Svar oppgaver gartner3utgave

Instructor’s Manual
Macroeconomics
Third Edition

Susanne Burri
Manfred Gärtner

For further instructor material
please visit:

www.pearsoned.co.uk/gartner
ISBN: 978-0-273-71791-1

© Manfred Gärtner 2009
Lecturers adopting the main text are permitted to download and photocopy the manual as required.


Pearson Education Limited
Edinburgh Gate
Harlow
Essex CM20 2JE
England
and
Associated Companies around the world
Visit us on the World Wide Web at:
www.pearsoned.co.uk
---------------------------------This edition published 2009
© Manfred Gärtner 2009
The right of Susanne Burri to be identified as author of this work has been asserted by him in
accordance with the Copyright, Designs and Patents Act 1988.
ISBN: 978-0-273-71791-1

All rights reserved. Permission is hereby given for the material in this publication to be
reproduced for OHP transparencies and student handouts, without express permission of the
Publishers, for educational purposes only. In all other cases, no part of this publication may be
reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise without either the prior written permission of
the Publishers or a licence permitting restricted copying in the United Kingdom issued by the
Copyright Licensing Agency Ltd. Saffron House, 6-10 Kirby Street, London EC1N 8TS. This
book may not be lent, resold, hired out or otherwise disposed of by way of trade in any form of
binding or cover other than that in which it is published, without the prior consent of the
Publishers.

2
© Manfred Gärtner 2009


Contents
Chapters

Pages

1.

Macroeconomic essentials

2.

Booms and recessions (I): the Keynesian cross

13

3.

Money, interest rates and the global economy

22

4.

Exchange rates and the balance of payments

32

5.

Booms and recessions (II): the national economy

38

6.

Enter aggregate supply

48

7.

Booms and recessions (III): aggregate supply and demand

56

8.

Booms and recessions (IV): Dynamic aggregate supply and demand

66

9.

Economic growth (I): basics

74

10.

Economic growth (II): advanced issues

83

11.

Endogenous economic policy

91

12.

The European Monetary System and Euroland at work

96

13.

Inflation and central bank independence

103

14.

Budget deficits and public debt

110

15.

Unemployment and growth

116

16.

Sticky prices and sticky information: new perspectives
on booms and recessions I

123

Real business cycles: new perspectives on booms and recessions (II)

130

A primer in econometrics

136

17.
Appendix

3
© Manfred Gärtner 2009

5


Manfred Gärtner, Macroeconomics, 3rd Edition, Instructor’s Manual

Supporting resources
Visit www.pearsoned.co.uk/gartner to find valuable online resources
Companion Website for students
• Macroeconomic tutorials with interactive models, guided exercises, and animations, plus an
interactive road map connecting key concepts and models
• A data bank with macroeconomic time series for many countries, along with a graphing module
• Extensive links to valuable resources on the web, organised by chapter
• Self assessment questions to check your understanding, with instant grading
• Index cards to aid navigation of resources, plus chapter summaries, macroeconomic dictionaries
in several languages, and more
For instructors
• Downloadable Instructor’s Manual including the solutions to chapter exercises and questions
• Downloadable PowerPoint slides of all figures and tables from the book
For more information please contact your local Pearson Education sales representative
or visit www.pearsoned.co.uk/gartner

4
© Manfred Gärtner 2009


1
Macroeconomic essentials
Chapter focus
This chapter attempts three things:
1. Provide an international perspective of macroeconomic issues and data. Since it tries to cover the European
countries rather comprehensively plus the major players in the global economy, it can only feature a limited set of
the most important macroeconomic data. It is desirable to augment this streamlined international information
with a more detailed discussion of your own country’s national macroeconomic data and sources.
2. Repeat some basic macroeconomic concepts. These are being used extensively in the remainder of the book.
These include the circular flow of income as a first ‘model’ of the macroeconomy and the circular flow identity
that is related to it, the government budget and the balance of payments. The role of money is also already
introduced at this stage by tying it to the circular flow via the quantity equation. The book assumes that students
have previously taken an economic principles course. Then the first (and probably the next two) chapter(s) can be
dealt with rather quickly. In case this is the first encounter of students with macroeconomics, then the concise
treatment of Chapter 1 should be augmented with additional reading assignments from some principles text.
3. Motivate students that macroeconomics is an exciting field with an applied focus. To this end, the chapter
features a case study on the subprime crisis that started in 2007–2008 that demonstrates that even the basic
concepts introduced in this chapter provide some useful insights into the issues and policy choices surrounding
this crisis.
The chapter ends with an appendix on logarithms, logarithmic scales and growth rates. It provides an
understanding of the growth rates of products (say PY) and fractions (say M/P) and motivates the graphical
display of trended time series using logarithmic scales. In an attempt not to leave students with a less
mathematical mind behind, numerical illustrations that students may follow with their pocket calculator are
being used instead of formal proofs.

Additional case studies

Case study C1.1 Germany's current account before and after unification
Germany’s traditional current account surpluses,
which had culminated at 4.8% of GDP in 1989,
disappeared after unification. In the first full
calendar year after the two Germanies had merged
the current account dropped from a regular surplus
into a deficit the size of about 1% of GDP (see
Figure C1.1(a)).
The circular flow model and the identity of leaks and
injections, S – I
T– G
IM – EX
0, provides a
first clue as to what had happened. First note,
however, that while we are treating the current
account CA and net exports
as synonyms in
Chapter 1, and throughout most of the text, this is
only an approximation. The main difference between
the two aggregates in reality is that the current
account also includes transfers across borders that are
not related to the export and import of goods and
services. Examples are aid to developing countries, a

