Learning Objectives• Define and measure elasticity• Apply concepts of price elasticity,

cross-elasticity, and income elasticity• Understand determinants of elasticity• Show how elasticity affects revenue

• P & Q are inversely related by the law of demand so E is always negative– The larger the absolute value of E, the more sensitive buyers are to

a change in price

Price Elasticity of Demand (E)

•% Q

E% P

• Measures responsiveness or sensitivity of consumers to changes in the price of a good

Calculating Price Elasticity of Demand

• Price elasticity can be measured at an interval (or arc) along demand, or at a specific point on the demand curve– If the price change is relatively small, a point

calculation is suitable– If the price change spans a sizable arc along

the demand curve, the interval calculation provides a better measure

Computation of Elasticity Over an Interval

• When calculating price elasticity of demand over an interval of demand, use the interval or arc elasticity formula

Q PE

P Q

Average

Average

So, arc price elasticity of demand =

• Ep = Coefficient of arc price elasticity

• Q1 = Original quantity demanded

• Q2 = New quantity demanded

• P1 = Original price

• P2 = New price

2/)(2/)( 21

12

21

12

PP

PP

QQ

QQEp

Computation of Elasticity at a Point

• When calculating price elasticity at a point on demand, multiply the slope of demand (Q/P), computed at the point of measure, times the ratio P/Q, using the values of P and Q at the point of measure

• Method of measuring point elasticity depends on whether demand is linear or curvilinear

The Price Elasticity of Demand

• Point elasticity: measured at a given point of a demand (or a supply) curve.

1

1

εP

PdQx

dP Q=

The Price Elasticity of Demand

The point elasticity of a linear demand function can be expressed as:

1

1

Q

P

P

Q

p

The Price Elasticity of Demand

• Some demand curves have constant elasticity over the relevant range

• Such a curve would look like:Q = aP-b

where –b is the elasticity coefficient• This equation can be converted to

linear by expressing it in logarithms:log Q = log a – b(log P)

The Price Elasticity of Demand

• Elasticity differs along a linear demand curve.

Price Elasticity of Demand (E)

Elasticity Responsiveness E

Elastic

Unitary Elastic

Inelastic

% Q % P

% Q % P

% Q % P

E 1

E 1

E 1

Perfect elasticity: E = ∞Perfect inelasticity: E = 0

Factors Affecting Price Elasticity of Demand

• Availability of substitutes – The better & more numerous the substitutes for a

good, the more elastic is demand

• Percentage of consumer’s budget– The greater the percentage of the consumer’s

budget spent on the good, the more elastic is demand

• Time period of adjustment– The longer the time period consumers have to

adjust to price changes, the more elastic is demand

The Price Elasticity of Demand

• A long-run demand curve will generally be more elastic than a short-run curve.

• As the time period lengthens consumers find way to adjust to the price change, via substitution or shifting consumption

The Price Elasticity of Demand

• There is a relationship between the price elasticity of demand and revenue received.– Because a demand curve is downward

sloping, a decrease in price will increase the quantity demanded

– If elasticity is greater than 1, the quantity effect is stronger than the price effect, and total revenue will increase

Price Elasticity & Total Revenue

Elastic

Quantity-effect dominates

Unitary elastic

No dominant effect

Inelastic

Price-effect dominates

Price rises

Price falls

TR falls

TR rises

No change in TR

No change in TR

TR rises

TR falls

• As price decreases– Revenue rises when

demand is elastic.– Revenue falls when

it is inelastic.– Revenue reaches its

peak when elasticity of demand equals 1.

• Marginal Revenue: The change in total revenue resulting from changing quantity by one unit.

QuantityMR

Revenue Total

• Since MR measures the rate of change in total revenue as quantity changes, MR is the slope of the total revenue (TR) curve

Demand & Marginal Revenue

Unit sales (Q) Price TR = P Q MR = TR/Q

0 $4.50

1 4.00

2 3.50

3 3.10

4 2.80

5 2.40

6 2.00

7 1.50

$ 0

$4.00

$7.00

$9.30

$11.20

$12.00

$12.00

$10.50

--

$4.00

$3.00

$2.30

$1.90

$0.80

$0

$-1.50

Demand, MR, & TR

Panel A Panel B

• For a straight-line demand curve the marginal revenue curve is twice as steep as the demand.

• At the point where marginal revenue crosses the X-axis, the demand curve is unitary elastic and total revenue reaches a maximum.

