Chapter 6: Elasticity and
Demand
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved.
Elasticity
%  in dependent variable
%  in independen t variabl e
Price elasticity of demand
%  in quantity demanded
%  in price
6-2
Price Elasticity of Demand (E)
• Measures responsiveness or sensitivity of
consumers to changes in the price of a
good
 Q
E
 P
• 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
6-3
Sign of Price Elasticity of Demand
• The coefficient of the price elasticity of
demand is always negative
• It is intuitively more appealing to talk about
price elasticity in terms of its absolute
value.
6-4
6-4
Price Elasticity of Demand (E)
Table 6.1
Elasticity
Responsiveness
E
Elastic
%∆Q> %∆P E> 1
Unitary Elastic
%∆Q= %∆P E= 1
Inelastic
%∆Q< %∆P E< 1
6-5
Elastic Demand
6-6
6-6
Inelastic Demand
Demand becomes less elastic as
price declines along a linear
demand curve.
6-7
6-7
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
6-8
Price Elasticity & Total Revenue
Table 6.2
Elastic
Unitary elastic
Inelastic
%∆Q> %∆P%∆Q= %∆P%∆Q< %∆P
Quantity-effect
dominates
No dominant
effect
Price-effect
dominates
Price
rises
TR falls
No change in TR
TR rises
Price
falls
TR rises
No change in TR
TR falls
6-9
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
6-10
Factors Affecting Price Elasticity
of Demand
• Necessities versus Luxuries
• Luxuries have a more elastic demand
• Definition of the market
• The more finely defined the market the more
elastic the demand. The more aggregate the
definition of the market the more inelastic the
demand
hamburger < beef <all meat products
6-11
6-
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)
Q
100
Q P
Q
 Q



E
P
P Q
 P
100
P
6-12
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
6-13
Calculating Price Elasticity of
Demand
• Regression analysis provides a point estimate
• Arc elasticity is typically only used for teaching
purposes
6-14
6-
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 Average P
E

P Average Q
6-15
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
6-16
Price Elasticity for Linear
Demand
Q / Q Q p


.
p / p p Q
Q  a  bp
p
 b
Q
6–17
6-17
Point Elasticity When
Demand is Linear
•
Given Q = a + bP + cM + dPR, let income
& price of the related good take specific
values M and PR , respectively
•
Then express demand as Q = a′ + bP ,
where a′ = a + cM + dPR and the slope
parameter is b = ∆Q ∕ ∆P
6-18
Point Elasticity When
Demand is Linear
• Compute elasticity using either of the two
formulas below which give the same value for E
P
P
Eb
or E 
Q
PA
Where P and Q are values of price and quantity demanded
at the point of measure along demand, and A ( = –a′ ∕ b) is
the price-intercept of demand
6-19
Point Elasticity When
Demand is Curvilinear
• Compute elasticity using either of two equivalent
formulas below
Q P
P
E
 
P Q P  A
Where ∆Q ∕ ∆P is the slope of the curved demand at the
point of measure, P and Q are values of price and quantity
demanded at the point of measure, and A is the priceintercept of the tangent line extended to cross the price axis
6-20
Elasticity (Generally) Varies Along a
Demand Curve
• For linear demand, price and Evary 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 Q = aPb which has a constant
price elasticity (equal to b) for all prices
6-21
Constant elasticity demand
function
1. Q  P

log Q  log    log P
2. Q / P   (  ) P
 1
3.   ( Q / P )( P / Q )   (  ) P
 
 1
P
P 
6-22
Constant Elasticity of Demand
(Figure 6.3)
6-23
Constant elasticity demand
function
6-24
6-
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
TR
MR 
Q
6-25
Demand & Marginal Revenue
(Table 6.3)
TR = P  Q
MR = TR/Q
Unit sales (Q)
Price
0
$4.50
1
4.00
$4.00
$4.00
2
3.50
$7.00
$3.00
3
3.10
$9.30
$2.30
4
2.80
$11.20
$1.90
5
2.40
$12.00
$0.80
6
2.00
$12.00
$0
7
1.50
$10.50
$-1.50
$
0
--
6-26
Demand, MR, & TR
Panel A
(Figure 6.4)
Panel B
6-27
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
6-28
Proof
P  A  BQ
TR  PQ  ( A  BQ )Q  AQ  BQ
MR  TR / Q  A  2 BQ
2
6-29
6-
Marginal Revenue
6-30
6-
Total Revenue
6-31
6-
Linear Demand, MR, & Elasticity
(Figure 6.5)
6-32
MR, TR, & Price Elasticity
(Table 6.4)
Marginal
revenue
MR > 0
Total revenue
TR increases as
Q increases
(P decreases)
Price elasticity
of demand
Elastic
(│E│> 1)
MR = 0
TR is maximized
Unit Elastic
(│E│= 1)
MR < 0
TR decreases as
Q increases
Inelastic
(│E│< 1)
(P decreases)
6-33
Marginal Revenue & Price Elasticity
• For all demand & marginal revenue
curves, the relation between marginal
revenue, price, & elasticity can be
expressed as
1

MR  P  1  
E

6-34
Proof
MR  TR / Q
TR  P  Q  P(Q)  Q
 P Q 
TR / Q  P  (P / Q)  Q  P 1 
 
 Q P 
Q P


P Q
 1
MR  P 1  
 
6-35
6-
Marginal Revenue & Price Elasticity
Note that as E -
that MRP
1

MR  P 1  
E

6-36
6-
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
 Qd Qd M
EM 


 M M Qd
6-37
Normal Good
6-38
6-
Inferior Good
6-39
6-
Cross-Price Elasticity
• Cross-price elasticity (EXR) measures the
responsiveness of quantity demanded of good X
to changes in the price of related good R,
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
E XR
 QX QX PR



 PR PR QX
6-40
Substitute Good
6-41
6-
Interval Elasticity Measures
• To calculate interval measures of income &
cross-price elasticities, the following formulas
can be employed
Q Average M
EM 

M Average Q
E XR
Q Average PR


PR Average Q
6-42
Point Elasticity Measures
• For the linear demand function
Q = a + bP + cM + dPR, point measures of
income & cross-price elasticities can be
calculated as
M
EM  c
Q
E XR
PR
d
Q
6-43
6-44
6-
6-45
6-