causal relationship, a
week) Middle High income movement along a curve can only be caused by a
Low income income change in the independent variable (in this case price),
10 which influences the dependent variable (quantity
18 9 demanded), thus causing a movement from one point
8 on the curve to another. A shift of a curve, on the
26 7 other hand, is caused by a change in a variable that
6 was previously held constant under the ceteris paribus
34 5 assumption (the level of income). All variables that
4 can cause shifts of a demand curve are referred to as
42 3 determinants of demand, because they determine
2 the position of the demand curve. As you will learn in
50 1 Chapter 2 of the textbook, there are several important
determinants of demand, of which income is only one.
5price per pizza
(Olemooan $) Supply
4
Supply as a relationship between price
3 and quantity supplied
2 high income Supply involves the relationship between the price of a
1 low income good and the quantity of the good producers (or firms)
want to produce and sell. Table 6 shows the quantity of
middle income pizzas Olemooan pizza producers want to produce each
0 1 2 3 4 5 6 7 8 9 10 week at different possible prices (in Olemooan $). The
data in Table 6 are graphed in Figure 9 (see page 13),
quantity which shows that there is a positive (or direct)
(thousand pizzas per week) relationship between price and quantity: the higher the
price of pizzas, the more pizzas that Olemooan pizza
Figure 8 Demand curves at different income levels producers want to sell. The quantity of pizzas Olemooan
producers want to sell is called quantity supplied.
same as a downward shift. The meaning of a rightward
shift of a demand curve is exactly the same as an upward As in the case of demand, price is the independent
shift, and the meaning of a leftward shift of a demand variable and quantity supplied is the dependent
curve is the same as a downward shift, although there is variable, because the quantity supplied depends
a difference in how we can interpret them. on price. There is therefore a positive causal
relationship between price and quantity supplied.
If we view the curve as shifting to the right, we see that Again, as in the case of demand, supply curves measure
for a given price, Oloemooans increase their purchases of the independent variable, price, on the vertical axis and
pizzas as income rises. At a price of $3, they will buy 4000 the dependent variable, quantity, on the horizontal axis.
pizzas per week with a low income, 5000 pizzas with a
middle income, and 6000 pizzas with a high income. If we Shifts of the supply curve and the ceteris
view the curve as moving upward or downward, we see paribus assumption
how much Olemooans are willing to pay for a particular The amount of a good produced, such as pizzas,
quantity of pizzas as their income changes. For example, depends on more factors than just price. For example,
for the quantity of 6000 pizzas, they are willing to pay $2 it depends on the number of pizza producers; as this
per pizza with low incomes, $2.50 per pizza with medium number increases, the amount of pizzas produced will
incomes, and $3.00 per pizza with high incomes. also increase. In addition, it depends on the costs of
producing pizzas; if costs increase, it is likely that the
Usually, when studying demand curves, we amount of pizzas produced will fall.1
examine shifts as occurring in the rightward or
leftward directions, and less often in the upward and
downward directions.

1 The reasons for this are explained in Chapter 2 of the textbook.

© Cambridge University Press 2012 Economics for the IB Diploma 12

Quantitative techniques

Table 6 Supply of pizzas by Olemooan producers

Price per pizza Quantity supplied Leftward/rightward shifts and upward/
(Olemooan $) (thousand pizzas per week) downward shifts of the supply curve
Looking at Figure 10, we can see that a rightward shift
1 3 of the supply curve looks the same as a downward
2 4 shift, and a leftward shift looks the same as an upward
3 5 shift. The meaning of a rightward shift of a supply curve
4 6 is exactly the same as a downward shift, and the meaning
5 7
of a leftward shift of a supply curve is exactly the same as
price per pizza 5
(Olemooan $) an upward shift, though it is possible to interpret them
4 differently (as in the case of demand).

3 Viewing the curve move from left to right, we see
that for each price, pizza producers want to supply
2 more pizzas as their costs fall. At a price of $3, they
will supply 4000 pizzas when costs are high, 5000
1 when costs are medium, and 6000 when costs are
low. Viewing the curve move upward, we see what
0 12345678 price producers are willing to accept for pizzas as their
quantity costs change. To produce 5000 pizzas, for example,
they will want to accept a price of $2 if costs are
(thousand pizzas per week) low, $3 if costs are medium, and $4 if costs are high.

Figure 9 Supply curve: price of pizzas and quantity supplied Table 7 Supply of pizzas by Olemooan producers at different cost levels

Once again, as in the case of demand, we have more Price per Quantity Quantity Quantity
than two variables to deal with, but with the possibility pizza supplied supplied supplied
of showing only two of them at the same time in a (thousand (thousand (thousand
single supply curve. To address this problem we use the (Olemooan $) pizzas per pizzas per pizzas per
same method as with demand, which involves use of
the ceteris paribus assumption. We plot the relationship week) week) week)
between price and quantity supplied, on the Low costs Medium High costs
assumption that all other variables that can influence
the amount supplied are constant or unchanging. 14 costs 2
25
We can use the information in Table 7 to show what 36 3 3
happens to the supply curve when there are factors 47
other than price that affect the amount supplied. The 58 4 4
factor we will consider is the cost of producing pizzas.
The data in the column indicating ‘medium costs’ are 5 5
the same as those we used to plot the supply curve of
Figure 9. 6 6

Figure 10 graphs the supply curves corresponding 7
to each of the three cost levels. If Olemooan producers
have medium costs of production for pizzas and then 5
these costs decrease, the entire supply curve shifts to
the right, to the curve indicating ‘low costs’. This is price per pizza 4
called an ‘increase in supply’, and tells us that at each (Olemooan $)
possible price, producers will supply more pizzas than 3
before. If, however, costs of producing pizzas increase,
then the supply curve will shift to the left to the curve 2 high low costs
labelled ‘high costs’, meaning that at each possible price costs
producers want to supply fewer pizzas than before.
1

medium costs

0 12345678
quantity

(thousand pizzas per week)

Figure 10 Supply curves at different cost levels

© Cambridge University Press 2012 Economics for the IB Diploma 13

This is reasonable, because the higher the costs of Quantitative techniques
making pizzas, the higher must be the price to make it
worthwhile for producers to produce the pizzas. A shift of a curve can be caused only by changes
in variables that do not appear on the vertical or
Supply curve shifts are sometimes examined as horizontal axis of a graph. Such variables are
moves to the left or to the right (see Chapter 2 of called determinants of the curve, because they
the textbook) and sometimes as moves up or down determine the position of the curve on the graph.
(textbook Chapters 4 and 5). However, it is important Determinants include all the variables that are held
to note that when we speak of ‘an increase in supply’ or constant under the ceteris paribus assumption. If any
‘a decrease in supply’ we are always referring to leftward/ determinant changes, then the entire curve shifts.
rightward shifts. An increase in supply means that On the other hand, any change caused by a variable
more pizzas are sold at each price, while a decrease in that is plotted on the vertical or horizontal axis,
supply refers to fewer pizzas sold at each price. Since always leads to a movement along the curve.
we measure the amount of pizzas along the horizontal
axis, this means that supply increases or decreases Test your understanding 5
involve rightward or leftward shifts of the supply
curve. 1 Draw a demand curve for pizzas (it is not
necessary to use data) and show what is likely
Why, then, do we sometimes refer to upward to happen if (a) there is a change in the price of
and downward shifts of the supply curve? As you will pizzas, (b) there is an increase in the population
discover when you study Chapters 4 and 5, upward/ of Olemoo, and (c) there is a decrease in the
downward shifts are very convenient to use when population of Olemoo.
studying certain kinds of taxes and subsidies, and
their effects on firms’ supply curves. Taxes work to 2 Draw a supply curve for pizzas (it is not
increase firms costs’ of production, and as we know necessary to use data) and show what is likely
this results in a leftward shift of the supply curve to happen if (a) there is a change in the price of
(or a ‘decrease in supply’). But if we view this leftward pizzas, (b) there is an increase in the number of
shift as an upward shift, then it is actually possible to pizza producers, and (c) there is a decrease in the
measure the cost increase in our graph, which can be very number of pizza producers.
useful. Subsidies, on the other hand, are payments
by the government to firms, having the opposite Further topics on graphs
effects of taxes. They work to decrease firms’ costs
of production, resulting in a rightward shift of the Non-linear curves
supply curve (or an ‘increase in supply’). If we view this
rightward shift as a downward shift, we can again measure The curves discussed above, illustrating positive and
the decrease in production costs, which can also be very negative relationships, are linear, or straight-line curves.
useful. Many of the curves you will be studying in this course
at standard level will be linear. Higher level material
These points will become clearer to you as you will include some curves that are non-linear, or curved.
study the textbook. Everything that was said above regarding positive and
negative relationships applies to non-linear curves as well.
Distinguishing between a movement along
the supply curve and a shift of the curve Figure 11(a) shows two non-linear curves where the
Everything that was said above in connection with variables in both cases are positively (directly) related.
shifts versus movements along a demand curve The difference between them is that in (i), as we move
applies equally to the supply curve. A movement rightward along the x-axis the curve becomes steeper,
along a supply curve is caused only by changes in where as in (ii), the curve becomes less steep.
price, the independent variable. A shift of a supply
curve is caused by changes in variables previously In Figure 11(b), the two variables are negatively
held constant under the ceteris paribus assumption. All (indirectly) related to each other. Here, too, the
such variables are called determinants of supply, difference between the two curves lies in how their
because they determine the position of the supply steepness changes as we move rightward along the
curve. In Chapter 2, you will learn about several x-axis: in (i) steepness decreases and in (ii) steepness
different kinds of determinants of supply. increases. The curve in Figure 11(b)(ii) is the
production possibilities curve introduced in Chapter 1
This leads us to an important point that applies to of the textbook.
both demand and supply curves (as well as all other
curves):

© Cambridge University Press 2012 Economics for the IB Diploma 14

(a) Positive relationships (ii) Quantitative techniques
(i) curve becomes steeper
(ii) curve becomes less steep y (a) Maximum number of joggers

(i) maximum

y

0 x0 x
(ii)
(b) Negative relationships 0 low T' high
(i) curve becomes less steep temperature temperature
(ii) curve becomes steeper
temperature
(i)
y
y

