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CHAPTER3QuantitativeDemandAnalysisChapterOutline•Theelasticityconcept•Ownpriceelasticityofdemand–Elasticityandtotalrevenue–Factorsaffectingtheownpriceelasticityofdemand–Marginalrevenueandtheownpriceelasticityofdemand•Cross-priceelasticity–Revenuechangeswithmultipleproducts•Incomeelasticity•OtherElasticities–Lineardemandfunctions–Nonlineardemandfunctions•Obtainingelasticitiesfromdemandfunctions–Elasticitiesforlineardemandfunctions–Elasticitiesfornonlineardemandfunctions•RegressionAnalysis–Statisticalsignificanceofestimatedcoefficients–Overallfitofregressionline–Regressionfornonlinearfunctionsandmultipleregression3-2ChapterOverviewIntroduction•Chapter2focusedoninterpretingdemandfunctionsinqualitativeterms:–Anincreaseinthepriceofagoodleadsquantitydemandedforthatgoodtodecline.–Adecreaseinincomeleadsdemandforanormalgoodtodecline.•Thischapterexaminesthemagnitudeofchangesusingtheelasticityconcept,andintroducesregressionanalysistomeasuredifferentelasticities.3-3ChapterOverviewTheElasticityConcept•Elasticity–Measurestheresponsivenessofapercentagechangeinonevariableresultingfromapercentagechangeinanothervariable.3-4TheElasticityConceptTheElasticityFormula•Theelasticitybetweentwovariables,𝐺and𝑆,ismathematicallyexpressedas:𝐸𝐺,𝑆=%Δ𝐺%Δ𝑆•Whenafunctionalrelationshipexists,like𝐺=𝑓𝑆,theelasticityis:𝐸𝐺,𝑆=𝑑𝐺𝑑𝑆𝑆𝐺3-5TheElasticityConceptMeasurementAspectsofElasticity•Importantaspectsoftheelasticity:–Signoftherelationship:•Positive.•Negative.–Absolutevalueofelasticitymagnituderelativetounity:•𝐸𝐺,𝑆1𝐺ishighlyresponsivetochangesin𝑆.•𝐸𝐺,𝑆1𝐺isslightlyresponsivetochangesin𝑆.3-6TheElasticityConceptOwnPriceElasticity•Ownpriceelasticityofdemand–MeasurestheresponsivenessofapercentagechangeinthequantitydemandedofgoodXtoapercentagechangeinitsprice.𝐸𝑄𝑋𝑑,𝑃𝑋=%Δ𝑄𝑋𝑑%Δ𝑃𝑋–Sign:negativebylawofdemand.–Magnitudeofabsolutevaluerelativetounity:•𝐸𝑄𝑋𝑑,𝑃𝑋1:Elastic.•𝐸𝑄𝑋𝑑,𝑃𝑋1:Inelastic.•𝐸𝑄𝑋𝑑,𝑃𝑋=1:Unitaryelastic.3-7OwnPriceElasticityofDemandLinearDemand,Elasticity,andRevenue3-8QuantityPriceDemand$400$20$102030$540$15$30$25$351050607080LinearInverseDemand:𝑃=40−0.5𝑄Demand:𝑄=80−2𝑃•Revenue=$30×20=$600•Elasticity:−2×$3020=−3•Conclusion:Demandiselastic.Observation:Elasticityvariesalongalinear(inverse)demandcurveOwnPriceElasticityofDemandTotalRevenueTest•Whendemandiselastic:–Apriceincrease(decrease)leadstoadecrease(increase)intotalrevenue.•Whendemandisinelastic:–Apriceincrease(decrease)leadstoanincrease(decrease)intotalrevenue.