Chapter 5

Elasticity of

Demand and Supply

© 2009 South-Western/Cengage Learning

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Price Elasticity of Demand

ElasticityA measure of the responsiveness of Qd or Qs to a change in price or other economic variable

Price elasticity of demand% change in Qd for a 1% change in price

Price Elasticity of Demand

• εd = %ΔQd / %ΔP

= ΔQd / Qd

ΔP / P

= ΔQd x P

ΔP Qd

• Law of demand

• εd negative

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Categories of Elasticities

|ε| between 0 and 1• Inelastic

|ε| greater than 1• Elastic

|ε| = 1• Unit elastic

|ε| = infinite• Perfectly elastic

|ε| = 0• Perfectly inelastic 4

Midpoint FormulaUse the average Q and average P in the elasticity formula:

average Q = (Q1 + Q2) / 2

average P = (P1 + P2) / 2

ε = ΔQ / (average Q)

ΔP / (average P)

= (Q1 - Q2) / (Q1 + Q2)

(P1 - P2) / (P1 + P2)

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Elasticity and Total Revenue

• Total revenue = price * quantity• TR= p * q• As p decreases

– If D elastic, TR increases

– If D inelastic, TR decreases

– If D unit elastic, TR constant

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Price Elasticity and the Linear D curve

• Linear D curve– Constant slope

– Different elasticity

– D becomes less elastic as we move downward

• D upper half: elastic• D lower half: inelastic• D midpoint: unit elastic

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Exhibit 2Demand, price elasticity and total revenue

8

D

90

60

10

70

Pric

e pe

r un

it

$100

80

50403020

b

a

de

800500200100 Quantity per period1,000 0 900

Tot

al r

even

ue

$25,000

500 Quantity per period1,000 0

(a) Demand and price elasticity

(b) Total revenue

Total

revenue

Unit elastic, ED =1

Elastic, ED >1

Inelastic, ED <1

Where D is elastic,

a lower P increases TR

Where D is inelastic,

a lower P decreases TR

TR reaches a maximum

at the rate of output

where D is unit elastic

c

Exhibit 4Summary of price elasticity of demand

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Effects of a 10 percent increase in price

Absolute value of price elasticity

Type of demand

What happens toquantity demanded

What happens to total revenue

0 < εd < 1 Inelastic Drops by less than 10 percent

Increases by less than 10 percent

εd = 1 Unit elastic Drops by 10 percent

No change

1 < εd <∞ Elastic Drops by more than 10 percent

Decreases

Determinants of Price Elasticity of D

• εd is greater:

– The greater the availability of substitutes, and the more similar the substitutes

– The more important the good as a share of the consumer’s budget

– The longer the period of adjustment (time)

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Exhibit 5Demand becomes more elastic over time

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Dw

Pric

e pe

r un

it

$1.25

1.00

Dm

Quantity

per day

95 10075500

Dy

e

Dw: one week after the price increase

Dm: one month after the price increase

Dy: one year after the price increase

Dy is more elastic than Dm , which is more elastic than Dw

Elasticity Estimates

• Short run– Consumers have little time to adjust

• Long run– Consumers can fully adjust to a price

change

• Demand is more elastic in the long run

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Exhibit 6Selected price elasticities of D (absolute values)

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Product Short run Long run

Cigarettes (among adults)Electricity (residential)Air travelMedical care and hospitalizationGasolineMilkFish (cod)WineMoviesNatural gas (residential) AutomobilesChevrolets

-0.10.10.30.40.40.50.70.91.41.9-

0.41.92.40.91.5--

1.23.72.12.24.0

Income Elasticity of Demand

% change in Qd for a 1% change in income

εI = %ΔQd / %ΔI

•Normal goods (Qd increases when I increases)

– Positive income elasticity

•Inferior goods (Qd decreases when I increases)

– Negative income elasticity

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Income Elasticity of Demand

• Normal goods– Income inelastic

• Elasticity between 0 and 1• Necessities

– Income elastic• Elasticity > 1• Luxuries

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Exhibit 10Selected income elasticities of demand

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ProductIncomeElasticity Product

IncomeElasticity

WinePrivate educationAutomobilesOwner-occupied housingFurnitureDental serviceRestaurant mealsSpirits (‘hard’ liquor)ShoesChickenClothing

5.032.462.451.491.481.421.401.211.101.060.92

Physicians’ servicesCoca-ColaBeefFoodCoffeeCigarettesGasoline and oilRental housingPorkBeerFlour

0.750.680.620.510.510.500.480.430.18-0.09-0.36

Cross-Price Elasticity of Demand

% change in Q demanded of one good for a 1% change in the price of another good– εX,Y = %ΔQX / %ΔPY

– If positive: X and Y are substitutes

– If negative: X and Y are complements

– If zero: X and Y are unrelated

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Price Elasticity of Supply

Price elasticity of supply% change in Qs for a 1 percent change

in price

εs = %ΔQs / %ΔP

•Law of supply

•εs positive

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Constant Elasticity Supply Curves

• Perfectly elastic S curve

– Horizontal; εs = ∞

– Producers supply 0 at a price below P

• Perfectly inelastic S curve

– Vertical; εs = 0

– Goods in fixed supply

• Unit-elastic S curve– %∆p = %∆q – S is a ray from the origin 19

Determinants of Supply Elasticity

• εs is greater:

– cost and feasibility of storage

– production process

– the longer the period of adjustment (time)

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Exhibit 9Supply becomes more elastic over time

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Sw

Pric

e pe

r un

it

1.00

$1.25

Quantity per day110 2000 100 140

Sm

Sy

Sw: one week after the price increase

Sm: one month after the price increase

Sy: one year after the price increase

Sw is less elastic than Sm , which is less elastic than Sy

Price Elasticity and Tax Incidence

• Tax– Decrease in S by the amount of tax

• S shifts upward by the tax

• Tax incidence– distribution of the tax burden

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Price Elasticity and Tax Incidence

• The more price elastic the D:– The more tax producers pay

– The less tax consumers pay

• The more elastic the S:– The less tax producers pay

– The more tax consumers pay

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Price Elasticity and Tax Incidence

• The issue of tax incidence depends on the relationship between εd and εs

If |εd| > εs

producers bear more of the burden of the tax

If |εd| < εs

consumers bear more of the burden of the tax

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