(b) Minimum household energy consumption

0 x0 x

Figure 11 Non-linear curves

minimum

Maximum and minimum points of 0 low T'' high
variables in non-linear curves temperature temperature
Sometimes a variable that is plotted in a non-linear
relationship reaches a maximum, which is a ‘highest’ tt
point, or a minimum, which is a ‘lowest’ point. These
kinds of points are illustrated in Figure 12. In part Figure 12 Non-linear curves with maximum and minimum points
(a) temperature is measured on the horizontal axis,
and the number of joggers on the vertical axis. When minimum because there is no need for heating or air
it is very cold there are few joggers; as temperature conditioning. The curve up to T’’ shows a negative
increases, the number of joggers increases, but beyond relationship between the two variables, and beyond T’’
a certain temperature, T’, it gets too hot to jog, and it becomes a positive relationship.
the number of joggers begins to fall. At temperature
T’, the number of joggers is maximum. Therefore, Illustrating two variables that are not
the curve up to T’ shows a positive relationship, and related to each other
beyond T’ it becomes a negative relationship. Sometimes, we may run into variables that are not
related to each other. This means that as one variable
In part (b) the horizontal axis again measures changes, the other variable remains the same. Two
temperature, with household energy consumption such relationships are shown in Figure 13. In part
appearing on the vertical axis. At low temperatures (a), we see that as fruit consumption increases, the
energy consumption is high because of heating,
and at high temperatures it is high because of air
conditioning. There is a temperature in between
the two extremes, T’’, where energy consumption is

© Cambridge University Press 2012 Economics for the IB Diploma 15

Quantitative techniques

(a) Haircuts and fruit consumption price
()5
number of haircuts per year 4 S
3
2
1

0 10 20 30 40 50 60 70
quantity

0 fruit consumptionprice of textbooks Figure 14 Calculating areas in a graph
(b) Textbook prices and number of pizzas bought
price of the good increases (see page 12). We can see
0 average number of pizzas bought that when price is €2 per unit, the firm sells 30 units;
per person per week when the price rises to €3 per unit, the firm sells 50
units. What is the firm’s total revenue (TR) at each
Figure 13 Unrelated variables price? Since TR = P × Q , when price is €2, TR = €2 × 30
= €60, and when price is €3, TR = €3 × 50 = €150. These
number of haircuts per year remains constant, i.e. values for TR can be shown graphically as areas. Since
fruit consumption does not have any effect on the the area of a rectangle can be found by multiplying
number of haircuts. In part (b) we see that the number two of its adjacent sides (two sides that connect at a
of pizzas bought per person each week remains point), it follows that TR = €60 is shown by the light
constant as the price of textbooks changes; in other green rectangle, and TR = €150 is shown by the sum
words, textbook price changes have no effect on pizza of the dark plus light green shaded regions. Note that
consumption. In both these examples, we say the two the dark green area alone is the difference between the
variables are independent of each other. two, or €90 (= €150 − €60).

Test your understanding 6

In Figure14, assume that the price increases to
€4 per unit. (a) What quantity of output will be
sold at that price? (b) What is the firm’s total
revenue at the new price? (c) By how much has the
firm’s total revenue increased compared to when
the price was €3 per unit?

Calculating areas in a graph Graphs and diagrams in relation
In some situations, some areas in a graph may have to theories and models
a particular meaning that we may want to calculate. The terms ‘graph’ and ‘diagram’ are often used
For example, an important concept in economics is interchangeably, and although their meanings
total revenue (abbreviated as TR), which is the total certainly overlap, they are not identical. ‘Diagram’ is a
amount of income that a firm receives for selling its broader term than ‘graph’, as all graphs are diagrams,
output. Total revenue is calculated by multiplying the yet not all diagrams are graphs. A diagram is any two-
number of items of a good sold, or quantity (Q), by the dimensional representation of information, which
price (P) of the good. Therefore, TR = P × Q. We can may be non-numerical, i.e. may not involve numbers
see this graphically in Figure 14, which plots price on (although there are many exceptions). A graph,
the vertical axis and quantity on the horizontal axis. in a most general sense, is a type of diagram that
The curve shown is a supply curve (S), indicating that usually displays variables using numbers or quantities
the quantity of a good sold by the firm increases as the (though here, too, there are many exceptions). Graphs

© Cambridge University Press 2012 Economics for the IB Diploma 16

Quantitative techniques

are extremely useful in presenting and analysing 3 Linear functions and linear
numerical information, or statistics or data. equations

Many of the figures presented above consist of In this section we examine graphs of supply and
diagrams that are graphs, as they all present variables demand and the equations that describe them, as well
that take on numerical values. On the other hand, the as some of their properties.
diagrams in Figures 11–13 would usually not be called
‘graphs’, because they present information about In a functional relation between two variables, the
variables in a non-numerical way. dependent variable is a function of the independent
variable: the dependent variable changes in response
In economics, when we discuss theories and use to changes in the independent variable. A function
models to illustrate theories, we make very heavy is expressed as an equation. In this course, we will
use of diagrams that show relationships between be using only linear functions, or equations that
variables, but without the use of numbers to measure represent straight (not curved) lines in a graph.
different values of the variables. In fact, it is not
necessary to plot data to show how variables relate According to mathematical convention, the
to each other. For example, the relationship between dependent variable in a function is plotted on the
price (P) and quantity supplied (Q) could be redrawn vertical axis and the independent variable on the
as in Figure 15(a); the relationship between price (P) horizontal axis. This practice is followed by the
and quantity demanded (Q) could be shown as in sciences and social sciences including economics,
Figure 15(b). Neither of these diagrams presents any with one major exception: demand and supply functions,
numerical information, yet we can still immediately where the axes for dependent and independent variables are
see the positive relationship in the first diagram and reversed. The practice of reversing the axes dates back
the negative relationship in the second. Most often, to the famous British economist Alfred Marshall, who
the shape or steepness of curves, either on their adopted the custom of plotting price (the independent
own, or drawn together with other curves in the variable) on the vertical axis in the 19th century. These
same diagram, are all we need in order to be able to functions must therefore be interpreted differently from the
make use of the information they provide to develop standard mathematical way.
theories and illustrate them with models.
The supply function
(a) Supply curve: a positive relationship
PS Understanding the equation
of a supply function
0Q You may recall that supply involves a positive causal
relationship between price and quantity supplied.
(b) Demand curve: a negative relationship The data in Table 8 represent a positive, linear
P relationship between price, P, in $, and quantity
supplied, Q s, in thousand units of good Alpha
D supplied per day. The data in Table 8 are graphed in
0Q Figure 16(a), where you can clearly see the positive
relation between P and Q s.
Figure 15 Non-numerical diagrams showing relationships between
variables Table 8 Data for a supply curve: positive linear relationship

© Cambridge University Press 2012 Quantity supplied Price (P, in $) Point on graph
(Q s, in thousand units (independent (Figure 16(a))

of Alpha per day) variable) A
(dependent variable) B
0 C
5 20 D
40 E
10 60 F
80
15 100

20

25

30

Economics for the IB Diploma 17

(a) Graphing from data in a table Quantitative techniques

P($) Both c and d are known as parameters, and in this
100 F context refer to the quantities that define a particular
linear functional relation. The information in Table 8
90 determines the values of the parameters c and d, and
once we have the values for c and d, we will have the
80 E linear equation that describes the data in this table.

70 The value of c is the value of the dependent
variable when the independent variable
60 D slope = Qs = 5 = 1 is equal to zero
p 20 4
In Table 8, the dependent variable is Q s and the
50 independent variable is P. We can see immediately

40 C that when P is equal to zero, Q s is equal to 5.
Therefore, c = 5.
30

20 B

10 The value of d is the slope
The slope is defined as the change in the dependent
A variable divided by the change in the independent
0 5 10 15 20 25 30 35 40 Q variable, between any two points on a line. We can
calculate the slope from the information in Table
value of Qs 8. Since Q s is the dependent variable and P is the
when P = 0 independent variable, the slope is defined as:

(thousand units per day)

(b) Graphing from the supply function

P($)

100 Qs = c + dp
is
90 1 slope = ΔQs = Q1 − Q2
80 Qs = 5 + 4 p ΔP P1 − P2

70

60 where Q1 and Q2 are two quantities and P1 and P2 are
the corresponding two prices. Note that this is the
50 slope = 1 = parameter d
4 same as:

40

30 slope = ΔQs = Q2 − Q1
20 (10, 20) ΔP P2 − P1

10 (7.5, 10) However, you must be consistent; i.e.
(5, 0)
slope = Q2 − Q1 would be wrong.
0 5 10 15 20 25 30 35 40 Q P1 − P2

parameter c Taking points A and B, we have:
(thousand units per day)

Figure 16 Graphing the supply curve ΔQ s = 10 − 5 = 5, and ΔP = 20 − 0 = 20.
Therefore,
The equation of a supply function
d = slope = ΔQs = 5 = 1
ΔP 20 4

(positive linear function) If we use points C and D, we have ΔQ s = 20 − 15 = 5,
and ΔP = 60 − 40 = 20. Therefore, ΔQs = 5 = 1, which
The equation of a linear supply function is given by:
ΔP 20 4
Q s = c + dP is the same as before. In fact, the slope of a straight line
is constant, or the same, no matter which two points
where we use to calculate it. You can see this by finding the
slope between any two other points in Table 8.
Q s = quantity supplied, the dependent variable
P = the independent variable The fact that the slope in the supply function
Q s = c + d P has a positive sign (+d) indicates that there
c = the value of the dependent variable when the is a positive relationship between the two variables,
P and Q s.
independent variable, P, is equal to zero

d = the slope, where slope = ΔQs and is the
ΔP

coefficient of the independent variable, P.

© Cambridge University Press 2012 Economics for the IB Diploma 18

Quantitative techniques

Specifying the supply function that joining three points does not produce a straight
line, we know that we have made a mistake). To find
Since c = 5, and d = 1 , the equation for the supply points, we can set P equal to different values and solve
4 for Q s (though it is possible also to set Q s equal to
different values and solve for P).
function in Table 8 is:
Using our supply equation
Qs 1P
4
1P
Using this equation, we can find any value of Qs, Qs 4
given a value of P. Suppose P = 52.7:

Qs = 5 + 1 (52.7) = 5 + 13.2 = 18 2 it is simplest to begin by setting P = 0, which gives Qs
4 = 5, where 5 is the parameter c. This gives us the point

(5,0) on the line. To find a second point, we can set

Similarly, we can find any value of P, given a value P = 10, which gives Qs =5+ 1 (10) = 5 + 2.5 = 7.5;
of Q s. Suppose Q s = 25: 4

25 = 5 + 1 P ⇒ 20 = 1 P ⇒ P = 80. this gives us the point (7.5,10). Setting P = 20, we have
4 4
1
Qs = 5+ 4 (20) = 5+5 = 10, or the point (10,20).

