管理经济学（原书第14版） 课件 第12章　具有市场力的企业的管理决策

Chapter12ManagerialDecisionsforFirmsWithMarketPowerMANAGERIALECONOMICSFoundationsofBusinessAnalysisandStrategyFourteenthEditionCHRISTOPHERR.THOMAS©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.LearningObjectives12.1Definemarketpoweranddescribethemeasurementofmarketpower.12.2Explainwhyentrybarriersarenecessaryforlong-runmarketpoweranddiscussmajortypesofentrybarriers.12.3-12.5Findtheprofit‐maximizingoutput,price,andinputusageforamonopolistandmonopolisticcompetitor.12.6Employempiricallyestimatedorforecasteddemand,averagevariablecost,andmarginalcosttocalculateprofit‐maximizingoutputandpriceformonopolisticormonopolisticallycompetitivefirms.12.7Selectproductionlevelsatmultipleplantstominimizethetotalcostofproducingagiventotaloutputforafirm.2MonopolyandMonopolisticCompetitionAmonopolyisasinglefirmthatproducesagoodforwhichtherearenoclosesubstitutesinamarketthatotherfirmsarepreventedfromenteringbecauseofabarriertoentry.Monopolisticcompetition

isamarketconsistingofalargenumberoffirmssellingadifferentiatedproductwithlowbarrierstoentry.Marketpoweristheabilitypossessedbyallprice-settingfirmstoraisepricewithoutlosingallsales,whichcausestheprice-settingfirm’sdemandtobedownward-sloping.3MeasurementofMarketPower1Degreeofmarketpowerisinverselyrelatedtothepriceelasticityofdemand.Thelesselasticthefirm’sdemand,thegreateritsdegreeofmarketpower.Thefewerclosesubstitutesforafirm’sproduct,thesmallertheelasticityofdemand(inabsolutevalue)andthegreaterthefirm’smarketpower.Whendemandisperfectlyelastic(demandishorizontal),thefirmhasnomarketpower.4MeasurementofMarketPower2Lernerindexmeasuresproportionateamountbywhichpriceexceedsmarginalcost:Equalszerounderperfectcompetition.Increasesasmarketpowerincreases.Alsoequals−1∕E,whichshowsthattheindex(andmarketpower)variesinverselywithelasticity.Thelowertheelasticityofdemand(absolutevalue),thegreatertheindexandthedegreeofmarketpower.5MeasurementofMarketPower3Ifconsumersviewtwogoodsassubstitutes,cross-priceelasticityofdemandispositive.Thehigherthepositivecross-priceelasticity,thegreaterthesubstitutabilitybetweentwogoods,andthesmallerthedegreeofmarketpowerforthetwofirms.Marketdefinitionistheidentificationoftheproducersandproductsthatcompeteforconsumersinaparticulargeographicarea.6BarrierstoEntryEntryofnewfirmsintoamarketerodesmarketpowerofexistingfirmsbyincreasingthenumberofsubstitutes.Afirmcanpossessahighdegreeofmarketpoweronlywhenstrongbarrierstoentry

