Chapter 06--Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter...

8/19/2019 Chapter 06--Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06Chapter 06

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Copyright © 2008 by the McGraw-Hill Companies, Inc. All

McGraw-Hill"IrwinManagerial #conomics,

Managerial Economics ThomaMaurininth edition

Copyright © 2008 by the McGraw-Hill Companies, Inc. AllMcGraw-Hill"IrwinManagerial #conomics,

Managerial Economics ThomaMaurininth edition

Chapter 6

Elasticity and Demand


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Managerial EconomicsManagerial Economics

6-2

•

P & Q are inversely related by the law ofdemand so E is always negative

• The larger the absolute value of E , the moresensitive 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


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6-3


Elasticity Responsiveness E

Elastic

Unitary Elastic

Inelastic

% Q % P ∆ >∆

% Q % P ∆ =∆

% Q % P ∆ 1

E = 1

E < 1

Table 6.1


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6-4


• 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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6-5

Price Elasticity & Total Revenue

Elastic

Quantity-effectdominates

nitary elastic

!o dominanteffect

"nelastic

Price-effectdominates

PricerisesPricefalls

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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6-6

Factors Affectin Price Elasticity

of Demand • #vailability 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 theconsumers budget spent on the good, themore elastic is demand

• %ime period of adustment• The longer the time period consumers have

to ad!ust to price changes, the more elasticis demand


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6-7

Calculatin Price Elasticity of

Demand • Price elasticity can be calculatedby multiplying the slope of demand

' Q/ P ( times the ratio of price to

quantity ' P/Q(

% Q E % P

∆= ∆

Q

Q P

P

∆ ×

= ∆ ×

100

100

Q P P Q

∆= ×∆

ll


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6-8

Calculatin Price Elasticity of

Demand • Price elasticity can be measured atan 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 si"able arcalong the demand curve, the intervalcalculation provides a better measure

M i l E iM i l E i


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6-9

Computation of Elasticity !ver an

"nterval • *hen calculating price elasticity ofdemand over an interval of

demand) use the interval or arc

elasticity formula

Q P E P Q∆= ×∆

AverageAverage

M i l E iM i l E i


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6-

Computation of Elasticity at a

Point • *hen calculating price elasticity at apoint on demand) multiply the slope of

demand '

Q/

P () computed at the point

of measure) times the ratio P/Q# usingthe values of P and Q at the point of

measure

•

Method of measuring point elasticitydepends on whether demand is linear or

curvilinear

M i l E iM i l E i


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6-

Point Elasticity $hen Demand is

%inear • R

R ,

Q a bP cM dP

ˆ ˆ M P

= + + ++iven ) let income &price of the related good ta,e specific

values and respectively

•

R

Q a' bP ˆ ˆ a' a cM dP

b Q P

= += + +

= ∆ ∆

%hen epress demand as ) where

and the slope parameter

is

M i l E iM i l E i


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6-


%inear • .ompute elasticity using either of the twoformulas below which give the same value

for E

P P E b E Q P A

= =−

or

#here and are values of price and $uantity demandedat the point of measure along demand, andis the price%intercept of demand

P Q A ( a'/ b )= −

M i l E iM i l E i


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6-


Curvilinear • .ompute elasticity using either of twoequivalent formulas below

Q P P E P Q P A

∆= × =∆ −

#here is the slope of the curved demand at

the point of measure, and are values of price and$uantity demanded at the point of measure, and isthe price%intercept of the tangent line e&tende

Q P

P Q A

∆ ∆

d tocross the price%a&is

M i l E iM i l E i


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6-

Elasticity (enerally) 'aries Alon

a Demand Curve• /or linear demand) price and E

vary

directly

• The higher the price, the more elastic is

demand• The lo'er the price, the less elastic is

demand

• /or curvilinear demand) no general rule

about the relation between price andquantity

(pecial case of 'hich has a constantprice elasticity )e$ual to * for all prices

bQ aP

b

=• (pecial case of 'hich has a constantprice elasticity )e$ual to * for all prices

bQ aP

b

=•

M i l E iM i l E i


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6-

Constant Elasticity of Demand(Fiure 6)



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6-

*arinal Revenue

• Marginal revenue ( MR) is the change

in total revenue per unit change in

output

• 0ince MR measures the rate of

change in total revenue as quantity

changes) MR is the slope of the total

revenue (TR) curve

TR MR

Q

∆=∆



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6-

Demand & *arinal Revenue

(Ta+le 6)Unit sales (Q) Price TR = P Q MR = TR/ Q+ -./+

0 -.++

1 2./+

2 2.0+

- 1.3+

/ 1.-+

4 1.++

5 0./+

+

-.++

5.++

6.2+

00.1+

01.++

01.++

0+./+

%%

-.++

2.++

1.2+

0.6+

+.3+

+

%0./+



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6-

Demand# *R# & TR (Fiure 6,)

Panel A Panel B



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6-

Demand & *arinal Revenue

• *hen inverse demand is linear) P

= A + BQ (A > , B ! )

• 7arginal revenue is also linear,intersects the vertical )price* ais atthe same point as demand, & is t'iceas steep as demand

MR = A + "BQ



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6-

%inear Demand# *R# & Elasticity

(Fiure 6-)



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6-

*R# TR# & Price Elasticity

Marginalrevenue

%otal revenuePrice elasticity

of demand

MR 8 + Elastic) E 8 0*

MR 9 + Unit elastic) E 9 0*

MR : + Inelastic) E : 0*

Unit elastic

) E 9 0*

Inelastic) E : 0*

Elastic) E 8 0*

Table 6.4

TR decreases asQ increases

) P decreases*

TR is maimi"ed

TR increases asQ increases) P decreases*



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6-

*arinal Revenue & Price Elasticity

• /or all demand & marginal revenue

curves) the relation between marginal

revenue) price) & elasticity can be

epressed as

11

MR P E

= +



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6-

"ncome Elasticity

• "ncome elasticity ( E M ) 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 M E

% M M Q

∆ ∆= = ×

∆ ∆



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6-

Cross.Price Elasticity

• .ross-price elasticity ( E #$ ) measures the

responsiveness of quantity demanded of

good # to changes in the price of related

good $ ) holding the price of good # & allother demand determinants for good #

constant

• Positive 'hen the t'o goods are substitutes

• Negative 'hen the t'o goods are complements

# # $

#$

$ $ #

% Q Q P E

% P P Q

∆ ∆= = ×

∆ ∆



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6-

"nterval Elasticity *easures

• %o calculate interval measures of

income & cross-price elasticities) the

following formulas can be employed

M

Q M E

M Q∆= ×∆

Average

Average

R

#R

R

P Q E P Q

∆= ×∆

AverageAverage



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6

Point Elasticity *easures

•

# # $ Q a bP cM dP ,= + + +/or the linear demand function

point

measures of income & cross-price

elasticities can be calculated as

M

M E c

Q=

R

#R

P E d

Q=

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