The equation of a linear supply function is given We could go on finding more points; however, as
by Q s = c + dP, where Q s is quantity supplied (the
dependent variable), P is price (the independent explained above, this is not necessary. Now the points
variable), c is the value of Q s when P = 0, and d is
the slope (given by ΔQs ). can be plotted. They appear in Figure 16(b).

ΔP When we have a graph of the general supply

function Q s = c + d P, we can attach specific
interpretations to the parameters c and d. We know

from our discussion above that c is equal to the value

The positive sign of the slope (+d) indicates that of the dependent variable, Q s, when the independent
the supply function represents a positive (direct) variable, P, is equal to zero. When the dependent
relationship between P and Q s.
variable is plotted on the horizontal axis, as in the

supply function, we can re-phrase this to mean that

c is the point on the horizontal axis that is cut by the

line. This is known as the horizontal intercept

Graphing the supply curve (an intercept is a point on an axis that is cut by

We can graph (or plot) the curve that corresponds to the graphed line). You can see in Figure 16 that the

this linear function by plotting the data of Table 8. horizontal intercept is the point (5,0).

However, you need to know how to graph the curve by The parameter d, or slope, is the coefficient of the

using the equation Qs = 5 + 1 P without the use of data. independent variable, P, defined as ΔQs . Since Q s is
4 plotted on the horizontal axis, ΔQs ΔP to the
refers
To make a graph, we must first decide which variable ΔP

will be plotted on which axis. This is very important, horizontal change divided by the vertical change between

because depending on which variable is plotted on which any two points on the line.

axis, we get a different linear curve.

Since we are graphing a supply function, we

know (from our discussion above) that price, P (the When the dependent variable appears on the
horizontal axis, in the equation of a supply function
independent variable), must be measured on the vertical of the form Q s = c + dP, the parameter c is equal to
the horizontal intercept, and the parameter d, or
axis, and quantity supplied, Qs (the dependent variable), slope, is equal to the horizontal change divided by
on the horizontal axis. We begin by labelling the axes the vertical change.

correctly. Price on the vertical axis is measured in $,

and quantity on the horizontal axis is measured in

‘thousand units per day’.

To find the linear curve that corresponds to our

function (equation), we need to find at least two An important note on the slope
As noted above, the practice of reversing the axes
points on the curve, since any two points define a of the dependent and independent variables gives
rise to different graphs. It also gives rise to different
straight line. In practice, it may be a good idea to find

a third point to check our calculations (if we find

© Cambridge University Press 2012 Economics for the IB Diploma 19

Quantitative techniques

interpretations of the parameters c and d in the The demand function
function Q s = c + dP. Suppose that according to the
correct mathematical practice, P, the independent Understanding the equation
variable, is plotted on the horizontal axis, and Q s, of a demand function
the dependent variable, on the vertical axis. In this Demand, you may remember, involves a negative
case, the parameter c is the vertical intercept, or causal relationship between price and quantity
the point on the vertical axis that is cut by the line, demanded. The data in Table 9 show a negative, linear
and the parameter d, or slope, is equal to the vertical relationship between price, P, in $, and quantity
change divided by the horizontal change between any demanded, Qd, in thousand units of good Alpha
two points on the line, commonly known as ‘rise over demanded per day. These data are graphed in
run’. (This is most likely the interpretation of the slope Figure 17(a).
that you are familiar with.) You can try plotting the
graph to see that the linear curve will be very different Table 9 Data for a demand curve: negative linear relationship
from that graphed in Figure 16. However, in the
context of economics, this would be incorrect. Quantity Price (P, in $) Point on graph
demanded (Qd, (independent (Figure 17(a))
Test your understanding 7 in thousand units
variable) A
1 State the equation of a linear supply function, of Alpha per B
and explain the meaning of the two variables day) (dependent 0 C
and the two parameters. 10 D
variable) 20 E
2 Explain the meaning of ‘slope’, and define it for 30 F
the case where the dependent variable is plotted 100 40
on the horizontal axis. 50
80
3 Explain the significance of a positive slope.
60
4 Given the data in the following table, find the
corresponding linear function (equation). 40

Q s (dependent variable) P (independent variable) 20
50 0
0
100 25
The equation of a demand function
150 50
(negative linear function)
200 75
The equation of a demand function is given by:
250 100
Qd = a − bP
300 125
where
350 150
Qd = the dependent variable
5 Using the equation you found in question 4, P = the independent variable
(a) find the values of Q s when P = 17, 25, 37, and
(b) find the values of P when Q s = 60, 75, 80. a = the value of the dependent variable when the

6 Using the equation you found in question 4, independent variable, P, is equal to zero
graph the corresponding curve by finding points
that do not appear in the table of question 4, −b = the slope (where slope = ΔQd), and is the
following the economics practice of putting the ΔP
dependent variable on the horizontal axis.
coefficient of the independent variable, P.
7 (a) State the horizontal intercept of the curve
that corresponds to the equation of question You can see that both variables, Qd and P, and both
4, and identify it on your graph. (b) What parameters, a and −b, have the same interpretation as
parameter in a supply equation does the
horizontal intercept correspond to? in a supply function, or a positive linear function; the

demand function differs only in that the slope has a

negative sign. This means there is a negative relation

between the two variables, Qd and P, shown also in
Table 9.

Specifying the demand function
Finding the parameters a and −b will allow us to
specify the equation describing this relationship of
Table 9. Since a represents the value of Qd when P = 0,
we can see immediately in Table 9 that a = 100.

© Cambridge University Press 2012 Economics for the IB Diploma 20

(a) Graphing from data in a table Quantitative techniques
P($)
Similarly, we can find any value of P, given a value
60 of Qd. If Qd = 25,

50 F E 25 = 100 − 2 P ⇒ 2 P = 75 ⇒ P = 37.5
40
30 D The equation of a linear demand function is given
by Qd = a − bP, where Qd is quantity demanded (the
20 ΔQd C dependent variable), P is price (the independent
10 Δp variable), a is the value of Qd when P = 0, and −b is
slope = = – 20 = –2 B the slope (given by ΔQd ).
10 A
ΔP
0 10 20 30 40 50 60 70 80 90 100 Q
The negative sign of the slope (−b) indicates that the
(thousand units per day) demand function represents a negative (indirect)
relationship between P and Qd.
value of Qd
when P = 0 Graphing the demand curve
To plot the curve that corresponds to the equation
(b) Graphing from the demand function Qd = 100 − 2 P (assuming we do not have the data
P($) in Table 9), we must find at least two points on the
line. We already have one, which is the parameter a
60 Qd = a – 6p = 100, meaning that Qd = 100 when P = 0, i.e. point
50 is (100,0). To get a second point, we can let P = 10, in
40 Qd = 100 – 2p which case Qd = 100 − 2 (10) = 100 − 20 = 80, which is
point (80,10). For a third point, if P = 20, Qd = 100 − 2
30 (20) = 60, or point (60,20). We can now plot the three
points.
20 (60, 20)
slope = –2 = The points are plotted in Figure 17(b). Note that
10 parameter –b (80, 10) as in the case of the supply curve, we obtain the
(100, 0) demand curve by plotting the dependent variable on the
horizontal axis and the independent variable on the
0 10 20 30 40 50 60 70 80 90 100 Q vertical axis.

(thousand units per day) We can now make a similar point as in the case of
the supply function:
parameter
a When the dependent variable appears on the
horizontal axis, in the equation of a demand
Figure 17 Graphing the demand curve function of the form Qd = a − bP, the parameter
a is equal to the horizontal intercept, and the
We know that −b = the slope, where the slope = ΔQd; parameter −b, or slope, is equal to the horizontal
ΔP change divided by the vertical change.
taking points B and C in Table 9, we find:
An important note on the slope
ΔQd = 60 − 80 = −20, and ΔP = 20 − 10 = 10. Therefore, The point made earlier (page 19) concerning the
practice of reversing the axes in supply functions
slope = ΔQd = −20 = −2 applies equally to demand functions. The slope we are
ΔP 10 calculating by plotting the dependent variable on the
horizontal axis is different than if we had followed the
(Remember the point made earlier about the need correct mathematical practice.
to be consistent in subtracting values of variables.)
The negative sign of the slope indicates the negative Economics for the IB Diploma 21
(indirect) relationship between variables P and Qd.

The equation we are looking for is therefore:

Qd = 100 − 2 P

Using this equation we can find any value of Qd,
given P. For example, if P = 30,

Qd = 100 − 2 (30) = 40

© Cambridge University Press 2012

Test your understanding 8 Quantitative techniques

1 State the equation of a linear demand function, the relevant portions of supply curves in part (a), and
and explain the meaning of the two variables the relevant portions of demand curves in part (b).
and the two parameters.
In the general supply function, Qs = c + dP, we
2 Explain the significance of the negative slope of know that the parameter c represents the horizontal
the demand function. intercept. Looking at Figure 18 (a), we can see that
c can have a negative value, as in S1, or a positive
3 Given the data in the accompanying table, find value, as in S2. This means that glancing at a supply
the corresponding linear function (equation). function with numerical values for c, we can see if
Qd (dependent variable) P (independent variable) the corresponding curve is of the form S1 or S2. For
50 0 example, a function Qs = −20 + 10P is of the form S1;
45 2 Qs = 20 + 5P is of the form S2.
40 4
35 6 When the parameter c has a negative value, we
30 8 are not interested in calculating c (the horizontal
25 10 intercept) as this represents a range of the curve where
20 12 Qs is negative, and we do not want to plot negative Qs
15 14
10 16 (a) Supply curves

