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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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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
Price Elasticity of Demand (E)
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
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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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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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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Point Elasticity $hen Demand is
%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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Point Elasticity $hen Demand is
Curvilinear • .ompute elasticity using either of twoequivalent formulas below
Q P P E P Q P A
∆= × =∆ −
#here is the slope of the curved demand at
the point of measure, and are values of price and$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
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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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Constant Elasticity of Demand(Fiure 6)
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*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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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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Demand# *R# & TR (Fiure 6,)
Panel A Panel B
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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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%inear Demand# *R# & Elasticity
(Fiure 6-)
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*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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*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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"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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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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"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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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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