•Whendemandisunitaryelastic:–Totalrevenueismaximized.3-9OwnPriceElasticityofDemandExtremeElasticities3-10QuantityDemandPricePerfectlyInelastic𝐸𝑄𝑋𝑑,𝑃𝑋=0Demand𝐸𝑄𝑋𝑑,𝑃𝑋=−∞PerfectlyelasticOwnPriceElasticityofDemandFactorsAffectingtheOwnPriceElasticity•Threefactorscanimpacttheownpriceelasticityofdemand:–Availabilityofconsumptionsubstitutes.–Time/Durationofpurchasehorizon.–Expenditureshareofconsumers’budgets.3-11OwnPriceElasticityofDemandElasticityandMarginalRevenue•Themarginalrevenuecanbederivedfromamarketdemandcurve.–Marginalrevenuemeasurestheadditionalrevenueduetoachangeinoutput.•Thislinkrelatesmarginalrevenuetotheownpriceelasticityofdemandasfollows:𝑀𝑅=𝑃1+𝐸𝐸–When−∞𝐸−1then,𝑀𝑅0.–When𝐸=−1then,𝑀𝑅=0.–When−1𝐸0then,𝑀𝑅0.3-12OwnPriceElasticityofDemandDemandandMarginalRevenue3-13Quantity0𝑃MR3Price6DemandOwnPriceElasticityofDemand16UnitaryMarginalRevenue(MR)Cross-PriceElasticity•Cross-priceelasticity–MeasuresresponsivenessofapercentchangeindemandforgoodXduetoapercentchangeinthepriceofgoodY.𝐸𝑄𝑋𝑑,𝑃𝑌=%Δ𝑄𝑋𝑑%Δ𝑃𝑌–If𝐸𝑄𝑋𝑑,𝑃𝑌0,then𝑋and𝑌aresubstitutes.–If𝐸𝑄𝑋𝑑,𝑃𝑌0,then𝑋and𝑌arecomplements.3-14Cross-PriceElasticityCross-PriceElasticityinAction•Supposeitisestimatedthatthecross-priceelasticityofdemandbetweenclothingandfoodis-0.18.Ifthepriceoffoodisprojectedtoincreaseby10percent,byhowmuchwilldemandforclothingchange?−0.18=%∆𝑄𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔𝑑10⇒%∆𝑄𝐶𝑙𝑜𝑡ℎ𝑖𝑛𝑔𝑑=−1.8–Thatis,demandforclothingisexpectedtodeclineby1.8percentwhenthepriceoffoodincreases10percent.3-15Cross-PriceElasticityCross-PriceElasticity•Cross-priceelasticityisimportantforfirmssellingmultipleproducts.–Pricechangesforoneproductimpactdemandforotherproducts.•Assessingtheoverallchangeinrevenuefromapricechangeforonegoodwhenafirmsellstwogoodsis:∆𝑅=𝑅𝑋1+𝐸𝑄𝑋𝑑,𝑃𝑋+𝑅𝑌𝐸𝑄𝑌𝑑,𝑃𝑋×%∆𝑃𝑋3-16Cross-PriceElasticityCross-PriceElasticityinAction•Supposearestaurantearns$4,000perweekinrevenuesfromhamburgersales(X)and$2,000perweekfromsodasales(Y).Iftheownpriceelasticityforburgersis𝐸𝑄𝑋,𝑃𝑋=−1.5andthecross-priceelasticityofdemandbetweensodasandhamburgersis𝐸𝑄𝑌,𝑃𝑋=−4.0,whatwouldhappentothefirm’stotalrevenuesifitreducedthepriceofhamburgersby1percent?∆𝑅=$4,0001−1.5+$2,000−4.0−1%=$100–Thatis,loweringthepriceofhamburgers1percentincreasestotalrevenueby$100.3-17Cross-PriceElasticityIncomeElasticity•Incomeelasticity–MeasuresresponsivenessofapercentchangeindemandforgoodXduetoapercentchangeinincome.𝐸𝑄𝑋𝑑,𝑀=%Δ𝑄𝑋𝑑%Δ𝑀–If𝐸𝑄𝑋𝑑,𝑀0,then𝑋isanormalgood.–If𝐸𝑄𝑋𝑑,𝑀0,then𝑋isaninferi