Chapter 2 Elasticity P50-63 Chapter 2 Elasticity P50-63.

Chapter 2ElasticityP50-63

Chapter 2ElasticityP50-63

ELASTICITYELASTICITY

• Defining elasticityDefining elasticity– the the responsivenessresponsiveness of demand and supply of demand and supply

– Firm might want a measure of how demand will Firm might want a measure of how demand will respond to an increase in pricerespond to an increase in price

– Government might want a measure of Government might want a measure of sensitivity of petrol demand to a tax increasesensitivity of petrol demand to a tax increase

– Sainsbury’s might want to know how supply of Sainsbury’s might want to know how supply of organic veg will respond to a price fall.organic veg will respond to a price fall.

Market supply and demandMarket supply and demand

Quantity

Pri

ce

O Q1

P1

a

S1

D

Quantity

Pri

ce

O Q2 Q1

P1

P2

b

S2

S1

D

a


Quantity

Pri

ce

O Q2 Q1

P1

P2

S2

S1

D

D'

a

b


Quantity

Pri

ce

O Q3 Q2 Q1

P1

P2

P3

c

S2

S1

D

D'

a

b



• ElasticityElasticity– use of proportionate or percentage changesuse of proportionate or percentage changes

• E.g.Price elasticity of demand (E.g.Price elasticity of demand (PPdd): ):

• Some books write Some books write pp

pricepriceinchange

QuantityQuantityinchange

P pd



• E.g.Price elasticity of demand (E.g.Price elasticity of demand (PPdd): ):

• Some books write Some books write pp

priceinchange

QuantityinchangeP pd %

%


•

priceinchange

QuantityinchangeP pd %

%

pricepriceinchange

QuantityQuantityinchange

P pd

0

4

8

12

16

20

0 100 200 300 400 500 600 700 800Quantity (tonnes: 000s)

Pri

ce (

pen

ce p

er k

g)

Demand

Price(pence per kg)

4

8

12

16

20

Market demand(tonnes 000s)

700

500

350

200100

A

B

C

D

E

Point

A

B

C

D

E

Market demand for potatoes Market demand for potatoes (monthly)(monthly)

Elasticity FormulaElasticity Formula

0

01

0

01

PPP

QQQ

P Dpd

A move from B to A…. A move from B to A….

0

01

0

01

PPP

QQQ

P Dpd

Price(pence per kg)

4

8

12

16

20


700

500

350

200100

A

B

C

D

E

Point

884

500500700

Dpd

P

Price(pence per kg)

4

8

12

16

20


700

500

350

200100

A

B

C

D

E

Point A move from B to A…. A move from B to A…. A move from B to A…. A move from B to A….

84

500200

D

pdP

2152

D

pdP

1

2.5

2

D

pdP

1

2.5

2 D

pdP

5

4 D

pdP



– the sign (positive or negative)the sign (positive or negative)

– the value (greater or less than one)the value (greater or less than one)

– Here Here

5

4 D

pdP

–Sign is negative and less than 1Sign is negative and less than 1

–We say that the demand curve is inelastic at this pointWe say that the demand curve is inelastic at this point


• If the elasticity of demand was If the elasticity of demand was

• Greater than 1 Greater than 1 - we would say it was - we would say it was elasticelastic..

• Less than 1 – InelasticLess than 1 – Inelastic

• Note Note elasticity of demand is negativeelasticity of demand is negative (usually) so (usually) so when we say it is greater than one we mean the when we say it is greater than one we mean the ABSOLUTE number is greater than oneABSOLUTE number is greater than one

• E.g. 4 > 1 - so more elasticE.g. 4 > 1 - so more elastic

• What does inelastic demand mean?What does inelastic demand mean?• Consider Consider Total ExpenditureTotal Expenditure on a good on a good• Total ExpenditureTotal Expenditure = ( = (P x QP x Q))

Total expenditure or Total RevenueTotal expenditure or Total Revenue

P(£)

Q (millions of units per period of time)

D

0

1

2

3

4

0 1 2 3 4 5

P(£)


