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.

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---------------------------------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

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ISBN: 978-0-273-71791-1

All rights reserved. Permission is hereby given for the material in this publication to be

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Publishers.

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© 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

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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

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© 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

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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

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6%

2%

2%

3%

4%

1%

0

0

0

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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

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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/

.

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€ /

1,600

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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.

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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.

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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

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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

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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

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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.

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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 .

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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.

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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

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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

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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

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∆

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.

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(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

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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.

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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.

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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

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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

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

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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

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6%

2%

2%

3%

4%

1%

0

0

0

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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

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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/

.

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€ /

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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.

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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.

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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

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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

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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

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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.

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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 .

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(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.

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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

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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

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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

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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.

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(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

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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.

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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.

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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

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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

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