McGraw-Hill/Irwin

Managerial Economics & Business Strategy

Chapter 3 Quantitative Demand Analysis

Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved.

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”

E G

,

S

 % 

G

% 

S

If

E G,S

> 0, then

S

and

G

are directly related.

If

E G,S

< 0, then

S

and

G

are inversely related.

If

E G,S

= 0, then

S

and

G

are unrelated.

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 The Elasticity Concept Using Calculus An alternative way to measure the elasticity of a function G = f(S) is

E G

,

S



dG dS S G

If

E G,S

> 0, then

S

and

G

are directly related.

If

E G,S

< 0, then

S

and

G

are inversely related.

If

E G,S

= 0, then

S

and

G

are unrelated.

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Own Price Elasticity of Demand

E Q X

,

P X

 % 

Q X

% 

P X d

 Negative according to the “law of demand.” Elastic: Inelastic:

E Q X

,

P X E Q X

,

P X

 1  1 Unitary:

E Q X

,

P X

 1

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Perfectly Elastic & Inelastic Demand Price Price D D Quantity Perfectly Elastic (

E Q X

,

P X

  ) Quantity Perfectly Inelastic (

E Q X

,

P X

 0 )

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 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.

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P

100 Elasticity, Total Revenue and Linear Demand

TR

0 10 20 30 40 50

Q

0

Q

3-8

P

100 80 Elasticity, Total Revenue and Linear Demand

TR

0 10 20 30 40 50

Q

800 0 10 20 30 40 50

Q

3-9

Elasticity, Total Revenue and Linear Demand

TR P

100 80 60 1200 0 10 20 30 40 50

Q

800 0 10 20 30 40 50

Q

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Elasticity, Total Revenue and Linear Demand

TR P

100 80 60 40 1200 0 10 20 30 40 50

Q

800 0 10 20 30 40 50

Q

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Elasticity, Total Revenue and Linear Demand

P

100 80 60 40 20 0 10 20 30 40 50

Q TR

1200 800 0 10 20 30 40 50

Q

3-12

Elasticity, Total Revenue and Linear Demand

P

100 80 60 40 20 Elastic 0 10 20 30 40 50

Q TR

1200 800 0 10 20 Elastic 30 40 50

Q

3-13

Elasticity, Total Revenue and Linear Demand

P

100 80 60 40 20 Elastic Inelastic 0 10 20 30 40 50

Q TR

1200 800 0 10 Elastic 20 30 40 50

Q

Inelastic

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Elasticity, Total Revenue and Linear Demand

P

100 80 60 40 20 Elastic

TR

Unit elastic Inelastic 1200 0 10 20 30 40 50

Q

800 Unit elastic 0 10 Elastic 20 30 40 50

Q

Inelastic

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Demand, Marginal Revenue (MR) and Elasticity

P

100 80 60 40 20 0 10 Elastic 20 Unit elastic 40 MR Inelastic 50

Q

  For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0.

When – MR > 0, demand is elastic; – MR = 0, demand is unit elastic; – MR < 0, demand is inelastic.

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Elasticity and Marginal Revenue

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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.

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Cross-Price Elasticity of Demand

E Q X

,

P Y

 % 

Q X

% 

P Y d

If

E QX,PY

> 0, then

X

and

Y

are substitutes.

If

E QX,PY

< 0, then

X

and

Y

are complements.

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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

 

R X

 1 

E Q X

,

P X

 

R Y E Q Y

,

P X

  % 

P X

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Cross-Price Elasticity in Action

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Income Elasticity

E Q X

,

M

 % 

Q X

% 

M d

If

E QX,M

> 0, then

X

is a normal good.

If

E QX,M <

0, then

X

is a inferior good.

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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.

  Impact of advertising campaigns.

And lots more!

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Example 1: Pricing and Cash Flows   AT&T needs to boost revenues in order to meet it’s marketing goals.

 According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64. To accomplish this goal, should AT&T raise or lower it’s price?

3-25

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.

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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

Answer: Calls Increase!

Calls would increase by 25.92 percent!