4 Using the equation you found in question 3, (a) P S1
find the values of Qd when P = 3, P = 4.2, P = 11; I
(b) find the values of P when Qd = 27.5, Qd = 35, II S2
Qd = 42.5. vertical
intercept
5 Using the equation you found in question 3,
graph the demand curve, by finding points 0Q
that do not appear in the table in question 3, horizontal
following the economics practice of putting the intercept
dependent variable on the horizontal axis.
III IV
6 Using your equation from question 3, calculate
the vertical and horizontal intercepts, and (b) Demand curves P
identify them in your graph of question 5. II
vertical
7 What parameter in a demand equation does the intercept
horizontal intercept correspond to?
I
8 For each of the following equations, state
whether they describe a positive or negative 0 horizontal Q
relationship, and explain why. III intercept D1
(a) Q = −5 + 7P
(b) Q = 17 − 5P IV
(c) Q = 10 + 15P
D2
Graphing the relevant parts of demand Figure 18 The relevant portions of supply and demand curves
and supply curves
Economics for the IB Diploma 22
When we plot supply and demand curves, we are
interested only in those portions of the curves that
appear in quadrant I (defined on page 8), i.e. that have
only positive values for both the Q and P variables (it
is not possible to have negative prices or quantities). In
Figure18, the bold-face portions of the curves indicate

© Cambridge University Press 2012

Quantitative techniques

values. Instead, finding the vertical intercept is more P
useful, as this is the point where the supply curve
begins. For example, suppose S1 in Figure 18(a) is 6 S1
given by Q s = −20 + 10P (graphed in Figure 19). We 5 Qs = –20 + 10P
know the vertical intercept is where Q = 0; therefore,
setting Q = 0 in the equation we solve for P: 4 (40, 4)
3 S2
Q = 0 = −20 +10P ⇒ 20 = 10P ⇒ P = 2 2 (0, 2) Qs = 20 + 5P
1
giving the vertical intercept at point (0,2). We can Z
therefore plot the solid portion of the curve, for (20, 0)
positive values only.
-20 -10 0 10 20 30 40 50 Q
In the case of S2 in Figure 18(a), the parameter c has -1
a positive value (in this range Q s is positive); therefore,
the horizontal intercept represents the beginning -2
of the supply curve. Given a function Q = 20 + 5P,
graphed in Figure 19, we set P = 0 (as we have done in -3
other examples above), and find Q = 20; therefore, the
horizontal intercept is at the point (20,0). -4

In Figure 18(b), the demand curve D2 is meaningless Figure 19 Examples of vertical and horizontal intercepts in supply
as all P and Q values are negative. All other demand functions
curves take the form of D1, where the vertical and
horizontal intercepts define the endpoints of the The answer to this question is that supply curves
demand curve. that have a positive c do not actually begin at a point
on the horizontal intercept; they have a lower limit,
In some cases, you may be asked to graph a demand which is at a price that is greater than zero. This could
or supply curve within a particular price range. For be at a point such as z on S2 in Figure 19. The point z
example, if you are asked to graph the supply function represents the lowest price that a firm would accept in
Q s = 20 + 5P within a price range of P = 0 to P = 4, this order to produce and sell its good. This is a price that
means simply that the supply curve should begin at allows the firm to cover at least some of its costs. You
the price of 0 and end at the price of 4. You can simply will learn about this price in Chapter 7 of the textbook.2
calculate the value of Q s for P = 0, which is Q s = 20, or
point (20,0) and the value of Q s for P = 4, which is Q s Therefore, graphing the supply curve all the way
= 40, or point (40,4), and plot these two points as the to the horizontal axis is a mathematical convenience
end points of the supply curve. You will then have a that we can use when we are not given a lower limit
supply curve like the unbroken part of S2 in Figure 19. for price. Similarly, plotting a demand curve all the
way to the horizontal axis is also a mathemathical
(We have not considered vertical and horizontal convenience, since at a price of zero consumers are
curves, which are special cases; you will learn about likely to demand much more than the Q given by the
these in the textbook.) horizontal intercept.

A note on supply and demand curves Test your understanding 9
We have seen that the parameter c can take on positive
or negative values. If c has a negative value, the supply Plot each of the following equations, putting P
curve begins somewhere on the P axis, which means (in $) on the vertical axis, and graphing only the
that the firm would only be willing to begin supplying relevant portions of the curves.
its product at a price which is greater than zero; this is
shown by S1 in Figure 18(a). However, what if c has a (a) Q s = −20 + 10P, up to price P = 7.
positive value? A positive c means that Q s > 0 when (b) Q s = 10 + 15P, from the horizontal intercept to
P = 0, or that the firm would be willing to begin
supplying its product when the price of the product is price P = 4.
zero; this is shown by S2 in Figure 18(a). Yet how is this
possible; what firm would be willing to produce and (c) Q d = 15 − 5P, from the vertical intercept to the
‘sell’ a good if it cannot sell at a price that is greater horizontal intercept.
than zero?
(d) Q d = 10 − 2P, from P = 1 to P = 4.

2 As you will learn in Chapter 7, this price is the ‘shut-down’ price, which for a perfectly competitive firm is equal to minimum average
variable cost in the short run, and is equal to minimum average total cost in the long run.

© Cambridge University Press 2012 Economics for the IB Diploma 23

Shifts in demand and supply curves Quantitative techniques

Rightward and leftward shifts in curves: Q = 80, which is 20 units to the left of the initial Q
finding the new equation intercept of Q = 100.
The parameters a (in the demand function Q d = a − bP)
and c (in the supply function Q s = c + dP) have a very Shifts in the supply function
important meaning: they represent all the variables
that are held constant under the ceteris paribus In the supply function Qs = 5 + 1 P, representing a
assumption in the relationship between Q s or Q d and 4
P. We now want to see what happens to a linear curve firm’s supply curve for good Alpha (see Table 8), c = 5,
when the parameter a or c changes.
which means that when P = 0, the quantity supplied
We know from our earlier discussion (pages 11
and 12) that any change in a determinant of a would be 5 thousand units per day. (You may want to
functional relation, in other words, any change in
one of the factors held constant by use of the ceteris bear in mind the point made earlier, page 23, that a
paribus assumption, leads to a shift of the curve. This
is exactly what happens if there is a change in the supply curve that begins at the Q intercept when
parameters a or c.
c > 0 is a mathematical convenience, since no firm
Shifts in the demand function
Figure 20(a) shows shifts that occur when there is a would supply its product at a price of zero.) Suppose
change in the parameter a in the demand function
Qd = a − bP. In the function Qd = 100 − 2P, representing there is a fall in costs of production, resulting in an
consumers’ daily demand for Alpha (see Table 9),
parameter a = 100, meaning that consumers would want increase in supply of 10 thousand units per day at
100 thousand units of the good each day if
P = 0. Suppose then that consumers’ income increases, every price. This means that when P = 0, the quantity
so that at each price, they want to buy 10 thousand
additional units of the good. This means that when supplied would be 5 + 10 = 15, i.e. 15 thousand units
P = 0, consumers will want to buy 100 + 10 = 110,
actually 110 thousand units; therefore, a increases from per day of Alpha.
a = 100 to a = 110. This gives rise to a new equation:
(a) Demand curve shifts
Q d = 110 − 2P P($)

The new equation is graphed in Figure 20(a), and 60 demand curve shifts right
results in a parallel rightward shift of the demand 50 Qd = 100 – 2P (increases) by 10 thousand units
curve by 10 units at every price, or actually 10 40 Qd = 110 – 2P
thousand units (which are measured along the
horizontal axis). The new Q intercept is at Q = 110, 30 Qd = 80 – 2P
which is 10 units to the right of the old Q intercept of
Q = 100. 20

On the other hand, suppose that a fall in demand curve shifts
income leads to a decrease in consumer demand of
20 thousand units at each price (relative to the initial 10 left (decreases) by
demand curve). This means that when P = 0,
consumers will want to buy 100 − 20 = 80, i.e. 80 20 thousand units
thousand units; therefore, a falls from a = 100 to
a = 80. This results in the equation: 0 10 20 30 40 50 60 70 80 90 100 110 Q
(thousand units per day)
Q d = 80 − 2P
(b) Supply curve shifts
In Figure 20(a), the graph of this equation shows a P($)
parallel leftward shift of the demand curve by 20 units
at every price, or actually 20 thousand units (measured 100
along the horizontal axis). The new Q intercept is at
90
© Cambridge University Press 2012
80 Qs = –5 + 41P Qs = 5 + 1 P
4
supply curve 1
70 shifts left 4
Qs = 15 + P
(decreases) by

60 10 thousand
units

50 supply curve
shifts right

40 (increases) by
10 thousand

units

30

20

10

0 5 10 15 20 25 30 35 40 Q
(thousand units per day)

Figure 20 Shifts in linear demand and supply curves

Economics for the IB Diploma 24

Therefore, the parameter c increases from c = 5 to Quantitative techniques

c = 15, and the new equation becomes: Test your understanding 10

Qs = 15 + 1P 1 Using your graphs from the questions in Test
4 your understanding 9, show (by graphing) what
will happen to each curve if:
When the above equation is graphed, there (a) in the function Q s = −20 + 10P, there is an
increase in supply of 10 units at every price
emerges a new linear curve parallel to the initial one, (b) in the function Q s = 10 + 15P there is a
decrease in supply of 30 units at every price
beginning at the point where Q = 15, occurring when (c) in the function Q d = 15 − 5P there is a
decrease in demand of 5 units at every price
P = 0, or point (15,0), as shown in Figure 20(b). Since (d) in the function Q d = 10 − 2P there is an
increase in demand of 2 units at every price.
the parameter c increased from 5 to 15, this means
2 State the new equation for each of the changes
that the curve has shifted rightward by the amount in question 1.

of 10 units of Q (= 15 − 5); note that this is actually 10

thousand units of Q, since Q is measured in thousands

of units. Therefore, for each value of P, the entire new

curve lies 10 thousand units of Q to the right of the

initial curve.

