managerial economics rganizational production and cost

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bri75829_ch05.qxd8/13/087:07PMPage142ProductionandCostCHAPTER5CHAPTEROUTLINEProductionFunctionsReturnstoScaleReturnstoaFactorChoiceofInputsProductionIsoquantsIsocostLinesCostMinimizationChangesinInputPricesCostsCostCurvesShortRunversusLongRunMinimumEfficientScaleLearningCurvesEconomiesofScopeProfitMaximizationFactorDemandCurvesCostEstimationSummaryAppendix:TheFactor-BalanceEquationheglobaldemandforsteelhasincreasedinrecentyearsdueinparttomajorconstructionprojectsincountries,suchasChinaandIndia.ConstructionTcrewshavebeenparticularlybusyinChinaonprojectsrelatedtothe2008BeijingOlympics,the2010ShanghaiWorldExposition,andnewhousing.Whiletheworldproductionofsteelalsohasincreased,thenetresulthasbeenanin-creaseinsteelpricesfromtheirhistoriclevels.Intheearly1990s,steelsoldforunder$100perton.Atyearend2007,thepricewas$545perton.Thismorethanfivefoldincreaseinthepriceofsteelfarexceedstherateofinflation,whichwasabout50percentoverthesameperiod.Steelpricesnotonlyincreasedoverthisperiodbutalsodisplayedhighvolatility.Inspring2002thepricewasaslowas$222,butbyfall2004ithadin-creasedtoabove$700.Itsubsequentlyretreatedtounder$500inlate2005,butbymid-2006approached$650. bri75829_ch05.qxd8/13/087:07PMPage143Chapter5ProductionandCost143Automobilemanufacturersareamajoruserofsteel.Highsteelpricesprovidestrongincentivestothesecompaniestofindwaystomitigatethepriceincrease,forexample,bysubstitutingawayfromsteeltowardrelativelylessexpensiveproductionmaterials.Considertheiractionsduringthe1990swhensteelpricesbegantheirrecentassent.In1994,domesticsteelpricesincreasedastheU.S.economyrecoveredfromarecession.1Indeed,thesteelmarketwasthestrongestithadbeenin20years:Specifically,steelpriceshadrisenfrombelow$90toover$135pertonbetween1992and1994.Aftersignificantpriceincreasesearlierintheyear,domesticsteelcompanieswereplanningtoincreasesheet-steelpricesbyanother10percentatyear’send.Inthetightelectrogalvanizedmar-kets,priceincreasesashighas20percentwereexpected.(Infact,in1995,pricesexceeded$142perton.)Tocountertheeffectsoftheincreaseindomesticsteelprices,U.S.autocompaniesactivelypursuednewoverseassuppliers.Forinstance,inJuly1994,GeneralMotorsin-vitedbidsforsheetsteelfromforeigncompaniessuchasSidmar,Solldac,Thyssen,andKlockner.Theincreasesinsteelpricesaffectedbothcompanies’pricingandoutputde-cisions.TheincreasesinsteelpricesalsoplacedpressureonU.S.automakerstouseotherrawmaterialsintheproductionprocess.Forexample,autocompaniesincreasedtheiruseofaluminuminengines,transmissions,bodycomponents,heatingandcoolingsystems,andsuspensionsystemsin1995.2(Aluminumpriceshadbeenrelativelystable;theywere$.534perpoundatthebeginningof1992and$.533inJanuary1994.)Potentialapplicationsfocusedonreplacingcastironorsteelwithaluminum.Inaddi-tion,autocompaniesincreasedresearchonnewwaystouseplastics,magnesium,andrecyclablematerialsintheirproductionprocess.Thisexampleraisesanumberofquestionsthatareofinteresttomanagers.First,howdofirmschooseamongsubstitutableinputsintheproductionprocess?Howdoestheoptimalinputmixchangewithchangesintheinputprices?Howdochangesininputpricesaffecttheultimatecostofproductionandtheoutputchoicesoffirms?Inthischapterweaddresstheseandrelatedquestions.Majortopicsincludeproductionfunc-tions,choiceofinputs,costs,profitmaximization,costestimation,andfactordemandcurves.Intheappendix,wederivethefactor-balanceequation.ProductionFunctionsAproductionfunctionisadescriptiverelationthatlinksinputswithoutput.Itspecifiesthemaximumfeasibleoutputthatcanbeproducedforgivenamountsofinputs.Pro-ductionfunctionsaredeterminedbytheavailabletechnology.Productionfunctionscanbeexpressedmathematically.Forinstance,givencurrenttechnology,anautomobilesupplierisabletotransforminputslikesteel,aluminum,plastics,andlaborintofinishedautoparts.Initsmostgeneralform,theproductionfunctionisexpressedasQf(x1,x2,...xn)(5.1)whereQisthequantityproducedandx1,x2,...xnarethevariousinputsusedintheproductionprocess.1Detailsofthisexamplearefrom“GeneralMotorsEyesImportstoCounterPriceIncreases,”MetalBulletin(July11,1994),21.2A.Wrigley(1994),“AutomotiveAluminumUseClimbingin1995’sModels:AutomotiveApplicationsWillUseSome120MillionLbs.in1995,”AmericanMetalMarket(August9),1. bri75829_ch05.qxd8/13/087:07PMPage144144Part2ManagerialEconomicsMANAGERIALAPPLICATIONSIncreasingReturnstoScaleatVolkswagenInordertocompeteglobally,VWandVolvohavelonghadacooperativerelationshipwherebyVWmodifiesorinstallsVWenginesincertainVolvocars.ThisallowsVWtoproduceproportionallymoreengineswithaproportionallysmallerincreaseininputs,therebyincreasingVW’sproductivity.SomeoftheseproductivitygainscanbepassedthroughtoVolvointermsoflowerenginecosts.Thisisanexampleofincreasingreturnstoscale.