Turkish family living in Germany sending money to
their parents in Ankara, or the contributions of the
German government to international organizations
such as NATO, the United Nations, or the European
Union. Since such things also constitute leakages
out of the circular flow of income, the current

account is actually a more precise measure of a
country’s net leakages to the rest of the world than
net exports.
It is often argued that the dramatic shift in Germany’s
current account was the result of rising government
budget deficits triggered by public investment in
East Germany’s infrastructure and transfer
payments to the East. This interpretation is often
motivated by comparing West Germany’s last full
budget in the year before unification, 1989, with the
years that followed. This implies that unification
drove a more or less balanced government budget

5
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

into deficit by some 3% of GDP. Panel (b) in Figure
C1.1, shows that this is a misleading story. The year
1989 is clearly atypical, given that the budget had
been in deficit for years before and exceeded 2% of
GDP in 1988 already. Ignoring 1989 as exceptional,
unification increased the budget deficit only by
about 1% point from 2% to 3% of GDP.
In terms of the circular flow identity: while the
increase of the budget deficit

may have
caused the current account to deteriorate, its
magnitude of 1% point only partly explains the
change in the current account by some 5 points.
What seems to have mattered much more is the
change in private net savings
documented in
panel (c) of Figure C1.1.

While private savings exceeded investment by some
6% of GDP before unification, this difference
dropped to about 2% after unification. This accounts
for the remaining change in the current account that
was not explained by the change in the government
budget deficit.
Of course, the change in private net savings also
reflects government policies towards the eastern
part of Germany. Net savings did not fall because
savings fell, but because investment increased due
to investment bonus packages put into action by the
Kohl government. Figure C1.2 shows that savings
were still about the same in 1995 as they had been
10 years earlier, while investment had risen by
about 4% points.
Using stylized, rounded numbers for the time
before and after unification Table C1.1 summarizes
the observed changes: the current account deficit
rose to – 4% to 1%. One percentage point of this
reflects the change in government spending
behaviour, i.e. the increase of the budget deficit

from 2% to 3% of GDP. The remaining 4 percentage
points (that is, the remaining 80%) of the change in
the current account reflect the change in net private
savings, which dropped from 6% to 2% of GDP.

Figure C1.2
Table C1.1
1986-1990
1991-1995

Figure C1.1
6
© Manfred Gärtner 2009

6%
2%

2%
3%

4%
1%

0
0
0


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Exercises
Exercise 1.1
The following are nominal incomes for some European countries in 2007, expressed in US dollars:
A 42,700; B 40,710; CH 59,880; D 38,860; DK 54,910; E 29,450; F 38,500; GB 42,740; GR 29,630; I 33,540; IRL 48,140;
LUX 75,880; N 76,450; NL 45,820; P 18,950; S 46,060. Real incomes are as follows: A 38,140; B 34,790; CH 43,870; D
33,530; DK 36,300; E 30,820; F 33,600; GB 33,800; GR 32,330; I 29,850; IRL 37,090; LUX 63,590; N 53,320; NL 39,310;
P 20,890; S 36,590.
(a) What is your country’s price level relative to the United States price level of 1 (If your country is
not included, choose any country)?
(b) Rank your country and any two other countries according to their price levels.
(a) To compute relative price levels, we use the data on nominal and real incomes given in the exercise.
From the definition of real income (cf. pg. 3) it follows that for any country i, real income can be
expressed as nominal income divided by the price level:
/
If we rearrange this equation and solve for the price level, we get
/
The price levels relative to the United States are:
⁄
⁄
⁄
⁄
⁄
⁄
⁄
⁄
⁄
⁄
⁄

⁄
⁄
⁄
⁄
⁄

⁄
⁄

⁄1
42,700⁄38,140
1.12
⁄1
40,710⁄34,790
1.17
⁄
⁄1
59,880/43,870
1.36
⁄
⁄1
38,860/33,530
1.16
⁄
⁄1
54,910/36,300
1.51
⁄
⁄1
29,450/30,820

0.96
⁄
⁄1
38,500/33,600
1.15
⁄
⁄1
42,740/33,800
1.26
⁄
⁄1
29,630/32,330
0.92
⁄
⁄1
33,540/29,850
1.12
⁄
⁄1
48,140/37,090
1.30
⁄
⁄1
75,880/63,590
1.19
⁄
⁄1
76,450/53,320
1.43
⁄

⁄1
45,820/39,310
1.17
⁄
⁄1
18,950/20,890
0.91
⁄
⁄1
46,060/36,590
1.26

(b) Denmark (DK) has the highest price level, followed by N, CH, IRL, GB, S, LUX, B, NL, D, F, I, A, E,
GR and P.

Exercise 1.2
Which of the following transactions constitute leakages, and which ones injections?
(a) The home country receives aid from the International Monetary Fund.
(b) Immigrant workers transfer their salaries to their home countries.
(c) Domestic firms invest in foreign countries.
(d) The government raises taxes and uses the proceeds to buy computers abroad.
Any part of domestic income that does not generate demand for domestically produced goods and services is a
leakage. Any exogenous demand for domestically produced goods, coming from some source other than
domestic income, is an injection into the circular flow of income.
(a) Injection
(b) Leakage
(c) Leakage
(d) Leakage
7
© Manfred Gärtner 2009

rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Exercise 1.3
Table 1.5 contains data for the Netherlands, Germany and Spain in 2006. All numbers are in billions of US
dollars. Fill in the missing numbers, following the logic of the circular flow model.
The numbers missing in Table 1.5 have been added in bold type in Table I1.1 below. Generally, the missing
numbers can be calculated using the circular flow identity and simplified definitions of the budget deficit and the
current account, respectively:
:

