Copyright © 2010 by the McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin Managerial Economics & Business Strategy Chapter 3 Quantitative Demand Analysis

3-2 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

3-3 The Elasticity Concept  How responsive is variable “G” to a change in variable “S” 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 The Elasticity Concept Using Calculus  An alternative way to measure the elasticity of a function G = f(S) is 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 Own Price Elasticity of Demand  Negative according to the “law of demand.” Elastic: Inelastic: Unitary:

3-6 Perfectly Elastic & Inelastic Demand D Price Quantity D Price Quantity

3-7 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.

3-8 Elasticity, Total Revenue and Linear Demand QQ P TR

3-9 Elasticity, Total Revenue and Linear Demand QQ P TR

3-10 Elasticity, Total Revenue and Linear Demand QQ P TR

3-11 Elasticity, Total Revenue and Linear Demand QQ P TR

3-12 Elasticity, Total Revenue and Linear Demand QQ P TR

3-13 Elasticity, Total Revenue and Linear Demand QQ P TR Elastic

3-14 Elasticity, Total Revenue and Linear Demand QQ P TR Inelastic Elastic Inelastic

3-15 Elasticity, Total Revenue and Linear Demand QQ P TR Inelastic Elastic Inelastic Unit elastic

3-16 Demand, Marginal Revenue (MR) and Elasticity  For a linear inverse demand function, MR(Q) = a + 2bQ, where b < 0.  When –MR > 0, demand is elastic; –MR = 0, demand is unit elastic; –MR < 0, demand is inelastic. Q P Inelastic Elastic Unit elastic MR

3-17 Elasticity and Marginal Revenue 

3-18 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.

3-19 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.

3-20 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:

3-21 Cross-Price Elasticity in Action 

3-22 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.

3-23 Income Elasticity in Action  Suppose that the income elasticity of demand for transportation is estimated to be 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?

3-24 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!

3-25 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  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?

3-26 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.

3-27 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?

3-28 Answer: Calls Increase! Calls would increase by percent!

3-29 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  If competitors reduced their prices by 4 percent, what would happen to the demand for AT&T services?

3-30 Answer: AT&T’s Demand Falls! AT&T’s demand would fall by percent!

3-31 Interpreting Demand Functions  Mathematical representations of demand curves.  Example: –Law of demand holds (coefficient of P X is negative). –X and Y are substitutes (coefficient of P Y is positive). –X is an inferior good (coefficient of M is negative).

3-32 Linear Demand Functions and Elasticities  General Linear Demand Function and Elasticities: Own Price Elasticity Cross Price Elasticity Income Elasticity

3-33 Elasticities for Linear Demand Functions In Action 

3-34 Log-Linear Demand  General Log-Linear Demand Function:

3-35 Elasticities for Nonlinear Demand 

3-36 Graphical Representation of Linear and Log-Linear Demand P Q Q D D LinearLog Linear P

3-37 Regression Line and Least Squares Regression 

3-38 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R0.87 R Square0.75 Adjusted R Square0.72 Standard Error Observations10.00 ANOVA DfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept Price

3-39 Evaluating Statistical Significance 

3-40 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R0.87 R Square0.75 Adjusted R Square0.72 Standard Error Observations10.00 ANOVA DfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept Price

3-41 Evaluating Overall Regression Line Fit: R- Square  Regression Analysis

3-42 Evaluating Overall Regression Line Fit: F- Statistic  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. Regression Analysis

3-43 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R0.87 R Square0.75 Adjusted R Square0.72 Standard Error Observations10.00 ANOVA DfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept Price Regression Analysis

3-44 Excel and Least Squares Estimates SUMMARY OUTPUT Regression Statistics Multiple R0.89 R Square0.79 Adjusted R Square0.69 Standard Error9.18 Observations10.00 ANOVA DfSSMSFSignificance F Regression Residual Total CoefficientsStandard Errort StatP-valueLower 95%Upper 95% Intercept Price Advertising Distance Regression Analysis

3-45 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.