7/31/2019 Chap3 (Bayes)

1/37

Managerial Economics &

Business Strategy

Chapter 3

Quantitative Demand Analysis

McGraw-Hill/IrwinMichael R. Baye, Managerial Economics andBusiness Strategy Copyright 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

7/31/2019 Chap3 (Bayes)

2/37

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

7/31/2019 Chap3 (Bayes)

3/37

The Elasticity Concept

How responsive is variable G to a change

in variable S

IfEG,S > 0, then S and G are directly related.

IfEG,S < 0, then S and G are inversely related.

S

GE SG

%

%,

IfEG,S = 0, then S and G are unrelated.

3-3

7/31/2019 Chap3 (Bayes)

4/37

The Elasticity Concept Using

Calculus An alternative way to measure the elasticity

of a function G = f(S) is

G

S

dS

dGE SG ,

IfEG,S > 0, then S and G are directly related.

IfEG,S < 0, then S and G are inversely related.

IfEG,S = 0, then S and G are unrelated.

3-4

7/31/2019 Chap3 (Bayes)

5/37

Own Price Elasticity of

Demand

Negativeaccording to the law of demand.

Elastic:Inelastic:

Unitary:

X

d

X

PQ

P

QE

XX

%

%,

1,

XX PQE

1, XX PQE

1, XX PQE

3-5

7/31/2019 Chap3 (Bayes)

6/37

Perfectly Elastic &

Inelastic Demand

)(ElasticPerfectly , XX PQE

D

Price

Quantity

D

Price

Quantity

)0(InelasticPerfectly , XX PQE

3-6

7/31/2019 Chap3 (Bayes)

7/37

Own-Price Elasticity

and Total Revenue Elastic

Increase (a decrease) in price leads to a decrease (anincrease) 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

7/31/2019 Chap3 (Bayes)

8/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

0 010 20 30 40 50

3-8

7/31/2019 Chap3 (Bayes)

9/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

0 10 20 30 40 50

80

800

0 10 20 30 40 50

3-9

7/31/2019 Chap3 (Bayes)

10/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

80

800

60 1200

0 10 20 30 40 500 10 20 30 40 50

3-10

7/31/2019 Chap3 (Bayes)

11/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

80

800

60 1200

40

0 10 20 30 40 500 10 20 30 40 50

3-11

7/31/2019 Chap3 (Bayes)

12/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

80

800

60 1200

40

20

0 10 20 30 40 500 10 20 30 40 50

3-12

7/31/2019 Chap3 (Bayes)

13/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

80

800

60 1200

40

20

Elastic

Elastic

0 10 20 30 40 500 10 20 30 40 50

3-13

7/31/2019 Chap3 (Bayes)

14/37

Elasticity, Total Revenue and Linear

Demand

QQ

PTR

100

80

800

60 1200

40

20

Inelastic

Elastic

Elastic Inelastic

0 10 20 30 40 500 10 20 30 40 50

3-14

7/31/2019 Chap3 (Bayes)

15/37

Elasticity, Total Revenue and Linear

Demand

QQ

P TR

100

80

800

60 1200

40

20

Inelastic

Elastic

Elastic Inelastic

0 10 20 30 40 500 10 20 30 40 50

Unit elastic

Unit elastic

3-15

7/31/2019 Chap3 (Bayes)

16/37

Demand, Marginal Revenue (MR)

and Elasticity For a linear inverse

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

When MR > 0, demand is

elastic;

MR = 0, demand is unitelastic;

MR < 0, demand isinelastic.

Q

P

100

80

60

40

20

Inelastic

Elastic

0 10 20 40 50

Unit elastic

MR

3-16

7/31/2019 Chap3 (Bayes)

17/37

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 consumers

budgets tend to be more inelastic than goods for which

consumers spend a large portion of their incomes.

3-17

7/31/2019 Chap3 (Bayes)

18/37

Cross Price Elasticity of

Demand

IfEQX,PY

> 0, thenXand Yare substitutes.

IfEQX,PY< 0, thenXand Yare complements.

Y

d

X

PQ P

QE

YX

%

%

,

3-18

7/31/2019 Chap3 (Bayes)

19/37

Income Elasticity

IfEQX

,M> 0, thenXis a normal good.

IfEQX,M< 0, thenXis a inferior good.

M

QE

d

X

MQX

%

%,

3-19

7/31/2019 Chap3 (Bayes)

20/37

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!

3-20

7/31/2019 Chap3 (Bayes)

21/37

Example 1: Pricing and Cash

Flows According to an FTC Report by Michael

Ward, AT&Ts own price elasticity of

demand for long distance services is -8.64. AT&T needs to boost revenues in order to

meet its marketing goals.