0

Table I1.1
Saving S

Investment
I

Taxes T

174

Netherlands
Germany
Spain

527
380

520
260

Government
expenditure
G
179
563

Budget
deficit

Imports
IM

Exports
EX

Current
account

421
1149

469
1304
327

155
77

4
25

Source: World Bank, Eurostat

Exercise 1.4
You head your country's central bank and must determine the amount of money to circulate next year. You
know that every euro circulates four times a year. The statistical office forecasts that production will remain
unchanged at 1,000 barrels of whisky (the only good produced in your country) next year.
(a) What is the slope of the aggregate supply curve if the production of whisky remains constant as
forecasted?
(b) Compute the price of one barrel of whisky if you fix the money supply at €4,000.
(c) What would be the price of one barrel of whisky if the velocity of money circulation rose to five
while the money supply remained at €4,000?
(d) Given the rising velocity of money circulation from (c) and constant production of whisky, how
would you fix the money supply if your targeted price level was €5 per barrel of whisky?
(e) What is the price of whisky if output rises to 1,600 barrels in the following year while the money
supply remains at €4,000 and money circulates four times a year?
(a) Since the quantity of whisky produced remains constant no matter what the price level is, the
aggregate supply curve is vertical in quantity-price space.
(b) Plugging the numbers given in the exercise into the quantity equation (
€4,000

4

) we get

1,000

This can be solved for

€16/

to obtain

.

(c) Plugging the new numbers into the quantity equation we get
€4,000

5

1,000

This can be solved for

to get

€20/

.

(d) Again we can plug in the numbers into the quantity equation, this time to compute
€

5

€5/

This yields

:

1,000
€1,000.

(e) Plugging the new numbers into the quantity equation we get €4,000
Solving the equation yields

€10/

.

8
© Manfred Gärtner 2009

4

€ /

1,600


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Exercise 1.5
Some time after an increase in the money supply from 50 billion to 100 billion units, the government of country
A learns that the price level has increased from 100 to 150 although the velocity of money circulation has
remained constant. What does that tell you about the slope of the aggregate supply curve?
The quantity equation
suggests that the money supply and the price level of country A should rise
by the same proportions if output and the velocity of money remain constant. In our example, the money supply
has doubled (i.e. it has risen by 100%) while the price level has risen by 50% only. With the velocity of money
remaining constant, output – or aggregate supply – must therefore have increased as well. This means that
the aggregate supply curve has a positive (finite) slope in quantity-price space: An increase in prices raises
output.

Exercise 1.6
The government of country B plans to spend €10,000 next year. Due to political constraints, taxes cannot exceed
€5,000. Eighty percent of the budget deficit will be financed by issuing government bonds to the private sector,
the rest by issuing bonds to the central bank in exchange for money.
(a) Compute the anticipated change in the money supply if neither international trade nor
international capital movements take place.
(b) What will be the effect on the price level if real output stays constant at Y = 10,000 and V at 4?
(c) Compute the anticipated change in the money supply if international trade in goods takes place,
but international capital movements are still forbidden. The statistical office forecasts a current
account deficit of €3,000.
(d) Can you think of arguments that render the assumption of a constant level of real production
(employed above) implausible?
(a) The increase in the money supply equals the amount of bonds issued to the central bank, which is
€1,000.
20% of €5,000, i.e. €1,000: ∆
∆
(b) We can use the quantity equation and our knowledge of the increase in the money supply to

compute the change in the price level.
Let
and
denote the current period money supply and price level. The quantity equation after
the increase of the money supply can then read
∆

∆

or, in expanded form

∆

Since the quantity equation holds in the current period, i.e. since
out these terms from the above expanded equation to get
∆

∆

∆

.
, we can cancel

.

Solving this for the change in the price level yields
∆P

∆M

V⁄Y

€1,000

4⁄10,000

0.4.

(c) If we consider an economy that engages in international trade, the money supply is determined
not only by the amount of government bonds issued to the central bank, but also by the amount of
). If there is a current account
foreign currency reserves the central bank holds (
deficit, the country imports more than it exports. The private demand for foreign currency thus
exceeds its supply by €3,000, which means that the central bank has to reduce its foreign currency
reserves by €3,000 in order to add to the foreign currency supply. This follows from
0,
0 and
∆
. To determine how this changes the money supply we can write:
∆

∆

∆

€1,000

€3,000

€2,000.

(d) Changes in government spending and the money supply may influence the interest rate (crowding
out; cf. chapter 3) and/or the exchange rate (depending on the level of capital mobility and the
exchange rate regime; chapters 4 and 5) and thus affect real output.

9
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Exercise 1.7
A country’s net foreign assets stand at 500. Next year’s exports are expected to be 30, expected imports are 20.
The central bank will not intervene in the foreign exchange market. What are the country's net foreign assets by
the end of next year?
In the absence of central bank intervention in the foreign exchange market, the change in foreign assets is
determined by the current account balance, i.e. by the difference between exports and imports:
∆

30

20

10.

The new level of net foreign assets is therefore

∆

500

10

510.

Exercise 1.8
Consider Figure 1.15. The graph shows a stylized demand curve for DVD recorders.

Figure 1.15
(a)
(b)
(c)
(d)

(e)
(f)
(g)
(h)

What are the endogenous variables in this model?
The price of a DVD recorder is 1,500 Swiss francs. What is the quantity demanded?
If the price fell to only one-third of its previous level, what would market demand be?
The supply curve can be described by the following equation:
500 0.000025
Draw the curve into the diagram in Figure 1.10.
Determine the equilibrium price level and the quantity sold graphically.
It becomes unfashionable to waste time in front of the TV. Show how this change of preferences

affects market demand. What will be the effect on the equilibrium price level and quantity?
Due to a new technology it becomes cheaper to produce DVD recorders. How will that affect the
diagram above?
The government introduces a tax on DVDs. How will that affect the diagram? What happens if
the government introduces a tax on visits to the cinema but does not levy a tax on DVDs?

