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Elasticity and its Application
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Definition of Elasticity
• Elasticity measures the responsiveness of one variable to changes in another variable
• How much does Y (dependent variable) change if X changes by 1% (independent variable)
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Examples
• Price elasticity of demand
• Income elasticity of demand
• Cross price elasticity of demand
• Price elasticity of supply
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Price Elasticity of Demand(PD)
• Responsiveness of quantity demanded to a change in price
• The percentage change in quantity demanded, resulting from a 1% change in price
PD = %QD / %P
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Pri
ce
O Q3 Q2 Q1
P1
P2
P3
c
S2
S1
D
D'
a
b The effect on price of a shift in supply
depends on the responsiveness of
demand to a change in price.
Market supply and demand
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Determinants of PD
• Availability of close substitutes
• Necessities versus luxuries
• Definition of the market
• Time horizon
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0
2
4
6
8
10
0 10 20 30 40 50
P (£)
Q (000s)
Demand
Measuring elasticity using the arc methodMeasuring elasticity using the arc method
m
n
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0
2
4
6
8
10
0 10 20 30 40 50
P (£)
Q (000s)
Q P
mid Q mid PPd =
Demand
m
n
Q = 10
P = –2
Mid P
7
Mid Q15
Measuring elasticity using the arc methodMeasuring elasticity using the arc method
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0
2
4
6
8
10
0 10 20 30 40 50
P (£)
Q (000s)
Q P
mid Q mid PPd =
10 2 15 7
=
Demand
m
n
Q = 10
P = –2
Mid P
7
Mid Q15
Measuring elasticity using the arc methodMeasuring elasticity using the arc method
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0
2
4
6
8
10
0 10 20 30 40 50
P (£)
Q (000s)
Q P
mid Q mid PPd =
10 2 15 7
=
= 2.33
Demand
m
n
Q = 10
P = –2
Mid P
7
Mid Q15
Measuring elasticity using the arc methodMeasuring elasticity using the arc method
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PD &Consumer Expenditure
• Total Consumer Expenditure / Firm’s total revenue
TE (TR) = P x Q
• Applications to pricing decisions
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Elastic Demand
• Elasticity greater than 1 (PD
• Effect of price change
– P rises: TE falls
– P falls: TE rises
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P(£)
Q (millions of units per period of time)
0
aD
Elastic demand between two pointsElastic demand between two points
Expenditure fallsas price rises
4
20
5
10
b
Expenditure risesas price falls
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Inelastic Demand
• Elasticity less than 1 (PD• Effects of a price change
– P rises: TE rises
– P falls: TE falls
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a4
20
P(£)
Q (millions of units per period of time)
0
D
Expenditure risesas price rises
Inelastic demand between two pointsInelastic demand between two points
8
15
c Expenditure fallsas price falls
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Special cases
• PD = 0 (Perfectly Inelastic Demand)
• PD = (Perfectly Elastic Demand)
• PD = 1 (Unit Elastic Demand)
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P2
P
QO Q1
P1
D
b
a
Perfectly inelastic demand (PD = 0)Perfectly inelastic demand (PD = 0)
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Q2
P
QO Q1
P1 Da b
Perfectly elastic demand (PD = )Perfectly elastic demand (PD = )
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P
QO 40
20
D
100
8
a
Unit elastic demand (PD = 1)
b
Expenditure stays thesame as price changes
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Price Elasticity of Supply(PS)
• Responsiveness of quantity supplied to a change in price
• The percentage change in quantity supplied, resulting from a 1% change in price
PS = %QS / %P
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Price elasticity of supplyPrice elasticity of supplyP
Q O
P0
Q0
S1
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P
Q O
P1
Q2
P0
Q0 Q1
S2
S1
Price elasticity of supplyPrice elasticity of supply
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Income elasticity ofdemand (YD)
• Responsiveness of demand to a change in consumer incomes
• The percentage change in quantity demanded, resulting from a 1% change in consumers income
YD = %QD / %Y
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Income elasticity ofdemand (YD)
• Normal goods:– Positive income elasticity– If the income increases (decreases) the
quantity demanded increases (decreases)– Example: Clothing, wine
• Inferior goods:– Negative income elasticity– If the income increases (decreases) the
quantity demanded decreases (increases)– Example: public transport
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Cross-Price Elasticity ofDemand (CDab)
• The responsiveness of demand for one good to a change in the price of another.
• The percentage change in quantity demanded of one good, resulting from a 1% change in price of another good.
CDab = %QDa / %Pb
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Cross-Price Elasticity ofDemand (CDab)
• Substitutes:– Positive cross-price elasticity– If the price of good B increases the demand for good
A increases– Example: hamburgers & burritos
• Complements:– Negative income elasticity– If the price of good B increases the demand for good
A decreases– Example: crude oil & cars
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Why are elasticity useful?
• Managers– Price elasticity of demand: Pricing strategy– Cross-price elasticity of demand: Defining the
company’s market– Income elasticity: Forecast long-term demand
• Government policy– Price elasticity of demand: Decision on Tax rate– Cross-price elasticity of demand: Competitive forces
in a market
