Strategy
Chapter 3
Quantitative
Demand Analysis
McGraw-Hill/Irwin
Overview
I. The Elasticity Concept
– Own Price Elasticity
– Elasticity and Total Revenue
– Cross-Price Elasticity
– Income Elasticity
II. Demand Functions
– Linear
– Log-Linear
III. Regression Analysis
3-2
The Elasticity Concept
 How responsive is variable “G” to a change in
variable “S”
EG , S
%G

%S
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
3-3
The Elasticity Concept Using
Calculus
 An alternative way to measure the elasticity of
a function G = f(S) is
EG , S
dG S

dS G
If EG,S > 0, then S and G are directly related.
If EG,S < 0, then S and G are inversely related.
If EG,S = 0, then S and G are unrelated.
3-4
Own Price Elasticity of Demand
EQX , PX
%QX

%PX
d
 Negative according to the “law of demand.”
Elastic:
EQ X , PX  1
Inelastic: EQ X , PX  1
Unitary:
EQ X , PX  1
3-5
Perfectly Elastic & Inelastic Demand
Price
Price
D
D
Quantity
PerfectlyElastic(EQX ,PX  )
Quantity
PerfectlyInelastic( EQX , PX  0)
3-6
Own-Price Elasticity
and Total Revenue
 Elastic
– Increase (a decrease) in price leads to a
decrease (an increase) in total revenue.
 Inelastic
– Increase (a decrease) in price leads to an
increase (a decrease) in total revenue.
 Unitary
– Total revenue is maximized at the point where
demand is unitary elastic.
3-7
Elasticity, Total Revenue
and Linear Demand
P
100
TR
0
10
20
30
40
50
Q
0
Q
3-8
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
3-9
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
3-10
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
40
800
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
3-11
Elasticity, Total Revenue
and Linear Demand
P
100
TR
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
3-12
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Elastic
80
1200
60
40
800
20
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
Elastic
3-13
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
50
Q
Inelastic
3-14
Elasticity, Total Revenue
and Linear Demand
P
100
TR
Unit elastic
Elastic
Unit elastic
80
1200
60
Inelastic
40
800
20
0
10
20
30
40
50
Q
0
10
Elastic
20
30
40
50
Q
Inelastic
3-15
Demand, Marginal Revenue (MR)
and Elasticity
 For a linear
inverse demand
function, MR(Q) =
a + 2bQ, where b
< 0.
 When
P
100
Elastic
Unit elastic
80
60
Inelastic
40
20
0
10
20
40
MR
50
Q
– MR > 0, demand is
elastic;
– MR = 0, demand is
unit elastic;
– MR < 0, demand is
inelastic.
3-16
Elasticity and Marginal Revenue
3-17
Factors Affecting the
Own-Price Elasticity
 Available Substitutes
– The more substitutes available for the good, the more
elastic the demand.
 Time
– Demand tends to be more inelastic in the short term than
in the long term.
– Time allows consumers to seek out available substitutes.
 Expenditure Share
– Goods that comprise a small share of consumer’s budgets
tend to be more inelastic than goods for which consumers
spend a large portion of their incomes.
3-18
Cross-Price Elasticity of Demand
EQX , PY
%QX

%PY
d
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.
3-19
Predicting Revenue Changes
from Two Products
Suppose that a firm sells two related goods.
If the price of X changes, then total revenue
will change by:
 


R  RX 1  EQX , PX  RY EQY ,PX  %PX
3-20
Cross-Price Elasticity in Action
3-21
Income Elasticity
EQX , M
%QX

%M
d
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is a inferior good.
3-22
Income Elasticity in Action
 Suppose that the income elasticity of
demand for transportation is estimated to
be 1.80. If income is projected to decrease
by 15 percent,
 what is the impact on the demand for
transportation?
 is transportation a normal or inferior good?
3-23
Uses of Elasticities




