Some Techniques ofSome Techniques ofEconomic AnalysisEconomic Analysis

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics• Use of diagrams in economics

O

Entertainment

Exp

endi

ture

(£)

Individual’s income (£)

Food

Effect of a rise in incomeEffect of a rise in income

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics

• Use of diagrams in economics

• Representing statistics

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

• Use of diagrams in economics

• Representing statistics– time-series data

UK Unemployment and economic growth: 1998 Q1 – 2002 Q1UK Unemployment and economic growth: 1998 Q1 – 2002 Q1U

ne

mp

loym

en

t (m

illio

ns)

1998 1999 2000 2001 2002

UK Unemployment and economic growth: 1998 Q1 – 2002 Q1UK Unemployment and economic growth: 1998 Q1 – 2002 Q1U

ne

mp

loym

en

t (m

illio

ns)

1998 1999 2000 2001 2002

UK Unemployment and economic growth: 1998 Q1 – 2002 Q1UK Unemployment and economic growth: 1998 Q1 – 2002 Q1U

ne

mp

loym

en

t (m

illio

ns)

1998 1999 2000 2001 2002

Ec

on

om

ic g

row

th (%

)

UK Unemployment and economic growth: 1998 Q1 – 2002 Q1UK Unemployment and economic growth: 1998 Q1 – 2002 Q1U

ne

mp

loym

en

t (m

illio

ns)

1998 1999 2000 2001 2002

Ec

on

om

ic g

row

th (%

)

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

Cross-section data:The distribution of UK pre-tax income

Cross-section data:The distribution of UK pre-tax income

0

10

20

30

40

50

60

Poorest 20% Next 20% Middle 20% Next 20% Richest 20%

Per

cen

tag

e o

f to

tal

ho

use

ho

ld i

nco

me

Cross-section data:The distribution of UK pre-tax income

Cross-section data:The distribution of UK pre-tax income

Cross-section data:The distribution of UK pre-tax income

Cross-section data:The distribution of UK pre-tax income

1977

42%42%

4%4%

10%10%

18%18%

26%26%

Cross-section data:The distribution of UK pre-tax income

Cross-section data:The distribution of UK pre-tax income

2000/1

15%15%

7%7%

2%2%51%51%

25%25%

1977

42%42%

4%4%

10%10%

18%18%

26%26%

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

0

25

50

75

100

0 10 000 20 000 30 000 40 000 50 000 60 000

Kg

pu

rch

ase

d p

er

yea

r

Consumer income (£ per year)

ConsumerConsumerincome (£)income (£)

Kg purchasedKg purchasedper yearper year

05 000

10 00015 00020 000

10254570

100

Using graphs with different scales: scale 1Using graphs with different scales: scale 1

0

25

50

75

100

0 10 000 20 000 30 000 40 000 50 000 60 000

Consumption of a foodstuff(per person)

Kg

pu

rch

ase

d p

er

yea

r

Consumer income (£ per year)

ConsumerConsumerincome (£)income (£)

Kg purchasedKg purchasedper yearper year

05 000

10 00015 00020 000

10254570

100

Using graphs with different scales: scale 1Using graphs with different scales: scale 1

0

100

200

300

400

0 5000 10 000 15 000 20 000

Kg

pu

rch

ase

d p

er

yea

r

Consumer income (£ per year)

ConsumerConsumerincome (£)income (£)

05 000

10 00015 00020 000

Kg purchasedKg purchasedper yearper year

10254570

100

Using graphs with different scales: scale 2Using graphs with different scales: scale 2

0

100

200

300

400

0 5000 10 000 15 000 20 000

Kg

pu

rch

ase

d p

er

yea

r

Consumer income (£ per year)

Consumption of a foodstuff(per person)

ConsumerConsumerincome (£)income (£)

05 000

10 00015 00020 000

Kg purchasedKg purchasedper yearper year

10254570

100

Using graphs with different scales: scale 2Using graphs with different scales: scale 2