Suppose, instead, that relative to the initial

function Qs = 5 + 1 P, there is an increase in costs of
4

production, resulting in a decrease in daily supply Upward and downward shifts in curves:
finding the new curve and equation
of 10 thousand units at every price. This means that On pages 11 and 13 above, it was noted that
rightward/leftward shifts of curves can also be viewed
when P = 0, Q s = −5 units. The parameter c decreases as upward/downward shifts. This is especially relevant
from 5 to −5, and the new equation becomes: to supply curves, which in some cases are considered
as shifting to the right or to the left (Chapter 2) and
Qs = −5 + 1 P other times upward or downward (Chapters 4 and 5).
4
It is convenient to consider supply curve shifts as
In this case, the supply curve shifts to the left by going in the up/down direction in the study of certain
kinds of taxes called indirect taxes, as well as subsidies, as
10 units of Q (actually 10 thousand units) at every both of these have the effect of changing firms’ costs of
production. (Remember that subsidies are payments by
price. The new curve can be graphed by finding points the government to firms, and are therefore the opposite
of taxes.) The reason is that the vertical difference between
that lie 10 units to the left of the initial supply curve. the old and new supply curves represents the change in the

Note that c = −5 means that Q s = −5 when P = 0, which firm’s costs of production due to the indirect tax or subsidy.
is in the negative range of Q. In fact, the supply curve

begins at Q = 0, where P = 20 (or the vertical intercept),

found by setting Q = 0 and solving:

0 = −5 + 1P ⇒ 5 = 1P ⇒ P = 20
4 4

Note that in the case of all changes in the

parameters a and c, the slope of the curves remained

the same, explaining why the new curves are in all The case of indirect taxes

cases parallel to the initial ones. Let’s consider the following example. We begin with
1
the supply function Qs = 5 + 4 P, which is the same

In curves described by the linear functions, as the function considered above (page 19). Suppose
Q d = a - bP or Q s = c + dP, a change in parameters a
or c indicates a change in a variable that was held the government imposes an indirect tax on good
constant under the ceteris paribus assumption,
and causes a parallel shift of the curve. If a or c Alpha produced by firms of $40 per unit of Alpha sold.
increases, there is a rightward shift by the amount
of the increase (measured along the horizontal This will cause the supply curve to shift upward by the
axis); if a or c decreases, there is a leftward shift by
the amount of the decrease (measured along the amount of $40 for each quantity of Alpha sold. The
horizontal axis).
pre-tax and after-tax supply curves are shown in

Figure 21(a), with the vertical difference between S1
and S2 representing the tax per unit.

We would now like to find the equation of the

new supply curve. To do this, we use the following

rule. Given a supply function of the general form

3 You may be surprised to see that we subtract t from P when we are shifting the supply curve upward. The reason is that subtracting t from P actually
means we are shifting the axes downward, thus actually moving the supply curve upward.

© Cambridge University Press 2012 Economics for the IB Diploma 25

Quantitative techniques

Q s = c + dP, whenever there is an upward shift of the equation we found earlier (page 25), when the curve of
function by t units, we replace P by P − t.3 The new
the equation Qs = 5 + 1 P shifted to the left due to
supply function therefore becomes: 4

Q s = c + d(P − t) a decrease in supply of 10 thousand units because of an

In our case, t = 40. Therefore, given our pre-tax increase in costs of production. This is not surprising,

equation of Qs = 5 + 1 P, the new, after-tax equation is because in fact the two shifts are identical. If you
4
1 1 examine Figure 20(b) and Figure 21(a), you will see
4 4
Qs = 5 + (P − 40) ⇒ Qs = 5 + P − 10 that the two curves are also identical. They have just

Qs −5 1 P been derived differently. Table 10 summarises the two
4
= + ways of deriving the new supply curve and equation.

You may now notice something interesting. The Table 10 Leftward shift and upward shift in the supply curve

after-tax equation we have derived is identical to the Initial equation: QS = 5 + 1 P
4

(a) An indirect tax shifts the curve up Decrease in supply: Indirect tax: upward shift
P($) leftward shift

100 Increase in production costs A tax of $40 per unit causes
causes a decrease in supply an increase in production
90 S2 = –5 + 1 P S1 of 10 units at every price. costs for every quantity
80 Qs 4 Qs supplied.
1
70 = 5 + 4 P

60 tax Supply curve shifts leftward Supply curve shifts upward
by 10 units measured along by $40 measured along the
50 per the horizontal axis. vertical axis.
unit

40 = $40 To find the new supply To find the new supply
function: find the new c,
supply curve which is c − 10 = 5 − 10 = −5, function: rewrite supply
and rewrite supply function function as Qs = 5 + ¼ (P − 40)
30 shifts up by $40 using parameter c = −5. and simplify.

20
10

0 5 10 15 20 25 30 35 40 Q Final equation: Qs = −5 + 1 P
(thousand units per day) 4

(b) A subsidy shifts the curve down The case of subsidies

P($) We can now consider the case of a subsidy, which

100 results in a decrease in the firm’s costs of production.

90 We begin with the same initial supply function as
80
70 S1 = 5 + 41 P S2 before, Q s = 5 + 1 P, and suppose that the government
Qs Qs 4
41 P
= 15 + grants a subsidy to firms of $40 per unit of Alpha sold.

60 subsidy This will cause the supply curve to shift downward by
per unit

50 = $40 the amount of $40 for each quantity of Alpha sold. The

40 pre-subsidy and after-subsidy supply curves are shown
30 supply curve
in Figure 21(b), with the vertical difference between S1
shifts down and S2 representing the subsidy per unit.
20 by $40
10 To find the equation of the new supply curve, we

use the following rule. Given a supply function of the

0 5 10 15 20 25 30 35 40 Q general form Qs = c + dP, whenever there is a downward
(thousand units per day) shift of the function by s units, we replace P by P + s.4

The new supply function therefore becomes:

Figure 21 Upward/downward shifts of the supply curve Q s = c + d(P + s)

4 Note that this is the exact opposite of what we did to find the new supply function when a tax was imposed (page 25). We now add s to P in order to
shift the supply curve downward, because by doing so we are shifting the axes upward, thus actually moving the supply curve downward.

© Cambridge University Press 2012 Economics for the IB Diploma 26

Since in our case s = $40, our equation of Qs = 5 + 1 P, Quantitative techniques
after the subsidy becomes: 4
Test your understanding 11
Qs = 5 + 1 (P + 40) ⇒ Qs = 5 + 1 P + 10
4 4 1 Using your graphs from the questions in Test
1 your understanding 9, show (by graphing) what
Qs = 15 + 4 P. will happen to the supply curves if:
(a) in the supply curve given by Qs = −20 + 10P,
The equation (after the subsidy) we have just the government grants a subsidy of $1 per
derived is the same as the equation we found when unit of the good; show the per unit subsidy
there is an increase in supply of 10 thousand units in your diagram;
due to a fall in costs of production. Again, this has (b) in the supply curve given Qs = 10 + 15P, the
occurred because the two shifts are identical. The two government imposes a tax of $2 per unit
resulting supply curves are also identical, as you can of the good; show the per unit tax in your
see by comparing Figure 20(b) with Figure 21(b). diagram.
Table 11 summarises the results.
2 Find the new supply equations that result after
Table 11 Rightward shift and downward shift in the supply curve the changes described in question 1 occur.

Initial equation: QS = 5 + 1 P 3 Compare the graphs you drew in question 1
4 above with the graphs you drew for Test your
understanding 10, question 1 parts (a) and (b),
Increase in supply: Subsidy: downward shift and explain why they are the same. Are the
rightward shift corresponding equations also the same? (They
should be.)
Decrease in production costs A subsidy of $40 per
causes an increase in supply unit causes a decrease in The slope
of 10 units at every price. production costs for every
quantity supplied. Interpreting changes in parameters –b
and d (the slope)
Supply curve shifts rightward Supply curve shifts downward When the slope of a linear demand function (−b) or
linear supply function (d) changes, the steepness of the
by 10 units measured along by $40 measured along the curve changes. Suppose that we have a supply function,
Q s = 10 + 4P, shown as S1 in Figure 22(a). If the slope
the horizontal axis. vertical axis. changes from 4 to 5, the new equation becomes:

To find the new supply To find the new supply Q s = 10 + 5P
function: find the new c,
which is c + 10 = 5 + 10 = 15, function: rewrite supply also shown in Figure 22(a). Note that the larger value
and rewrite supply function function as Qs = 5 + ¼ (P + 40) of the slope (5 > 4) has made the curve flatter.
using parameter c = 15. and simplify.
A demand function, Q d = 50 − 5P, is shown in
Final equation: QS = 15 + 1 P Figure 22(b). If the slope changes from −5 to −10, the
4 new equation becomes:

If you are given a supply function and are asked to Q d = 50 − 10P
graph the corresponding supply curve, and then to
graph a new supply curve following a change of some which can also be seen in Figure 22(b). Note that the
kind, you must be very careful to consider the nature larger absolute value of the slope has made the curve
of the change. If it involves a change in supply, you flatter (the absolute value is the numerical value
must shift the supply curve leftward or rightward by without the minus sign. Therefore, the absolute value
the amount of the change in supply. If it involves an of −10 is 10).
indirect tax or subsidy, you must use the information
to shift the supply curve upward or downward by the (When the dependent variable is plotted on the
amount of the tax or subsidy per unit of output. vertical axis (as in the usual mathematical practice),
the opposite holds: the larger the absolute value of the
All changes in supply (increases or decreases) are slope, the steeper the line.)
analysed as rightward or leftward shifts of the
supply curve. Indirect taxes and subsidies are Economics for the IB Diploma 27
analysed as upward and downward shifts of the
supply curve because of their effect on firms’ costs
of production.

© Cambridge University Press 2012

Quantitative techniques

(a) Supply curve: positive relationship same is not true of non-linear curves, whose slope is
continuously changing.
P

10 S1 Comparing slopes of linear curves
Qs = 10 + 4P in different diagrams
8 S2 It was stated above that the greater the absolute value
of the slope, the flatter the curve if the dependent
6 variable is on the horizontal axis, and the steeper the
4 Qs = 10 + 5P curve if the dependent variable is on the vertical axis.
You should be careful to note, however, that these
2 points apply only to curves that are drawn in the same
diagram that uses the same units, or that are drawn in
0 10 20 30 40 50 Q the same scale. If two curves are in different diagrams
with different scales, it is not possible to compare the
(b) Demand curve: negative relationship slopes by reference to the steepness of the linear curves.