(a) Endogenous variables are determined within the model. To describe their behaviour is the very
purpose of the model. In the above model, the price and the quantity are endogenous variables.
(b) The quantity demanded at a price of 1,500 Swiss francs can be read off the graph; it is approximately
24 million units (The more exact number is 23,333,333 units).
(c) One third of 1,500 Swiss francs is 500 Swiss francs. The quantity demanded at a price level of 500
Swiss francs is 50 million units; this can be read off the graph.
(d) The supply curve is drawn into Figure I1.1. According to the equation given, the intercept of the supply
curve (
0) is at
500. For every price increase of 250 Swiss francs, 10 million additional units are
supplied.
10
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Figure I1.1
(e) The equilibrium price and the quantity sold in equilibrium can be read off the intersection of the
demand and supply curve. The equilibrium price is 1,250 Swiss francs, the equilibrium quantity is
30 million units.
(f)

The change in preferences induces consumers to demand fewer DVD recorders at any given price level.
Graphically, this is equivalent to the demand curve shifting left (or down). After the shift has occurred,
the new equilibrium price and amount will necessarily be lower than the initial equilibrium values (see
Figure I1.2).

Figure I1.2
(g) The new technology makes it possible to produce more DVD recorders at any given price level.
Graphically, this is equivalent to the supply curve shifting right (or down). After the shift has occurred,
the new equilibrium price will be lower and the new equilibrium quantity will be higher than the old
equilibrium values (see Figure I1.3).

Figure I1.3
11
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

(h) The tax on DVDs has an adverse effect on the demand for DVD recorders since DVDs and DVD
recorders are complements. Hence, the demand for DVD recorders falls at any given price level, and the
demand curve will shift to the left (or down).
By contrast, a tax on visits to the cinema will stimulate the demand for DVD recorders, since DVD
recorders (together with DVDs) are a substitute for visits to the cinema. Hence the demand of DVD
recorders rises at any given price level and the demand curve shifts to the right (see Figure I1.4).

Figure I1.4

12
© Manfred Gärtner 2009


2
Booms and recessions (I): the Keynesian cross
Chapter Focus
This chapter brings students all the way from the use of the circular flow of income ‘model’ in Chapter 1 as a
descriptive device to setting the circular flow of income up as a genuine model with a unique equilibrium in
Chapter 2. Introducing the concept of a macroeconomic equilibrium constitutes a big step. When the circular
flow of income is being used merely as a descriptive device, the circular flow identity holds at all times. Income
may be at any level as long as we permit investment demand to comprise both planned (voluntary) and
unplanned (involuntary) investment. While such a descriptive model helps streamline our thinking about what
seems an incomprehensible macroeconomic reality, it does not explain why income is at a unique level, and at no
other.
To build a model with a unique equilibrium requires the following:
1.

The introduction of behavioural equations: the consumption function, the investment function, the export
function and the import function. These functions are being kept deliberately simple in order to arrive at a
first macroeconomic model, the Keynesian cross, quickly, without distracting detours. If so desired, and if
time permits, refined discussions of one or more of the behavioural equations may be discussed in more
detail:
– the permanent income or life cycle hypothesis of consumption;
– the q theory of investment;
– or the role of the J curve in international trade.
As said, these detours are being avoided in Chapter 2. The only refinement offered is a brief discussion of how
consumption and investment decisions depend on expected future movements of income, which leads to the result
that marginal consumption out of a transitory increase in income is much smaller than out of a permanent
increase in income.

2.

The distinction between planned and unplanned investment and, hence, spending. It is important to stress
that equilibrium income defined as a situation in which income equals all planned spending defines a point of
gravity only. Actual income in any given year may well deviate from this. But market forces will eventually
move income towards this gravity point.

Additional case studies
Case study C2.1 The 2008 US stimulus package
As the US subprime mortgage crisis unfolded at the
beginning of 2008, President Bush and Congress
responded to rising fears of a severe economic
slowdown with calls for a swift economic stimulus
package. On 13 February the president signed a
$152 billion fiscal stimulus package into law which
granted tax rebates of up to $1,200 to most people
who had paid income taxes in 2007. Figure C2.1
shows how these rebates affected US disposable
income and consumption and puts developments
into perspective.
Figure C2.1
13
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

The lower line reveals that short-lived increases in

income may be expected to generate only small, if
any, responses in consumption, in particular at
times when households worry about their savings,
their future income and the security of their jobs.

The drop in consumption during the second half of
2008, when income was still rising, gives proof of
increased saving efforts in order to make up for lost
wealth and prepare for an uncertain future.

Exercises
Exercise 2.1
Consider French real output between 1900 and 1994 as given in Figure 2.16. Add your guess of the paths of
steady-state income and potential income to the graph.
See Figure I2.1. It is important to note that French potential income and French steady-state income coincided in
the years between 1900 and 1914, and again in the years between 1970 and 1994. The deviations of potential
income from its secular trend (i.e. steady-state income) were caused by the two world wars. Subsequent
reversions indicate transition dynamics.

Figure I2.1
Exercise 2.2
Figure 2.20 displays the evolution of real GDP between 1978 and 2002 for the United States and France.
(a) Try to identify business cycles, marking peaks and troughs on the graphs.
(b) Identify the US position in 1991 in a diagram with prices on the vertical axis and income on the
horizontal axis. Mark potential income, steady-state income and actual income.
Two US economists, Arthur F. Burns and Wesley C. Mitchell, claimed half a century ago that the typical business
cycle lasts between 6 and 32 quarters.
(c) Does this agree with your findings?
(a) See Figures I2.2 and I2.3.
(b) Figure 2.20 shows no deviation of potential income from steady-state income for the United States. There

was, in other words, no massive reduction of the capital stock in the years between 1978 and 2002.
Potential income can thus be assumed to match steady-state income. Moreover, the US business cycle
reached a trough in 1991 (cf. Figure I2.2). This means that by definition, actual income was below
potential income in 1991, which is reflected by the actual income line in Figure I2.4.
(c) According to Figures I2.2 and I2.3, entire business cycles last approximately 9 years or 36 quarters in the
United States and approximately 8 years or 32 quarters in France. They are thus at (or above) the upper
bound of what Burns and Mitchell consider to be a typical business cycle period.

