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# Managerial Economics

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### Managerial Economics

2. 2. Overview I. The Elasticity Concept Own Price Elasticity Elasticity and Total Revenue Cross-Price Elasticity Income Elasticity II. Demand Functions Linear Log-Linear Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
3. 3. The Elasticity Concept • How responsive is variable “G” to a change in variable “S” % ΔG EG , S = % ΔS If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
4. 4. The Elasticity Concept Using Calculus • An alternative way to measure the elasticity of a function G = f(S) is dG S EG , S = dS G If EG,S > 0, then S and G are directly related. If EG,S < 0, then S and G are inversely related. If EG,S = 0, then S and G are unrelated. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
5. 5. Own Price Elasticity of Demand %ΔQX d EQX , PX = %ΔPX • Negative according to the “law of demand.” Elastic: EQX , PX > 1 Inelastic: EQX , PX < 1 Unitary: EQX , PX = 1 Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
6. 6. Perfectly Elastic & Inelastic Demand Price Price D D Quantity Quantity Perfectly Elastic ( EQ X ,PX = −∞) Perfectly Inelastic ( EQX , PX = 0) Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
7. 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. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
8. 8. Elasticity, Total Revenue and Linear Demand P TR 100 0 10 20 30 40 50 Q 0 Q Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
9. 9. Elasticity, Total Revenue and Linear Demand P TR 100 80 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
10. 10. Elasticity, Total Revenue and Linear Demand P TR 100 80 60 1200 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
11. 11. Elasticity, Total Revenue and Linear Demand P TR 100 80 60 1200 40 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
12. 12. Elasticity, Total Revenue and Linear Demand P TR 100 80 60 1200 40 20 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
13. 13. Elasticity, Total Revenue and Linear Demand P TR 100 Elastic 80 60 1200 40 20 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elastic Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
14. 14. Elasticity, Total Revenue and Linear Demand P TR 100 Elastic 80 60 1200 Inelastic 40 20 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elastic Inelastic Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
15. 15. Elasticity, Total Revenue and Linear Demand P TR 100 Elastic Unit elastic 80 Unit elastic 60 1200 Inelastic 40 20 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elastic Inelastic Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
16. 16. 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. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
17. 17. Cross Price Elasticity of Demand %ΔQX d EQX , PY = %ΔPY If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
18. 18. Income Elasticity %ΔQX d EQX , M = %ΔM If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is a inferior good. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
19. 19. Uses of Elasticities • Pricing. • Managing cash flows. • Impact of changes in competitors’ prices. • Impact of advertising campaigns. • Merger analysis Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
20. 20. 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? Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
21. 21. 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. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
22. 22. 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? Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
23. 23. Answer • Calls would increase by 25.92 percent! %ΔQX d EQX , PX = −8.64 = %ΔPX %ΔQX d − 8.64 = − 3% − 3% × (− 8.64 ) = %ΔQX d %ΔQX = 25.92% d Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
24. 24. 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? Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
25. 25. Answer • AT&T’s demand would fall by 36.24 percent! %ΔQX d EQX , PY = 9.06 = %ΔPY %ΔQX d 9.06 = − 4% − 4% × 9.06 = %ΔQX d %ΔQX = −36.24% d Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
26. 26. Interpreting Demand Functions • Mathematical representations of demand curves. • Example: QX = 10 − 2 PX + 3PY − 2 M d • X and Y are substitutes (coefficient of PY is positive). • X is an inferior good (coefficient of M is negative). Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
27. 27. Linear Demand Functions • General Linear Demand Function: QX = α 0 + α X PX + α Y PY + α M M + α H H d PY M P EQX , PX = α X X EQX , PY = αY EQX , M = α M QX QX QX Own Price Cross Price Income Elasticity Elasticity Elasticity Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
28. 28. Example of Linear Demand • Qd = 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. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
29. 29. Log-Linear Demand • General Log-Linear Demand Function: ln Q X d = β 0 + β X ln PX + βY ln PY + β M ln M + β H ln H Own Price Elasticity : βX Cross Price Elasticity : β Y Income Elasticity : βM Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
30. 30. Example of Log-Linear Demand • ln(Qd) = 10 - 2 ln(P). • Own Price Elasticity: -2. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
31. 31. Graphical Representation of Linear and Log-Linear Demand P P D D Q Q Linear Log Linear Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
32. 32. 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. • Managers can quantify the impact of changes in prices, income, advertising, etc. Michael R. Baye, Managerial Economics and Business Strategy, 5e. Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.