D

0

1

2

3

4

0 1 2 3 4 5


0

1

2

3

4

0 1 2 3 4 5

Consumers’ total expenditure Consumers’ total expenditure ==

firms’ total revenuefirms’ total revenue==

£2 x 3m = £6m£2 x 3m = £6m

P(£)


D


P =£2 and Q = 3mP =£2 and Q = 3m


• Price elasticity of demand and consumer Price elasticity of demand and consumer expenditure (expenditure (P x QP x Q))– effects of a price change on expenditure: effects of a price change on expenditure:

elastic demandelastic demand

P(£)


0

aD4

20

Elastic demand between two pointsElastic demand between two points

TR=

4x20=80

P(£)


0

b

aD

5

4

10 20

Expenditure fallsas price rises

Elastic demand between two pointsElastic demand between two points

5x10=50

TR=

4x20=80



elastic demandelastic demand– effects of a price change on expenditure: effects of a price change on expenditure:

inelastic demandinelastic demand

Inelastic demand between two pointsInelastic demand between two points

P(£)


0

a

D

4

20

TR=

4x20=80

P(£)


0

c

a

D

8

4

15 20

Expenditure risesas price rises

Inelastic demand between two pointsInelastic demand between two points

TR=

4x20=80

8x15=120

ElasticityElasticity

• Elastic demand: Elastic demand:

• Total RevenueTotal Revenue fallsfalls when when P risesP rises

• ININelastic demand: elastic demand:

• Total RevenueTotal Revenue risesrises when when P risesP rises



– the sign (positive or negative)the sign (positive or negative)

– the value (greater or less than one)the value (greater or less than one)

• Price elasticity of demand (Price elasticity of demand (PPdd):):

DeterminantsDeterminants of Elasticity:of Elasticity:

–number and closeness of substitute goodsnumber and closeness of substitute goods

–the proportion of income spent on the goodthe proportion of income spent on the good

–timetime



elastic demandelastic demand– effects of a price change on expenditure: effects of a price change on expenditure:

inelastic demandinelastic demand– extreme casesextreme cases

Totally inelastic demand (Totally inelastic demand (PPDD = 0)= 0)

P

QO Q1

P1

D

a

P

QO Q1

P1

P2

D

b

a



0

01

0

01

PPP

QQQ

P Dpd


0

01

0

00

PPP

QQQ

P pd


0

0

01

0

00

PPP

QQQ

P pd

P

QO Q1

P1

P2

D

b

a


Note TR has still risen, but PPDD

= 0= 0

Infinitely elastic demand (PD = )Infinitely elastic demand (PD = )

P

QO Q1

P1 Da

P

QO Q1

P1

Q2

Dba

Infinitely elastic demand (PD = )Infinitely elastic demand (PD = )

Why Infinitely Elastic?Why Infinitely Elastic?

0

01

0

01

PPP

QQQ

P pd


0

00

0

01

PPP

QQQ

P pd


0

0

01

0P

QQQ

P pd


00

01

QQQ

P pd


00

01

Q

QQ

P pd

P

QO Q1

P1

Q2

Dba

Note strictly speaking this should be a negative number, i.e.,

Infinitely elastic demand (PD = - )



..and total revenue rises when p falls!

P

QO Q1

P1

Q2

Dba





..really saying p falls by teeny weeny tiny amount!

P

QO Q1

P1

Q2

Dba





..OR total revenue falls when p rises!

Unit elastic demand (Unit elastic demand (PPDD = -1)= -1)

P

QO 40

20

D

a

This is a very special case

We will see this in more detail later

P

QO 40

20

100

D8

a

b


TR=

20 x 40

=800

8 x 100=800

P

QO 40

20

100

D8

a

b


TR=

20 x 40

=800

8 x 100=800

When PPDD = -1, Total = -1, Total

Revenue Revenue stays the stays the same when P risessame when P rises


• In Economics instead of writing QIn Economics instead of writing Q1 1 - Q- Q00 , we , we

use the notation use the notation QQ1 1 - Q- Q00= = QQ, ,

• wherewhere means means ‘‘change inchange in’’

• So:So:

0

01

0

01

PPP

QQQ

Pd

0

0

PPQQ

Arc v Point ElasticityArc v Point Elasticity

• Earlier we calculated the elasticity when Earlier we calculated the elasticity when moving between B and A. The answer wasmoving between B and A. The answer was

• -4/5-4/5

• You might expect that moving from A to B You might expect that moving from A to B would produce the same result. Let’s would produce the same result. Let’s check.check.