14
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Figure I2.2

Figure I2.3

Figure I2.4

Exercise 2.3
Consider an economy with the following data (note that
actual investment):
750

500

0

250

is planned investment, which may not coincide with
250

1,000

(a) Is this economy’s circular flow in equilibrium in the sense that firms do not have to change inventories
involuntarily?
(b) Translate the above data into a diagram with demand on the vertical axis and income on the horizontal
axis.
Add the assumption
0.75 .
15
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

(c) Draw the aggregate-expenditure and the actual-expenditure lines. Identify demand-determined income
in equilibrium in your graph and analytically.
(d) What happens to equilibrium income if government expenditure increases by 500 units? Show your
result in a graph and verify that it is supported by the multiplier formula of Equation 2.9.
(e) Using a graph, show what happens if net exports fall from 250 to 100.
(f) Using a graph, show what happens if the marginal propensity to consume rises from 0.75 to 0.8.
(a) The circular flow is not in equilibrium since planned (aggregate) demand
750 500 250 250

1,750 exceeds output (1,000). Firms have to undertake unplanned negative investment of 250 instead.
(b) See Figure I2.5.

Figure I2.5
(c) See Figure I2.6. Since consumption now depends on income, the aggregate-expenditure line slopes
upward in income-expenditure space. The intersection of the aggregate-expenditure line with the actualexpenditure line determines equilibrium income. Equilibrium income can be derived analytically by
solving the circular flow equation:
0.75
500 250 250 for , which yields
4,000. Note that
we implicitly used the multiplier 1⁄ 1 0.75
4.

Figure I2.6
(d) At the old level of government expenditure, the aggregate-expenditure line intersects the vertical axis at
1,000. If government expenditure increases by 500 units, the new intercept is at 1,500 and equilibrium
income (which can be found at the point where the aggregate-expenditure and the actual-expenditure
line intersect) amounts to
6,000. This can be verified by using the formula ∆
1⁄1
]∆ .
Plugging in
0.75 and ∆
500 yields ∆
2,000, which confirms the graphical result in Figure I2.7.

16
© Manfred Gärtner 2009

rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Figure I2.7
(e) The decline in exports makes the aggregate-expenditure line shift downward by 150 units and the new
intercept with the vertical axis is at 850. The new point of intersection with the actual-expenditure line is
at
3,400 (see Figure I2.8). This can be verified by computing ∆
1⁄1
]∆
with ∆
150
and
0.75, which yields ∆
600.

Figure I2.8
(f)

If the marginal propensity to consume changes, the slope of the aggregate-expenditure line changes. In
our case increases from 0.75 to 0.8, which makes the aggregate-expenditure line steeper ( actually is
the slope of the aggregate-expenditure line). If we compute income for the initial values of investment,
government consumption, and net exports, we have to solve the equation
0.8
500 250 250
for , which yields
5,000 (see Figure I2.9).

Figure I2.9

17
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Exercise 2.4
One effect of German unification was a rise in demand for most Western countries’ exports. However, the
impact differed considerably among European countries, depending on the multipliers that transform an
exogenous change in demand into a change in income.
Consider the Netherlands and the United Kingdom. The share of imports in Dutch GDP is 52%, the share of
imports in British GDP is 27%. Assume that these average import propensities are also the marginal propensities
to import. Assume, further, that for both countries the marginal propensity to consume is 80% and the average
tax rate is 30%. What is the slope of the aggregate supply curve if the production of whisky remains constant as
forecasted?
(a) Calculate the equilibrium effect of an exogenous increase of export demand by 100 units on Dutch and
British GDP.
(b) Employ the successive-rounds interpretation of the multiplier. By how much has income increased after
round #3 in total?

(a) The multiplier for an open economy with taxes is
.
For the Netherlands this yields a multiplier of
.

.

.

1.042.

For the United Kingdom the multiplier is
.

.

.

1.408.

The increases in income induced by the hike in export demand are thus 104.2 for the Netherlands and
140.8 for the United Kingdom.

(b) The results derived above hold in equilibrium after the full multiplier effect has played out. This means
that the increases in income calculated above will be reached only after an infinite number of virtual
rounds. However, most of the increase in income is reached after the first few rounds. We will thus trace
the evolution of income over the first three rounds only.
In round #1, only the direct effect of the increased export demand on income occurs, hence ∆
∆
100. This holds both for the Netherlands and the United Kingdom. In round #2, the additional output
feeds into consumption and import demand. The incremental increase in output in this second round is
∆

1

]∆ .

Plugging in ∆
100 and the given values for the marginal propensity to import, the tax rate and the
marginal propensity to consume we get
∆

0.8 1

0.3

0.52]

100

4.

100

29.

for the Netherlands and
∆

0.8 1

0.3

0.27]

for the United Kingdom.
In round #3, the incremental output of round #2, ∆ , feeds into consumption and import demand.

