需求分析与需求估计

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第四讲需求分析与需求估计 主要内容一需求关系二需求的价格弹性三需求的收入弹性四需求的交叉弹性五弹性在管理决策中的应用六需求估计的市场研究方法需求函数的统计估计 经济分析与决策需求分析生产和成本分析产品、定价和产出量决策资本支出分析经济、政治与社会环境经营状况（趋势、周期和季节性影响）要素市场状况（资本、劳动和原材料）竞争者反应与策略性反应组织架构与规则限制现金流量风险厂商价值（股东的财富） HealthCare&CigarettesRaisingcigarettetaxesreducessmokingInCanada,$4forapackofcigarettesreducedsmoking38%inadecadeButcigarettetaxesalsohelpsfundhealthcareinitiativesTheissuethen,shouldwefindataxratethatmaximizestaxrevenues?Orataxratethatreducessmoking? 一、需求关系需求表、需求曲线与需求函数。消费者的基本问题——花得起的条件下最大化效用——需求函数。价格变化引起需求量的变化。收入效应；替代效应。耐用品与非耐用品对生产者的派生需求。 Reasonsthatpriceandquantityarenegativelyrelatedinclude:incomeeffect--asthepriceofagooddeclines,theconsumercanpurchasemoreofallgoodssincehisorherrealincomeincreased.substitutioneffect--asthepricedeclines,thegoodbecomesrelativelycheaper.Arationalconsumermaximizessatisfactionbyreorganizingconsumptionuntilthemarginalutilityineachgoodperdollarisequal: 二、需求的价格弹性需求的决定因素厂商是否可控？这些因素变化对需求量的影响有多大？定量！案例3-1——两种不同机制：Ford&Pizzahut。价格弹性PriceElasticity ED=%changeinQ/%changeinPShortcutnotation:ED=%Q/%PApercentagechangefrom100to150is50%Apercentagechangefrom150to100is-33%Forarcelasticities,weusetheaverageasthebase,asin100to150is+50/125=40%,and150to100is-40%ArcPriceElasticity--averagesoverthetwopointsDarcpriceelasticityED=DQ/[(Q1+Q2)/2]DP/[(P1+P2)/2]AveragepriceAveragequantity 二、需求的价格弹性计算实例1—P63李维斯牛仔裤的需求弹性。计算实例2—P63NBA公司索价。案例3-2——《麦肯电讯》。价格与收益的关系——表3-4。图3-2。当需求弹性绝对值<1时，价格上升（下降）将造成消费者的总支出的的增加（减少）。当需求弹性绝对值>1时，价格上升（下降）将造成消费者的总支出的的减少（增加）。当需求弹性绝对值=1时，价格上升（下降）将造成消费者的总支出的的不变。 IfED=-1,unitelasticIfED>-1,inelastic,e.g.,-0.43IfED<-1,elastic,e.g.,-4.0priceelasticregionunitelasticinelasticregionStraightlinedemandcurveexamplequantity PerfectlyElastic|ED|=BandPerfectlyInelastic|ED|=0DD’DD’ 二、需求的价格弹性边际收益与弹性的关系MR=P(1+1/ED)总收益函数取最大值时，单位弹性+MR=0。对任何需求弹性不足的产品，厂商都力求提高价格。案例3-3——大众汽车入侵北美市场。图3-3。影响弹性的因素 Theavailabilityandtheclosenessofsubstitutesmoresubstitutes,moreelasticThemoredurableistheproductDurablegoodsaremoreelasticthannon-durablesThepercentageofthebudgetlargerproportionofthebudget,moreelasticThelongerthetimeperiodpermittedmoretime,generally,moreelasticconsiderexamplesofbusinesstravelversusvacationtravelforallthreeabove. 三、需求的收入弹性需求的收入弹性衡量是某些商品需求量的变化对收入变化的反应程度。EY=%Q/%Y=(Q/Y)(Y/Q)pointincomeEY=DQ/[(Q1+Q2)/2]arcincomeDY/[(Y1+Y2)/2]elasticity低收入弹性（0-1）+高收入弹性（>1）。奢侈品一般具有高收入弹性，必需品具有低收入弹性 IfEY>0,thenitisanormalorincomesuperiorgoodsomegoodsareLuxuries:EY>1withahighincomeelasticitysomegoodsareNecessities:EY<1withalowincomeelasticityIfEYisnegative,thenit’saninferiorgoodConsidertheseexamples:ExpendituresonnewautomobilesExpendituresonnewChevroletsExpenditureson1996ChevyCavalierswith150,000milesWhichoftheaboveislikelytohavethelargestincomeelasticity?Whichoftheabovemighthaveanegativeincomeelasticity? 四、需求的交叉弹性明显影响一种商品的另一个因素是相关商品的价格替代品与互补品。EX=%QA/%PB=(QA/PB)(PB/QA)替代品EX>0；互补品EX<0。案例3-4——Staples的传真纸和钉书钉更贵。P77。 PROBLEM:Findthepointpriceelasticity,thepointincomeelasticity,andthepointcross-priceelasticityatP=10,Y=20,andPs=9,ifthedemandfunctionwereestimatedtobe:QD=90-8·P+2·Y+2·PsIsthedemandforthisproductelasticorinelastic?Isitaluxuryoranecessity?Doesthisproducthaveaclosesubstituteorcomplement?Findthepointelasticitiesofdemand. AnswerFirstfindthequantityatthesepricesandincome:QD=90-8·P+2·Y+2·Ps=90-8·10+2·20+2·9=90-80+40+18=68ED=(Q/P)(P/Q)=(-8)(10/68)=-1.17whichiselasticEY=(Q/Y)(Y/Q)=(2)(20/68)=+.59whichisanormalgood,butanecessityEX=(QA/PB)(PB/QA)=(2)(9/68)=+.26whichisamildsubstitute 五、弹性在管理决策中的应用企业的销售量相对于企业不能控制的外部变量的交叉弹性，对于企业最有效地应对竞争对手的竞争策略和制定最合适的成长战略都是非常关键的。