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# Chapter 3

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• 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
• Own Price Elasticity
• Elasticity and Total Revenue
• Cross-Price Elasticity
• Income Elasticity
• II. Demand Functions
• Linear
• Log-Linear
• III. Regression Analysis
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• 3. The Elasticity Concept
• How responsive is variable “G” to a change in variable “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. 3-
• 4. The Elasticity Concept Using Calculus
• An alternative way to measure the elasticity of a function G = f(S) is
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. 3-
• 5. Own Price Elasticity of Demand
• Negative according to the “law of demand.”
Elastic: Inelastic: Unitary: 3-
• 6. Perfectly Elastic & Inelastic Demand D Price Quantity D Price Quantity 3-
• 7. 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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• 8. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 0 0 10 20 30 40 50 3-
• 9. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 0 10 20 30 40 50 80 800 0 10 20 30 40 50 3-
• 10. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 0 10 20 30 40 50 0 10 20 30 40 50 3-
• 11. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 40 0 10 20 30 40 50 0 10 20 30 40 50 3-
• 12. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 40 20 0 10 20 30 40 50 0 10 20 30 40 50 3-
• 13. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 40 20 Elastic Elastic 0 10 20 30 40 50 0 10 20 30 40 50 3-
• 14. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 40 20 Inelastic Elastic Elastic Inelastic 0 10 20 30 40 50 0 10 20 30 40 50 3-
• 15. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 80 800 60 1200 40 20 Inelastic Elastic Elastic Inelastic 0 10 20 30 40 50 0 10 20 30 40 50 Unit elastic Unit elastic 3-
• 16. 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.
Q P 100 80 60 40 20 Inelastic Elastic 0 10 20 40 50 Unit elastic MR 3-
• 17. 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.
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• 18. Cross Price Elasticity of Demand If E Q X ,P Y > 0, then X and Y are substitutes. If E Q X ,P Y < 0, then X and Y are complements. 3-
• 19. Income Elasticity If E Q X ,M > 0, then X is a normal good. If E Q X ,M < 0, then X is a inferior good. 3-
• 20. 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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• 21. 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?
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• 22. 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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• 23. 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?
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• Calls would increase by 25.92 percent!
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• 25. 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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• AT&T’s demand would fall by 36.24 percent!
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• 27. Interpreting Demand Functions
• Mathematical representations of demand curves.
• Example:
• 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).
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• 28. Linear Demand Functions and Elasticities
• General Linear Demand Function and Elasticities:
Own Price Elasticity Cross Price Elasticity Income Elasticity 3-
• 29. Example of Linear Demand
• Q d = 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.
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• 30. 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.
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• 31. An Example
• Use a spreadsheet to estimate the following log-linear demand function.
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• 32. Summary Output 3-
• 33. Interpreting the Regression Output
• The estimated log-linear demand function is:
• ln(Q x ) = 7.58 - 0.84 ln(P x ).
• 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(P X ) variable explains only 17 percent of the variation in ln(Q x ).
• F -statistic significant at the 1 percent level.
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• 34. 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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