Post on 26-Dec-2015
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
Market supply and demandMarket supply and demand
Quantity
Pri
ce
O Q2 Q1
P1
P2
S2
S1
D
D'
a
b
Market supply and demandMarket supply and demand
Quantity
Pri
ce
O Q3 Q2 Q1
P1
P2
P3
c
S2
S1
D
D'
a
b
Market supply and demandMarket supply and demand
ELASTICITYELASTICITY
• 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
ELASTICITYELASTICITY
• 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
priceinchange
QuantityinchangeP pd %
%
ELASTICITYELASTICITY
•
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
Market demand(tonnes 000s)
700
500
350
200100
A
B
C
D
E
Point
884
500500700
Dpd
P
Price(pence per kg)
4
8
12
16
20
Market demand(tonnes 000s)
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
ELASTICITYELASTICITY
• ElasticityElasticity– use of proportionate or percentage changesuse of proportionate or percentage changes
– 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
ELASTICITYELASTICITY
• 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(£)
Q (millions of units per period of time)
D
0
1
2
3
4
0 1 2 3 4 5
Total expenditure or Total RevenueTotal expenditure or Total Revenue
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(£)
Q (millions of units per period of time)
D
Total expenditure or Total RevenueTotal expenditure or Total Revenue
P =£2 and Q = 3mP =£2 and Q = 3m
ELASTICITYELASTICITY
• 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(£)
Q (millions of units per period of time)
0
aD4
20
Elastic demand between two pointsElastic demand between two points
TR=
4x20=80
P(£)
Q (millions of units per period of time)
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
ELASTICITYELASTICITY
• 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– 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(£)
Q (millions of units per period of time)
0
a
D
4
20
TR=
4x20=80
P(£)
Q (millions of units per period of time)
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
ELASTICITYELASTICITY
• ElasticityElasticity– use of proportionate or percentage changesuse of proportionate or percentage changes
– 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
ELASTICITYELASTICITY
• 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– 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
Totally inelastic demand (Totally inelastic demand (PPDD = 0)= 0)
Elasticity FormulaElasticity Formula
0
01
0
01
PPP
QQQ
P Dpd
Elasticity FormulaElasticity Formula
0
01
0
00
PPP
QQQ
P pd
Elasticity FormulaElasticity Formula
0
0
01
0
00
PPP
QQQ
P pd
P
QO Q1
P1
P2
D
b
a
Totally inelastic demand (Totally inelastic demand (PPDD = 0)= 0)
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
Why Infinitely Elastic?Why Infinitely Elastic?
0
00
0
01
PPP
QQQ
P pd
Why Infinitely Elastic?Why Infinitely Elastic?
0
0
01
0P
QQQ
P pd
Why Infinitely Elastic?Why Infinitely Elastic?
00
01
QQQ
P pd
Why Infinitely Elastic?Why Infinitely Elastic?
00
01
Q
P pd
P
QO Q1
P1
Q2
Dba
Note strictly speaking this should be a negative number, i.e.,
Infinitely elastic demand (PD = - )
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
Note strictly speaking this should be a negative number, i.e.,
Infinitely elastic demand (PD = - )
Note strictly speaking this should be a negative number, i.e.,
Infinitely elastic demand (PD = - )
..really saying p falls by teeny weeny tiny amount!
P
QO Q1
P1
Q2
Dba
Note strictly speaking this should be a negative number, i.e.,
Infinitely elastic demand (PD = - )
Note strictly speaking this should be a negative number, i.e.,
Infinitely elastic demand (PD = - )
..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
Unit elastic demand (Unit elastic demand (PPDD = -1)= -1)
TR=
20 x 40
=800
8 x 100=800
P
QO 40
20
100
D8
a
b
Unit elastic demand (Unit elastic demand (PPDD = -1)= -1)
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
ELASTICITYELASTICITY
• 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
Market demand(tonnes 000s)
700
500
350
200100
A
B
C
D
E
Point
448
700700500
pdP
Price(pence per kg)
4
8
12
16
20
Market demand(tonnes 000s)
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
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 pd
P
A move from B to A…. A move from B to A…. A move from B to A…. A move from B to A….
Whoops, before we found that elasticity of demand was –4/5 now
What is going on here.
ELASTICITYELASTICITY
• 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.
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.
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
52
10
P
Q
Note15
7.2
10
dP
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
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.
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
35
3.2
10
dP
52
10
P
Q
Note
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
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 (£)
Which demand curve is the more Which demand curve is the more elastic?elastic?
P (£)
Q Q
Suppose instead both demand curves were on the same graph
P (£)
Which demand curve is the more Which demand curve is the more elastic?elastic?
P (£)
Q Q
P (£)
Suppose instead both demand curves were on the same graph
Which demand curve is the more Which demand curve is the more elastic?elastic?
P (£)
Q
Suppose instead both demand curves were on the same graph
Now we have a common point, so we can say flatter line is more elastic
.. It has the smaller slope
ELASTICITYELASTICITY
• 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
Pd = (1 / slope) x P/Q
Measuring elasticity at a pointMeasuring elasticity at a point
P
Q
50
30
0 40 100
D
r
Pd = (1 / slope) x P/Q
= 100/50 x 30/40
Measuring elasticity at a pointMeasuring elasticity at a point
P
Q
50
30
0 40 100
D
r
Pd = (1 / slope) x P/Q
= 100/50 x 30/40
= 60/40
Measuring elasticity at a pointMeasuring elasticity at a point
P
Q
50
30
0 40 100
D
r
Pd = (1 / slope) x P/Q
= 100/50 x 30/40
= 60/40
= 1.5
Measuring elasticity at a pointMeasuring elasticity at a point
ELASTICITYELASTICITY
• Price elasticity of supplyPrice elasticity of supply
– measurementmeasurement
0
0
PP
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)
ELASTICITYELASTICITY
0
0
PP
P S
S
spS
P
4 8121620
Q
100200350530700
abcde
ELASTICITYELASTICITY
64150100
spSP
P
4 8121620
Q
100200350530700
abcde
ELASTICITYELASTICITY
12
3.3
2
4
6.
15
10
64150100
SP
P
4 8121620
Q
100200350530700
abcde
ELASTICITYELASTICITY
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
Supply in different time periodsSupply in different time periods
Very Short Run
Supply is Inelastic
D1
D2
Si SS
P1
P3
P2
Q1 Q3
P
Q O
a
b
c
Supply in different time periodsSupply in different time periods
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
Supply in different time periodsSupply in different time periods
Long Run
ELASTICITYELASTICITY
• 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
Y
D
DpD
ELASTICITYELASTICITY
DDpp> 0 Normal Good
• 0-1 Normal Necessity
• >1 Luxury or superior good
• spending proportionally more as Income rises
DDpp < 0 Inferior Good
ELASTICITYELASTICITY
• 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
ELASTICITYELASTICITY
• 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