Hence
∆

1

∆

0.8 1

]∆ , which yields
0.3

0.52]

4

0.16

for the Netherlands, and
∆

0.8 1

0.3

0.27]

29

8.41

for the United Kingdom.
The additional output resulting after the first three rounds can be determined by computing ∆
∆
∆ , which yields 100 4 0.16 104.16 for the Netherlands and 100 29 8.41 137.41 for the
18
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

United Kingdom. Hence, both countries are very close to reaching the new equilibrium values after as
little as three rounds.
Exercise 2.5
In the summer of 1991 the German parliament imposed a surcharge of 7.5% on the personal and corporate
income tax (the so-called Solidaritätszuschlag), promising that this tax surcharge would be removed after one
year. However, following a decision in March 1993 the solidarity surcharge was reintroduced in January 1995
and was still in effect in 1996. What would you expect aggregate consumption to look like, starting at the first
announcement of the solidarity surcharge? Does it make any difference whether individuals believed the
government’s pledge that the surcharge would be removed after one year?
Following the permanent income hypothesis, we would predict that temporary changes in income do not
strongly affect consumption. Hence, the first announcement should have only slightly lowered consumption
given the government’s pledge to remove the tax surcharge after one year. However, if consumers did not believe
the government’s announcement and instead anticipated that the tax surcharge was to persist for the years to
come, they should have consumed considerably less due to the anticipated sizeable fall in permanent (disposable)
income.

Exercise 2.6

Figure 2.21 shows quarterly data for nominal GDP and nominal consumption in France. (Both time series are
deviations from a non-linear trend.) What is your interpretation of these time series in the light of the hypothesis
that consumption only responds to permanent changes of income?

Figure 2.21
It is apparent from Figure 2.18 that deviations from trend are more pronounced for nominal GDP than for
nominal consumption (GDP is ‘more volatile’ than consumption). This supports the permanent income
hypothesis, which postulates that consumption does not react strongly to changes in income if these are
considered to be only temporary.

Exercise 2.7
Consider an economy characterized by
, with
0.75,
0,
250,
250, and
, with
500 and
5,000. Note that investment depends on the interest rate.
(a) Assume that, because of increasingly pessimistic expectations of investors, autonomous investment
decreases from 500 to 300. The interest rate and all other exogenous variables stay constant. Calculate
the resulting change in income.
(b) At the same time the interest rate decreases from 0.06 to 0.05. Calculate the effect on equilibrium
income.
(a) From

we get (by using the parameter values given above)

0.75

i.e.

4

250
500

250
5,000

5,000

,

, and
19
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

∆

4

∆ .

By plugging in the given autonomous investment decrease of 200 we get

∆

4

200

800, i.e. the resulting change in income is

800.

(b) A decline of the interest rate from 0.06 to 0.05 increases equilibrium income by 200 units:
∆

4

5,000

∆

20,000

0.01

200.

Combining the effects of the autonomous investment decrease and the decline of the interest rate on
equilibrium income yields ∆
800 200
600.

Exercise 2.8
Consider the economy of Exercise 2.7, except that consumption now depends on disposable income:
.
The government increases expenditure from 250 to 750 (i.e. ∆
500). This additional expenditure is financed
partly by taxes, which account for 50% of government revenue, and partly by issuing bonds. This sudden
appearance of huge quantities of government bonds on the capital market drives up interest rates from 0.05 to
0.06. What is the effect of all these changes on equilibrium income? Would it have been better to finance the
expenditure entirely by taxes (then ∆
∆
500 and ∆
0 ?
The aggregate-expenditure function reads
, which can be solved for Y to get
].
By plugging in the given parameter values we can compute the overall change in equilibrium income:
∆

4

∆

∆

∆ ]

4

0.75

250

500

5,000

0.01]

1,050.

Without bond financing (and assuming that the interest rate stays constant) ∆
∆

4

∆ ]

∆

4

0.75

500

500]

∆

500 and, therefore,

500.

Thus the multiplier under the restriction ∆
∆ , the balanced budget multiplier, is ∆ ⁄∆
1.
Without bond financing, the effect of the increase in government spending on income would have been much
smaller. Given the above parameter values, refraining from bond financing is not the most favourable option.

Exercise 2.9
Investment decisions not only depend on the interest rate but also on expectations of the future overall economic
situation, represented by future GDP.
(a) Through what channels might Y enter the investment decision?
(b) Assume that, to form their expectations about future GDP, investors simply extrapolate today’s GDP,
i.e.
. Moreover, assume that these expectations enter the investment function in the following
form (note that we neglect the influence of the interest rate):
.
(i)
(ii)

How will this modification affect the multiplier?
Derive the multiplier for this case, in which Y influences investment.

(a) Expectations about future booms or recessions co-determine expectations about future revenues and
profits and therefore the firms' propensity to invest.
(b) From Y = c × Y + G + NX + α × Y, we can derive the (investment-augmented) multiplier 1/(1 – c – α). If
α + c < 1, this multiplier is higher than the multiplier that does not consider the influence of output on
investment.
Exercise 2.10

An open economy exhibits the following aggregate-expenditure function:
AE = C+ I + G + NX
where C = c(Y–T) and T = tY. I, G and NX are exogenous variables.
20
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

(a) The country enters a war, which boosts government expenditure G. Show the effect on income

in the
Keynesian cross.
(b) You recognize that the actual increase in Y is smaller than the one you found in question (a). What
factors may be responsible for this ‘too small’ multiplier? Specify the variants that go with the given
aggregate-expenditure function and illustrate them in the Keynesian cross.
(a) See Figure I2.10. An increase in government expenditure shifts the aggregate-expenditure curve
upwards. Because of the multiplier, the effect on Y is larger than the original increase in G.

Figure I2.10
(b) We implicitly assumed that all parameters and exogenous variables remain constant. But in reality this
need not be the case. It is rather likely that people increase their savings rate (thereby reducing their
propensity to consume ) because of the uncertainty during wartime. Also, the government might
increase the tax rate to finance its war expenditure. A higher and a lower make the aggregateexpenditure curve flatter (In Figure I2.11, the vertical axis intercept remains the same). It is furthermore
possible that the autonomous expenditure components
and fall during wartime, which would
result in a downward-shift of the aggregate-expenditure curve. Figure I2.11 shows that with all the
mentioned changes, the resulting increase in is smaller than in (a).

