23735854 elasticity and demand

8/14/2019 23735854 Elasticity and Demand

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he McGraw-Hill Series

anagerialEconomics ThomasMauriceeighth edition

Chapter 6

Elasticity and Demand


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ManagerialEconomics2

The McGraw-Hill Series2

P& Q are inversely related by the law ofdemand soEis always negative

The larger the absolute value ofE, the moresensitive buyers are to a change in price

Price Elasticity of Demand (E)

Measures responsiveness or sensitivity

of consumers to changes in the price of

a good

% Q

E% P

=


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Elasticity Responsiveness E

Elastic

Unitary Elastic

Inelastic

% Q % P >

% Q % P =

% Q % P 1

E =1

E


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Percentage change in quantity

demandedcan be predicted for a given

percentage change in price as:

% Qd = % PxE Percentage change in price required for

a given change in quantity demanded

can be predicted as:

% P= % QdE


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Price Elasticity & Total Revenue

Elastic

Q-effect dominates

Unitary elastic

No dominant effect

Inelastic

P-effect dominates

Pricerises

Pricefalls

TR falls

TR rises

No change in TR

No change in TR

TR rises

TR falls

% Q % P > % Q % P = % Q % P


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Factors Affecting Price Elasticity

of Demand Availability of substitutes

The better & more numerous the substitutesfor a good, the more elastic is demand

Percentage of consumers budget The greater the percentage of theconsumers budget spent on the good, themore elastic is demand

Time period of adjustment The longer the time period consumers have toadjust to price changes, the more elastic isdemand


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i l i


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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, apoint calculation is suitable

If the price change spans a sizable arcalong the demand curve, the intervalcalculation provides a better measure

M i l E i


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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

Q PEP Q

=

AverageAverage

M i l E i


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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 pointof measure, times the ratioP/Q, using thevalues ofPand Q at the point of measure

Method of measuring point elasticity

depends on whether demand is linear or

curvilinear

M i l E i


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Point Elasticity When Demand is

Linear

R

R ,

Q a bP cM dP

M P

= + + +Given , let income &

price of the related good take specific

values and respectively

R

Q a' bP a' a cM dP

b Q P

= += + +

=

Then express demand as , where

and the slope parameter

is

M i l E i


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Point Elasticity When Demand is

Linear Compute elasticity using either of the two

formulas below which give the same value

forE

P P E b E Q P A

= =

or

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

P Q A ( a'/ b )=


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M i l E i


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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

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

bQ aP

b

=Special case of which has a constantprice elasticity (equal to ) for all prices

bQ aP

b

=

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Constant Elasticity of Demand(Figure 6.3)



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Computation of Elasticity Over an

Interval

Marginal revenue (MR) is the change

in total revenue per unit change in

output

SinceMR measures the rate of

change in total revenue as quantity

changes,MR is the slope of the total

revenue (TR) curveTR

MRQ

=



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Demand & Marginal Revenue(Table 6.3)

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

0 $4.50

1 4.002 3.50

3 3.10

4 2.805 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



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Demand, MR, & TR (Figure 6.4)

Panel A Panel B



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Demand & Marginal Revenue

When inverse demand is linear, P

= A + BQ

Marginal revenue is also linear,intersects the vertical (price) axis atthe same point as demand, & is twiceas steep as demand

MR = A + 2BQ

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Linear Demand, MR, & Elasticity

(Figure 6.5)



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TR decreases asQ increases

TR is maximized

TR increases asQ increases

MR, TR, & Price Elasticity

Marginalrevenue

Total revenue Price elasticity ofdemand

MR > 0 Elastic (E>1)

MR = 0 Unit elastic(E= 1)

MR < 0 Inelastic (E 1)

Table 6.4



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Marginal Revenue & Price Elasticity

For all demand & marginal revenue

curves, the relation between marginal

revenue, price, & elasticity can be

expressed as

11

MR P E

= +



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Income Elasticity

Income elasticity (EM) measures the

responsiveness of quantity demanded

to changes in income, holding the price

of the good & all other demanddeterminants constant

Positive for a normal good

Negative for an inferior goodd d

M

d

% Q Q ME

% M M Q

= =



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Cross-Price Elasticity

Cross-price elasticity (EXY) measures the

responsiveness of quantity demanded of

goodXto changes in the price of related

good Y, holding the price of goodX& allother demand determinants for goodX

constant

Positive when the two goods are substitutes

Negative when the two goods are complements

X X Y

XY

Y Y X

% Q Q P E

% P P Q

= =



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Interval Elasticity Measures

To calculate interval measures of

income & cross-price elasticities, the

following formulas can be employed

M

Q ME

M Q=

Average

Average

R

XR

R

PQEP Q

=

AverageAverage



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Point Elasticity Measures

X X Y Q a bP cM dP ,= + + +For the linear demand function

point

measures of income & cross-price

elasticities can be calculated as

M

ME c

Q=

R

XR

PE d

Q=

23735854 elasticity and demand

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