1. 3-1 Quantitative Demand Analysis

2. Overview I. The Elasticity Concept n Own Price Elasticity n Elasticity and Total Revenue n Cross-Price Elasticity n Income Elasticity II. Demand Functions n Linear n Log-Linear III. Regression Analysis 3-2

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. 3-3

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. 3-4

5. Own Price Elasticity of Demand Negative according to the “law of demand.” Elastic: Inelastic: Unitary: 3-5

6. Perfectly Elastic & Inelastic Demand D Price Quantity D Price Quantity 3-6

7. Own-Price Elasticity and Total Revenue Elastic n Increase (a decrease) in price leads to a decrease (an increase) in total revenue. Inelastic n Increase (a decrease) in price leads to an increase (a decrease) in total revenue. Unitary n Total revenue is maximized at the point where demand is unitary elastic. 3-7

8. Elasticity, Total Revenue and Linear Demand QQ P TR 100 001020 304050 3-8

9. Elasticity, Total Revenue and Linear Demand QQ P TR 100 01020 304050 80 800 0 10 20 304050 3-9

10. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 01020 304050 01020 304050 3-10

11. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 40 01020 304050 01020 304050 3-11

12. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 40 20 01020 304050 01020 304050 3-12

13. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 40 20 Elastic 01020 304050 01020 304050 3-13

14. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 40 20 Inelastic Elastic Inelastic 01020 304050 01020 304050 3-14

15. Elasticity, Total Revenue and Linear Demand QQ P TR 100 80 800 60 1200 40 20 Inelastic Elastic Inelastic 01020 304050 01020 304050 Unit elastic 3-15

16. Demand, Marginal Revenue (MR) and Elasticity For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0. When n MR > 0, demand is elastic; n MR = 0, demand is unit elastic; n MR < 0, demand is inelastic. Q P 100 80 60 40 20 Inelastic Elastic 01020 4050 Unit elastic MR 3-16

17. Factors Affecting Own Price Elasticity n Available Substitutes The more substitutes available for the good, the more elastic the demand. n Time Demand tends to be more inelastic in the short term than in the long term. Time allows consumers to seek out available substitutes. n 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. 3-17

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. 3-18

19. 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: 3-19

20. 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

21. 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

22. 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

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. 3-23

24. 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

25. Answer Calls would increase by 25.92 percent! 3-25

26. 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

27. Answer AT&T’s demand would fall by 36.24 percent! 3-27

28. Interpreting Demand Functions Mathematical representations of demand curves. Example: n Law of demand holds (coefficient of P X is negative). n X and Y are substitutes (coefficient of P Y is positive). n X is an inferior good (coefficient of M is negative). 3-28

29. Linear Demand Functions and Elasticities General Linear Demand Function and Elasticities: Own Price Elasticity Cross Price Elasticity Income Elasticity 3-29

30. 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

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

32. Example of Log-Linear Demand ln(Q d ) = 10 - 2 ln(P). Own Price Elasticity: -2. 3-32

33. P Q Q D D LinearLog Linear Graphical Representation of Linear and Log-Linear Demand P 3-33

34. Conclusion Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. Managers can quantify the impact of changes in prices, income, advertising, etc. 3-34