Figure I2.11

21
© Manfred Gärtner 2009


3
Money, interest rates and the global economy
Chapter focus
This chapter develops the IS-LM model (also called the global economy model) and discusses its two constituent
markets, the goods market and the money market. The goods market, which was already introduced in Chapter
2, is refined by making investment depending on the interest rate. Considerable space is devoted to the money
market, reflecting latest developments. The chapter also shows how the goods and the money market interact,
and brings a first encounter with monetary and fiscal policy.
Recent years brought an engaged discussion among academic teachers on whether we should continue to teach
IS-LM with a fully spelled out money market in which the central bank exercises discretionary control over the
money supply; or instead focus on the currently predominant practice of conducting monetary policy via a
monetary policy rule that may feature the interest rate or the money supply as an instrument. There are good
arguments in favour of both.
In our judgement, the conventional approach is more difficult to teach, but also more complete and, therefore,
more robust. Treating the interest rate as the monetary policy instrument simplifies the analysis enormously. The
price to be paid is that extraordinary events such as bank runs, liquidity traps or even the implications of risk
premiums appear more difficult to teach without a fully worked-out money market. The unfolding of the global
economic crisis that follows the US subprime mortgage crisis of 2007–2008 seems to suggest that this price may
indeed be high.
The third edition has expanded the treatment of the money market considerably by giving interest rate targeting
and monetary policy rules their proper place while still using the conventional treatment of the money market
(meaning a focus on the interaction between supply and demand) as a foundation. After working through
Chapter 3, students should be familiar with both approaches and know how they are related. The key insight that

this chapter attempts to convey is that the qualitative properties of the IS-LM model are not dependent on
whether we represented the money market by an LM curve or use a policy rule (called an LM curve in this
chapter).

Additional case studies
Case study C3.1 Liquidity traps and Japan’s prolonged recession
Japan’s long economic slump experienced during
the second half of the 1990s baffled many observers.
While the real money supply increased by almost
40% between 1996 and 2000, income rose by a barely
observable 3.2%. So contrary to what we have
learned from this chapter’s analysis, monetary
policy in this case does not really seem to have an
effect on income worth talking about. Does this
mean the model is of no help in trying to
understand Japan’s recent slump? One might be
tempted to think so. And, in fact, the simple version
of the model developed above fails to account
for Japan’s experience. A generalized version,

however, will provide new insights and an
interesting application.
In this textbook most relationships are drawn as
straight lines, as in the
curve. This is easy to
draw, can be based on simple linear equations, and
under most circumstances is a useful approximation
of a (possibly) more complicated reality. That is the
case in most circumstances, but in extreme situations
this is sometimes not so.

Recall that the
curve slopes upwards because,
when interest rates go down and bonds lose part of
their advantage as a store of value, individuals hold
larger shares of their wealth in the form of money.

22
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

Since bonds lose their dominance as a store of value
completely once the interest rate is at (or near) zero,
the
curve cannot extend into the region of
negative interest rates. To avoid this, the
curve
must become flatter as i falls, becoming horizontal
at or just above a zero interest rate. The existence of
a horizontal segment of the
curve does not really
matter as long as the
curve intersects
on the
upward sloping section. This is the configuration
that we have in mind in this textbook. In the
unlikely case that the

intersects
where it is
flat, we have a problem. Then the economy is in a
liquidity trap.

that the public was prepared to hold this additional
nominal wealth in the form of money, the interest
rate could not go down any further. As a
consequence, the money supply increase could not
stimulate investment demand and income. The
economy stayed very much where it was in 1996.
Table C3.1 gives key data for the Japanese economy.
Table C3.1
1996

2000

Real GDP ( )

514,852

531,133

Real money supply ( / )

163,201

227,210

Price Index ( )

100.0

101.4

Interest rate ( )

0.59%

0.25%

Food for thought
Japan raised government spending several times in
order to get out of the recession, with little effect.
What might be the cause(s) of this? In the spirit of
the quantity equation, we concluded in Chapter 1
that a money supply increase raises nominal
income
. In Japan neither
nor
rose to a
relevant extent. How does this fit in with the
quantity equation?
Figure 1
The possibility of a liquidity trap is a well-known
concept and had been taught to generations of
students.
However,
recent
generations

of
economists considered the liquidity trap to be dead
– an academic nicety that did not have any basis in
the real world. That is, until US economist Paul
Krugman came forward with the suggestion that
Japan had fallen into a liquidity trap in the 1990s.
Figure 1 sketches Japan’s experience according to
this argument.
Suppose Japan was in the situation indicated in
1996. Putting this point on the horizontal part of
Japan’s
curve appears justified by a 1996 interest
rate of 0.59%, barely above zero. In the course of the
next four years, the nominal money supply rose by
some 40%, as did the real money supply, since
prices did not change much. This shifted the
curve massively to the right, into the dark blue
position. Since the interest rate was already so low

Food for thought – possible answers
Regarding the ineffective increase in government
spending, some other demand category must have
been reduced, leading to a very small multiplier.
As for the increase in the money supply, we can see
by looking at the quantity equation
that if
increased without affecting either or ,
then the velocity of money circulation must have
fallen. This may be the case because at near zero
interest rates, speculative and precautionary money

holdings increased.

Exercises
Exercise 3.1
Which of the following variables are flow variables, and which are stock variables?
(a) A nation’s GDP.
(b) A firm’s cars and machines.
(c) The gold reserves in the vaults of your country’s central bank.
(d) Ferrari Testarossa sales between 1987 and 2008.
(e) Aggregate investment.
(f) British lager consumption per capita in 2007.
(g) The number of Rioja bottles in your cellar.
23
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

(h) The profits of your country’s central bank in 2009.
(i) The number of all Škoda models registered in Warsaw.
Remember: A flow variable is measured over a period of time, while a stock variable is measured at a point in
time.
(a) A nation’s GDP – flow.