企业应该关心影响自己产品需求的所有重要变量及其影响。实例。 假设某公司销售X产品，估计的需求回归方程如下。这里Qx是X产品的销售量（百万磅/年），Px是X产品的价格（美元/磅），I是可支配收入（万亿美元/年），Py是竞争品的价格（美元/磅），Ps是互补品的价格（美元/磅），A是广告支出（10万美元/年）。假设今年Px=2.00，I=2.50，Py=1.80，Ps=0.50，A=1.00。⑴计算今年X品牌的销售量。⑵分别求出需求价格弹性、需求收入弹性、竞争品交叉弹性、互补品交叉弹性、广告弹性？⑶假设企业计划明年提高X产品价格5%，广告支出增加12%，个人支配收入会提高4%，竞争品价格提高7%，互补品价格降低8%。依据以上计算结果，估计明年的销售量是多少？ 六、需求估计的市场研究方法对本厂商产品的需求关系越了解，越有可能采取使厂商产生最大利润和现金流量的方法。管理问题——公共运输的需求。影响因素？三种重要的市场研究方法：消费者调查+消费者的焦点小组+市场试验。消费者调查一组样本消费者的调查。购买意愿+价格敏感程度+广告了解程度等。 七、需求函数的统计估计计量经济学方法。 StatisticalEstimationofDemandFunctions:PlotHistoricalDataLookattherelationshipofpriceandquantityovertimePlotitIsitademandcurveorasupplycurve?Theproblemisthisdoesnotholdotherthingsequalorconstant.quantityPrice2000200319992001200220042001Isthiscurvedemandorsupply? Stepstotake:Specificationofthemodel--formulatethedemandmodel,selectaFunctionalFormlinearQ=a+b•P+c•YdoubleloglogQ=a+b•logP+c•logYquadraticQ=a+b•P+c•Y+d•P2Estimatetheparameters--determinewhicharestatisticallysignificanttryothervariables&otherfunctionalformsDevelopforecastsfromthemodel SpecifyingtheVariablesDependentVariable--quantityinunits,quantityindollarvalue(asinsalesrevenues)IndependentVariables--variablesthoughttoinfluencethequantitydemandedInstrumentalVariables--proxyvariablesfortheitemwantedwhichtendstohavearelativelyhighcorrelationwiththedesiredvariable:e.g.,TastesTimeTrend FunctionalForms:LinearLinearQ=a+b•P+c•YTheeffectofeachvariableisconstant,asinQ/P=bandQ/Y=c,wherePispriceandYisincome.TheeffectofeachvariableisindependentofothervariablesPriceelasticityis:ED=(Q/P)(P/Q)=b•P/QIncomeelasticityis:EY=(Q/Y)(Y/Q)=c•Y/QThelinearformisoftenagoodapproximationoftherelationshipinempiricalwork. FunctionalForms:MultiplicativeorDoubleLogMultiplicativeQ=A•Pb•YcTheeffectofeachvariabledependsonalltheothervariablesandisnotconstant,asinQ/P=bAPb-1YcandQ/Y=cAPbYc-1Itisdoublelog(logisthenaturallog,alsowrittenasln)LogQ=a+b•LogP+c•LogYthepriceelasticity,ED=btheincomeelasticity,EY=cThispropertyofconstantelasticitymakesthisapproacheasytouseandpopularamongeconomists. SimpleLinearRegressionYt=a+bXt+ttimesubscripts&errortermFind“bestfitting”linet=Yt-a-bXtt2=[Yt-a-bXt]2.mint2=[Yt-a-bXt]2.Solution:slopeb=Cov(Y,X)/Var(X)andintercepta=mean(Y)-b•mean(X)_XY_YaDXDY SimpleLinearRegression:Assumptions&SolutionMethodsThedependentvariableisrandomAstraightlinerelationshipexistserrortermhasameanofzeroandafinitevariancetheindependentvariablesareindeedindependentSpreadsheets-suchasExcel,Lotus1-2-3,QuatroPro,orJoeSpreadsheetStatisticalcalculatorsStatisticalprogramssuchasMinitabSASSPSSForeProfitMystat Sherwin-WilliamsCaseTenregionswithdataonpromotionalexpenditures(X)andsales(Y)Result:Y=120.755+.434XOneuseofaregressionistomakepredictions.Ifaregionhadpromotionalexpendituresof185,thepredictionisY=201.045,bysubstituting185forXTheregressionoutputwilltellusalsothestandarderroroftheestimate,se.Inthiscase,se=22.799Approximately95%predictionintervalisY2se.Hence,thepredictedrangeisanywherefrom155.447to246.643. T-testsDifferentsampleswouldyielddifferentcoefficientsTestthehypothesisthatcoefficientequalszeroHo:b=0Ha:b0RULE:Ifabsolutevalueoftheestimatedt>Critical-t,thenREJECTHo.Wesaythatit’ssignificant!Theestimatedt=(b-0)/bThecriticaltis:LargeSamples,criticalt2N>30SmallSamples,criticaltisonStudent’stDistribution,pageB-3atendofbook,usuallycolumn0.05.D.F.