E Q X

,

P X

  8 .

64  % 

Q

%

X



P X d

  8 .

64 3 %     % 

Q X

 3 % 8 .

64  

d

% 

Q X d

% 

Q X d

 25 .

92 %

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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?

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Answer: AT&T’s Demand Falls!

AT&T’s demand would fall by 36.24 percent!

E Q X

,

P Y

 9 .

06  % 

Q

%

X



P Y d

9 .

06  %  

Q X

4 %

d

 4 %  9 .

06  % 

Q X d

% 

Q X d

  36 .

24 %

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Interpreting Demand Functions  Mathematical representations of demand curves.

 Example:

Q X d

 10  2

P X

 3

P Y

 2

M

– Law of demand holds (coefficient of P X is negative).

– X and Y are substitutes (coefficient of P Y 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:

Q X d

  0  

X P X

 

Y P Y

 

M M

 

H H E Q X

,

P X

 

X P X

Own Price Elasticity

Q X E Q X

,

P Y

 

Y P Y Q X

Cross Price Elasticity

E Q X

,

M

 

M M

Income Elasticity

Q X

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Elasticities for Linear Demand Functions In Action

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Log-Linear Demand  General Log-Linear Demand Function: ln

Q X d

  0  

X

ln

P X

 

Y

ln

P Y

 

M

ln

M

 

H

ln

H

Own Price Elasticity : Cross Price Elasticity : Income Elasticity :  X  Y  M

3-34

Elasticities for Nonlinear Demand

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P Graphical Representation of Linear and Log-Linear Demand P Linear D Q Log Linear D Q

3-36

Regression Line and Least Squares Regression

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Excel and Least Squares Estimates

SUMMARY OUTPUT

Regression Statistics

Multiple R R Square Adjusted R Square Standard Error 0.87

0.75

0.72

112.22

Observations 10.00

ANOVA Regression Residual Total Intercept Price

Df

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

t Stat F

23.94

Significance F

0.0012

P-value

6.69 0.0002

-4.89 0.0012

Lower 95% Upper 95%

1068.87

-3.82

2194.07

-1.37

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Evaluating Statistical Significance

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Excel and Least Squares Estimates

SUMMARY OUTPUT

Regression Statistics

Multiple R R Square Adjusted R Square Standard Error 0.87

0.75

0.72

112.22

Observations 10.00

ANOVA Regression Residual Total Intercept Price

Df

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

t Stat F

23.94

Significance F

0.0012

P-value

6.69 0.0002

-4.89 0.0012

Lower 95% Upper 95%

1068.87

-3.82

2194.07

-1.37

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Regression Analysis Evaluating Overall Regression Line Fit: R- Square

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Regression Analysis Evaluating Overall Regression Line Fit: F Statistic

 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.

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Regression Analysis Excel and Least Squares Estimates

SUMMARY OUTPUT

Regression Statistics

Multiple R R Square Adjusted R Square Standard Error 0.87

0.75

0.72

112.22

Observations 10.00

ANOVA Regression Residual Total Intercept Price

Df

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

t Stat F

23.94

Significance F

0.0012

P-value

6.69 0.0002

-4.89 0.0012

Lower 95% Upper 95%

1068.87

-3.82

2194.07

-1.37

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Regression Analysis Excel and Least Squares Estimates

SUMMARY OUTPUT

Regression Statistics

Multiple R R Square Adjusted R Square Standard Error Observations 0.89

0.79

0.69

9.18

10.00

ANOVA Regression Residual Total Intercept Price Advertising Distance

Df

3 6 9

SS

1920.99

505.91

2426.90

Coefficients Standard Error

135.15

20.65

-0.14

0.06

0.54

-5.78

0.64

1.26

MS

640.33

84.32

F

7.59

Significance F

0.182

t Stat

6.54

P-value

0.0006

-2.41 0.0500

0.85 0.4296

-4.61 0.0037

Lower 95% Upper 95%

84.61

185.68

-0.29

0.00

-1.02

-8.86

2.09

-2.71

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Conclusion

 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.

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