(Note,in1999,FordpurchasedVolvo’scardivision.)Source:B.Mitchener,A.Latour,andS.Moore(1998),“VW-VolvoTalksSuggestSuccessIsn’tEnoughtoEnsureIndependenceinAutomotiveIndustry,”TheWallStreetJournal(July2),A17.Tosimplifytheexposition,supposethattheautopartinthisexampleispro-ducedfromjusttwoinputs—steelandaluminum.Anexampleofaspecificproductionfunction3inthiscontextisQS12A12(5.2)whereSispoundsofsteel,Aispoundsofaluminum,andQisthenumberofautopartsproduced.Withthisproductionfunction,100poundsofsteeland100poundsofaluminumwillproduce100autopartsovertherelevanttimeperiod,400poundsofsteeland100poundsofaluminumwillproduce200autoparts,andsoon.4ReturnstoScaleThetermreturnstoscalereferstotherelationbetweenoutputandtheproportionalvari-ationofallinputstakentogether.Withconstantreturnstoscale,a1percentchangeinallinputsresultsina1percentchangeinoutput.Forexample,Equation(5.2)presentsaproductionfunctionwithconstantreturnstoscale.Ifthefirmuses100poundsofeachinput,itproduces100autoparts.Ifthefirmincreasesbothinputsby1percentto101pounds,itproduces101autoparts.5Withincreasingreturnstoscale,a1percentchangeinallinputsresultsinagreaterthan1percentchangeinoutput.AnexampleofsuchaproductionfunctionisQSA(5.3)Here,100poundsofsteeland100poundsofaluminumproduce10,000autoparts,while101poundsofsteelandaluminumproduce10,201autoparts(a2percentincreaseinoutput).Firmsoftenexperienceincreasingreturnstoscaleoveratleastsomerangeofoutput.Onemajorreasonisthatafirmoperatingonalargerscalecanengageinmoreextensivespecialization.Forinstance,ifanautomobilecompanyhasonlythreeemploy-eesandthreemachines,eachemployeeandeachmachinehastoperformamyriadof3ThisproductionfunctionisanexampleofaCobb-Douglasproductionfunction,whichtakesthegeneralformQSA.Cobb-Douglasproductionfunctionsareusedfrequentlyinempiricalestimation.Notallfirms,however,haveproductionprocessesthatarewelldescribedbythisparticulartypeofproductionfunction.410012100121010100,and40012100122010200.5[(1001.01)12][(1001.01)12]101. bri75829_ch05.qxd8/13/087:07PMPage145Chapter5ProductionandCost145tasksforthecompanytoproduceautomobiles.Giventhebroadarrayoftasksthateachworkerandmachinehastoperform,efficiencyislikelytobelow.Incontrast,alargefirmemployingthousandsofworkersandmachinescanengageinmuchgreaterspe-cialization.(AsnotedinChapter3,specializationoftenproducesefficiencygains.)Withdecreasingreturnstoscale,a1percentchangeinallinputsresultsinalessthan1percentchangeinoutput.AnexampleisQS13A13(5.4)Thelikelihoodthatafirmwillchoosetooperatewhereitexperiencesdecreasingreturnstoscaleisopentodebate.Someeconomistsarguethatfirmsshouldseldomdisplaydecreasingreturnstoscale.Ifafacilityofagivensizecanproduceagivenoutput,whycan’tthefirmsimplyreplicatethatfacilityandproducetwicetheoutputwithtwicetheinputs?Indeed,mostempiricalstudiesonthesubjectsuggestthatthetypicalfirmini-tiallyexperiencesincreasingreturnstoscale,followedbyconstantreturnstoscaleoveraquitebroadrangeofoutput.Ontheotherhand,severalempiricalstudiesindicatethatsomefirmsprobablydoexperiencedecreasingreturnstoscale.6Also,casualobservationsuggeststhatsomelargerfirmssufferfrominefficienciestoagreaterextentthandosmallerfirms—forexample,coordinationandcontrolproblemsbecomemoresevereasafirmbecomeslarger.