P Slope and elasticity
10 The slope, defined as ΔQ , measures the responsiveness
8 Qd = 50 – 5P
6 ΔP
4 of the dependent variable to changes in the
2 Qd = 50 – 10P independent variable. You can see this in Figure 22.
In part (a), suppose there is a change in P (the
0 10 20 30 40 50 Q independent variable) from 4 to 5. What will be the
effects on the dependent variable Qs? In the supply
Figure 22 Changes in the slope of linear curves (with the dependent curve defined by Q s = 10 + 4P, when P = 4, Q s = 26;
variable on the horizontal axis) when P = 5, Q s = 30. Therefore, Qs increases by 4
units. In the flatter supply curve defined by Q s =
In a linear demand or supply function, Q d = a − bP 10 + 5P, when P = 4, Q s = 30; when P = 5, Q s = 35,
or Q s = c + dP, a change in the slope (−b or d) results i.e. it increases by 5 units. Therefore, there is a larger
in a change in the steepness of the curve. When the responsiveness in Q s when the curve is flatter.

dependent variable is plotted on the horizontal axis, The idea of responsiveness of one variable to
changes in another variable is very important in
the larger the absolute value of the slope, the flatter economics, and we will encounter it repeatedly
throughout this course. Therefore, the slope is
the line. an important concept. However, as a measure of
responsiveness it suffers from a serious limitation: it
Test your understanding 12 depends on the particular units used to measure the
variables. If units change, the slope also changes; the
1 State the new equation for each of the following use of different units means that responsiveness is not
changes: (a) in the function Q s = −20 + 10P, the comparable by use of the slope.
slope changes to +25, and (b) in the function
Q d = 15 − 5P, the slope changes to −10. Economists therefore use a closely related concept
to measure responsiveness, called elasticity. Whereas
2 For each of the following linear equations where slope measures responsiveness in absolute terms, elasticity
the dependent variable Q, is plotted on the
horizontal axis, state whether the new curve measures responsiveness in percentage terms:
will become flatter or steeper. (a) in Q s = 5 + 20P
the slope changes to 15, (b) in Q d = 4 − 12P the slope = ΔQ elasticity = %ΔQ = ΔQ
slope changes to −8, (c) in Q s = −3 + 7P the slope ΔP %ΔP Q
changes to 9, and (d) in Q d = 2 − 15P the slope
changes to −17. ΔP
P
It should be noted that the slope of a straight line
is always constant, meaning that it is the same no = ΔQ × P = slope × P
matter on what part of the line it is measured. The ΔP Q Q

The concept of elasticity will be studied in Chapter 3
of the textbook.

© Cambridge University Press 2012 Economics for the IB Diploma 28

Solving simultaneous linear equations to Quantitative techniques
calculate equilibrium price and quantity
To check our results we could substitute P = 3 into
Suppose we are given a linear demand function Q d = the supply equation as well:
45 − 5P, and a linear supply function Q s = −30 + 20P.
The two curves defined by the two functions have Q s = −30 + 20(3) = −30 + 60 = 30
a point of intersection, or a point where they cross
each other, which we would like to find as this has a Since both methods give the same result, we can be
major economic significance. We can find the point of fairly confident that our calculations are correct.
intersection by graphing the two curves, as in Figure 23,
which shows that the two curves cross each other at the Therefore, the point of intersection is (30,3), or
point where P = 3 and Q = 30, or the point (30,3). where P = 3 and Q = 30. As we will discover in
Chapter 2, this price and quantity combination is
However, we would like to find the point of known as equilibrium price and quantity.
intersection mathematically, because this gives far
more accurate results. To do this, we must solve for P Test your understanding 13
and Q using the equations of the demand and supply
functions. This is done in the following way. 1 You are given the following demand function:
Qd = 10−2P, where Qd is quantity of good Beta
We have the following two equations: demanded in thousands of units per week, and P
is the price of Beta in $. (a) Identify the horizontal
Q d = 45 − 5P (the demand function) intercept. (b) Calculate the vertical intercept.
Q s = −30 + 20P (the supply function) (c) Identify the slope. (d) Graph the curve that
corresponds to this function. (e) Explain whether
In addition, we know that Q d = Q s at the point this is a positive or negative relationship; how
where the two curves cross, since at that point does your answer relate to the slope? (f) Assume
quantity demanded is equal to quantity supplied. the parameter 10 increases to 14; show this
Therefore, we can set the demand and supply graphically (up to a price P = 5) and explain in
functions equal to each other: words the meaning of this shift. (g) State the new
equation. (h) Starting with the initial demand
Q d = Q s can be written as function, assume the slope changes to −1; state
45 − 5P = −30 + 20P the new demand equation and explain what will
happen to the steepness of the demand curve.
Solving for P, we have:
2 You are given the following supply function:
45 + 30 = 5P + 20P ⇒ 75 = 25P Q s = −3 + 3P, where Qs is quantity of good Beta
supplied in thousands of units per week, and P is
P= 75 =3 the price of Beta in $. (a) Identify the horizontal
25 intercept; should this be included in a graph
of the supply curve? (b) Calculate the vertical
We now need to find Q. To do this, we substitute intercept. (c) Identify the slope. (d) Graph the
curve that corresponds to this function from
P = 3 into either the demand or supply function above, P = 1 to P = 4. (e) Explain whether this is a
positive or negative relationship; how does
and solve for Q: your answer relate to the slope? (f) Assume
that the parameter −3 changes to −1; show this
Q d = 45 − 5(3) = 45 − 15 = 30 graphically and explain in words the meaning of
this shift. (g) State the new equation.
P (h) Assume the slope changes to 2; state the new
9 supply equation and explain what will happen
to the steepness of the supply curve.
8
3 (a) Using the demand function, Q d = 10 − 2P,
7 and the supply function, Q s = −3 + 3P, where
Q d and Q s refer to thousands of units of Beta
6 per week and P is in $, solve for P and Q and
5 Qs = –30 + 20P determine equilibrium price and quantity.
(b) Plot the two curves on the same graph from
4 P = 1 to P = 4; is their point of intersection the
same as the one you calculated for P and Q?
3 (30, 3)
2
1 Qd = 45 – 5P

0 10 20 30 40 50 60 70 80 Q

Figure 23 Demand and supply curves and their point of intersection

© Cambridge University Press 2012 Economics for the IB Diploma 29

Quantitative techniques

4 (a) Calculate Q d and Q s that would result at (a) Q plotted on horizontal axis (b) Q plotted on vertical axis
a price of $4. (b) What is the excess (or extra)
quantity of Beta supplied at P = $4? (a) Q (b)
6
5 (a) Calculate Q d and Q s that would result at
a price of $2. (b) What is the excess (or extra) P 35
quantity of Beta demanded at P = $2?
24
6 Suppose there is an increase in demand for Beta
of 2000 units at each price. (a) Find the new 13 inverse D
demand equation. (b) Find the new equilibrium
price and quantity by solving the equations. D
(c) Graph the new demand curve in your 2
diagram for question 3 above and identify the 0 1 2 3 4 5 6Q 1
equilibrium price and quantity. Do they match
with your calculations? 0 1 2 3P

7 Solve the following equations for P and Q: Figure 24 Demand curves Qd = 6 – 2P
Q s = 10 + 5 P and Q d = 50 − 5P.
with the curve in part (b), you will see that they are
Using a graphics display calculator (GDC) different. In fact, the curve that appears in Figure 24(b) is
to graph functions and find equilibrium incorrect from an economics perspective, because it plots Q
price and quantity on the vertical axis and P on the horizontal axis.

You are permitted to use a graphics display calculator In order to find the correct graph of the demand
(GDC) when taking a higher level paper 3 exam. A curve on your calculator, the demand function Qd =
GDC can be used mainly to help you graph functions. 6 − 2P has to be expressed in a way so that when the
However, you should note that a GDC is not essential to calculator graphs it, Qd will appear on the horizontal
answering paper 3 questions. This section is intended to axis and P on the vertical axis. In other words, the
guide you through how you can use a GDC for higher variables in the function y = f (x), must be identified as
level paper 3, should you decide you would like to do so. y = P (plotted on the vertical axis) and x = Qd (plotted
on the horizontal axis. For this to happen, the demand
Graphing a demand function using a GDC function Qd = 6 − 2P must be rewritten so that P is
A GDC expresses functions in the following way: expressed as a function of Q. This involves taking the
initial demand function and solving for P:
y = f (x)
1
which means that the variable y is a function of x, and Qd = 6 − 2P ⇒ 2P = 6 − Qd ⇒ P = 3 − 2 Qd
where y is always plotted on the vertical axis, and
x is always plotted on the horizontal axis. 1 as a
The equation Pca=ll3ed−th2eQind,vewrsheedreemPainsdexfupnrectsisoend. In
Suppose you are asked to graph the following function of Q, is
demand function:
graphing the inverse demand function, the GDC will
Qd = 6 − 2P
provide the correct demand curve, as in Figure 24(a).
The Q intercept is Q = 6, and the P intercept is P = 3
(obtained by setting Q d = 0 = 6 − 2P ⇒ 2P = 6 ⇒ P = 3). The reason is that now the calculator has correctly
This demand curve is graphed in Figure 24(a).
identified P as the variable y that is plotted on the
Suppose now you wanted to use your GDC to
graph Qd = 6 − 2P. If you were to write the demand vertical axis, and Q d as the variable×that is plotted on
function as the horizontal axis.

y = 6−2x In practice, you do not have to calculate the inverse

where you have set y = Qd and x = P, and you put this demand function yourself, as the GDC can do it for
into your calculator to get its graph, the graph that
will appear on your screen will look like the graph you, and then graph it. To get the correct graph, enter
in Figure 24(b). If you compare the curve in part (a)
the initial demand function Q d = 6 − 2P into the
© Cambridge University Press 2012 calculator, and ask it to graph the inverse function (the

steps for this are described at the end of this chapter).

This will provide you with the correct graph of the

demand curve.