exist.Conditionsthatmakeitunprofitablefornewfirmstoenteramarketinwhicheconomicprofitsarebeingearnedbytheexistingfirms.7CommonEntryBarriers1BarrierscreatedbygovernmentPatents,licenses,exclusivefranchises.EconomiesofscaleWhenlong-runaveragecostdeclinesoverawiderangeofoutputrelativetodemandfortheproduct,theremaynotberoomforanewfirmtoentertheindustryonalargeenoughscaletocompete.EssentialinputbarriersOnefirmcontrolsacrucialinputintheproductionprocess.BrandloyaltiesStrongcustomerallegiancetoexistingfirmsmaykeepnewfirmsfromfindingenoughbuyerstomakeentryworthwhile.8CommonEntryBarriers2Consumerlock-inPotentialentrantscanbedeterrediftheybelievehighswitchingcostsmakepreviousconsumptiondecisionsverycostlytochange.Switchingcostsareincurredbyconsumerswhentheyswitchtonewordifferentproductsorservices.Networkexternalities(networkeffects)Occurwhenbenefitorutilityaconsumerderivesfromconsumingagooddependspositivelyonthenumberofotherconsumerswhousethegood.SunkcostsEntrycosts(whicharesunkcosts)canserveasabarrieriftheyaresohighthatthefirmcannotexpecttoearnenoughfutureprofittomakeentryworthwhile.9DemandandMarginalRevenueforaMonopolistMarketdemandcurveisthefirm’sdemandcurve.Themonopolistmustlowerpricetoselladditionalunitsofoutput.Marginalrevenueislessthanpriceforallbutthefirstunitsold.WhenMRispositive(negative),demandiselastic(inelastic).Forlineardemand,MRisalsolinear,hasthesameverticalinterceptasdemand,andistwiceassteep.10Figure12.1DemandandMarginalRevenueFacingaMonopolistAccessthetextalternativeforslideimages.11Short-RunProfitMaximizationforMonopolyMonopolistwillproducewhereMR=SMCaslongasTRatleastcoversthefirm’stotalavoidablecost(TR≥TVC).Priceforthisoutputisgivenbythedemandcurve.IfTR<TVC(or,equivalently,P<AVC),thefirmshutsdownandlosesonlyfixedcosts.IfP>ATC,firmmakeseconomicprofit.IfATC>P>AVC,firmincursalossbutcontinuestoproduceinshortrun.12Table12.1ProfitMaximizationforSouthwestLeatherDesigns(1)(2)(3)(4)(5)(6)(7)Output(Q)Price(P)TotalRevenue(TR=PQ)TotalCost(TC)MarginalRevenueMarginalCostProfit(π)0$40.00$0$40,000––$−40,0001,00035.0035,00042,000$35.00$2.00−7,0002,00032.5065,00043,50030.001.5021,5003,00028.0084,00045,50019.002.0038,5004,00025.00100,00048,50016.003.0051,5005,00021.50107,50052,5007.504.0055,0006,00018.92113,52057,5006.025.0056,0207,00017.00119,00063,7505.486.2555,2508,00015.35122,80073,7503.8010.0049,0509,00014.00126,00086,2503.2012.5039,75013Figure12.2ProfitMaximizationforSouthwestLeatherDesigns:ChoosingOutputAccessthetextalternativeforslideimages.14Figure12.3Short-RunProfit-MaximizingEquilibriumUnderMonopolyAccessthetextalternativeforslideimages.15Figure12.4Short-RunLossMinimizationUnderMonopolyAccessthetextalternativeforslideimages.16Long-RunProfitMaximizationforMonopolyThemonopolistmaximizesprofitbychoosingtoproduceoutputwhereMR=LMC,aslongasP≥LAC.WillexitindustryifP<LAC.Monopolistwilladjustplantsizetotheoptimallevel.Optimalplantiswheretheshort-runaveragecostcurveistangenttothelong-runaveragecostattheprofit-maximizingoutputlevel.17Figure12.5Long-RunProfitMaximizationUnderMonopolyAccessthetextalternativeforslideimages.18Profit-MaximizingInputUsage1Marginalrevenueproduct(MRP)

istheadditionalrevenueearnedwhenthefirmhiresonemoreunitoftheinput.Ifchoosetoproduce:IftheMRP

ofanadditionalunitofinputisgreaterthanthepriceofinput,thatunitshouldbehired.EmployamountofinputwhereMRP

=inputprice=w.Profit-maximizinglevelofinputusageproducesexactlythatlevelofoutputthatmaximizesprofit.19Profit-MaximizingInputUsage2Averagerevenueproduct(ARP)