(b) A firm’s cars and machines – stock.
(c) The gold reserves in the vaults of your country’s central bank – stock.
(d) Ferrari Testarossa sales between 1987 and 2008 – flow.
(e) Aggregate investment – flow.

(f) British lager consumption per capita in 2007 – flow.
(g) The number of Rioja bottles in your cellar – stock.
(h) The profits of your country’s central bank in 2009 – flow.
(i) The number of all Škoda models registered in Warsaw – stock.
Exercise 3.2
Recall the quantity equation from Chapter 1:
. In this chapter, the velocity of money circulation
was assumed to be constant. Is this assumption reasonable in the light of the model of money demand? How
would you expect to change with an increase in the interest rate? Assume that the interest rate remains at its
new higher level, with and unchanged. How does this affect the price level?
A higher interest rate raises the opportunity costs of holding money and thereby reduces the demand for money.
It should thus be expected that an increase in the interest rate leads to an increase in the velocity of money. Given
that people still spend the same amount, i.e. given that consumption remains the same, the average monetary unit
will have to circulate more often once people hold less money. In the case of Germany, this conjecture is
supported by empirical evidence. In the short run, increases of the short-term interest rate tended to coincide with
an increase of the velocity of M1. Hence, given that and remain constant, an increase in the interest rate will
increase the price level.

Exercise 3.3
(a) In recent years, a number of institutional and technical innovations, such as cash machines, have made
it less and less expensive to obtain cash. Explain the consequences of this development by using the
model of money demand in the text. If this trend continues, will average cash holdings decrease or
increase?
(b) How do decreasing transaction costs affect the LM curve? (Hint: start with the money demand equation
and show how transaction costs determine the slope of the money demand function. Look at two
different interest rates, including
0. Then work your way through to Figure 3.6 and decide whether
– with lower transaction costs – a given increase in money supply leads to a larger or to a smaller shift
of the
curve.)

(a) The innovations reduce the transaction costs for obtaining money, i.e. for converting other types of
wealth such as interest bearing assets into cash. Given the same opportunity costs of holding money (the
level of the interest rate), this will make it worthwhile to hold less money and make more trips to the
bank. Therefore, average cash holdings will decrease.

(b) Decreasing transaction costs make the money demand curve rotate counter-clockwise around its
horizontal-axis intercept, i.e. the demand curve becomes flatter (see the left-hand side of Figure I3.1 for a
graphical illustration of this). Lower transaction costs imply that less money is demanded at any positive
interest rate level (c.f. solution to Exercise 3.3.a). They furthermore imply that money demand becomes
more sensitive to changes in the interest rate, since for a given increase in the interest rate the resulting
decrease in money demand will be more pronounced. (This could be proven by noting that for any
positive interest rate, money demand is now lower thanks to decreased transaction costs. At an interest
rate of zero, however, the money demand should remain constant since holding money here involves no
24
© Manfred Gärtner 2009


rd

Manfred Gärtner, Macroeconomics, 3 Edition, Instructor’s Manual

opportunity costs. Analytically it follows that sinking transaction costs correspond to a higher in the
money demand function. At an interest rate of zero, money demand, i.e.
, is independent of
transaction costs. Furthermore, an increase of corresponds to a rotation of the money demand curve
⁄
(
1/
) around its horizontal-axis intercept.)

It follows that the
curve is flatter at lower transaction costs as well. To see why, consider that a given
increase in income, ∆ , moves the money demand curve by ∆ to the right (i.e. ∆ ⁄∆
); this change
is the same under both transaction cost regimes since is unaffected by transaction costs. While ∆ ⁄∆
remains unaffected by changing transaction costs, ∆ ⁄∆
/ decreases when h increases (i.e. when
transaction costs decrease). This means that the change of the interest rate needed to bring the money
market back to equilibrium after an increase in income becomes smaller once transaction costs fall. The
curve must thus become flatter. A quick look at the formula of the
curve (
/
/ )
helps understand this. An increase in makes the
curve flatter.

Figure I3.1
It is relatively easy to see that with lower transaction costs, a given increase in the money supply leads to
a smaller shift of the
curve. In the left-hand panel, we see that an increase in the money supply leads
to a smaller decrease in the interest rate when transaction costs are low (analytically ∆ ⁄∆
∆ ⁄∆
1/
becomes smaller in absolute terms when h increases). Since the change in the interest rate
∆ ⁄∆
1/ corresponds to the ‘vertical shift’ of the
curve in the right hand panel, this shift will
also be smaller. (Also note that the ‘horizontal shift’ of the
curve, ∆ ⁄∆
1/ , remains unaffected

by transaction costs.)

Exercise 3.4
Consider Table 3.1, which shows end-of-month exchange rates for the British pound (GBP), the US dollar (USD)
and the Chinese yuan (CNY) versus the euro (EUR) during the first half of 2008. Which month recorded the
largest appreciation of the euro versus the dollar? How many yuan did one dollar cost in Mai? In which months
did the yuan appreciate against the pound?
Table 3.1
GBP/EUR
USD/EUR
CNY/EUR

January
0.7477
1.4870
10.679

February
0.7652
1.5121
10.786

March
0.7958
1.5812
11.078

April
0.7901
1.5540

10.858

May
0.7860
1.5508
10.765

June
0.7922
1.5764
10.805

The second row shows the price of euro expressed in US dollars. If the euro appreciates, the price of euro
increases. The month with the (absolutely and relatively) largest appreciation was thus March.
To calculate the price of one yuan in US dollars in May 2008, we first note that for one euro, one had to pay 10.765
yuan. For this one euro, one then received 1.5508 dollar. So one dollar cost 10.765/1.5508 6.9416 yuan.
Formally:
.
.

6.9416.

To determine in which months the yuan appreciated against the pound, we first calculate the exchange rate
(direct notation) CNY/GBP:
25
© Manfred Gärtner 2009