ElasticityElasticity

1. A definition & determinants of elasticity1. A definition & determinants of elasticity• Price elasticityPrice elasticity

2. Elasticity & consumer expenditure2. Elasticity & consumer expenditure

3. Measurement of elasticity3. Measurement of elasticity• Arc methodArc method• Point methodPoint method

4. Other measures of elasticity 4. Other measures of elasticity

1. Definitions and determinants1. Definitions and determinants

If price rises, demand will fallIf price rises, demand will fall• By how much?By how much?

• Responsiveness of demand – elasticityResponsiveness of demand – elasticity

DefinitionsDefinitions ‘‘the the responsivenessresponsiveness of demand and of demand and

supply to changes in price’supply to changes in price’ Price elasticity of demand Price elasticity of demand ((PPdd))::

• ‘‘The responsiveness of quantity demanded The responsiveness of quantity demanded to a change in price’to a change in price’

figfigQuantity

Pric

e

O Q2 Q1

P1

S1

D

a

Market supply and demandMarket supply and demand

Quantity

Pric

e

O Q2 Q1

P1

P2

b

S2

S1

D

a

Market supply and demandMarket supply and demand

figfigQuantity

Pric

e

O Q3 Q2 Q1

P1

P2

P3

c

S2

S1

D

D'a

b

Market supply and demandMarket supply and demand

Determinants of Determinants of PPdd

Why does the price elasticity vary?Why does the price elasticity vary?• 1. number and closeness of substitute goods1. number and closeness of substitute goods

The larger the number of substitute goods (that satisfy the The larger the number of substitute goods (that satisfy the

same need), the greater (same need), the greater (PPdd) will be) will be E.g. holidays v. electricityE.g. holidays v. electricity

• 2. 2. the proportion of income spent on the goodthe proportion of income spent on the good If this is high, a price rise will force a substantial reduction in If this is high, a price rise will force a substantial reduction in

demanddemand

• 3. Time3. Time Time to adjust spending patternsTime to adjust spending patterns Short run – inelasticShort run – inelastic Long run - elasticLong run - elastic

2. Elasticity and consumer expenditure2. Elasticity and consumer expenditure

Total expenditure (TE) Total expenditure (TE)

= = P x Q P x Q

= Total Revenue (TR)= Total Revenue (TR)

See figureSee figure

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

0

1

2

3

4

0 1 2 3 4 5

Total expenditureTotal expenditure

Elasticity & consumer expenditureElasticity & consumer expenditure

What happens to TE (and TR) as price What happens to TE (and TR) as price changes?changes?

A) elastic demandA) elastic demand

• PP, Q, Q proportionately more (TE proportionately more (TE))

• P P , Q , Q proportionately more (TE proportionately more (TE ) )

P(£)

Q (millions of units per period of time)

0

aD4

20

Elastic demand between two pointsElastic demand between two points

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

Elasticity & consumer expenditureElasticity & consumer expenditure

B) inelastic demandB) inelastic demand

• PP, Q, Q proportionately less (TE proportionately less (TE ))

• P P , Q , Q proportionately less (TE proportionately less (TE ))

Inelastic demand between two pointsInelastic demand between two points

P(£)

Q (millions of units per period of time)

0

a

D

4

20

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

P

QO Q1

P1

P2

D

b

a

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

P

QO Q1

P1

Q2

Dba

Infinitely elastic demand (PD = )

P

QO 40

20

100

D8

a

b

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

3. Measurement of elasticity3. Measurement of elasticity

Elasticity varies along the demand ( & supply) Elasticity varies along the demand ( & supply) curvecurve Price-elastic (>1)Price-elastic (>1) price-inelastic(0-1)price-inelastic(0-1) unitary (=1)unitary (=1)

(1) arc method (between two points on D)(1) arc method (between two points on D) price elasticity of demand: price elasticity of demand: Q/QQ/Q ÷ ÷ P/PP/P using the average or 'mid-point' methodusing the average or 'mid-point' method

Q/average QQ/average Q ÷ ÷ P/average PP/average P

0

2

4

6

8

10

0 10 20 30 40 50

P (£)

Q (000s)

m

n

Q Pmid Q mid PPd =

Demand

Measuring elasticity using the arc methodMeasuring elasticity using the arc method

0

2

4

6

8

10

0 10 20 30 40 50

P (£)

Q (000s)

m

n

Q Pmid Q mid PPd =

10 2 15 7=

= 10/15 x 7/2 = 70/30= 7/3 = 2.33

Demand

Measuring elasticity using the arc methodMeasuring elasticity using the arc method

Measurement of elasticityMeasurement of elasticity

(2) The Point Method(2) The Point Method• Price elasticity of demandPrice elasticity of demand

dQ / dP x P / QdQ / dP x P / Q

• ‘‘d’ – infinitesimally small change (see calculus)d’ – infinitesimally small change (see calculus)

• dQ / dP – rate of change of quantity demanded dQ / dP – rate of change of quantity demanded with respect to pricewith respect to price

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

= dQ/dP i.e. invert dP/dQ (-50/100)

= 100/50 =-2 = /40) = -2 (0.75) = 1.5

Measuring elasticity at a pointMeasuring elasticity at a point

4. Other measures of elasticity4. Other measures of elasticity

Income elasticity of demandIncome elasticity of demand ‘…‘…the responsiveness of demand to a change in the responsiveness of demand to a change in

consumer income, Y.’consumer income, Y.’• Luxuries (>1), necessities (0-1),inferior goods(<0)Luxuries (>1), necessities (0-1),inferior goods(<0)

Cross-price elasticity of demandCross-price elasticity of demand ‘…‘…responsiveness of demand for one product to a responsiveness of demand for one product to a

change in the price of another product.’change in the price of another product.’ Substitutes or complementsSubstitutes or complements

Price elasticity of supplyPrice elasticity of supply Definition & determinants?Definition & determinants?