Managerial Economics &
Business Strategy
Overview
I. The Elasticity Concept
Chapter 3
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Quantitative Demand Analysis
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Own Price Elasticity
Elasticity and Total Revenue
Cross-Price Elasticity
Income Elasticity
II. Demand Functions
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Linear
Log-Linear
III. Regression Analysis
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
The Elasticity Concept
Own Price Elasticity of
Demand
• How responsive is variable “G” to a change
in variable “S”
EG ,S =
% ∆G
% ∆S
EQX , PX =
EQ X , PX > 1
Elastic:
Inelastic: EQ X , PX < 1
- S and G are inversely related
Unitary:
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
EQX , PX = 1
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Perfectly Elastic &
Inelastic Demand
Elasticity Calculation
Price
D
D
Quantity
Perfectly Elastic
d
• Negative according to the “law of demand”
+ S and G are directly related
Price
%∆QX
%∆PX
Quantity
Suppose in the Lincoln Market, at a price of
$1.00 per gallon, 90 (thousand gallons) per
week are sold. Some world event happens
(a war) that causes price to rise to $1.25 per
gallon. Weekly sales fall to 88 (thousand
gallons) per week. What is the price
elasticity of demand?
Perfectly Inelastic
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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Own-Price Elasticity
and Total Revenue
Elasticity Calculation
From the definition of own price elasticity :
% change in P/ % change in Q, we can
operationalize this as by finding the average arc
price elasticity:
E =( Q2-Q1/ P2-P1) x ( P2+P1/ Q2+Q1) so
E = (88-90/1.25-1) x (1.25+1/88+90)
E = -2/.25 x 2.25/178 = - 0.102
which is relatively inelastic.
• Elastic
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• Inelastic
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Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Factors Affecting
Own Price Elasticity
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8
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Inelastic
4
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2
D
3
4
5
Quantity
Time
• Demand tends to be more inelastic in the short term than in
the long term.
• Time allows consumers to seek out available substitutes.
6
2
Available Substitutes
• The more substitutes available for the good, the more elastic
the demand.
Elastic
1
Total revenue is maximized at the point where demand
is unitary elastic.
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Elasticity, TR, and Linear
Demand
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Increase (a decrease) in price leads to an increase (a
decrease) in total revenue.
• Unitary
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Price
Increase (a decrease) in price leads to a decrease (an
increase) in total revenue.
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, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Cross Price Elasticity of
Demand
Income Elasticity
EQX , PY =
% ∆QX
% ∆PY
d
+ Substitutes
- Complements
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
EQ X , M =
% ∆QX
% ∆M
d
+ Normal Good
- Inferior Good
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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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, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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?
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, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Answer
• Calls would increase by 25.92 percent!
EQX , PX = −8.64 =
% ∆QX
% ∆PX
d
d
% ∆QX
− 3%
d
− 3% × (− 8.64 ) = %∆QX
− 8.64 =
d
%∆QX = 25.92%
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Example 3: Impact of a change
in a competitor’s price
Answer
• 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?
• AT&T’s demand would fall by 36.24 percent!
EQ X , PY = 9.06 =
% ∆Q X
%∆PY
d
d
% ∆Q X
− 4%
d
− 4% × 9.06 = %∆Q X
9.06 =
d
%∆Q X = −36.24%
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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Demand Functions
• Mathematical representations of demand curves
• Example:
Specific Demand Functions
• Linear Demand
d
Q X = 10 − 2 PX + 3PY − 2 M
• X and Y are substitutes (coefficient of PY is
positive)
• X is an inferior good (coefficient of M is
negative)
•
•
•
•
d
Q X = α 0 + α X PX + α Y PY + α M M + α H H
PX
QX
Own Price
Elasticity
EQ X , PX = α X
EQX , PY = α Y
PY
QX
EQX ,M = α M
Income
Elasticity
Cross Price
Elasticity
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Example of Linear Demand
Log-Linear Demand
ln Q X d = β 0 + β X ln PX + βY ln PY + β M ln M + β H ln H
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
Own Price Elasticity :
Cross Price Elasticity :
Income Elasticity :
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Example of Log-Linear
Demand
M
QX
βX
βY
βM
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
P
P
• ln Qd = 10 - 2 ln P
• Own Price Elasticity: -2
D
D
Q
Linear
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Q
Log Linear
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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Regression Analysis
• Used to estimate demand functions
• Important terminology
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Least Squares Regression: Y = a + bX + e
Confidence Intervals
t-statistic
R-square or Coefficient of Determination
F-statistic
An Example
• Use a spreadsheet to estimate log-linear
demand
ln Qx = β 0 + β x ln Px + e
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Summary Output
Interpreting the Output
• Estimated demand function:
Regression Statistics
Multiple R
0.41
R Square
0.17
Adjusted R Square
0.15
Standard Error
0.68
Observations
41.00
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ANOVA
df
Regression
Residual
Total
SS
1.00
39.00
40.00
MS
Coefficients Standard Error
7.58
1.43
-0.84
0.30
Intercept
ln(P)
F
3.65
18.13
21.78
3.65
0.46
t Stat
5.29
-2.80
7.85
P-value
0.000005
0.007868
Significance F
0.01
Lower 95%
Upper 95%
4.68
10.48
-1.44
-0.23
• How good is our estimate?
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Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Summary
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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.
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
ln Qx = 7.58 - 0.84 lnPx
Own price elasticity: -0.84 (inelastic)
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, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Sample Exam Problem
Variable
Coefficient S. Error
Constant
100
5.00
P
-2.50
?
PY
-1.20 0.5
M
0.10
?
t-stat
?
4.0
?
2.5
R2 = .75 # of Observations = 200
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
5
Sample Exam Problem
Fill in the table and assuming the null
hypothesis is that the coefficient is zero in
each case.
Find the price elasticity of demand assuming
average income is $2000, P=$100 and PY is
$5. Will revenue fall or rise is price is
lowered?
Sample Exam Problem
Variable
Coefficient S. Error
Constant
100
5.00
P
-2.50
0.625
-1.20 0.5
PY
M
0.10
0.04
t-stat
20.0
-4.0
-2.4
2.5
R2 = .75 # of Observations = 200
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Sample Exam Problem
Sample Exam Problem
Q = 100 – 2.5P – 1.2 PY +.1M demand fn.
Q = 100 – 2.5P – 1.2*5 + .1*2000
Q = 294 – 2.5P demand curve
E = -2.5*P/Q so P = 100 implies Q = 44
E = -250/44 = -5.68 so highly elastic
Lower price and revenue will rise.
Given the demand curve we just calculated,
what price maximizes total revenue? What
is elasticity at that price?
We have Q = 294 – 2.5P and TR = Q*P so
TR = (294 – 2.5P)P = 294P –P2
dTR/dP = 294-5P = 0 or P = $58.8 and Q =
147 so E = -2.5* (58.8/147) = -1
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
Sample Exam Problem
Sample Exam Problem
Marginal revenue by definition is dTR/dQ.
MR >0 implies elastic demand
MR< 0 implies inelastic demand
MR=0 implies unitary elastic demand
The demand cure is Q = f(P) but we need
P = g(Q) or inverse demand curve to obtain
the MR curve (to find dTR/dQ)
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
From previous slide: Q = 294 – 2.5P
Solve for P in terms of Q:
2.5P = 294 – Q or
P = 117.6 – 0.4Q .
TR(Q) = P*Q = (117.6-0.4Q)Q
MR = dTR/dQ = 117.6 – 0.8Q
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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Sample Exam Problem
By definition, MR = 0 implies we have
maximized total revenue. Solving:
117.6 – 0.8Q = 0 implies Q = 147
Substitute into inverse demand curve:
P = 117.6 – 0.4*147 so P = $58.8
Just like a couple of slides back. Note, we
checked that E=1 at that price.
Michael R. Baye, Managerial Economics and Business Strategy, 4e. ©The McGraw-Hill Companies, Inc. , 2002
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