Graphing a supply curve using a GDC
Graphing a supply curve with the help of a GDC is
identical to graphing a demand curve. Suppose you

Economics for the IB Diploma 30

want to graph the function Qs = 2 + 2P. This graph Quantitative techniques
appears in Figure 25(a). If your GDC graphs this
If you are asked to find P and Q graphically, this
function, it will come up with what appears in follows simply from your graphs of the demand and
supply curves that you have already produced using
Figure 25(b), which is incorrect because Q has been a GDC to graph the inverse demand function and
the inverse supply function. This graph appears in
plotted on the vertical axis and P on the horizontal axis. Figure 26(a), which shows that equilibrium P = 1 and
equilibrium Q = 4, and the demand and supply curves
The GDC will find the correct supply curve by plotting are correctly drawn.

the inverse supply function, which involves expressing P The only further use that a GDC can have in the
context of finding equilibrium P and Q is to help you
as a function of Qs. The inverse supply function in check the accuracy of your calculations or of your
graphs. This can be done in the following way.
this case would be P = −1 + 1 Q s. However, you need
2 Enter the demand function, Qd = 6 − 2P, and the
supply function, Qs = 2 + 2P, into the calculator, and
not solve for P yourself to find the inverse function, ask it to graph them and find the point of intersection.
However, you must be very careful here. The calculator
as the calculator will do it for you. You simply enter will provide you with a graph as in Figure 26(b), which
provides you with the correct values of P and Q, but the
the initial supply function into the GDC, and ask it to wrong curves. As you can see in Figure 26(b), the point of
intersection occurs at Q = 4 and P = 1, which are the same
graph the inverse function. values for P and Q as in Figure 24(a); however, the curves
are incorrect because they plot Q on the vertical axis and P
Given a demand or supply function, to graph the on the horizontal axis. Therefore, you can only use this
demand curve or supply curve using a GDC, enter method to check that the values for P and Q you have
the function into the calculator and ask it to graph calculated are correct.
the inverse function. The graph that will appear will
be the correct demand or supply curve. In fact, considering the time constraints in an exam,
it may not be worthwhile for you to go to such lengths
Finding the equilibrium price to check your calculations.5
and quantity
Price and quantity at the point of equilibrium Shifts in the functions
correspond to the value of P and the value of Q Once you have graphed demand and/or supply curves,
where the demand curve and supply curve intersect you may be asked to find a new demand curve, or a
(cross each other). As we saw earlier, this point of new supply curve, following changes in the parameter
intersection can be found (a) graphically, which a in the function Q d = a − b P, or in the parameter c
involves reading off your graph of the demand and
supply curves the values of P and Q at the point where
they cross, or (b) mathematically, which involves
solving the demand and supply equations for P and Q.

If you are asked to find equilibrium P and Q
mathematically, your GDC will not be of any use, as it
does not do the necessary manipulations.

(a) Q plotted on horizontal axis (b) Q plotted on vertical axis (a) Q plotted on horizontal axis (b) Q plotted on vertical axis
Q Q
(a) 6 (b) (a) 6 (b)
P P
3 5 inverse S 3 5 inverse S
2S 4 2S 4

13 13
D
0 1 2 3 4 5 6Q 2 inverse D
1 0 1 2 3 4 5 6Q 2
1

0 1 2 3P 0 1 2 3P

Figure 25 Supply curves Qs = 2 + 2P Figure 26 Demand, supply and equilibrium P and Q

5 It is also possible for you to calculate the inverse demand function and the inverse supply function, by solving in each case for P, enter these new
equations into the calculator, and ask it to find the point of intersection. In this case, you will get both the correct values for P and Q, and the correct
demand and supply curves. However, this is very time-consuming, and is not recommended.

© Cambridge University Press 2012 Economics for the IB Diploma 31

in the function Qs = c + dP. You may then be asked to Quantitative techniques
graph the new demand or supply curve.
and is the coefficient of P in a demand function or a
A GDC cannot help you here, unless you are able supply function. Given a demand function such as Q d
to first find the new equation that results following = 6 − 2 P, suppose you are told that the slope changes
a change in the parameter a or c. The method for to −3. Your GDC cannot be used unless you first find
finding such new equations was explained in detail the new function; to do this simply replace −2 by −3,
above (pages 24 and 25). Once you have found a thus getting Q d = 6 − 3P.
new equation, enter it into the calculator and ask it
to graph the inverse function. This will give you the If you were asked to graph the new curve that
graph of the new demand curve or new supply curve results after a change in the slope, you could put the
that you require. new function into the calculator and ask for a graph of
the inverse function.
For example, suppose you are given the demand
function Q d = 6 − 2P, where Q is in thousand kilograms If you were asked whether the new curve will
(kg) of good Zeta per week, and P is price in $; you are be steeper or flatter than the initial curve (without
told that following a successful advertising campaign graphing), you could graph them anyway, and
for Zeta, there is increase in demand of 2000 kg per compare the inverse functions of the initial and final
week, and you are asked to plot the new demand demand functions with respect to their steepness; in
curve. You must find the new demand function before other words, compare the steepness of the inverse
you can use your GDC. In the new demand function, function of Q d = 6 − 2P with the steepness of the
the Q intercept, which initially was 6, increases by 2 to inverse function of Q d = 6 − 3P. Note, though that this
become 8. Therefore, the new function is: may be tricky, because when you view both graphs at
the same time on your screen, it may be confusing to
Qd = 8 − 2 P determine which curve is which.

If you put this function into the calculator and ask Therefore, it may not worth your time to use your
it to graph the inverse function, you will be shown the GDC for this purpose. To figure out whether the new
new demand curve. curve will be steeper or flatter, all you have to do
is remember the simple rule: the greater the absolute
However, you should ask yourself whether it is worth value of the slope, the flatter the curve. Since −3 has a
your time to do this. If you have already plotted the greater absolute value than −2, you can conclude
curve for Qd = 6 − 2P, and you have found the new Q (without the help of a GDC) that the new curve will
intercept, which is 8, all you have to do is draw a new be flatter.
demand curve parallel to the initial one, beginning
at the Q intercept of Q = 8. This is so simple to do, that Steps for using a GDC to find inverse
the use of a GDC would not be a good use of your time. demand and supply functions and
equilibrium price and quantity
Changes in the slope The process of graphing inverse functions on a GDC
The slope was defined as the change in the dependent differs according to the type of GDC. The steps for
variable (Q) divided by the change in the independent Casio and Texas Instruments (TI) GDCs are explained
variable (P) between any two points on a linear curve, below. In both cases we will use the same demand and
supply functions used above.

© Cambridge University Press 2012 Economics for the IB Diploma 32

Casio Quantitative techniques
How to plot an inverse function on a Casio
1 From the main menu, use the arrow keys to mark the window
GRAPH.

2 Press EXE.

3 Type in the function y = 6 − 2x. (The variable x is below the
red ALPHA button.)

4 Press EXE.

5 Press F6. Note that this function corresponds to Figure
24(b), i.e. Q = 6 − 2s with Q plotted on the vertical axis.

6 Press F4.

7 Press F4 again. (This asks the calculator to draw the inverse
function.) You will get the graph of the inverse function,
i.e. Q = 6 − 2x with Q plotted on the horizontal axis, along
with the original function. Note that the inverse function
corresponds to Figure 24(a), which is the correct graph of
the demand function.

© Cambridge University Press 2012 Economics for the IB Diploma 33

Quantitative techniques

How to find the point of intersection of two straight lines (a demand function and a supply function) on a Casio
1 From the main menu, use the arrow keys to mark the window
GRAPH.

2 Press EXE.

3 Type in the function y = 6 − 2x. Press EXE to go to the
second line and then type the next function,
y = 2 + 2x.

4 Press EXE.

5 Press F6 to plot both functions. Note that this corresponds
to Figure 26(b).

6 Press the SHIFT key and then the F5 (also known as
G-Solv) key to display the following window.

7 Press the F5 key (for intersection). This gives the values
of x and y at the point of intersection. However, you must
remember that x = 1 corresponds to P = 1 and y = 4 to
Q = 4; therefore, while the point of intersection is correct,
the curves are incorrect, because they plot Q on the
vertical axis.

© Cambridge University Press 2012 Economics for the IB Diploma 34

Texas Instruments Quantitative techniques
How to plot an inverse function on a TI
1 Press the Y = key and type in the function y = 6 − 2x. (You
will find the symbol x next to the green ALPHA button.)

2 Press the GRAPH key to plot this function. Note that this
function corresponds to Figure 24(b), i.e. Q = 6 − 2x with Q
plotted on the vertical axis.

3 Press the 2ND key and then the DRAW key to display the
following window.

4 Scroll down to number 8 or just press 8. (This asks the
calculator to draw the inverse function.)

5 Press the VARS key.

6 Press the right arrow to mark Y-VARS and then press
ENTER.

7 This window is displayed. Press ENTER.

8 This window is displayed.
9 Press ENTER again. You will see the graph of the inverse

function, i.e. Q = 6 − 2x with Q plotted on the horizontal
axis, along with the original function. Note that the inverse
function corresponds to Figure 24(a), which is the correct
graph of the demand function.

© Cambridge University Press 2012 Economics for the IB Diploma 35

Quantitative techniques

How to find the point of intersection of two straight lines (a demand function and a supply function) on a TI
1 Press the Y = key and type in the function y = 6 − 2x. Press
ENTER to go to the second line and then type the next
function, y = 2 + 2x.

2 Press GRAPH to plot both functions. Note that this
corresponds to Figure 26(b).

3 Press the 2ND key and then the CALC key to display the
following window.

4 Press the number 5 (for intersection).

5 Press ENTER 3 times. This gives the values of x and y at the
point of intersection. However, you must remember that x
= 1 corresponds to P = 1 and y = 4 to Q = 4; therefore, while
the point of intersection is correct, the curves are incorrect,
because they plot Q on the vertical axis.

It may be noted that on both the Casio and the TI, Test your understanding 14
it is also possible to use the simultaneous equation
facility to find the point of intersection of two lines. Answer the questions below for each of the
following demand and supply equations.
Concluding comments (i) Qd = 10 − 5P; Qs = 2 + 3P
The main use of a GDC for higher level paper 3 is as (ii) Qd = 45 − 5P; Qs = −30 + 20P
an aid to graphing demand and supply curves. For this (iii) Qd = 60 − 20P; Qs = 20 + 20P
purpose, you must learn how to find graphs of inverse
functions on your calculator, where P is expressed as a 1 Graph the demand and supply equations, and
function of Q. Beyond that, you must understand the find the equilibrium price and quantity on your
meaning of the parameters of the demand and supply graph (a) without the use of a GDC, and (b)
functions (the Q intercept and the slope) and how to using a GDC to find the inverse functions. (c)
find a new function given a change in any of these, as Compare your results to make sure they agree.
the GDC can be of no use to you in this respect. If you
learn how to plot the curves of demand and supply 2 Compare the two methods and determine which
functions quickly and accurately, it is most likely that of the two you find more convenient.
a GDC will not be of much use to you, except for
simple arithmetic calculations, and possibly as a check 3 Find the equilibrium price and quantity
for the accuracy of your work. mathematically, and compare with the results of
your graph to make sure they agree.
© Cambridge University Press 2012
4 Find the equilibrium price and quantity using your
GDC, and compare with your results in your graph.

