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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
    3-
  • 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.
    3-
  • 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.
    3-
  • 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!
    3-
  • 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?
    3-
  • 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.
    3-
  • 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?
    3-
  • 24. Answer
    • Calls would increase by 25.92 percent!
    3-
  • 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?
    3-
  • 26. Answer
    • AT&T’s demand would fall by 36.24 percent!
    3-
  • 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).
    3-
  • 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.
    3-
  • 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.
    3-
  • 31. An Example
    • Use a spreadsheet to estimate the following log-linear demand function.
    3-
  • 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.
    3-
  • 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.
    3-