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Chapter 3Quantitative Demand AnalysisCopyright 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Chapter OutlineThe elasticity conceptOwn price elasticity of demandElasticity and total revenueFactors affecting the own price elasticity of demandMarginal revenue and the own price elasticity of demandCross-price elasticityRevenue changes with multiple productsIncome elasticityOther ElasticitiesLinear demand functionsNonlinear demand functionsObtaining elasticities from demand functionsElasticities for linear demand functionsElasticities for nonlinear demand functionsRegression AnalysisStatistical significance of estimated coefficientsOverall fit of regression lineRegression for nonlinear functions and multiple regression3-2Chapter Overview2IntroductionChapter 2 focused on interpreting demand functions in qualitative terms:An increase in the price of a good leads quantity demanded for that good to decline.A decrease in income leads demand for a normal good to decline.This chapter examines the magnitude of changes using the elasticity concept, and introduces regression analysis to measure different elasticities.3-3Chapter Overview3The Elasticity ConceptElasticity Measures the responsiveness of a percentage change in one variable resulting from a percentage change in another variable.

3-4The Elasticity Concept4The Elasticity Formula3-5The Elasticity Concept5Measurement Aspects of Elasticity3-6The Elasticity Concept6Own Price Elasticity3-7Own Price Elasticity of Demand7Linear Demand, Elasticity, and Revenue3-8QuantityPriceDemand$400$20$102030$540$15$30$25$351050607080Observation: Elasticity varies along a linear (inverse) demand curveOwn Price Elasticity of Demand8Total Revenue TestWhen demand is elastic:A price increase (decrease) leads to a decrease (increase) in total revenue.When demand is inelastic:A price increase (decrease) leads to an increase (decrease) in total revenue.When demand is unitary elastic:Total revenue is maximized. 3-9Own Price Elasticity of Demand9Extreme Elasticities3-10QuantityDemandPricePerfectly InelasticDemandPerfectly elasticOwn Price Elasticity of Demand10Factors Affecting the Own Price ElasticityThree factors can impact the own price elasticity of demand:Availability of consumption substitutes.Time/Duration of purchase horizon.Expenditure share of consumers budgets.3-11Own Price Elasticity of Demand11Elasticity and Marginal Revenue3-12Own Price Elasticity of Demand12Demand and Marginal Revenue3-13Quantity0MR3Price6ElasticDemandOwn Price Elasticity of Demand16InelasticUnitaryMarginal Revenue (MR)Cross-Price Elasticity3-14Cross-Price Elasticity14Cross-Price Elasticity in Action3-15Cross-Price Elasticity15Cross-Price Elasticity3-16Cross-Price Elasticity16Cross-Price Elasticity in Action3-17Cross-Price Elasticity17Income Elasticity3-18Income Elasticity18Income Elasticity in Action3-19Income Elasticity19Other ElasticitiesOwn advertising elasticity of demand for good X is the ratio of the percentage change in the consumption of X to the percentage change in advertising spent on X.Cross-advertising elasticity between goods X and Y would measure the percentage change in the consumption of X that results from a 1 percent change in advertising toward Y.3-20Other ElasticitiesElasticities for Linear Demand Functions3-21Obtaining Elasticities From Demand Functions21Elasticities for Linear Demand Functions In Action3-22Obtaining Elasticities From Demand Functions22Elasticities for Nonlinear Demand Functions3-23Obtaining Elasticities From Demand Functions23Elasticities for Nonlinear Demand FunctionsIn Action3-24Obtaining Elasticities From Demand Functions24Regression AnalysisHow does one obtain information on the demand function?Published studies.Hire consultant.Statistical technique called regression analysis using data on quantity, price, income and other important variables.3-25Regression Analysis25Regression Line and Least Squares Regression3-26Regression Analysis26Excel and Least Squares Estimates3-27SUMMARY OUTPUTRegression StatisticsMultiple R0.87R Square0.75Adjusted R Square0.72Standard Error112.22Observations10.00ANOVADfSSMSFSignificance FRegression1301470.89301470.8923.940.0012Residual8100751.6112593.95Total9402222.50CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept1631.47243.976.690.00021068.872194.07Price-2.600.53-4.890.0012-3.82-1.37Regression Analysis27Evaluating Statistical Significance3-28Regression Analysis28Excel and Least Squares Estimates3-29SUMMARY OUTPUTRegression StatisticsMultiple R0.87R Square0.75Adjusted R Square0.72Standard Error112.22Observations10.00ANOVADfSSMSFSignificance FRegression1301470.89301470.8923.940.0012Residual8100751.6112593.95Total9402222.50CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept1631.47243.976.690.00021068.872194.07Price-2.600.53-4.890.0012-3.82-1.37Regression Analysis29Evaluating Overall Regression Line Fit: R- Square3-30Regression Analysis30Evaluating Overall Regression Line Fit: Adjusted R-Square3-31Regression Analysis31Evaluating Overall Regression Line Fit: F-StatisticA 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.3-32Regression Analysis32Excel and Least Squares Estimates3-33SUMMARY OUTPUTRegression StatisticsMultiple R0.87R Square0.75Adjusted R Square0.72Standard Error112.22Observations10.00ANOVADfSSMSFSignificance FRegression1301470.89301470.8923.940.0012Residual8100751.6112593.95Total9402222.50CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept1631.47243.976.690.00021068.872194.07Price-2.600.53-4.890.0012-3.82-1.37Regression Analysis33Regression for Nonlinear Functions and Multiple Regression3-34Regression Analysis34Excel and Least Squares Estimates3-35SUMMARY OUTPUTRegression StatisticsMultiple R0.89R Square0.79Adjusted R Square0.69Standard Error9.18Observations10.00ANOVADfSSMSFSignificance FRegression31920.99640.337.590.182Residual6505.9184.32Total92426.90CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept135.1520.656.540.000684.61185.68Price-0.140.06-2.410.0500-0.290.00Advertising0.540.640.850.4296-1.022.09Distance-5.781.26-4.610.0037-8.86-2.71Regression Analysis35ConclusionElasticities 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.3-3636