A move from A to B…. A move from A to B….

0

0

PPQQ

P pd

Price(pence per kg)

4

8

12

16

20


700

500

350

200100

A

B

C

D

E

Point

448

700700500

pdP

Price(pence per kg)

4

8

12

16

20


700

500

350

200100

A

B

C

D

E

Point A move from B to A…. A move from B to A…. A move from B to A…. A move from B to A….

1172

4472

pdP

A move from B to A…. A move from B to A…. A move from B to A…. A move from B to A….

7

2

1

1.

7

2

1172

pdP


7

2 pd

P


Whoops, before we found that elasticity of demand was –4/5 now

What is going on here.


• The answer is to measure elasticity by the The answer is to measure elasticity by the arcarc method: method:

• arc elasticityarc elasticity– using the average or 'mid-point'using the average or 'mid-point'

Eg. In the term (QEg. In the term (Q1 1 - Q- Q00) / ) / QQ**

• Instead of using Instead of using QQ00 or or QQ11 under the line, we under the line, we

use the mid-point between the two. use the mid-point between the two.

0

4

8

12

16

20

0 100 200 300 400 500 600 700 800Quantity (tonnes: 000s)

Pri

ce (

pen

ce p

er k

g)

Demand

A

B

C

D

E

Arc MethodArc Method

PmidPQmidQ

Pd

64

600200

dP

0

4

8

12

16

20

0 100 200 300 400 500 600 700 800

Quantity (tonnes: 000s)

Pri

ce (

pen

ce p

er k

g)

Demand

A

B

C

D

E

Market demand for potatoes Market demand for potatoes (monthly)(monthly)

2

1

4

2

4

6.6

2

64

600200

d

d

P

P

• Now since using mid-point elasticity is the Now since using mid-point elasticity is the same whether we are moving from point A same whether we are moving from point A to B or point B to A.to B or point B to A.

• From now on when we write P or Q we will From now on when we write P or Q we will mean the mid-point. mean the mid-point.

PPQQ

Pd

We can simplify the formula for We can simplify the formula for elasticity to :elasticity to :

PPQQ

Pd

P

P

Q

Q

.Q

P

P

Q.

Elasticity along a straight line demand curve.Elasticity along a straight line demand curve.

P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

Q

P

P

QP

d.


P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

52

10

P

Q

Note15

7.2

10

dP


P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

33.23

7

dP

15

7.5

dP

Now look lower down the lineNow look lower down the line

P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

Q

P

P

QP

d.


P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

35

3.2

10

dP

52

10

P

Q

Note


P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

35

3.5

dP

428.07

3

dP

So along the line the elasticity variesSo along the line the elasticity varies

P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

Elastic

INElastic

So along the line the elasticity variesSo along the line the elasticity varies

P (£)

Q (000s)

Demand

0

2

4

6

8

10

0 10 20 30 40 50

Highly Elastic

Inelastic

Portion

Which demand curve is the more Which demand curve is the more elastic?elastic?

P (£)

Q Q

Can’t really say – elasticity varies along the length. So it depends

P (£)


P (£)

Q Q

Suppose instead both demand curves were on the same graph

P (£)


P (£)

Q Q

P (£)



P (£)

Q


Now we have a common point, so we can say flatter line is more elastic

.. It has the smaller slope


• Measurement of elasticity: We also use a Measurement of elasticity: We also use a concept called point elasticityconcept called point elasticity

• If you haven’t A-level maths you can come If you haven’t A-level maths you can come back to this is a few weeks. Ignore for now.back to this is a few weeks. Ignore for now.

