Slide 1Chapter OutlineIntroductionThe Elasticity ConceptThe Elasticity FormulaMeasurement Aspects of ElasticityOwn Price ElasticityLinear Demand, Elasticity, and RevenueTotal Revenue TestExtreme ElasticitiesFactors Affecting the Own Price ElasticityElasticity and Marginal RevenueDemand and Marginal RevenueCross-Price ElasticityCross-Price Elasticity in ActionCross-Price ElasticityCross-Price Elasticity in ActionIncome ElasticityIncome Elasticity in ActionOther ElasticitiesElasticities for Linear Demand FunctionsElasticities for Linear Demand Functions In ActionElasticities for Nonlinear Demand FunctionsElasticities for Nonlinear Demand Functions In ActionRegression AnalysisRegression Line and Least Squares RegressionExcel and Least Squares EstimatesEvaluating Statistical SignificanceExcel and Least Squares EstimatesEvaluating Overall Regression Line Fit: R- SquareEvaluating Overall Regression Line Fit: Adjusted R-SquareEvaluating Overall Regression Line Fit: F-StatisticExcel and Least Squares EstimatesRegression for Nonlinear Functions and Multiple RegressionExcel and Least Squares EstimatesConclusionCHAPTER 3Quantitative Demand Analysis© 2014 by McGraw-Hill Education. All Rights Reserved.Chapter Outline•The elasticity concept•Own price elasticity of demand–Elasticity and total revenue–Factors affecting the own price elasticity of demand–Marginal revenue and the own price elasticity of demand•Cross-price elasticity–Revenue changes with multiple products•Income elasticity•Other Elasticities–Linear demand functions–Nonlinear demand functions•Obtaining elasticities from demand functions–Elasticities for linear demand functions–Elasticities for nonlinear demand functions•Regression Analysis–Statistical significance of estimated coefficients–Overall fit of regression line–Regression for nonlinear functions and multiple regressionCopyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-2Chapter OverviewIntroduction•Chapter 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.Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-3Chapter OverviewThe Elasticity Concept•Elasticity –Measures the responsiveness of a percentage change in one variable resulting from a percentage change in another variable.Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-4The Elasticity ConceptThe Elasticity Formula•The elasticity between two variables, and , is mathematically expressed as:•When a functional relationship exists, like , the elasticity is:• Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-5The Elasticity ConceptMeasurement Aspects of Elasticity•Important aspects of the elasticity:–Sign of the relationship: •Positive. •Negative.–Absolute value of elasticity magnitude relative to unity:• is highly responsive to changes in .• is slightly responsive to changes in .• Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-6The Elasticity ConceptOwn Price Elasticity•Own price elasticity of demand –Measures the responsiveness of a percentage change in the quantity demanded of good X to a percentage change in its price.–Sign: negative by law of demand.–Magnitude of absolute value relative to unity:•: Elastic.•: Inelastic.•: Unitary elastic.• Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-7Own Price Elasticity of DemandLinear Demand, Elasticity, and RevenueCopyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-8QuantityPriceDemand$400$20$102030$540$15$30$25$3510 50 6070 80Linear Inverse Demand: Demand: •Revenue = $•Elasticity: •Conclusion: Demand is elastic. •Revenue = $•Elasticity: •Conclusion: Demand is unitary elastic. •Revenue = $•Elasticity: •Conclusion: Demand is inelastic. Observation: Elasticity varies along a linear (inverse) demand curveOwn Price Elasticity of DemandTotal Revenue Test•When 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. Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-9Own Price Elasticity of DemandExtreme ElasticitiesCopyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-10QuantityDemandPricePerfectly Inelastic����, ��=0 Demand����, ��=− ∞ Perfectly elasticOwn Price Elasticity of DemandFactors Affecting the Own Price Elasticity•Three factors can impact the own price elasticity of demand:–Availability of consumption substitutes.–Time/Duration of purchase horizon.–Expenditure share of consumers’ budgets.Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-11Own Price Elasticity of DemandElasticity and Marginal Revenue•The marginal revenue can be derived from a market demand curve.–Marginal revenue measures the additional revenue due to a change in output.•This link relates marginal revenue to the own price elasticity of demand as follows:–When then, .–When then, .–When then, .• Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-12Own Price Elasticity of DemandDemand and Marginal RevenueCopyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved. 2-13Quantity0� MR3Price6ElasticDemandOwn Price Elasticity of Demand16InelasticUnitaryMarginal Revenue (MR)Cross-Price Elasticity•Cross-price elasticity–Measures responsiveness of a percent change in demand for good X due to a percent change in the price of good Y. –If , then and are substitutes.–If , then and are complements.• Copyright © 2014 by the McGraw-Hill Companies, Inc. All rights reserved.3-14Cross-Price ElasticityCross-Price Elasticity in Action•Suppose it is estimated that the cross-price elasticity of demand between clothing and food is -0.18. If the price of food is projected to increase by 10 percent, by how much will demand for clothing change?–That is, demand