istheaveragerevenueperworker:RelevantrangeofMRPcurveisdownwardsloping,positiveportion,forwhichARP>MRP.ShutdowninshortrunifARP<MRPWhenARP<MRP,TR<TVC.20Figure12.6AMonopolyFirms’DemandforLaborAccessthetextalternativeforslideimages.21MonopolisticCompetitionLargenumberoffirmsselladifferentiatedproduct.Productsareclose(notperfect)substitutes.Marketismonopolistic.Productdifferentiationcreatesadegreeofmarketpower.Marketiscompetitive.Largenumberoffirms,easyentry.22ProfitMaximizationforMonopolisticCompetitionShort-runequilibriumisidenticaltomonopoly.Unrestrictedentry/exitleadstolong-runequilibriumandzeroeconomicprofits.AttainedwhendemandcurveforeachproduceristangenttoLAC.Atequilibriumoutput,P=LACandMR=LMC.23Figure12.7Short-RunProfitMaximizationUnderMonopolisticCompetitionAccessthetextalternativeforslideimages.24Figure12.8Long-RunEquilibriumUnderMonopolisticCompetitionAccessthetextalternativeforslideimages.25ImplementingtheProfit-MaximizingOutputandPricingDecision(Step1)GeneralrulesforimplementationShouldthefirmproduceorshutdown?Ifproductionoccurs,howmuchshouldthefirmproduce?Step1:EstimatedemandequationUsestatisticaltechniquesfromChapter7.Substituteforecastsofdemand-shiftingvariablesintoestimateddemandequationtoget:26ImplementingtheProfit-MaximizingOutputandPricingDecision(Step2)Step2:FindinversedemandequationSolveforP27ImplementingtheProfit-MaximizingOutputandPricingDecision(Steps3and4)Step3:SolveformarginalrevenueWhendemandisexpressedasP=A+BQ,marginalrevenueisStep4:EstimateAVCandSMCUsestatisticaltechniquesfromChapter10.28ImplementingtheProfit-MaximizingOutputandPricingDecision(Steps5and6)Step5:FindoutputwhereMR=SMCSetequationsequalandsolveforQ*.Thelargerofthetwosolutionsistheprofit-maximizingoutputlevel.Step6:Findprofit-maximizingpriceSubstituteQ*intoinversedemand:P*=A+BQ*Q*andP*areonlyoptimalifP≥AVC.29ImplementingtheProfit-MaximizingOutputandPricingDecision(Step7)Step7:CheckshutdownruleSubstituteQ*intoestimatedAVCfunction:IfP*≥AVC*,

produceQ*unitsofoutputandselleachunitforP*.IfP*<AVC*,

shutdownintheshortrun.30ImplementingtheProfit-MaximizingOutputandPricingDecision(Step8)Step8:ComputeprofitorlossProfit=π*=TR−TC

=

(PxQ*)−[(AVCxQ*)−TFC]=

(P−AVC)Q*−TFCIfP<AVC,firmshutsdownandprofitis−TFC.31MaximizingProfitatAztecElectronics:AnExample1Aztecpossessesmarketpowerviapatentsandsellsadvancedwirelessstereoheadphones.Estimationofdemandandmarginalrevenue:32MaximizingProfitatAztecElectronics:AnExample

2Solveforinversedemand:33MaximizingProfitatAztecElectronics:AnExample

3Determinethemarginalrevenuefunctionfromtheinversedemandfunction(sameP-intercept,twiceassteep):P=100–0.002QMR=100–0.004Q34Figure12.9DemandandMarginalRevenueforAztecElectronicsAccessthetextalternativeforslideimages.35MaximizingProfitatAztecElectronics:AnExample4Estimationofaveragevariablecostandmarginalcost:GiventheestimatedAVCequation:Then,36MaximizingProfitatAztecElectronics:AnExample5Outputdecision:SetMR=SMCandsolveforQ*37MaximizingProfitatAztecElectronics:AnExample6Outputdecision:SolveforQ*

usingthequadraticformula38MaximizingProfitatAztecElectronics:AnExample7Pricingdecision:SubstituteQ*intoinversedemand.P*=100−0.002(6,000)=$8839MaximizingProfitatAztecElectronics:AnExample8Shutdowndecision:ComputeAVCat6,000units:=$34.BecauseP=$88>$34=ATC,Aztecshouldproduceratherthanshutdown.40MaximizingProfitatAztecElectronics:AnExample9

41Figure12.10ProfitMaximizationatAztecElectronicsAccessthetextalternativeforslideimages.42MultiplantFirmsIfafirmproducesintwoplants,AandB:ThetotalcostofproducinganygivenleveloftotaloutputisminimizedwhenproductionisallocatedsothatThetotalmarginalcostcurveisthehorizontalsummationofallplants’marginalcostcurves,whichgivestheadditiontototalcostattributabletoincreasingtotaloutputbyoneunit.Profitmaximizingtotaloutputiswhere43Figure12.11AMultiplantFirmAccessthetextalternativeforslideimages.44Figure12.12MultiplantProductionatMercantileExpressAccessthetextalternativeforslideimages.45Summary1Price-settingfirmspossessmarketpower.Amonopolyexistswhenasinglefirmproducesandsellsaparticulargoodorserviceforwhichtherearenogoodsubstitutesandnewfirmsarepreventedfromenteringthemarket.Monopolisticcompetitionariseswhenthemarketconsistsofalargenumberofrelativelysmallfirmsthatproducesimilar,butslightlydifferentiated,productsandhavesomemarketpower.Afirmcanpossessahighdegreeofmarketpoweronlywhenstrongbarrierstotheentryofnewfirmsexist.Intheshortrun,themanagerofamonopolyfirmwillchoosetoproducewhereMR=SMC,ratherthanshutdown,aslongastotalrevenueatleastcoversthefirm’stotalvariablecost(TR≥TVC).46Summary2Inthelongrun,themonopolistmaximizesprofitbychoosingtoproducewhereMR=LMC,unlesspriceislessthanlong-runaveragecost(P<LAC),inwhichcasethefirmexitstheindustry.Forfirmswithmarketpower,marginalrevenueproduct(MRP)isequaltomarginalrevenuetimesmarginalproduct:MRP=MR×MP.WhetherthemanagerchoosesQorL

tomaximizeprofit,theresultinglevelsofinputusage,output,price,andprofitarethesame.Short-runequilibriumundermonopolisticcompetitionisexactlythesameasformonopoly.47Summary3Long-runequilibriuminamonopolisticallycompetitivemarketisattainedwhenthedemandcurveforeachproduceristangenttothelong-runaveragecostcurve.Eightstepscanbeemployedforprofitmaximizationforamonopolyormonopolisticallycompetitivefirm:(1)estimatedemandequation,(2)findinversedemandequation,(3)solveformarginalrevenue,(4)estimateaveragevariablecostandmarginalcost,(5)findoutputlevelwhereMR=SMC,(6)findprofit-maximizingprice,(7)checktheshutdownrule,and(8)computeprofit/loss.Afirmproducingintwoplants,A