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

– questions of distribution

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

– questions of distribution

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

– questions of distribution

– real and nominal values

• Use of diagrams in economics

• Representing statistics– time-series data

– cross-section data

• Getting a true picture from statistics– selective use of data

– graphical presentation

– absolute and proportional values

– questions of distribution

– real and nominal values

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index

• Index numbers– constructing an index

Constructing an index:UK manufacturing and service industry output: 1995 = 100

Constructing an index:UK manufacturing and service industry output: 1995 = 100

Constructing an index:UK manufacturing and service industry output: 1995 = 100

Constructing an index:UK manufacturing and service industry output: 1995 = 100

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes

• Index numbers– constructing an index – using index numbers to measure

percentage changes

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

Constructing a weighted average indexConstructing a weighted average index

Constructing a weighted average indexConstructing a weighted average index

Constructing a weighted average indexConstructing a weighted average index

Constructing a weighted average indexConstructing a weighted average index

Constructing a weighted average indexConstructing a weighted average index

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships– simple linear functions

• as a table• as a graph• as an equation

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships– simple linear functions

• as a table• as a graph• as an equation

Graph of the saving function: S = 0.2YGraph of the saving function: S = 0.2Y

National income(£bn per year)

Total saving(£bn per year)

01020304050

02468

10

Sa

vin

g (£

bn)

National income (£bn)

a

a

S = 0.2Y

0

2

4

6

8

10

12

14

0 10 20 30 40 50

National income(£bn per year)

Total saving(£bn per year)

01020304050

02468

10

Sa

vin

g (£

bn)

National income (£bn)

b

b

S = 0.2Y

0

2

4

6

8

10

12

14

0 10 20 30 40 50

Graph of the saving function: S = 0.2YGraph of the saving function: S = 0.2Y

National income(£bn per year)

Total saving(£bn per year)

01020304050

02468

10

Sa

vin

g (£

bn)

National income (£bn)

c

c

S = 0.2Y

0

2

4

6

8

10

12

14

0 10 20 30 40 50

Graph of the saving function: S = 0.2YGraph of the saving function: S = 0.2Y

National income(£bn per year)

Total saving(£bn per year)

01020304050

02468

10

S = 0.2Y

Sa

vin

g (£

bn)

National income (£bn)

def d

e

f

0

2

4

6

8

10

12

14

0 10 20 30 40 50

Graph of the saving function: S = 0.2YGraph of the saving function: S = 0.2Y

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5

x y

012345

a

a

Y = 4 + 2x 4 6 8101214

y

x

Graph of the function: y = 4 + 2xGraph of the function: y = 4 + 2x

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5

x y

012345

b

b

4 6 8101214

y

x

Y = 4 + 2x

Graph of the function: y = 4 + 2xGraph of the function: y = 4 + 2x

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5

x y

012345

c

c

4 6 8101214

y

x

Y = 4 + 2x

Graph of the function: y = 4 + 2xGraph of the function: y = 4 + 2x

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5

x y

012345

def

d

4 6 8101214

y

x

e

fY = 4 + 2x

Graph of the function: y = 4 + 2xGraph of the function: y = 4 + 2x

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5

x y

012345

4 6 8101214

y

x

1

cd

c

d

2

Y = 4 + 2x

Graph of the function: y = 4 + 2xGraph of the function: y = 4 + 2x

SOME TECHNIQUES OF ECONOMIC ANALYSISSOME TECHNIQUES OF ECONOMIC ANALYSIS

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships– simple linear functions

• as a table• as a graph• as an equation

– non-linear functions

• Index numbers– constructing an index – using index numbers to measure

percentage changes– price index– use of weighted averages

• Functional relationships– simple linear functions

• as a table• as a graph• as an equation

– non-linear functions

0

5

10

15

20

25

30

0 1 2 3 4 5 6

x y

0123456

a

a

4132025282928

y

x

Graph of the function: y = 4 + 10x – x2Graph of the function: y = 4 + 10x – x2

0

5

10

15

20

25

30

0 1 2 3 4 5 6

y

x

x y

0123456

b 4132025282928

b

Graph of the function: y = 4 + 10x – x2Graph of the function: y = 4 + 10x – x2

0

5

10

15

20

25

30

0 1 2 3 4 5 6

y

x

x y

0123456

c

4132025282928

c

Graph of the function: y = 4 + 10x – x2Graph of the function: y = 4 + 10x – x2

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7

Q C

01234567

a

a

20263444567086

104

y

x

A total cost function: C = 20 + 5Q + Q2A total cost function: C = 20 + 5Q + Q2

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7

b

y

x

Q C

01234567

b20263444567086

104

A total cost function: C = 20 + 5Q + Q2A total cost function: C = 20 + 5Q + Q2

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7

c

y

x

Q C

01234567

c

20263444567086

104

A total cost function: C = 20 + 5Q + Q2A total cost function: C = 20 + 5Q + Q2

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7

y

x

Q C

01234567

abcdefgh

20263444567086

104

cb

d

a

e

f

g

hA total cost function: C = 20 + 5Q + Q2A total cost function: C = 20 + 5Q + Q2

Q C

01234567

d

d

20263444567086

104

y

x

1

11

0

10

20

30

40

50

60

70

80

90

100

110

0 1 2 3 4 5 6 7

A total cost function: C = 20 + 5Q + Q2A total cost function: C = 20 + 5Q + Q2

DIFFERENTIATIONDIFFERENTIATION

• Elementary differentiation

– the rules

• Finding the maximum or minimum point of a curve

– differentiating the equation

– setting it equal to zero

• Is it a maximum or a minimum?

– differentiating a second time

• Elementary differentiation

– the rules

• Finding the maximum or minimum point of a curve

– differentiating the equation

– setting it equal to zero

• Is it a maximum or a minimum?

– differentiating a second time

-25

-20

-15

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

Q 0 1 2 3 4 5 6 7 8 9 10 -20 -9 0 7 12 15 16 15 12 7 0

A total profit function:= –20 + 12Q – Q 2A total profit function:= –20 + 12Q – Q 2

Q

Q 0 1 2 3 4 5 6 7 8 9 10 -20 -9 0 7 12 15 16 15 12 7 0

d / dQ = 0

Q

-25

-20

-15

-10

-5

0

5

10

15

20

0 1 2 3 4 5 6 7 8 9 10

A total profit function:= –20 + 12Q – Q 2A total profit function:= –20 + 12Q – Q 2

DIFFERENTIATIONDIFFERENTIATION

• Elementary differentiation

– the rules

• Finding the maximum or minimum point of a curve

– differentiating the equation

– setting it equal to zero

• Is it a maximum or a minimum?

– differentiating a second time

– the second derivative test

• Elementary differentiation

– the rules

• Finding the maximum or minimum point of a curve

– differentiating the equation

– setting it equal to zero

• Is it a maximum or a minimum?

– differentiating a second time

– the second derivative test

Un

em

plo

yme

nt (

%)

Unemployment

1989 1990 1991 1992

4

5

6

7

8

9

10

11

12

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3-10

-5

0

5

10

15When is good news really good?When is good news really good?

Un

em

plo

yme

nt (

%)

Ra

te of ch

ang

e in un

emplo

ymen

t (%)

Unemployment

Rate of changein unemployment

1989 1990 1991 1992

4

5

6

7

8

9

10

11

12

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3-10

-5

0

5

10

15When is good news really good?When is good news really good?

Un

em

plo

yme

nt (

%)

Ra

te of ch

ang

e in un

emplo

ymen

t (%)

Unemployment

Rate of changein unemployment

1989 1990 1991 1992

4

5

6

7

8

9

10

11

12

Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3 Q4 Q1 Q2 Q3-10

-5

0

5

10

15When is good news really good?When is good news really good?