Linear Demand, MR, & Elasticity

• Some sample elasticities– Coffee: short run -0.2, long run -0.33– Kitchen and household appliances: -

0.63– Meals at restaurants: -2.27– Airline travel in U.S.: -1.98– Beer: -0.84, Wine: -0.55

MR, TR, & Price Elasticity

Marginal revenue Total revenue

Price elasticity of demand

MR > 0 Elastic (E> 1)

MR = 0 Unit elastic (E= 1)

MR < 0 Inelastic (E< 1)

Unit elastic (E= 1)

Inelastic (E< 1)

Elastic (E> 1)

TR decreases as Q increases (P decreases)

TR is maximized

TR increases as Q increases (P decreases)

Marginal Revenue & Price Elasticity

• For all demand & marginal revenue curves, the relation between marginal revenue, price, & elasticity can be expressed as

11MR PE

The Cross-Elasticity of Demand

• Cross-elasticity of demand: The percentage change in quantity consumed of one product as a result of a 1 percent change in the price of a related product.

B

AX P

QE

%

%

The Cross-Elasticity of Demand

• Arc Elasticity

2/)(2/)( 21

12

21

12

BB

BB

AA

AAx PP

PP

QQ

QQE

The Cross-Elasticity of Demand

• Point Elasticity

B

B

A

AX P

P

Q

QE

The Cross-Elasticity of Demand

• The sign of cross-elasticity for substitutes is positive.

• The sign of cross-elasticity for complements is negative.

• Two products are considered good substitutes or complements when the coefficient is larger than 0.5.

Predicting Revenue Changes from Two Products

Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by:

XPQYPQX PERERRXYXX

%1 ,,

Income Elasticity• Income Elasticity of Demand:

The percentage change in quantity demanded caused by a 1 percent change in income.

Y

QEY

%

%

Income Elasticity• Arc Elasticity

2/)(2/)( 21

12

21

12

YY

YY

QQ

QQEY

Income Elasticity• Categories of income

elasticity– Superior goods: EY >

1

– Normal goods: 0 >EY

>1– Inferior goods –

demand decreases as income increases: EY < 0

Other Elasticity Measures

• Elasticity is encountered every time a change in some variable affects quantities.– Advertising expenditure– Interest rates– Population size

Uses of Elasticities• Pricing.• Managing cash flows.• Impact of changes in competitors’ prices.• Impact of economic booms and recessions.• Impact of advertising campaigns.• And lots more!

Example 1: Pricing and Cash Flows

• According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64.

• AT&T needs to boost revenues in order to meet it’s marketing goals.

• To accomplish this goal, should AT&T raise or lower it’s price?

Answer: Lower price!• Since demand is elastic, a reduction in

price will increase quantity demanded by a greater percentage than the price decline, resulting in more revenues for AT&T.

Example 2: Quantifying the Change

• If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

Answer• Calls would increase by 25.92 percent!

%92.25%

%64.8%3

%3

%64.8

%

%64.8,

dX

dX

dX

X

dX

PQ

Q

Q

Q

P

QE

XX

Example 3: Impact of a change in a competitor’s

price• According to an FTC Report by

Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06.

• If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

Answer• AT&T’s demand would fall by 36.24 percent!

%24.36%

%06.9%4

%4

%06.9

%

%06.9,

dX

dX

dX

Y

dX

PQ

Q

Q

Q

P

QE

YX

Elasticity of Supply• Price Elasticity of Supply: The

percentage change in quantity supplied as a result of a 1 percent change in price.

• If the supply curve slopes upward and to the right, the coefficient of supply elasticity is a positive number.

Price %

SuppliedQuantity %E

S

Elasticity of Supply• Arc elasticity

2/)(2/)( 21

12

21

12

PP

PP

QQ

QQEs

Elasticity of Supply• When the supply curve is more

elastic, the effect of a change in demand will be greater on quantity than on the price of the product.

• With a supply curve of low elasticity, a change in demand will have a greater effect on price than on quantity.

Interpreting Demand Functions

• Mathematical representations of demand curves.

• Example:

• X and Y are substitutes (coefficient of PY is positive).

• X is an inferior good (coefficient of M is negative).

MPPQ YXd

X 23210

Linear Demand Functions

• General Linear Demand Function:

HMPPQ HMYYXXd

X 0

Own PriceElasticity

Cross PriceElasticity

IncomeElasticity

X

XXPQ Q

PE

XX,

XMMQ Q

ME

X,

X

YYPQ Q

PE

YX,

Example of Linear Demand

• Qd = 10 - 2P.• Own-Price Elasticity: (-2)P/Q.• If P=1, Q=8 (since 10 - 2 = 8).• Own price elasticity at P=1, Q=8:

(-2)(1)/8= - 0.25.

0ln ln ln ln lndX X X Y Y M HQ P P M H

M

Y

X

:Elasticity Income

:Elasticity Price Cross

:Elasticity PriceOwn

Log-Linear Demand• General Log-Linear Demand Function:

Example of Log-Linear Demand

• ln(Qd) = 10 - 2 ln(P).• Own Price Elasticity: -2.

P

Q Q

D D

Linear Log Linear

Graphical Representation of Linear and Log-Linear

DemandP