Economics for the IB Diploma 36

Introduction to the IB Economics
exam papers

Learning outcomes, command terms All command terms are classified in four categories
and assessment objectives called ‘assessment objectives’ (AOs). There is a
progression of AOs regarding the demands made on
The IB Economics guide (for first examinations in the student, beginning from AO1, which is the lowest
May 2013) contains detailed learning outcomes for level of demand, up to AO3, which is the highest level.
each syllabus topic and sub-topic. All these learning The fourth level, AO4, consists of command terms that
outcomes appear in the textbook and are displayed in are specific to particular skills and techniques, and do
green boxes under the corresponding heading where not correspond to any particular level of demand in
they are explained and discussed. relation to the other three AO levels.

The first word of each learning outcome consists The four AO levels and the corresponding
of a ‘command term’. The command terms specify command terms are outlined in the table below.
what students should be able to do with each learning All command terms are defined in the table on page 5
outcome in exams. of this section.

Assessment objective (AO) Explanation of assessment objectives Command terms The command terms
require students to:
AO1: knowledge and Demonstrate knowledge and define Learn and comprehend
understanding understanding of the syllabus describe the meaning of
contents, including current economic list information.
issues and data, as well as provide outline
definitions of syllabus economic terms. state Use their knowledge to
explain actual situations,
Demonstrate knowledge and and to break down ideas
understanding of higher level into simpler parts and see
topics. how the parts relate.

AO2: application and analysis Apply economic theories and analyse Rearrange component
concepts to real-world situations, apply ideas into a new whole
identify and interpret economic data, comment and make judgements
and demonstrate the extent to which distinguish based on evidence or a
information is used effectively. explain set of criteria.
suggest
Demonstrate application
and analysis of higher level
topics.

AO3: synthesis and evaluation Examine economic concepts and compare
theories, use these together with compare and contrast
examples to construct and present contrast
arguments, discuss and evaluate discuss
theories and information. evaluate
examine
Demonstrate economic synthesis justify
and evaluation of higher level to what extent
topics.

© Cambridge University Press 2012 Economics for the IB Diploma 1

Introduction to the IB Economics exam papers

Assessment objective (AO) Explanation of assessment objectives Command terms The command terms
require students to:
AO4: selection, use and Produce well-structured written calculate
application of a variety of material using appropriate construct Demonstrate selection
skills and techniques terminology; use correctly labelled derive and application of skills.
diagrams to explain concepts and determine
theories; select, interpret and analyse draw
extracts from news media; interpret identify
appropriate data sets. label
measure
Use quantitative techniques to plot
identify, explain and analyse show
economic relationships. show that
sketch
solve

Command terms and assessment of consumer surplus’, because ‘discuss’ is an AO3
objectives in exams command term.

The command term that appears at the beginning of Learning outcomes that use AO4 command terms,
each learning outcome in the textbook (and in the on the other hand, can only be examined by questions
IB Economics guide) corresponds to a particular AO using AO4 command terms. For example, the learning
level. An exam question on a learning outcome uses outcome, ‘Draw a supply curve’ could be examined by
a command term that is either from the same AO level, a question such as ‘Construct a supply curve’, since
or from a lower AO level; it cannot be from a higher AO ‘construct’ is an AO4 command term.
level.
Main features of examinations
For example, in the learning outcome, ‘Explain (external assessment)
the concept of consumer surplus’, ‘explain’ is an AO2
command term. An exam question could use the same Exams (external assessment) consist of two exam
command term as in the learning outcome, or it could papers for standard level (SL): paper 1 and paper 2.
say, ‘Analyse the concept of consumer surplus’, since They consist of three exam papers for higher level
‘analyse’ is also an AO2 command term. Alternatively, (HL): paper 1, paper 2 and paper 3. The tables below
an exam question could say, ‘Define consumer summarise the main features of each exam paper at
surplus’, since ‘define’ is an AO1 command term. An standard and higher levels.
exam question could not say ‘Discuss the concept

Paper 1 has the same structure for both standard and higher levels:

Duration of paper 1 Paper 1: SL and HL
Focus and structure of paper 1 1 hour and 30 minutes
Section A focuses on section 1 of the syllabus (microeconomics). Students must answer
Structure of questions and marks one question from a choice of two.
earned in paper 1
Section B focuses on section 2 of the syllabus (macroeconomics). Students must
answer one question from a choice of two.
Each question consists of two parts, (a) and (b). Students must answer both parts.

Part (a) earns a maximum of 10 marks, and part (b) a maximum of 15 marks, making a
total of 25 marks for the question.

(continued over)

© Cambridge University Press 2012 Economics for the IB Diploma 2

Introduction to the IB Economics exam papers

Assessment objectives in paper 1 Paper 1: SL and HL
Part (a) of the questions examines assessment objectives 1, 2 and 4.

Maximum marks earned in paper 1, Part (b) of the questions examines assessment objectives 1, 2, 3 and 4.
and percentage in total IB Economics Since the student must answer two questions, paper 1 earns a maximum of 50 marks.
grade
Paper 1 accounts for 40% of the student’s overall grade at standard level, and 30% of
the student’s overall grade at higher level.

Paper 2 has the same structure for both standard and higher levels:

Duration of paper 2 Paper 2: SL and HL
Focus and structure of paper 2
1 hour and 30 minutes

Section A focuses on section 3 of the syllabus (international economics), though
students may be required to draw on other parts of the syllabus. Students must answer
one question from a choice of two.

Structure of questions and marks Section B focuses on section 4 of the syllabus (development economics), though
earned in paper 2 students may be required to draw on other parts of the syllabus. Students must answer
one question from a choice of two.

Paper 2 consists of data response questions. Each question consists of four parts, (a),
(b), (c) and (d), which are based on a text/data provided. Students must answer all
parts.

Part (a) is sub-divided into 2 parts, (i) and (ii), each of which is worth 2 marks; therefore
part (a) is worth a maximum of 4 marks.

Part (b) is worth a maximum of 4 marks.

Part (c) is worth a maximum of 4 marks.

Part (d) is worth a maximum of 8 marks.

Assessment objectives in paper 2 Therefore, each question earns a maximum of 20 marks.
Part (a) of the questions examines assessment objective 1.

Part (b) of the questions examines assessment objectives 1, 2, and 4.

Part (c) of the questions examines assessment objectives 1, 2 and 4.

Maximum marks earned in paper 2, Part (d) of the questions examines assessment objectives 1, 2 and 3.
and percentage in total IB Economics Since the student must answer two questions, paper 2 earns a maximum of 40 marks.
grade
Paper 2 accounts for 40% of the student’s overall grade at standard level, and 30% of
the student’s overall grade at higher level.

© Cambridge University Press 2012 Economics for the IB Diploma 3

Introduction to the IB Economics exam papers

Paper 3 is for HL only:

Duration of paper 3 Paper 3: HL
Focus and structure of paper 3
1 hour
Structure of questions and marks
earned in paper 3 Paper 3 focuses on the entire syllabus, including SL/HL core and HL topics. Students
must answer two questions from a choice of three.
Assessment objectives in paper 3
Each question consists of several parts, (a), (b), (c) and so on. The number of parts varies
from question to question. Students must answer all parts.

Each question earns a maximum of 25 marks.

Paper 3 examines assessment objectives 1, 2 and 4.

Maximum marks earned in paper 3, Since the student must answer two questions, paper 3 earns a maximum of 50 marks.
and percentage in total IB Economics Paper 3 accounts for 20% of the student’s overall grade at higher level.
grade

© Cambridge University Press 2012 Economics for the IB Diploma 4

Introduction to the IB Economics exam papers

Definitions of command terms

All command terms are listed below alphabetically, together with their corresponding AO levels and definitions.

Command term Definition asks students to:

Analyse AO2 Break down in order to bring out the essential elements or structure.
Apply AO2 Use an idea, equation, principle, theory or law in relation to a given problem or issue.
Calculate AO4 Obtain a numerical answer showing the relevant stages in the working.
Comment AO2 Give a judgment based on a given statement or result of a calculation.
Compare AO3 Give an account of the similarities between two (or more) items or situations, referring to both (all)

Compare and of them throughout.
contrast AO3 Give an account of similarities and differences between two (or more) items or situations, referring to
Construct
Contrast both (all) of them throughout.
AO4 Display information in a diagrammatic or logical form.
Define AO3 Give an account of the differences between two (or more) items or situations, referring to both (all)
Derive
Describe of them throughout.
Determine AO1 Give the precise meaning of a word, phrase, concept or physical quantity.
Discuss AO4 Manipulate a mathematical relationship to give a new equation or relationship.
AO1 Give a detailed account.
Distinguish AO4 Obtain the only possible answer.
Draw AO3 Offer a considered and balanced review that includes a range of arguments, factors or hypotheses.

Evaluate Opinions or conclusions should be presented clearly and supported by appropriate evidence.
Examine AO2 Make clear the differences between two or more concepts or items.
AO4 Represent by means of a labelled, accurate diagram or graph, using a pencil. A ruler (straight edge)
Explain
Identify should be used for straight lines. Diagrams should be drawn to scale. Graphs should have points
Justify correctly plotted (if appropriate) and joined in a straight line or smooth curve.
Label AO3 Make an appraisal by weighing up the strengths and limitations.
List AO3 Consider an argument or concept in a way that uncovers the assumptions and interrelationships of
Measure the issue.
Outline AO2 Give a detailed account including reasons or causes.
Plot AO4 Provide an answer from a number of possibilities.
Show AO3 Give valid reasons or evidence to support an answer or conclusion.
Show that AO4 Add labels to a diagram.
AO1 Give a sequence of brief answers with no explanation.
Sketch AO4 Obtain a value for a quantity.
AO1 Give a brief account or summary.
Solve AO4 Mark the position of points on a diagram.
State AO4 Give the steps in a calculation or derivation.
Suggest AO4 Obtain the required result (possibly using information given) without the formality of proof. ‘Show
To what extent that’ questions do not generally require the use of a calculator.
AO4 Represent by means of a diagram or graph (labelled as appropriate). The sketch should give a general
idea of the required shape or relationship, and should include relevant features.
AO4 Obtain the answer(s) using algebraic and/or numerical and/or graphical methods.
AO1 Give a specific name, value or other brief answer without explanation or calculation.
AO2 Propose a solution, hypothesis or other possible answer.
AO3 Consider the merits or otherwise of an argument or concept. Opinions and conclusions should be
presented clearly and supported with appropriate evidence and sound argument.

Source: IB Economics guide (First examinations 2013)

© Cambridge University Press 2012 Economics for the IB Diploma 5