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Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis McGraw-Hill/Irwin Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. 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 3-2 The Elasticity Concept How responsive is variable “G” to a change in variable “S” EG , S %G %S 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. 3-3 The Elasticity Concept Using Calculus An alternative way to measure the elasticity of a function G = f(S) is EG , S dG 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. 3-4 Own Price Elasticity of Demand EQX , PX %QX %PX d Negative according to the “law of demand.” Elastic: EQ X , PX 1 Inelastic: EQ X , PX 1 Unitary: EQ X , PX 1 3-5 Perfectly Elastic & Inelastic Demand Price Price D D Quantity PerfectlyElastic(EQX ,PX ) Quantity PerfectlyInelastic( EQX , PX 0) 3-6 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. 3-7 Elasticity, Total Revenue and Linear Demand P 100 TR 0 10 20 30 40 50 Q 0 Q 3-8 Elasticity, Total Revenue and Linear Demand P 100 TR 80 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q 3-9 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q 3-10 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q 3-11 Elasticity, Total Revenue and Linear Demand P 100 TR 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q 3-12 Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 40 800 20 0 10 20 30 40 50 Q 0 10 20 30 40 50 Q Elastic 3-13 Elasticity, Total Revenue and Linear Demand P 100 TR Elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 50 Q Inelastic 3-14 Elasticity, Total Revenue and Linear Demand P 100 TR Unit elastic Elastic Unit elastic 80 1200 60 Inelastic 40 800 20 0 10 20 30 40 50 Q 0 10 Elastic 20 30 40 50 Q Inelastic 3-15 Demand, Marginal Revenue (MR) and Elasticity For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0. When P 100 Elastic Unit elastic 80 60 Inelastic 40 20 0 10 20 40 MR 50 Q – MR > 0, demand is elastic; – MR = 0, demand is unit elastic; – MR < 0, demand is inelastic. 3-16 Elasticity and Marginal Revenue 3-17 Factors Affecting the 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. 3-18 Cross-Price Elasticity of Demand EQX , PY %QX %PY d If EQX,PY > 0, then X and Y are substitutes. If EQX,PY < 0, then X and Y are complements. 3-19 Predicting Revenue Changes from Two Products Suppose that a firm sells two related goods. If the price of X changes, then total revenue will change by: R RX 1 EQX , PX RY EQY ,PX %PX 3-20 Cross-Price Elasticity in Action 3-21 Income Elasticity EQX , M %QX %M d If EQX,M > 0, then X is a normal good. If EQX,M < 0, then X is a inferior good. 3-22 Income Elasticity in Action Suppose that the income elasticity of demand for transportation is estimated to be 1.80. If income is projected to decrease by 15 percent, what is the impact on the demand for transportation? is transportation a normal or inferior good? 3-23 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! 3-24 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? 3-25 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. 3-26 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? 3-27 Answer: Calls Increase! Calls would increase by 25.92 percent! EQX , PX %QX 8.64 %PX d %QX 8.64 3% d 3% 8.64 %QX d %QX 25.92% d 3-28 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? 3-29 Answer: AT&T’s Demand Falls! AT&T’s demand would fall by 36.24 percent! EQX , PY %QX 9.06 %PY d %QX 9.06 4% d 4% 9.06 %QX d %QX 36.24% d 3-30 Interpreting Demand Functions Mathematical representations of demand curves. Example: QX 10 2PX 3PY 2M d – Law of demand holds (coefficient of PX is negative). – X and Y are substitutes (coefficient of PY is positive). – X is an inferior good (coefficient of M is negative). 3-31 Linear Demand Functions and Elasticities General Linear Demand Function and Elasticities: QX 0 X PX Y PY M M H H d P EQX , PX X X QX Own Price Elasticity EQX , PY PY Y QX Cross Price Elasticity M EQX , M M QX Income Elasticity 3-32 Elasticities for Linear Demand Functions In Action 3-33 Log-Linear Demand General Log-Linear Demand Function: ln QX d 0 X ln PX Y ln PY M ln M H ln H Own PriceElasticity: X Cross PriceElasticity: Y IncomeElasticity: M 3-34 Elasticities for Nonlinear Demand 3-35 Graphical Representation of Linear and Log-Linear Demand P P D Linear D Q Log Linear Q 3-36 Regression Line and Least Squares Regression 3-37 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R 0.87 R Square 0.75 Adjusted R Square 0.72 Standard Error 112.22 Observations 10.00 ANOVA Df Regression Residual Total Intercept Price 1 8 9 SS 301470.89 100751.61 402222.50 Coefficients Standard Error 1631.47 243.97 -2.60 0.53 MS 301470.89 12593.95 F Significance F 23.94 0.0012 t Stat P-value Lower 95% Upper 95% 6.69 0.0002 1068.87 2194.07 -4.89 0.0012 -3.82 -1.37 3-38 Evaluating Statistical Significance 3-39 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R 0.87 R Square 0.75 Adjusted R Square 0.72 Standard Error 112.22 Observations 10.00 ANOVA Df Regression Residual Total Intercept Price 1 8 9 SS 301470.89 100751.61 402222.50 Coefficients Standard Error 1631.47 243.97 -2.60 0.53 MS 301470.89 12593.95 F Significance F 23.94 0.0012 t Stat P-value Lower 95% Upper 95% 6.69 0.0002 1068.87 2194.07 -4.89 0.0012 -3.82 -1.37 3-40 Regression Analysis Evaluating Overall Regression Line Fit: R- Square 3-41 Regression Analysis Evaluating Overall Regression Line Fit: FStatistic A measure of the total variation explained by the regression relative to the total unexplained variation. – The greater the F-statistic, the better the overall regression fit. – Equivalently, the P-value is another measure of the F-statistic. • Lower p-values are associated with better overall regression fit. 3-42 Regression Analysis Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R 0.87 R Square 0.75 Adjusted R Square 0.72 Standard Error 112.22 Observations 10.00 ANOVA Df Regression Residual Total Intercept Price 1 8 9 SS 301470.89 100751.61 402222.50 Coefficients Standard Error 1631.47 243.97 -2.60 0.53 MS 301470.89 12593.95 F Significance F 23.94 0.0012 t Stat P-value Lower 95% Upper 95% 6.69 0.0002 1068.87 2194.07 -4.89 0.0012 -3.82 -1.37 3-43 Regression Analysis Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R 0.89 R Square 0.79 Adjusted R Square 0.69 Standard Error 9.18 Observations 10.00 ANOVA Df Regression Residual Total Intercept Price Advertising Distance SS 1920.99 505.91 2426.90 MS 640.33 84.32 Coefficients Standard Error 135.15 20.65 -0.14 0.06 0.54 0.64 -5.78 1.26 t Stat 6.54 -2.41 0.85 -4.61 3 6 9 F Significance F 7.59 0.182 P-value Lower 95% Upper 95% 84.61 185.68 0.0006 0.0500 -0.29 0.00 0.4296 -1.02 2.09 0.0037 -8.86 -2.71 3-44 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. – A host of other things, including cost functions. Managers can quantify the impact of changes in prices, income, advertising, etc. 3-45