Elasticity and Demand

Price Elasticity of Demand (E)

• 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 price2

•% Q

E% P

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

Price Elasticity of Demand (E)

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Elasticity Responsiveness EElasticUnitary ElasticInelastic

% Q % P

% Q % P

% Q % P

E 1

E 1

E 1

Price Elasticity of Demand (E)

• Percentage change in quantity demanded can be predicted for a given percentage change in price as:

–%Qd = %P x E

• Percentage change in price required for a given change in quantity demanded can be predicted as:

–%P = %Qd ÷ E

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Price Elasticity & Total Revenue

5

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

% Q % P % Q % P % Q % P

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

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Calculating Price Elasticity of Demand

• Price elasticity can be calculated by multiplying the slope of demand (Q/P) times the ratio of price to quantity (P/Q)

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% QE

% P

Q

QP

P

100

100

Q P

P Q

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

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Computation of Elasticity Over an Interval

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

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Q PE

P Q

Average

Average

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

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Point Elasticity When Demand is Linear

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R

R ,

Q a bP cM dP

ˆ ˆM P

Given , let income & price of the related good take specific

values and respectively

R

Q a' bPˆ ˆa' a cM dP

b Q P

Then express demand as , where

and the slope parameter is

Point Elasticity When Demand is Linear

• Compute elasticity using either of the two formulas below which give the same value for E

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P PE b E

Q P A

or

Where and are values of price and quantity demandedat the point of measure along demand, and is the price-intercept of demand

P QA ( a'/ b )

Point Elasticity When Demand is Curvilinear

• Compute elasticity using either of two equivalent formulas below

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Q P PE

P Q P A

Where is the slope of the curved demand atthe point of measure, and are values of price and quantity demanded at the point of measure, and is the price-intercept of the tangent line extende

Q P

P QA

d to cross the price-axis

Elasticity (Generally) Varies Along a Demand Curve

• For linear demand, price and Evary directly– The higher the price, the more elastic is demand– The lower the price, the less elastic is demand

• For curvilinear demand, no general rule about the relation between price and quantity

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Special case of which has a constantprice elasticity (equal to ) f or all prices

bQ aPb

Special case of which has a constantprice elasticity (equal to ) f or all prices

bQ aPb

Constant Elasticity of Demand (Figure 6.3)

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Marginal Revenue

• Marginal revenue (MR) is the change in total revenue per unit change in output

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

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TRMR

Q

Demand & Marginal Revenue

$ 0

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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

$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

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Panel A Panel B

Demand & Marginal Revenue

• When inverse demand is linear, P = A + BQ (A > 0, B < 0)– Marginal revenue is also linear, intersects the

vertical (price) axis at the same point as demand, & is twice as steep as demand

MR = A + 2BQ

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Linear Demand, MR, & Elasticity

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MR, TR, & Price Elasticity

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Marginal revenue

Total revenuePrice 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

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11MR P

E

Income Elasticity

• Income elasticity (EM) measures the responsiveness of quantity demanded to changes in income, holding the price of the good & all other demand determinants constant– Positive for a normal good– Negative for an inferior good

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d dM

d

% Q Q ME

% M M Q

Cross-Price Elasticity• Cross-price elasticity (EXY) measures the

responsiveness of quantity demanded of good X to changes in the price of related good Y, holding the price of good X & all other demand determinants for good X constant– Positive when the two goods are substitutes– Negative when the two goods are complements

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X X YXY

Y Y X

% Q Q PE

% P P Q

Interval Elasticity Measures• To calculate interval measures of income & cross-

price elasticities, the following formulas can be employed

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M

Q ME

M Q

Average

Average

RXR

R

PQE

P Q

Average

Average

Point Elasticity Measures

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X X YQ a bP cM dP , For the linear demand function

pointmeasures of income & cross-priceelasticities can be calculated as

M

ME c

Q

RXR

PE d

Q