=#observations,minusnumberofindependentvariables,minusone.N<30 Sherwin-WilliamsCaseInthesimplelinearregression:Y=120.755+.434XThestandarderroroftheslopecoefficientis.14763.(Thisisusuallyavailablefromanyregressionprogramused.)Testthehypothesisthattheslopeiszero,b=0.Theestimatedtis:t=(.434–0)/.14763=2.939Thecriticaltforasampleof10,hasonly8degreesoffreedomD.F.=10–1independentvariable–1fortheconstant.TableB2showsthistobe2.306atthe.05significancelevelTherefore,|2.939|>2.306,sowerejectthenullhypothesis.Weinformallysay,thatpromotionalexpenses(X)is“significant.” CorrelationCoefficientWewouldexpectmorepromotionalexpenditurestobeassociatedwithmoresalesatSherwin-Williams.Ameasureofthatassociationisthecorrelationcoefficient,r.Ifr=0,thereisnocorrelation.Ifr=1,thecorrelationisperfectandpositive.Theotherextremeisr=-1,whichisnegative.r=-1r=+1r=0YYYXXX CoefficientofDetermination:R2R-squareisthepercentageofthevariationindependentvariablethatisexplained^–R2=[Yt-Yt]2/[Yt-Yt]2=SSR/SSTAsmorevariablesareincluded,R-squarerisesAdjustedR-square,however,candecline_XY_YYtYtpredicted^ AssociationandCausationRegressionsindicateassociation,butbewareofjumpingtotheconclusionofcausationSupposeyoucollectdataonthenumberofswimmersatabeachandthetemperatureandfind:Temperature=61+.04Swimmers,andR2=.88.Surelythetemperatureandthenumberofswimmersispositivelyrelated,butwedonotbelievethatmoreswimmersCAUSEDthetemperaturetorise.Furthermore,theremaybeotherfactorsthatdeterminetherelationship,forexamplethepresenceofrainorwhetherornotitisaweekendorweekday.Educationmayleadtomoreincome,andalsomoreincomemayleadtomoreeducation.Thedirectionofcausationisoftenunclear.Buttheassociationisverystrong. MultipleLinearRegressionMosteconomicrelationshipsinvolveseveralvariables.Wecanincludemoreindependentvariablesintotheregression.Todothis,wemusthavemoreobservations(N)thanthenumberofindependentvariables,andnoexactlinearrelationshipsamongtheindependentvariables.AtSherwin-Williams,besidespromotionalexpenses,differentregionschargedifferentsellingprices(SellPrice)andhavedifferentlevelsofdisposableincome(DispInc)Thenextslidegivestheoutputofamultiplelinearregression,multiple,becausetherearethreeindependentvariables Figure4.9Depvar:Sales(Y)N=10R-squared=.790AdjustedR2=.684StandardErrorofEstimate=17.417VariableCoefficientStderrorTPConstant310.24595.0753.263.017Promotion.0080.2040.038.971SellPrice-12.2024.582-2.663.037DispInc2.6773.1600.847.429 InterpretingMultipleRegressionOutputWritetheresultasanequation:Sales=310.245+.008Promotion-12.202SellPrice+2.677DispIncDoestheresultmakeeconomicsense?Aspromotionexpenserises,sodoessales.Thatmakessense.Asthesellingpricerises,sodoessales.Yes,that’sreasonable.Asdisposableincomerisesinaregion,sodoessales.Yup.That’sreasonable.Isthecoefficientonthesellingpricestatisticallysignificant?TheestimatedtvalueisgiveninFigure4.9tobe-2.663Thecriticaltvalue,with6(whichis10–3–1)degreesoffreedomintableB2is2.447Therefore|-2.663|>2.447,sorejectthenullhypothesis,andassertthatthesellingpriceissignificant! 案例3-5——飞跃北大西洋旅行的需求估计J.M.Cigliano估计了1965—1978美国与欧洲之间的空中旅行需求： 案例3-6——公共交通与城市拥挤北京广州等大城市城市拥护现象突出。公共交通是解决城市拥护的关键。公交降价是否有利于城市拥护现象的解决？