andB,shouldallocateproductionbetweenthetwoplantssothat48EndofMainContent©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.AccessibilityContent:TextAlternativesforImages50Figure12.1DemandandMarginalRevenueFacingaMonopolist-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandmarginalrevenueindollarsanditrangesfrom0to20.Thehorizontalaxisislabeledasquantityanditrangesfrom0to1,500.AdeclininglinelabeledMRbeginsat(0,20),fallslefttoright,passesthroughpoint(900,8),andendsat(1,500,0).Anotherdeclininglinebeginsat(0,20),fallslefttoright,passesthroughpointsBat(900,14),Aat(1,500,10),andendsatpointD.Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.51Figure12.2ProfitMaximizationforSouthwestLeatherDesigns:ChoosingOutput-TextAlternativeReturntoparent-slidecontainingimages.TheverticalaxisislabeledasPrice,marginalrevenue,andmarginalcostindollarsanditrangesfrom0to40inincrementsof10.Thehorizontalaxisislabeledasquantityandrangesfrom0to9,000inincrementsof1,000.ThefirstcurveislabeledasD,beginsat(0,40),fallslefttoright,passesthroughthepoint(1,000,35),(2,000,32.50),(3,000,28.50),(4,000,25.00),(5,000,21.50),(6,000,18.92),(7,000,17.00),(8,000,15.35),andendsat(9,000,14.00).ThesecondcurvelabeledMRbeginsat(500,35),fallslefttoright,passesthroughpoints(1,000,35),(2,000,30),(3,000,19.00),(4,000,16.00),(5,000,7.50),(6,000,6.02),(7,000,5.48),(8,000,3.80),andendsat(9,000,3.20).ThethirdcurvelabeledSMC,beginsat(500,2),riseslefttoright,(1,000,2),(2,000,1.50),(3,000,2.00),(4,000,3.00),(5,000,4.00),(6,000,5.00),(7,000,6.25),(8,000,10.00),andendsat(9,000,12.50).Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.52Figure12.3Short-RunProfit-MaximizingEquilibriumUnderMonopoly-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandcostindollars.Thehorizontalaxisislabeledquantity.AdeclininglinelabeledMRbeginsatthepointabove(0,7)andendsatapointinthefirstquadrant.AnotherdeclininglinelabeledDbeginsatapointabove(0,7),liesabovelineMR,andendsatapointinthefirstquadrant.AcurvelabeledATC,concaveup,beginsat(100,5.8),fallslefttoright,passesthroughpointCat(200,5),continuestoitslowestpoint,thenrisestotheright.AnothercurvelabeledSMC,beginsat(150,4),concaveup,risessteeplytotheright,intersectingbothlinesandthecurveATC,andextendsfromthetopright.AquadrilateralABCDisdrawnsuchthatvertexAisat(0,7),Bat(200,7),Cat(200,5),andDat(0,5).Thequadrilateralisshaded.Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.53Figure12.4Short-RunLossMinimizationUnderMonopoly-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandcostindollars.Thehorizontalaxisislabeledquantity.AdeclininglinelabeledMRbeginsatthepointneartheverticalaxis,fallslefttoright,andendsatapointinthefirstquadrant.AnotherdeclininglinelabeledDwithlessslopebeginsatapointnearandslightlyrightofthefirstline,fallslefttoright,passesthroughpointCat(50,75),andendsatapointnearthex-axisinthefirstquadrant.AcurvelabeledATC,concaveup,entersfromthetop,fallslefttoright,passesthroughpointBat(50,80),continuesitslowestpoint,andthenrisestotheright.AnothercurvelabeledAVCbeginsnearpointAat(0,80),concaveup,fallsslightlytotheright,passesthroughpointFat(50,65),reachesalowpoint,thenrisestotherightandendsclosetothecurveATC.AnothercurvelabeledSMC,beginsapproximatelyat(20,55),concaveup,fallslefttotheright,intersectsthelineMRat(50,50),thenrisestotheright,intersectingtheotherlineandcurves.AquadrilateralABCDisdrawnsuchthatvertexAisat(0,80),Bat(50,80),Cat(50,75),andDat(0,75).Thequadrilateralisshaded.Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.54Figure12.5Long-RunProfitMaximizationUnderMonopoly-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandcostindollars.Thehorizontalaxisislabeledquantity.AdeclininglinelabeledMRbeginsatanapproximatepoint(0,80),passesthroughpoint(350,22),andendsatapointnearthex-axis.AnotherdeclininglinelabeledDbeginsatapoint(0,80),haslessslopethanlineMR,passesthroughpointBat(350,55),andendsatapointnearthex-axis.Fourcurvesareplotted.ThefirstcurvelabeledLAC,concaveup,beginsat(175,65),fallslefttoright,passesthroughpointCat(350,50),continuestoitslowestpoint(800,30),thenrisestotheright.ThesecondcurvelabeledLMC,beginsat(175,25),concaveup,fallsslightlytotheright,toitslowestpoint(350,22),thenextendssteeplytothetopright.ThethirdcurveisasmallconcavecurvelabeledATCsubscript1,whichisdrawnandtouchespointCat(350,50).ThefourthcurvelabeledSMCsubscript1,concaveup,beginsat(200,175),riseslefttoright,passesthroughpoint(350,22),andexitsfromthetop.ArectangleABCDisdrawnsuchthatvertexAisat(0,55),Bat(350,55),Cat(350,50),andDat(0,50).Therectangleisshaded.Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.55Figure12.6AMonopolyFirms’DemandforLabor-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledmarginalrevenueproductandwage(dollars)anditrangesfrom0to58.Thehorizontalaxisislabeledunitoflaboranditrangesfrom0to500.ThecurveMRPequalsMRtimesMPandentersfromthetopclosetotheverticalaxis,fallslefttoright,throughpointsCat(300,58),pointA(400,45),andpointBat(500,30)andendsat(650,0).AnotherdashedcurvelabeledARPequalsPtimeAP,concavedown,begins(50,65),riseslefttoright,intersectingthefirstcurveatitshighpointapproximately(200,75),thenfallstotheright,andexits.AhorizontallinelabeledWsubscript1,beginsat(0,45),andextendsrightward,intersectingthecurveMRPatpointA.AnotherhorizontallinelabeledWsubscript2,beginsat(0,30),andextendsrightward,intersectingthecurveMRPatpointB.Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.56Figure12.7Short-RunProfitMaximizationUnderMonopolisticCompetition-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandcostindollars.Thehorizontalaxisislabeledquantity.AdeclininglinelabeledMRbeginsneartheverticalaxis,passesthroughapointdirectlyabove(Q,0),andendsatapointnearthex-axis.AnotherdeclininglinelabeledDbeginsabovethefirstline,haslessslopethanlineMR,passesthroughpointAat(Q,P),andendsatapointnearthex-axis.Twocurvesareplotted.ThefirstcurvelabeledATC,concaveup,beginsnearthey-axisbelowthefirstline,fallslefttoright,passesthroughpointBat(Q,C),thenrisestotheright.ThesecondcurvelabeledSMC,concaveup,nearthey-axis,riseslefttoright,passesthroughapointdirectlyabove(Q,0),andexitsfromthetop.ArectanglePABCisdrawnsuchthatvertexPisat(0,P),Aat(Q,P),Bat(Q,C),andCat(0,C).ThepointCisclosetotheorigin.Therectangleisshaded.Notethatthevaluesmentionedareapproximate.Returntoparent-slidecontainingimages.57Figure12.8Long-RunEquilibriumUnderMonopolisticCompetition-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandcostindollarsandthehorizontalaxisislabeledasquantity.AdeclininglinelabeledMRbeginsatapointontheverticalaxisandendsatapointnearthex-axis.AnotherdeclininglinelabeledDhaslessslope,beginsatthesamepointoforiginofthefirstline,andendsatapointrightoftheendpointofthefirstline.AcurvelabeledLAC,concaveup,beginsneartheverticalaxisabovetheoriginpointoflines,fallslefttoright,passesthroughapoint(Qbar,Pbar),continuesdownwardtoalowpoint,thenrisesupandtotheright.AnothercurvelabeledLMC,concaveup,beginsneartheverticalaxisbelowpointPontheverticalaxis,riseslefttoright,intersectsthelineandcurves,andexitsatthetopright.AnotherdecreasingdiagonallinelabeledDsubscriptmisdrawnintersectingbothcurves.Notethatthevaluesmentionedareapproximate.Returntoparent-slidecontainingimages.58Figure12.9DemandandMarginalRevenueforAztecElectronics-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledaspriceandmarginalrevenueindollarsanditrangesfrom0to100inincrementsof20units.Thehorizontalaxisislabeledoutput,Q,anditrangesfrom0to50,000.AdeclininglinelabeledMRequals100minus0.004Q,beginsat(0,100),andendsat(25,000,0).AnotherdeclininglinelabeledPequals100minus0.002Q,beginsat(0,100)andendsat(50,000,0).Notethevaluesmentionedaboveareapproximate.Returntoparent-slidecontainingimages.59Figure12.10ProfitMaximizationatAztecElectronics-TextAlternativeReturntoparent-slidecontainingimages.Theverticalaxisislabeledpriceandcostindollarsanditrangesfrom0to100.Thehorizontalaxisislabeled0to10,000inincrementsof2,000.AdeclininglinelabeledDcolonPequals100minus0.002Q,beginsat(0,100),andpassesthroughpointBat(6,000,88).AnotherdeclininglinelabeledMRequals100minus0.004Q,beginsat(0,100),andpassesthroughpointAat(6,000,76).AcurvelabeledSMCequals28minus0.01Qplus0.000003Qsquared,beginsat(0,28),fallslefttoright,reachesalowpointat(16,1,500),thenrisesthroughpointAat(6,000,76),andexitsatthetop.AnothercurvelabeledAVCequals28minus0.005Qplus0.000001Qsquared,beginsat(0,28),fallslefttoright,reachesalowpointat(2,000,24),andrisestotherightthroughpointSat(6,000,34).AparaboliccurvelabeledATCequ