Pricing.
Managing cash flows.
Impact of changes in competitors’ prices.
Impact of economic booms and
recessions.
 And lots more!
3-24
Example 1: Pricing and Cash Flows
 According to an FTC Report by Michael
Ward, AT&T’s own price elasticity of
demand for long distance services is -8.64.
 AT&T needs to boost revenues in order to
meet it’s marketing goals.
 To accomplish this goal, should AT&T
raise or lower it’s price?
3-25
 Since demand is elastic, a reduction in
price will increase quantity demanded by a
greater percentage than the price decline,
resulting in more revenues for AT&T.
3-26
Example 2: Quantifying the Change
 If AT&T lowered price by 3 percent, what
would happen to the volume of long
distance telephone calls routed through
AT&T?
3-27
Calls would increase by 25.92 percent!
EQX , PX
%QX
 8.64 
%PX
d
%QX
 8.64 
 3%
d
 3%   8.64  %QX
d
%QX  25.92%
d
3-28
Example 3: Impact of a Change
in a Competitor’s Price
 According to an FTC Report by Michael
Ward, AT&T’s cross price elasticity of
demand for long distance services is 9.06.
 If competitors reduced their prices by 4
percent, what would happen to the demand
for AT&T services?
3-29
AT&T’s demand would fall by 36.24 percent!
EQX , PY
%QX
 9.06 
%PY
d
%QX
9.06 
 4%
d
 4%  9.06  %QX
d
%QX  36.24%
d
3-30
Interpreting Demand Functions
 Mathematical representations of demand
curves.
 Example:
QX  10  2PX  3PY  2M
d
– Law of demand holds (coefficient of PX is negative).
– X and Y are substitutes (coefficient of PY is positive).
– X is an inferior good (coefficient of M is negative).
3-31
Linear Demand Functions and
Elasticities
 General Linear Demand Function and
Elasticities:
QX  0   X PX  Y PY  M M  H H
d
P
EQX , PX   X X
QX
Own Price
Elasticity
EQX , PY
PY
 Y
QX
Cross Price
Elasticity
M
EQX , M   M
QX
Income
Elasticity
3-32
Elasticities for Linear Demand Functions In
Action
3-33
Log-Linear Demand
 General Log-Linear Demand Function:
ln QX d  0   X ln PX  Y ln PY  M ln M  H ln H
Own PriceElasticity:  X
Cross PriceElasticity:  Y
IncomeElasticity:
M
3-34
Elasticities for Nonlinear Demand
3-35
Graphical Representation of
Linear and Log-Linear Demand
P
P
D
Linear
D
Q
Log Linear
Q
3-36
Regression Line and Least Squares
Regression
3-37
Excel and Least Squares Estimates
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.87
R Square
0.75
0.72
Standard Error
112.22
Observations
10.00
ANOVA
Df
Regression
Residual
Total
Intercept
Price
1
8
9
SS
301470.89
100751.61
402222.50
Coefficients Standard Error
1631.47
243.97
-2.60
0.53
MS
301470.89
12593.95
F
Significance F
23.94
0.0012
t Stat
P-value Lower 95% Upper 95%
6.69 0.0002
1068.87 2194.07
-4.89 0.0012
-3.82
-1.37
3-38
Evaluating Statistical Significance
3-39
Excel and Least Squares Estimates
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.87
R Square
0.75
0.72
Standard Error
112.22
Observations
10.00
ANOVA
Df
Regression
Residual
Total
Intercept
Price
1
8
9
SS
301470.89
100751.61
402222.50
Coefficients Standard Error
1631.47
243.97
-2.60
0.53
MS
301470.89
12593.95
F
Significance F
23.94
0.0012
t Stat
P-value Lower 95% Upper 95%
6.69 0.0002
1068.87 2194.07
-4.89 0.0012
-3.82
-1.37
3-40
Regression Analysis
Evaluating Overall Regression Line Fit: R- Square
3-41
Regression Analysis
Evaluating Overall Regression Line Fit: FStatistic
 A measure of the total variation explained
by the regression relative to the total
unexplained variation.
– The greater the F-statistic, the better the
overall regression fit.
– Equivalently, the P-value is another measure
of the F-statistic.
• Lower p-values are associated with better overall
regression fit.
3-42
Regression Analysis
Excel and Least Squares Estimates
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.87
R Square
0.75
0.72
Standard Error
112.22
Observations
10.00
ANOVA
Df
Regression
Residual
Total
Intercept
Price
1
8
9
SS
301470.89
100751.61
402222.50
Coefficients Standard Error
1631.47
243.97
-2.60
0.53
MS
301470.89
12593.95
F
Significance F
23.94
0.0012
t Stat
P-value Lower 95% Upper 95%
6.69 0.0002
1068.87 2194.07
-4.89 0.0012
-3.82
-1.37
3-43
Regression Analysis
Excel and Least Squares Estimates
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.89
R Square
0.79
0.69
Standard Error
9.18
Observations
10.00
ANOVA
Df
Regression
Residual
Total
Intercept
Price
Distance
SS
1920.99
505.91
2426.90
MS
640.33
84.32
Coefficients Standard Error
135.15
20.65
-0.14
0.06
0.54
0.64
-5.78
1.26
t Stat
6.54
-2.41
0.85
-4.61
3
6
9
F
Significance F
7.59
0.182
P-value Lower 95% Upper 95%
84.61
185.68
0.0006
0.0500
-0.29
0.00
0.4296
-1.02
2.09
0.0037
-8.86
-2.71
3-44
Conclusion
 Elasticities are tools you can use to quantify
the impact of changes in prices, income, and