Managerial Economics & Business Strategy

1. Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

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

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

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

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

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

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 2Q2 Note: MR looks like inverse demand (P = 10 – 2Q), but has twice the slope, which means MR < P. Why?

9. 10 Elastic: P , Qd , and TR  Unit Elastic: TR is maximized Price, MR 5 Inelastic: P , Qd , and TR D MR Quantity 2.5 5 When MR = 0 (i.e., slope of TR function is zero), TR is maximized Total Revenue 12.5 Quantity

10. Factors Affecting Own Price Elasticity • 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 • 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.

11. Cross Price Elasticity of Demand + Substitutes - Complements

12. Cross-Price Elasticity of Demand 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

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 PY is positive) • X is an inferior good (coefficient of M is negative)

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

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

23. constant elasticities Log-Linear Demand

24. P Q P D D Q Log Linear Linear

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

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

27. An Example • Go out and collect data on price and quantity • Cautionary note about identification. P S0 S1 $8 $6 D0 D improperly identified D1 Q 100 250 • Use a spreadsheet or statistical package (e.g., Minitab) to estimate demand:

28. Summary Output

29. Interpreting the Output • Estimated demand function: • ln Qx = 7.58 - 0.84 lnPx • 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 .17 indicates we explained only 17 percent of the variation • 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 • 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.