1. Managerial Economics & Business Strategy
Chapter 3
Quantitative Demand Analysis
McGraw-Hill/Irwin
Michael R. Baye, Managerial Economics and Business Strategy
Copyright © 2008 by the McGraw-Hill Companies, Inc. All rights reserved.

2. Overview I. The Elasticity Concept II. Demand Functions
3-2
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. The Elasticity Concept
3-3
The Elasticity Concept
How responsive is variable “G” to a change in variable “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.

4. The Elasticity Concept Using Calculus
3-4
The Elasticity Concept Using Calculus
An alternative way to measure the elasticity of a function G = f(S) is
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.

5. Own Price Elasticity of Demand
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Own Price Elasticity of Demand
Negative according to the “law of demand.”
Elastic:
Inelastic:
Unitary:

6. Perfectly Elastic & Inelastic Demand
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Perfectly Elastic & Inelastic Demand
Price
Price D D
Quantity
Quantity

7. Own-Price Elasticity and Total Revenue
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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.

8. Elasticity, Total Revenue and Linear Demand
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Elasticity, Total Revenue and Linear Demand P TR
100 10 20 30 40 50 Q Q

9. Elasticity, Total Revenue and Linear Demand
3-9
Elasticity, Total Revenue and Linear Demand P TR
100 80
800 Q 10 20 30 40 50 Q 10 20 30 40 50

10. Elasticity, Total Revenue and Linear Demand
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Elasticity, Total Revenue and Linear Demand P TR
100 80 60
1200
800 Q 10 20 30 40 50 Q 10 20 30 40 50

11. Elasticity, Total Revenue and Linear Demand
3-11
Elasticity, Total Revenue and Linear Demand P TR
100 80 60
1200 40
800 Q 10 20 30 40 50 Q 10 20 30 40 50

12. Elasticity, Total Revenue and Linear Demand
3-12
Elasticity, Total Revenue and Linear Demand P TR
100 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50

13. Elasticity, Total Revenue and Linear Demand
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Elasticity, Total Revenue and Linear Demand P TR
100
Elastic 80 60
1200 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic

14. Elasticity, Total Revenue and Linear Demand
3-14
Elasticity, Total Revenue and Linear Demand P TR
100
Elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

15. Elasticity, Total Revenue and Linear Demand
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Elasticity, Total Revenue and Linear Demand P TR
100
Unit elastic
Elastic
Unit elastic 80 60
1200
Inelastic 40 20
800 Q 10 20 30 40 50 Q 10 20 30 40 50
Elastic
Inelastic

16. Demand, Marginal Revenue (MR) and Elasticity
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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 unit elastic;
MR < 0, demand is inelastic. P
100
Elastic
Unit elastic 80 60
Inelastic 40 20 Q 10 20 40 50 MR

17. Factors Affecting Own Price Elasticity
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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.

18. Cross Price Elasticity of Demand
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Cross Price Elasticity of Demand
If EQX,PY > 0, then X and Y are substitutes.
If EQX,PY < 0, then X and Y are complements.

19. Predicting Revenue Changes from Two Products
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Predicting Revenue Changes from Two Products
Suppose that a firm sells to related goods. If the price of X changes, then total revenue will change by:

20. Income Elasticity If EQX,M > 0, then X is a normal good.
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Income Elasticity
If EQX,M > 0, then X is a normal good.
If EQX,M < 0, then X is a inferior good.

21. Uses of Elasticities Pricing. Managing cash flows.
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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!

22. Example 1: Pricing and Cash Flows
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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
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?

23. 3-23
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.

24. Example 2: Quantifying the Change
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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?

25. 3-25
Answer
Calls would increase by percent!

26. Example 3: Impact of a change in a competitor’s price
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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?

27. 3-27
Answer
AT&T’s demand would fall by percent!

28. Interpreting Demand Functions
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Interpreting Demand Functions
Mathematical representations of demand curves.
Example:
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).

29. Linear Demand Functions and Elasticities
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Linear Demand Functions and Elasticities
General Linear Demand Function and Elasticities:
Own Price
Elasticity
Cross Price
Elasticity
Income
Elasticity

30. Example of Linear Demand
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Example of Linear Demand
Qd = P.
Own-Price Elasticity: (-2)P/Q.
If P=1, Q=8 (since = 8).
Own price elasticity at P=1, Q=8:
(-2)(1)/8=

31. 3-31
Log-Linear Demand
General Log-Linear Demand Function:

32. Example of Log-Linear Demand
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Example of Log-Linear Demand
ln(Qd) = ln(P).
Own Price Elasticity: -2.

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

34. Regression Analysis One use is for estimating demand functions.
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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.

35. 3-35
An Example
Use a spreadsheet to estimate the following log-linear demand function.

36. 3-36
Summary Output

37. Interpreting the Regression Output
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Interpreting the Regression Output
The estimated log-linear demand function is:
ln(Qx) = ln(Px).
Own price elasticity: (inelastic).
How good is our estimate?
t-statistics of 5.29 and 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.

38. Conclusion
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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.