Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Managerial Economics &
Business Strategy
Chapter 3
Quantitative Demand Analysis
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Overview
I,Elasticities of Demand
? Own Price Elasticity
? Elasticity and Total Revenue
? Cross-Price Elasticity
? Income Elasticity
II,Demand Functions
? Linear
? Log-Linear
III,Regression Analysis
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Elasticities of Demand
? How responsive is variable,G” to a change
in variable,S”
+ S and G are directly related
- S and G are inversely related
S
G
E SG
?
?
?
%
%
,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Own Price Elasticity of
Demand
? Negative according to the,law of demand”
Elastic,
Inelastic,
Unitary,
X
d
X
PQ P
Q
E
XX ?
?
?
%
%
,
1,?XX PQE
1,?XX PQE
1,?XX PQE
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Perfectly Elastic &
Inelastic Demand
Perfectly Elastic
D
Price
Quantity
Perfectly Inelastic
D
Price
Quantity
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Elasticity,TR,and Linear
Demand
Price
Quantity
D
10
8
6
4
2
1 2 3 4 5
Elastic
Inelastic
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Factors Affecting
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,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Cross Price Elasticity of
Demand
+ Substitutes
- Complements
Y
d
X
PQ P
Q
E
YX ?
?
?
%
%
,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Income Elasticity
+ Normal Good
- Inferior Good
M
QE dX
MQ X ?
??
%
%
,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Uses of Elasticities
? Pricing
? Managing cash flows
? Impact of changes in competitors’ prices
? Impact of economic booms and recessions
? Impact of advertising campaigns
? And lots more!
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Answer,Lower price!
? 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,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Answer
? Calls would increase by 25.92 percent!
? ?
%92.25%
%64.8%3
%3
%
64.8
%
%
64.8
,
??
?????
?
?
??
?
?
???
d
X
d
X
d
X
X
d
X
PQ
Q
Q
Q
P
Q
E
XX
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
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 MCI and other competitors reduced their
prices by 4 percent,what would happen to
the demand for AT&T services?
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Answer
? AT&T’s demand would fall by 36.24 percent!
%24.36%
%06.9%4
%4
%
06.9
%
%
06.9
,
???
????
?
?
?
?
?
??
d
X
d
X
d
X
Y
d
X
PQ
Q
Q
Q
P
Q
E
YX
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Demand Functions
? Mathematical representations of demand curves
? Example,
? X and Y are substitutes (coefficient of PY is
positive)
? X is an inferior good (coefficient of M is
negative)
MPPQ YXdX 23210 ????
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Specific Demand Functions
? Linear Demand
HMPPQ HMYYXXdX ????? ????? 0
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity
X
X
XPQ Q
PE
XX ??,X
MMQ Q
ME
X
??,
X
Y
YPQ Q
PE
YX ??,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Example of Linear Demand
? Qd = 10 - 2P
? Own-Price Elasticity,(-2)P/Q
? If P=1,Q=8 (since 10 - 2 = 8)
? Own price elasticity at P=1,Q=8,
(-2)(1)/8= - 0.25
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
HMPPQ HMYYXXdX l o gl o gl o gl o gl o g 0 ????? ?????
M
Y
X
,E la s t ic it y I n c o m e
:E la s t ic it y P r ic e C r o s s
,E la s t ic it y P r ic eO w n
?
?
?
Log-Linear Demand
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Example of Log-Linear
Demand
? log Qd = 10 - 2 log P
? Own Price Elasticity,-2
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
P
Q
P
Q
D D
Linear Log Linear
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Regression Analysis
? Used to estimate demand functions
? Important terminology
? Least Squares Regression,Y = a + bX + e
? Confidence Intervals
? t-statistic
? R-square or Coefficient of Determination
? F-statistic
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
An Example
? Use a spreadsheet to estimate log-linear
demand
ePQ xxx ??? l o gl o g 0 ??
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary Output
R e gre s s i on S t a t i s t i c s
M ul t i pl e R 0, 4 1
R S qu a r e 0, 1 7
A dj us t e d R S qu a r e 0, 1 5
S t a nd a r d E r r or 0, 6 8
O bs e r v a t i on s 4 1, 0 0
A N O V A
df SS MS F S i gn i f i c a nc e F
R e gre s s i on 1, 0 0 3, 6 5 3, 6 5 7, 8 5 0, 0 1
R e s i du a l 3 9, 0 0 1 8, 1 3 0, 4 6
To t a l 4 0, 0 0 2 1, 7 8
C oe f f i c i e nt s S t a nd a r d E r r or t S t a t P - v a l ue Lo w e r 9 5 % U pp e r 9 5 %
I nt e r c e pt 7, 5 8 1, 4 3 5, 2 9 0, 0 0 0 0 0 5 4, 6 8 1 0, 4 8
l n( P ) - 0, 8 4 0, 3 0 - 2, 8 0 0, 0 0 7 8 6 8 - 1, 4 4 - 0, 2 3
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Interpreting the Output
? Estimated demand function,
? log Qx = 7.58 - 0.84 logPx
? Own price elasticity,-0.84 (inelastic)
? How good is our estimate?
? t-statistics of 5.29 and -2.80 indicate that the estimated
coefficients are statistically different from zero
? R-square of,17 indicates we explained only 17 percent
of the variation
? F-statistic significant at the 1 percent level,
Michael R,Baye,Managerial Economics and Business Strategy,3e,?The McGraw-Hill Companies,Inc.,1999
Summary
? Elasticities are tools you can use to quantify the impact
of changes in prices,income,and advertising on sales
and revenues,
? Given market or survey data,regression analysis can be
used to estimate,
? Demand functions
? Elasticities
? A host of other things,including cost functions
? Managers can quantify the impact of changes in prices,
income,advertising,etc,