– the formula for price elasticity of demand: the formula for price elasticity of demand: ddQ/Q/ddP x P/QP x P/Q

– the elasticity of a straight-line demand ‘curve’ the elasticity of a straight-line demand ‘curve’ (constant d(constant dQQ/d/dPP))

– the elasticity of a curved demand curve: dthe elasticity of a curved demand curve: dQQ/d/dPP is the tangent to the curveis the tangent to the curve

Measuring elasticity at a pointMeasuring elasticity at a point

P

Q

0

D

r

Pd = (1 / slope) x P/Q

P

Q

50

30

0 40 100

D

r



P

Q

50

30

0 40 100

D

r


= 100/50 x 30/40


P

Q

50

30

0 40 100

D

r


= 100/50 x 30/40

= 60/40


P

Q

50

30

0 40 100

D

r


= 100/50 x 30/40

= 60/40

= 1.5



• Price elasticity of supplyPrice elasticity of supply

– measurementmeasurement

0

0

PP

QQ

P S

S

spS

0

4

8

12

16

20

0 100 200 300 400 500 600 700 800

Pri

ce (

pen

ce p

er k

g)

Quantity (tonnes: 000s)

Supply

a

b

c

d

e

P

4 8121620

Q

100200350530700

abcde

Market supply of potatoes Market supply of potatoes (monthly)(monthly)


0

0

PP

QQ

P S

S

spS

P

4 8121620

Q

100200350530700

abcde


64150100

spSP

P

4 8121620

Q

100200350530700

abcde


12

3.3

2

4

6.

15

10

64150100

SP

P

4 8121620

Q

100200350530700

abcde


1 DpSP

So the Elasticity of Supply in this example =1 and it is positive

However, once again, it is possible to have elastic and inelastic

demand curves.

Supply in different time periods Supply in different time periods reflects different Elasticitiesreflects different Elasticities

D1

P1

Q1

P

Q O

a

D1

D2

P1

Q1

P

Q O

a

Supply in different time periodsSupply in different time periods

Suppose Demand rises,

How will supply react?

D1

D2

Si

P1

P2

Q1

P

Q O

a

b


Very Short Run

Supply is Inelastic

D1

D2

Si SS

P1

P3

P2

Q1 Q3

P

Q O

a

b

c


Medium Run

Supply is More Elastic

D1

D2

Si SS

SL

P1

P4

P3

P2

Q1 Q3 Q4

P

Q O

a

b

c

d


Long Run


• Income elasticity of demand (Income elasticity of demand (eta)eta)

• Measures the responsiveness of demand to Measures the responsiveness of demand to changes in incomechanges in income

YY

QQ

Y

D

DpD


DDpp> 0 Normal Good

• 0-1 Normal Necessity

• >1 Luxury or superior good

• spending proportionally more as Income rises

DDpp < 0 Inferior Good


• Cross-price elasticity of demandCross-price elasticity of demand

– Measures the responsiveness of a good to Measures the responsiveness of a good to changes in the price of other goodschanges in the price of other goods

B

B

A

DA

Dp

ppQQ

CABABD


• Cross-price elasticity of demandCross-price elasticity of demand

– Measures the responsiveness of a good to Measures the responsiveness of a good to changes in the price of other goodschanges in the price of other goods

DpABABD

C • If the elasticity is a If the elasticity is a positive positive number number

• A & B are A & B are substitutessubstitutes

• If the elasticity is a If the elasticity is a negativenegative number number

• A & B are A & B are complementscomplements

SUMMARYSUMMARY

• In this series of lectures based on Ch.2 of In this series of lectures based on Ch.2 of Sloman we have learnt aboutSloman we have learnt about

– The demand curveThe demand curveAnd Movements along versus Shifts inAnd Movements along versus Shifts in

– The supply curveThe supply curveAnd Movements along versus Shifts inAnd Movements along versus Shifts in

– Determination of Equilibrium :- D=SDetermination of Equilibrium :- D=SThe Effects of a variety of shiftsThe Effects of a variety of shifts

– ElasticityElasticityOf Demand, Supply, Income and Cross PriceOf Demand, Supply, Income and Cross Price

Chapter 2 Elasticity P50-63 Chapter 2 Elasticity P50-63.

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Transcript of Chapter 2 Elasticity P50-63 Chapter 2 Elasticity P50-63.