1. Managerial Economics & Business Strategy Chapter 3 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. Own Price Elasticity of Demand Negative according to the “law of demand” Elastic: Inelastic: Unitary:

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

5. Own-Price Elasticity and Total Revenue Elastic: Increase (a decrease) in price leads to a decrease (an increase) in total revenue. n E.G., %  in P leads to a larger %  in Q d  TR  Inelastic: Increase (a decrease) in price leads to an increase (a decrease) in total revenue. n E.G., %  in P leads to a smaller %  in Q d  TR  Unitary: Total revenue is maximized at the point where demand is unitary elastic. n E.G., %  in P leads to a same %  in Q d  TR remains unchanged and is maximized.

6. Linear Demand & Elasticity Suppose you have the following demand function: Therefore, Inverse Demand

7. =  3=  2/3 Linear Demand & Elasticity Price Quantity D 10 8 6 4 2 1 2 3 4 5 Elastic Inelastic Unit Elastic 5 2.5 =  1/4

8. Demand, Market Elasticity, TR and MR Using the demand function, find TR(Q) & MR. TR=P  Q, plug-in inverse demand function for P TR(Q)=10Q  2Q 2 Note: MR looks like inverse demand (P = 10 – 2Q), but has twice the slope, which means MR < P. Why?

9. Unit Elastic: TR is maximized Elastic: P , Q d , and TR  Inelastic: P , Q d , and TR  Total Revenue Quantity 12.5 When MR = 0 (i.e., slope of TR function is zero), TR is maximized MR Price, MR Quantity 10 52.5 5 D

10. Factors Affecting Own Price Elasticity n Available Substitutes The more substitutes available for the good, the more elastic the demand. –Firm demand curve will be more elastic than the market demand curve 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.

11. Cross Price Elasticity of Demand + Substitutes - Complements

12. When a firm’s revenues are derived from the sale of two goods, X and Y We can calculate the change in revenues when the price of good X changes as Cross-Price Elasticity of Demand

13. Income Elasticity + Normal Good - Inferior Good

14. 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?

15. 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.

16. 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?

17. Answer Calls would increase by 25.92 percent!

18. 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?

19. Answer AT&T’s demand would fall by 36.24 percent!

20. Information Found in Demand Functions Example: X and Y are substitutes (coefficient of P Y is positive) X is an inferior good (coefficient of M is negative)

21. Calculating Elasticities from Linear Demand Functions Linear Demand Own Price Elasticity Cross Price Elasticity Income Elasticity

22. Example of Linear Demand Given: P X =$40, P Y =$30, M=$48,000 Q X d = 100 - 2P X + 4P Y + ¼ M Find Q given the above data. Calculate Own-Price Elasticity. Calculate Cross-Price Elasticity. Calculate Income Elasticity.

23. Log-Linear Demand  constant elasticities

24. P Q P Q D D Linear Log Linear

25. Example of Log-Linear Demand ln Q d = 10 - 2 ln P Own Price Elasticity: -2 If price falls by 20%, by what percentage will Q d change?

26. Regression Analysis Used to estimate demand functions Important terminology (MBA 6041 and covered in the Baye Managerial textbook). n Least Squares Regression: Y = a + bX + e n Confidence Intervals n t-statistic n R-square n F-statistic

27. An Example Go out and collect data on price and quantity n Cautionary note about identification. P Q Use a spreadsheet or statistical package (e.g., Minitab) to estimate demand: D improperly identified $8 $6 100250 S1S1 S0S0 D1D1 D0D0

28. Summary Output

29. Interpreting the Output Estimated demand function: n ln Q x = 7.58 - 0.84 lnP x n Own price elasticity: -0.84 (inelastic) How good is our estimate? n t-statistics of 5.29 and -2.80 indicate that the estimated coefficients are statistically different from zero n R-square of.17 indicates we explained only 17 percent of the variation n F-statistic significant at the 1 percent level tells us that only 1% chance that estimated regression model fits the data purely by accident.

30. Summary n Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. n Given market or survey data, regression analysis can be used to estimate: Demand functions Elasticities A host of other things, including cost functions n Managers can quantify the impact of changes in prices, income, advertising, etc.