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# Chapter 3

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### Chapter 3

2. 2. Overview <ul><li>I. The Elasticity Concept </li></ul><ul><ul><li>Own Price Elasticity </li></ul></ul><ul><ul><li>Elasticity and Total Revenue </li></ul></ul><ul><ul><li>Cross-Price Elasticity </li></ul></ul><ul><ul><li>Income Elasticity </li></ul></ul><ul><li>II. Demand Functions </li></ul><ul><ul><li>Linear </li></ul></ul><ul><ul><li>Log-Linear </li></ul></ul><ul><li>III. Regression Analysis </li></ul>3-
3. 3. The Elasticity Concept <ul><li>How responsive is variable “G” to a change in variable “S” </li></ul>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. 4. The Elasticity Concept Using Calculus <ul><li>An alternative way to measure the elasticity of a function G = f(S) is </li></ul>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. 5. Own Price Elasticity of Demand <ul><li>Negative according to the “law of demand.” </li></ul>Elastic: Inelastic: Unitary: 3-
6. 6. Perfectly Elastic & Inelastic Demand D Price Quantity D Price Quantity 3-
7. 7. Own-Price Elasticity and Total Revenue <ul><li>Elastic </li></ul><ul><ul><li>Increase (a decrease) in price leads to a decrease (an increase) in total revenue. </li></ul></ul><ul><li>Inelastic </li></ul><ul><ul><li>Increase (a decrease) in price leads to an increase (a decrease) in total revenue. </li></ul></ul><ul><li>Unitary </li></ul><ul><ul><li>Total revenue is maximized at the point where demand is unitary elastic. </li></ul></ul>3-
8. 8. Elasticity, Total Revenue and Linear Demand Q Q P TR 100 0 0 10 20 30 40 50 3-
9. 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. 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. 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. 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. 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. 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. 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. 16. Demand, Marginal Revenue (MR) and Elasticity <ul><li>For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0. </li></ul><ul><li>When </li></ul><ul><ul><li>MR > 0, demand is elastic; </li></ul></ul><ul><ul><li>MR = 0, demand is unit elastic; </li></ul></ul><ul><ul><li>MR < 0, demand is inelastic. </li></ul></ul>Q P 100 80 60 40 20 Inelastic Elastic 0 10 20 40 50 Unit elastic MR 3-
17. 17. Factors Affecting Own Price Elasticity <ul><ul><li>Available Substitutes </li></ul></ul><ul><ul><ul><li>The more substitutes available for the good, the more elastic the demand. </li></ul></ul></ul><ul><ul><li>Time </li></ul></ul><ul><ul><ul><li>Demand tends to be more inelastic in the short term than in the long term. </li></ul></ul></ul><ul><ul><ul><li>Time allows consumers to seek out available substitutes. </li></ul></ul></ul><ul><ul><li>Expenditure Share </li></ul></ul><ul><ul><ul><li>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. </li></ul></ul></ul>3-
18. 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. 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. 20. Uses of Elasticities <ul><li>Pricing. </li></ul><ul><li>Managing cash flows. </li></ul><ul><li>Impact of changes in competitors’ prices. </li></ul><ul><li>Impact of economic booms and recessions. </li></ul><ul><li>Impact of advertising campaigns. </li></ul><ul><li>And lots more! </li></ul>3-
21. 21. Example 1: Pricing and Cash Flows <ul><li>According to an FTC Report by Michael Ward, AT&T’s own price elasticity of demand for long distance services is -8.64. </li></ul><ul><li>AT&T needs to boost revenues in order to meet it’s marketing goals. </li></ul><ul><li>To accomplish this goal, should AT&T raise or lower it’s price? </li></ul>3-
22. 22. Answer: Lower price! <ul><li>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. </li></ul>3-
23. 23. Example 2: Quantifying the Change <ul><li>If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T? </li></ul>3-
24. 24. Answer <ul><li>Calls would increase by 25.92 percent! </li></ul>3-
25. 25. Example 3: Impact of a change in a competitor’s price <ul><li>According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is 9.06. </li></ul><ul><li>If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services? </li></ul>3-
26. 26. Answer <ul><li>AT&T’s demand would fall by 36.24 percent! </li></ul>3-
27. 27. Interpreting Demand Functions <ul><li>Mathematical representations of demand curves. </li></ul><ul><li>Example: </li></ul><ul><ul><li>Law of demand holds (coefficient of P X is negative). </li></ul></ul><ul><ul><li>X and Y are substitutes (coefficient of P Y is positive). </li></ul></ul><ul><ul><li>X is an inferior good (coefficient of M is negative). </li></ul></ul>3-
28. 28. Linear Demand Functions and Elasticities <ul><li>General Linear Demand Function and Elasticities: </li></ul>Own Price Elasticity Cross Price Elasticity Income Elasticity 3-
29. 29. Example of Linear Demand <ul><li>Q d = 10 - 2P. </li></ul><ul><li>Own-Price Elasticity: (-2)P/Q. </li></ul><ul><li>If P=1, Q=8 (since 10 - 2 = 8). </li></ul><ul><li>Own price elasticity at P=1, Q=8: </li></ul><ul><li> (-2)(1)/8= - 0.25. </li></ul>3-
30. 30. Regression Analysis <ul><li>One use is for estimating demand functions. </li></ul><ul><li>Important terminology and concepts: </li></ul><ul><ul><li>Least Squares Regression model: Y = a + bX + e . </li></ul></ul><ul><ul><li>Least Squares Regression line: </li></ul></ul><ul><ul><li>Confidence Intervals. </li></ul></ul><ul><ul><li>t -statistic. </li></ul></ul><ul><ul><li>R- square or Coefficient of Determination. </li></ul></ul><ul><ul><li>F -statistic. </li></ul></ul>3-
31. 31. An Example <ul><li>Use a spreadsheet to estimate the following log-linear demand function. </li></ul>3-
32. 32. Summary Output 3-
33. 33. Interpreting the Regression Output <ul><li>The estimated log-linear demand function is: </li></ul><ul><ul><li>ln(Q x ) = 7.58 - 0.84 ln(P x ). </li></ul></ul><ul><ul><li>Own price elasticity: -0.84 (inelastic). </li></ul></ul><ul><li>How good is our estimate? </li></ul><ul><ul><li>t -statistics of 5.29 and -2.80 indicate that the estimated coefficients are statistically different from zero. </li></ul></ul><ul><ul><li>R -square of 0.17 indicates the ln(P X ) variable explains only 17 percent of the variation in ln(Q x ). </li></ul></ul><ul><ul><li>F -statistic significant at the 1 percent level. </li></ul></ul>3-
34. 34. Conclusion <ul><li>Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. </li></ul><ul><li>Given market or survey data, regression analysis can be used to estimate: </li></ul><ul><ul><li>Demand functions. </li></ul></ul><ul><ul><li>Elasticities. </li></ul></ul><ul><ul><li>A host of other things, including cost functions. </li></ul></ul><ul><li>Managers can quantify the impact of changes in prices, income, advertising, etc. </li></ul>3-
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