To accomplish this goal, should AT&Traise or lower its price?

3-21

7/31/2019 Chap3 (Bayes)

22/37

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.

3-22

7/31/2019 Chap3 (Bayes)

23/37

Example 2: Quantifying the

Change IfAT&T lowered price by 3 percent, what

would happen to the volume of long

distance telephone calls routed throughAT&T?

3-23

7/31/2019 Chap3 (Bayes)

24/37

Answer

Calls would increase by 25.92 percent.

%92.25%

%64.8%3

%3

%64.8

%

%64.8,

d

X

dX

d

X

X

d

XPQ

Q

Q

Q

P

QE

XX

3-24

7/31/2019 Chap3 (Bayes)

25/37

Example 3: Impact of a change

in a competitors price According to an FTC Report by Michael

Ward, AT&Ts cross price elasticity of

demand for long distance services is 9.06.

Ifcompetitors reduced their prices by 4

percent, what would happen to the demand

for AT&T services?

3-25

7/31/2019 Chap3 (Bayes)

26/37

Answer

AT&Ts demand would fall by 36.24 percent.

%24.36%

%06.9%4

%4

%06.9

%

%06.9,

d

X

dX

d

X

Y

d

XPQ

Q

Q

Q

P

QE

YX

3-26

7/31/2019 Chap3 (Bayes)

27/37

Interpreting Demand Functions

Mathematical representations of demand curves.

Example:

MPPQ YXd

X 23210

3-27

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).

7/31/2019 Chap3 (Bayes)

28/37

Linear Demand Functions and

Elasticities General Linear Demand Function and Elasticities:

HMPPQ HMYYXXd

X 0

Own Price

Elasticity

Cross Price

Elasticity

Income

Elasticity

X

X

XPQ Q

PE

XX

,X

MMQ

Q

ME

X

,X

YYPQ

Q

PE

YX,

3-28

7/31/2019 Chap3 (Bayes)

29/37

Example of Linear Demand

Qd = 10 - 2P.

Own-Price Elasticity: (-2)P/Q.

IfP=1, Q=8 (since 10 - 2 = 8).

Own price elasticity at P=1, Q=8:

(-2)(1)/8= - 0.25.

3-29

7/31/2019 Chap3 (Bayes)

30/37

0ln ln ln ln ln

d

X X X Y Y M HQ P P M H

M

Y

X

:ElasticityIncome

:ElasticityPriceCross

:ElasticityPriceOwn

Log-Linear Demand

General Log-Linear Demand Function:

3-30

7/31/2019 Chap3 (Bayes)

31/37

Example of Log-Linear

Demand ln(Qd) = 10 - 2 ln(P).

Own Price Elasticity: -2.

3-31

7/31/2019 Chap3 (Bayes)

32/37

P

Q Q

D D

Linear Log Linear

Graphical Representation of

Linear and Log-Linear Demand

P

3-32

7/31/2019 Chap3 (Bayes)

33/37

Regression Analysis

One use is for estimating demand functions.

Important terminology and concepts:

Least Squares Regression model: Y = a + bX + e. Least Squares Regression line:

Confidence Intervals.

t-statistic.

R-square or Coefficient of Determination.

F-statistic.

XbaY

3-33

7/31/2019 Chap3 (Bayes)

34/37

An Example

Use a spreadsheet to estimate the following

log-linear demand function.

0ln lnx x xQ P e

3-34

7/31/2019 Chap3 (Bayes)

35/37

Summary Output

Regression Statistics

Multiple R 0.41

R Square 0.17

Adjusted R Square 0.15

Standard Error 0.68

Observations 41.00

ANOVA

df SS MS F Significance F

Regression 1.00 3.65 3.65 7.85 0.01

Residual 39.00 18.13 0.46

Total 40.00 21.78

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 7.58 1.43 5.29 0.000005 4.68 10.48

ln(P) -0.84 0.30 -2.80 0.007868 -1.44 -0.23

3-35

7/31/2019 Chap3 (Bayes)

36/37

Interpreting the Regression

Output The estimated log-linear demand function is:

ln(Qx)= 7.58 - 0.84 ln(Px).

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 0.17 indicates the ln(PX) variable explains

only 17 percent of the variation in ln(Qx).

F-statistic significant at the 1 percent level.

3-36

3 37

7/31/2019 Chap3 (Bayes)

37/37

Conclusion

Elasticities are tools you can use to quantifythe impact of changes in prices, income, andadvertising on sales and revenues.

Given market or survey data, regressionanalysis 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.

3-37