(WefocusontheseorganizationalissuesinPart3.)Inourexamples,thereturnstoscalearethesameoverallrangesofoutput.Forinstance,Equation(5.2)alwaysdisplaysconstantreturnstoscale,whileEquation(5.4)alwaysdisplaysdecreasingreturns.Mostproductionfunctionsvaryinreturnstoscaleovertherangeofoutput.Mostfrequently,productionfunctionshaveincreasingreturnstoscalewhenoutputisrelativelylow,followedbyconstantreturnstoscaleasoutputcontinuestoincrease,andpossiblydecreasingreturnstoscalewhenoutputishigh.Othercombinationsarepossible.ReturnstoaFactorReturnstoafactorreferstotherelationbetweenoutputandthevariationinasingleinput,holdingotherinputsfixed.Returnstoafactorcanbeexpressedastotal,marginal,oraveragequantities.Thetotalproductofaninputisthescheduleofoutputobtainedasthatinputincreases,holdingotherinputsfixed.Themarginalproductofaninputisthechangeintotaloutputassociatedwithaone-unitchangeintheinput,holdingotherinputsfixed.Finally,theaverageproductisthetotalproductdividedbythenumberofunitsoftheinputemployed.Toillustratetheseconcepts,considertheproductionfunctioninEquation(5.2):QS12A12.Table5.1(page146)presentsthetotal,marginal,andaverageproductofS,holdingAfixedat9.7Forthisproductionfunction,totalproductincreasesasSincreases;marginalproduct,however,declines.ThismeansthatalthoughtotalproductincreaseswithS,itdoessoatadecreasingrate.Averageproductalsodecreasesovertheentirerange.Moregenerally,marginalandaverageproductsdonothavetodeclineovertheentirerangeofoutput.Indeed,manyproductionfunctionsdisplayincreasingmarginaland6Forexample,E.Berndt,A.Friedlaender,andJ.Chiang(1990),“InterdependentPricingandMarkupBehavior:AnEmpiricalAnalysisofGM,Ford,andChrysler,”workingpaper,NationalBureauofEconomicResearch,Cambridge,MA.7Theproductionfunctionassumesthatproductiondoesnothavetotakeplaceindiscreteunits.Forinstance,outputmightbeexpressedintons;clearlyproductioninfractionsoftonsispossible. bri75829_ch05.qxd8/13/087:07PMPage146146Part2ManagerialEconomicsUnitsUnitsTotalProductMarginalProductAverageProductofSofAofSofSofS193.003.003.00294.241.242.12395.200.961.73496.000.801.50596.700.701.34Table5.1ReturnstoaFactorThistableshowsthetotal,marginal,andaverageproductsofsteelfortheproductionfunctionQS12A12.Aluminumisheldfixedat9units.ThetotalproductofSisthetotaloutputforeachlevelofS;themarginalproductofSistheincrementaloutputfromoneadditionalunitofS;andtheaverageproductofSisoutputdividedbythetotalunitsofS.averageproductsoversomeranges.However,mostproductionfunctionsreachapointafterwhichthemarginalproductofaninputdeclines.Thisobservationofteniscalledthelawofdiminishingreturns(orlawofdiminishingmarginalproduct),whichstatesthatthemarginalproductofavariablefactoreventuallywilldeclineasitsuseisin-creased.Toillustratethisprinciple,considertheclassicexampleoffarmingaplotofland.Landisfixedat1acre,andnooutputcanbeharvestedwithoutanyworkers.If10bushelsofgraincanbeproducedbyoneworker,themarginalproductofthefirstunitoflaboris10bushels.Thechangeinoutputmightbeevengreaterasthefirmmovesfromonetotwoworkers.Forinstance,twoworkersmightbeabletoproduce25bushelsofgrainbyworkingtogetherandspecializinginvarioustasks.Themarginalproductoflaboris15bushelsandthus,overthisrange,marginalproductisincreasing.Eventually,asthefirmcontinuestoaddmoreworkers,whileholdinglandfixed,outputwillgrowataslowerrate.Atsomepoint,totaloutputmightactuallydeclinewithMANAGERIALAPPLICATIONSStudyingforanExam—theLawofDiminishingReturnsYourperformanceontheCPAexamdependsonbothyoureffortandaptitudeinthesubject.Youraptitudeislargelyafixedinput(e.g.,itishardtoincreaseyourbasicIQ).Effortontheotherhandissomethingyoucancontrolandvary.Forexample,ifyouarepreparingfortheCPAexam,youcouldspendmanyorfewhoursreadingbooksandworkingproblems.Thechoiceisyours.Ifyouexertnoeffort,youareunlikelytodowellontheexamandeasilycouldfail.Ifyoustudy,yourperformanceislikelytoimprove.Initially,asyoubegintoallocateadditionalhourstostudyingfortheexam,yourrateofimprovementmightbequitelarge.Forinstance,youmightexpecttoincreaseyourexamscoreby20pointsifyoustudyoneversusnohours.Asyoucontinuetospendmoretimeonstudyingfortheexam,yourrateofimprovement(marginalproductofeffort)islikelytodecline—youwillreachapointofdiminishingreturns.Indeedatsomepointyourexamscorecoulddeclinewithadditionaleffortasyoubecometootiredtotaketheexam—themarginalproductofeffortbecomesnegative.Basiceconomicssaysthatyoushouldstudyforanexamuptothepointwheretheincrementalbenefitsofstudyingadditionaltimeareequaltotheincrementalcosts.Thelawofdiminishingreturnsimpliesthattheincrementalbenefitswilleventuallybecomesmallerandpossiblynegative.Theincrementalcostsofstudyinganadditionalhourdependonyouropportunitycostoftime—forwhatelsecouldyouusethetime?ItisunlikelytobeoptimalforyoutospendadditionaltimestudyingfortheCPAexamifthatcausesyoutoneglectyourotherprofessionalresponsibilities. bri75829_ch05.qxd8/13/087:07PMPage147Chapter5ProductionandCost147Figure5.1ReturnstoaFactor:QACommonCaseThisfigureillustratesacommonpatternfortotalproduct,marginalproduct,andreturnstoafactor.Inthelowerpanel,marginalproductrises,thenTotalfalls,andeventuallybecomesnegative.Whenproductmarginalproductisrising(betweenzeroandS1),totalproductincreasesatanincreasingrate(thecurveisconvex)inthelowerpanel.Whenmarginalproductisfallingbutpositive(betweenS1andS2),Quantityofautopartstotalproductcontinuestoincreasebutdoessoatadecreasingrate.BeyondS2,marginalproductisnegativeandtotalproductfallswithadditionalSoutput.AverageproductisrisingwhereitisbelowmarginalproductandisfallingwhereitisaboveQ/Smarginalproduct.Averageandmarginalproductsareequalwhereaverageproductisatamaximum.perunitofsteelQuantityofautopartsAverageproductMarginalproductSS1S2Quantityofsteeladditionalworkersbecauseofcoordinationorcongestionproblems.Inthiscase,themarginalproductisnegative.Figure5.1illustratesreturnstoafactorinthiscommoncase.Theupperpaneldis-playstotalproduct,andthelowerpaneldisplaysmarginalandaverageproducts.AstheuseofinputSgoesfromzerotoS1,marginalproductrises.Overthisrangetotalprod-uctisconvex—totalproductincreasesatanincreasingrate.8AtS,diminishingreturns1setinandthemarginalproductbeginstofall.BetweenS1andS2,marginalproductispositiveandsototalproductcontinuestoincrease.However,itdoessoatadecreasingrate(thecurveisconcave).BeyondS2,marginalproductisnegative,hencetotaloutputfallswithincreasesinS.Averageproductisrisingwheremarginalproductisaboveaver-ageproductandisfallingwheremarginalproductisbelowaverageproduct.Marginal8Technicalnote:Themarginalproductatapointisequaltotheslopeofthetotalproductcurveatthatpoint(MPTP/S).Thus,marginalproductisdecreasingwhenthetotalcostcurveisconcaveandincreasingwhenitisconvex. bri75829_ch05.qxd8/13/087:07PMPage148148Part2ManagerialEconomicsMANAGERIALAPPLICATIONSBaseballBattingAveragesMarginalproductisaboveaverageproductwhenaverageproductisrisingandbelowaverageproductwhenaverageproductisfalling.Thisrelationisageneralpropertyofmarginalsandaverages.Ausefulillustrationisabaseballplayer’sbattingaverage.Thebattingaverageisdefinedasthenumberofhitsdividedbythenumberoftimesatbat.Supposeaplayerstartsagamewithanaverageof.300.Iftheplayergetstwohitswithfouratbats,themarginalbattingaverageforthedayis.500andtheplayer’sbattingaveragemustrise.Iftheplayergetsonehitwithfouratbats,themarginalis.250andtheoverallaveragemustdrop.productandaverageproductareequalwhereaverageproductisatitsmaximum.9Thisrelationisageneralrule.10Theaccompanyingboxonbaseballbattingaveragesillus-tratestheintuitionbehindthisrelation.ChoiceofInputsProductionIsoquantsMostproductionfunctionsallowsomesubstitutionamonginputs.Forexample,sup-posethatAlexiDyachenkoischiefoperatingofficer,managingafirmwiththeproduc-tionfunctionQS12A12,andhewantstoproduce100autoparts.Inthiscase,therearemanydifferentcombinationsofsteelandaluminumthatwillyield100autoparts.Forinstance,100autopartscanbeproducedusing100poundsofsteeland100poundsofaluminum,25poundsofsteeland400poundsofaluminum,or400poundsofsteeland25poundsofaluminum.Figure5.2displaysallthepossiblecombinationsofinputsthatcanbeusedtoproduceexactly100autoparts.Obviously,100autopartsalsocouldbeproducedwithmoreinputs—pointsaboveortotherightofapointonthisisoquant—butthosepointsrepresentinefficientproductionmethods.Thiscurveiscalledanisoquant(iso,meaningthesame,andquantfromquantity).Anisoquantshowsallinputcombinationsthatproducethesamequantityassumingefficientproduction.Thereisadifferentisoquantforeachpossiblelevelofproduction.Figure5.2showstheisoquantsfor100,200,and300autoparts.Productionfunctionsvaryintermsofhoweasilyinputscanbesubstitutedoneforanother.Insomecases,nosubstitutionispossible.Supposethatinordertoproduce100autopartsyoumusthave100poundsofaluminumand100poundsofsteel,toproduce200autopartsyoumusthave200poundsofaluminumand200poundsofsteel,andsoon.Havingextrasteeloraluminumwithouttheothermetalyieldsnoadditionaloutput—theymustbeusedinfixedproportions.AsshowninFigure5.3,isoquantsfromfixed-proportionproductionfunctionsareshapedasrightangles.Attheotherextremeareperfectsubstitutes:Theinputscanbesubstitutedfreelyoneforanother.Supposethatoneautopartalwayscanbeproducedusingeither2poundsofsteelor2poundsofaluminum.Inthiscase,thefirmcanproduce100autopartsbyusingeither200poundsofaluminumor200poundsofsteel,oranycombinationinbetween.Asshownin9Graphically,marginalproductistheslopeofalinedrawntangenttothetotalproductcurveofthatlevelofoutput;averageproductistheslopeofthelineconnectingapointonthetotalproductcurvewiththeorigin.10Averagesandmarginalsalsoareequalwhentheaverageisataminimum. bri75829_ch05.qxd8/13/087:07PMPage149Chapter5ProductionandCost149Figure5.2IsoquantsAAnisoquantdisplaysallpossiblewaystoproduceagivenquantity.Thereisadifferentisoquantforeachpossiblelevelofproduction.Thisfigureshowstheisoquantsfor100,200,and300autopartsfortheproductionfunctionQS12A12.300Quantityofaluminum200100SQuantityofsteelFigure5.3,thecorrespondingisoquantisastraightline.Mostproductiontechnologiesimplyisoquantsthatarebetweenthesetwoextremes.AsdepictedinFigure5.3,typicalisoquantshavecurvature,butarenotrightangles.Thedegreeofsubstitutabilityoftheinputsisreflectedinthecurvature:Theclosertheisoquantistoarightangle(themoreconvex),thelowerthedegreeofsubstitutability.Generally,isoquantsareconvextotheorigin(aspicturedinthecenterpanelinFigure5.3—thetypicalcase).ConvexityimpliesthatthesubstitutabilityofoneinputFigure5.3IsoquantsforFixedProportionProductionFunctions,PerfectSubstitutes,andtheNormalCaseProductionfunctionsvaryintermsofhoweasilyinputscanbesubstitutedforoneanother.Insomecases,inputsmustbeusedinfixedproportionsandnosubstitutionispossible.Here,isoquantstaketheshapeofrightangles.Attheotherextremeareperfectsubstitutes,wheretheinputscanbefreelysubstitutedforoneanother.Here,isoquantsarestraightlines.Mostproductionfunctionshaveisoquantsthatarebetweenthetwoextremes.Theisoquantsinthenormalcasehavecurvaturebutarenotrightangles.AAAQuantityofaluminumSSSQuantityofsteelQuantityofsteelQuantityofsteelFixedproportionsNormalcasePerfectsubstitutes bri75829_ch05.qxd8/13/087:07PMPage150150Part2ManagerialEconomicsMANAGERIALAPPLICATIONSSubstitutionofInputsinHomeBuildingBuildersinthePacificNorthwestuselargequantitiesofwoodintheconstructionofresidentialhouses.Forinstance,woodisusedforframing,siding,floors,roofs,andsoon.HomebuildersintheSouthwest(forexample,Arizona)usemuchmorestuccoandtileinhomeconstruction.Animportantreasonforthisdifferenceisthat,incontrasttothePacificNorthwest,theSouthwestdoesnothavelargenearbyforests.Thisexamplesuggeststhathomebuildersareabletosubstituteamonginputsinbuildingahome.HomebuildersintheSouthwest,however,stillusewoodtoframethehouse:Thesubstitutionofotherinputsforwoodisnotcomplete.foranotherdeclinesaslessofthefirstinputisused.Inourexample,ifthefirmisusingalargequantityofsteelandlittlealuminum,itcaneliminatearelativelylargequantityofsteelwiththeadditionofonlyasmallquantityofaluminumwhilekeepingoutputthesame(seeFigure5.2).Inthiscase,aluminumwouldbemuchbettersuitedthansteeltoconstructsomecomponentsoftheautopart.Butasthefirmuseshigherproportionsofaluminum,itsabilitytosubstitutealuminumforsteeldeclines:Steelisbettersuitedforothercomponents.Mostproductionprocessesdisplaythisproperty.IsocostLinesGiventhattherearemanywaystoproduceagivenlevelofoutput,howdoesAlexichoosethemostefficientinputmix?Theanswerdependsonthecostsoftheinputs.Supposethatthefirmfacescompetitiveinputmarketsandcanbuyasmuchofeachinputasitwantsatprevailingmarketprices.ThepriceofsteelisdenotedPs,whereasthepriceofaluminumisdenotedPa.Totalcost(TC)isequaltothesumofthequantitiesofeachinputusedintheproductionprocesstimestheirrespectiveprices.Thus,TCPsSPaA(5.5)IsocostlinesdisplayallcombinationsofSandAwiththesamecost.SupposePs$.50perpoundandPa$1perpound,andthegivencostlevelis$100.Inthiscase,$100$.50S$A(5.6)orequivalently,A1000.5S(5.7)MANAGERIALAPPLICATIONSGeneralMotorsIsShanghaiedInthelate1990s,GeneralMotorsparticipatedina$1.5billionjointventurewithastate-ownedenterpriseinChina.TheBuicksproducedattheresultingstate-of-the-artShanghaiplantwereconsideredtobethehighest-qualitycarsofthatmodelbeingproducedanywhereintheworld.Productioncosts,however,wereextremelyhigh.Oneimportantreasonforthehighcostswasgovernmentregulation.TheChinesegovernmentdictatedwhatproductscouldbebuilt,aswellashowmany,andatwhatprice.Thegovernmentalsorestrictedtheinputmix.Forinstance,in1999GMwasrequiredtouselocallymadecomponentsequaling40percentintermsofvalueand60percentin2000.ThusalthoughGMhassharedimportanttechnologywithitsChinesepartner,governmentconstraintshaveprecludedefficientproduction.Highcostshavelimitedthejointventure’sabilitytoexportcarstoothercountries.Source:LKraar(1999),“China’sCarGuy,”Fortune(October11),238–246. bri75829_ch05.qxd8/13/087:07PMPage151Chapter5ProductionandCost151Figure5.4IsocostCurvesAIsocostlinesdisplayallcombinations200ofinputsthatcostthesame.Inthisexample,Ps$.50perpoundandPa$1perpound.Thefigureshowsisocostlinesfor$100and$200ofexpenditures.Theslopeofanisocostlineis1times100theratiooftheinputprices—inthisQuantityofaluminumexample,0.5.Isocostlinesfordifferent$100line$200lineexpenditurelevelsareparallel.S200400QuantityofsteelFigure5.4graphsthisisocostline.Notethattheintercept,100,indicateshowmanypoundsofaluminumcouldbepurchasediftheentire$100werespentonaluminum.Theslopeof0.5is1timestheratioofthetwoprices(PsPa):Sincealuminumistwiceasexpensiveassteel,0.5poundsofaluminumcanbegivenupfor1poundofsteelandcostsremainthesame.Holdingthepricesoftheinputsconstant,isocostlinesfordifferentcostlevelsareparallel.Figure5.4illustratesthispropertyusingtheisocostlinesfor$100and$200.Notethatthefurtherawaythelineisfromtheorigin,thehigherthetotalcost.Thus,holdingoutputconstant,thefirmwouldliketobeonthelowestpossibleisocostline.Theslopeofanisocostlinechangeswithchangesintheratiooftheinputprices.AsdepictedinFigure5.5,ifthepriceofsteelincreasesto$1,thelinebecomessteeper(slopeof1).Here,thefirmmustgiveup1poundofaluminumtoobtain1poundofsteel.Alternatively,ifthepriceofsteelfallsto$.25(notdepictedinthefigure),thelinebe-comesflatter(slopeof–0.25).Inthiscase,thefirmhastogiveuponly0.25poundofaluminumforeverypoundofsteel.Similarly,theslopeofthelinealsochangeswithchangesinthepriceofaluminum.Whatdeterminestheslopeofthelinearetherelativeprices(recalltheslopeis–PsPa).Figure5.5IsocostLinesandAChangesinInputPrices100Thisfiguredepictstheeffectofchangesininputpricesontheslopesofisocostlines.Thesolidlineshowstheisocostlinewhenthepriceofaluminumis$1andthepriceofsteelis$.50.Thedottedlineshowstheisocostlinewherethepricesofbothinputsare$1.TotalcostQuantityofaluminumPs=$1.00Ps=$.50perpoundperpoundineachcaseis$100.S100200Quantityofsteel bri75829_ch05.qxd8/13/087:07PMPage152152Part2ManagerialEconomicsFigure5.6CostMinimizationAQ*Theinputmixthatminimizesthecostofproducinganygivenoutput,Q*,occurswhereanisocostlineistangenttotheA′relevantisoquant.Inthisexample,thetangencyoccursat(S*,A*).Thefirmwouldprefertobeonanisocostlineclosertotheorigin.However,thefirmA*wouldnothavesufficientresourcestoproduceQ*.ThefirmcouldproduceQ*usingotherinputmixes,suchas(S,A).QuantityofaluminumHowever,thecostofproductionwouldincrease.SS′S*QuantityofsteelCostMinimizationForanygivenlevelofoutput,Q*,Alexiwillwanttochoosetheinputmixthatmini-mizestotalcosts.AsshowninFigure5.6,thecost-minimizingmix(S*,A*)occursatthepointoftangencybetweentheisoquantforQ*withtheisocostline.Alexiwouldliketoproducetheoutputlessexpensively(usinganisocostlineclosertotheorigin).However,lower-costproductionisnotfeasible.AlexicouldselectotherinputmixestoproduceQ*.11Butanyotherinputmixwouldplacethefirmonahigherisocostline.Considerthecombination(S,A)inFigure5.6.Thiscombinationofinputsalsopro-ducesQ*unitsofoutput.Yetthisoutputcanbeproducedatalowercostbyusinglessaluminumandmoresteel.Intheappendixtothischapter,weshowthatattheoptimalinputmix,thefollowingconditionholds:MPsPsMPaPa(5.8)whereMPiisthemarginalproductofinputi.(RecallthatthemarginalproductofaninputisdescribedinTable5.1.)Condition(5.8)hasastraightforwardinterpretation.Theratioofthemarginalproducttopriceindicateshowmuchadditionaloutputcanbeobtainedbyspendinganextradollarontheinput.Attheoptimaloutputmixthisquantitymustbethesameacrossallinputs.Otherwise,itwouldbepossibletoincreaseoutputwithoutincreasingcostsbyreducingtheuseofinputswithlowratiosandin-creasingtheuseofinputswithhighratios.Forinstance,iftheratiois10unitsperdollarforaluminumand20unitsperdollarforsteel,thefirmcouldholdcostsconstantbutin-creaseoutputby10unitsbyspendingonelessdollaronaluminumandonemoredollaronsteel.Alexihasnotchosenanoptimalinputmixwhensuchsubstitutionispossible.11Notethesimilaritybetweenthiscostminimizationproblemandtheconsumer’sutilitymaximizationproblemintroducedinChapter2.Themathematicsarethesame—bothareconstrainedoptimizationproblems.Theconsumermaximizesutilityforagivenbudget.Costminimizationisequivalenttomaximizingoutputforagivenbudget(wherethebudgetisthatassociatedwiththelowest-costmethodofproducingtheoutput). bri75829_ch05.qxd8/13/087:07PMPage153Chapter5ProductionandCost153ACADEMICAPPLICATIONSMinimumWageLawsTheminimumwageintheUnitedStateswasincreasedto$5.85onJuly24,2007.Proponentsofthisactionarguedthatthepoorwouldbesubstantiallybetteroffasaresultofthisincrease.Theanalysisinthischapterindicateswhymanyeconomistsandpoliticiansareskepticalaboutthisclaim.Althoughitistruethattheincreaseinminimumwagemakessomeworkersbetteroffbyincreasingtheirwages,otherindividualswouldbemadeworseoff.Inparticular,theincreaseinthewagerateislikelytomotivatefirmstosubstituteawayfromlow-skilledworkerstowardmoreautomationandadditionalhigh-skilledworkers.Thus,thenumberofemployeeshiredattheminimumwageislikelytodeclinewithanincreaseinthewage.Estimatessuggestthatwhentheminimumwagewasincreasedfrom$3.35to$4.25,employmentamongteenagemenfellby7.29percent,andemploymentamongteenagewomenfellby11.34percent;employmentamongteenageblacksfellby10percent.Minimumwageworkerswhoretaintheirjobsarebetteroff;butindividualswhowantajob,yetcannotfindone,areworseoff.Source:D.Deere,K.Murphy,andF.Welch(1995),“Employmentandthe1990–1991Minimum-WageHike,”AmericanEconomicReview85:2,232–237.ChangesinInputPricesAnincreaseintherelativepriceofaninputwillmotivateAlexitouselessofthatinputandmoreofotherinputs.Figure5.7illustrateshowtheoptimalinputmixforproducingQ*changesasthepriceofsteelincreases:Alexichooseslesssteelandmorealuminumtoproducetheoutput.Thiseffectiscalledthesubstitutioneffect.Thestrengthofthesubsti-tutioneffectdependsonthecurvatureoftheisoquant.Thegreaterthecurvature,thelessAlexiwillsubstitutebetweenthetwoinputsforanygivenchangeinprices.Thesubstitu-tioneffecthelpsexplainthereactionsofautomobilecompaniestothe1994increasesindomesticsteelprices.Thesecompaniesincreasedtheiruseofforeignsteel.Theyalsosearchedforadditionalwaystoreplacesteelwithotherinputssuchasaluminum.Figure5.7OptimalInputMixandAChangesinInputPricesThisfigureillustrateshowtheoptimalinputQ*mixforproducingagivenoutput,Q*,changesasthepriceofaninputincreases.A*2Inthisexample,thepriceofsteelincreasesandthefirmuseslesssteelandmorealuminumtoproducetheoutput.ThisA*1effectiscalledthesubstitutioneffect.Thestrengthofthesubstitutioneffectdependsonthecurvatureoftheisoquant.TheQuantityofaluminumgreaterthecurvature,thelessthefirmwillsubstitutebetweenthetwoinputs.HighsteelLowsteelpricepriceSS*S*21Quantityofsteel bri75829_ch05.qxd8/13/087:07PMPage154154Part2ManagerialEconomicsANALYZINGMANAGERIALDECISIONS:ChoosingtheMixofPeopleandMachinestoTicketAirlineCustomersYouworkforanairlinecompanyasaticketoperations2.Plottheinputcombinationsinthetableonamanageratamajorairport.YourunitisresponsibleforgraphthatcontainsCSRsontheverticalaxisissuingboardingpassesto30,000customersperday.andmachinesonthehorizontalaxis.ConnectCurrentlyyouemploy80customerservicerepresenta-thepointsbylinestoapproximateanisoquanttives(CSRs)and10electronicticketingmachinestoaspicturedinFigure5.6.Addthecostmini-meetthisdemand.EachCSRispaidwagesandfringemizingisocostcurvetothegraph(youcanbenefitsof$150/day.Italsocostsyou$150/daytoderivethislinefromtheinputpricesandtheleaseeachmachine(priceincludesinstallation,soft-totalcostofthelow-costinputcombination).waresupport,andservicing).AcomputervendorHowdotheslopesoftheisocostcurveandhasofferedtoleaseyouadditionalelectronicticketingisoquantcompareattheoptimalinputmachinesatthisprice.Youestimatethatbyleasingcombination?10moremachinesyoucanmeetyourservicerequire-3.SupposethatthemarginalproductofCSRsmentswith30fewerCSRs.Shouldyouleasetheaddi-attheoptimalinputcombinationis1,000.tionalmachinesorcontinuetoserviceyourcustomersExplaininwordswhatthismeans.Whatiswithyourcurrentinputmix?themarginalproductofmachinesatthispoint?Explainwhy.1.Youconductadditionalanalysisandestimate4.Supposethatthecostofleasingamachinethatyoucanservicethe30,000customerswithdeclinesto$45/day.WhatisyournewthefollowingcombinationsofCSRsandma-optimalinputmix?Howdoesthisaffectchines.Calculatethetotalcostsforeachoftheseyourgraph?combinations.Whatcombinationofinputs5.Arethereanyotherfactorsthatshouldbeservesthecustomersatthelowestpossiblecost?consideredinmakingthisdecisionontheoptimalmixofmachinesandCSRs?CSRsTicketingMachinesDiscussbriefly.801050203030204015501260CostsWehaveanalyzedhowfirmsshouldchoosetheirinputmixtominimizecostsofpro-duction.Wenowextendthisanalysistofocusmorespecificallyoncostsofproducingdifferentlevelsofoutput.Analysisofthesecostsplaysanimportantroleinoutputandpricingdecisions.CostCurvesThetotalcostcurvedepictstherelationbetweentotalcostsandoutput.Conceptually,thetotalcostcurvecanbederivedfromtheisoquant/isocostanalysisdiscussedabove.Foreachfeasiblelevelofoutput,thereisaleast-costmethodofproduction—asdepicted bri75829_ch05.qxd8/13/087:07PMPage155Chapter5ProductionandCost155MANAGERIALAPPLICATIONSJobSeekersUseInternetPostingrésumésontheInternetisgrowinginpopularity.In1999,therewerealmostfivemillionrésumésontheInternet—200timesasmanyas1994,accordingtoComputerEconomics.Thenumberofjob-relatedWebsitesisexpectedtogrowfromabout200in1998to1,200in2002.Thisexplosivegrowthisaresponsetotheadvantagesofonlinejobsearches.Candidatescanreachalargeraudiencewithgreaterease.Andrecruiterscanreducepaperworkandtravel.Butthisfloodinjobcandidatessendingonlinerésuméshascreatedunexpectedheadachesforemployers.Somecompaniesaregettingthousandsofrésumésdumpedintotheire-mailboxeseachday.Others,fedupwithmasse-mailedrésumés,yearnforamorepersonaltouch.“Yougettonsofstufffrompeoplewhoaren’tqualified,”saysMichaelErbschloeofComputerEconomics,aCarlsbad,California,researchfirm.“Thecontentofthee-mailishorrible.Itbogsdownyourmailboxandyourserver.”Thusintheproductionofjoboffers,thereducedcostofdistributinginformationaboutthemselvesusingtheInternethasresultedinhugevolumeofe-mailasjobseekerssubstituteawayfrommoreexpensivealternatives.Source:S.Armour(1999),“OnlineRésumésBoggingDownEmployers,”Democrat&Chronicle(July19),1F.bythetangencybetweentheisoquantandtheisocostline.Thetotalcostcurvesimplydisplaysthecostofproductionassociatedwiththeisocostlineandthecorrespondingoutput.Forinstance,iftheleast-costmethodofproducing100autopartsis$1,000,onepointonthetotalcostcurveis(100,$1000).Iftheleast-costmethodofproducing200partsis$1,500,anotherpointis(200,$1,500).Marginalcostisthechangeintotalcostsassociatedwithaone-unitchangeinoutput.Averagecostistotalcostdividedbytotaloutput.Managerssometimesrefertomarginalcostasincrementalcost,whereastheyusethetermunitcosttorefertoaveragecost.Figure5.8(page156)displaysthetotal,marginal,andaveragecostcurvesforahypo-theticalfirm.(Thisfigureillustratesacommonpatternforcostcurves,althoughnotallfirmshavecostcurveswiththissameshape.)Theupperpanelindicatesthattotalcostincreaseswithoutput.BetweenzeroandQ1,totalcostincreasesbutatadecreasingrate(thecurveisconcave).Asshowninthelowerpanel,overthisrange,marginalcostdecreases.12PastQ,totalcostincreasesatanincreasingrate(thetotalcostcurveis1convex)andmarginalcostincreases.Averagecostisdecliningwheremarginalcostisbelowaveragecostandisrisingwheremarginalcostisaboveaveragecost.Averagecostequalsmarginalcostwhereaveragecostisatitsminimumpoint.Aspreviouslydis-cussed,theserelationsaregeneralrules:Theyapplytoaveragecostsandaverageprod-ucts,aswellasbattingaveragesandGPAs.ProductionFunctionsandCostCurvesWithconstantinputprices,theshapesofcostcurvesaredeterminedbytheunderlyingproductionfunction.Forinstance,iftheproductionfunctiondisplaysincreasingreturnstoscaleoversomerangeofoutput,long-runaveragecostmustdeclineoverthatrange.Withincreasingreturnstoscale,a1percentincreaseininputexpendituresresultsinagreaterthan1percentincreaseinoutputandaveragecostmustfall.Incontrast,withdecreasingreturnstoscale,a1percentincreaseininputexpendituresresultsinalessthan1percentincreaseinoutputandaveragecostmustrise.Finally,constant12Technicalnote:Themarginalcostatapointisthederivativeoftotalcost(MCTCQ).Graphically,itisequaltotheslopeofthetotalcostcurveatthatpoint.Thus,marginalcostdecreaseswhenthetotalcostcurveisconcaveandincreaseswhenitisconvex.Theaveragecostcurveistheslopeofthelineconnectingapointonthetotalcostcurvewiththeorigin. bri75829_ch05.qxd8/13/087:07PMPage156156Part2ManagerialEconomicsFigure5.8CostCurves$Thisfiguredisplaysthetotal,marginal,andaveragecostcurvesofahypotheticalfirm.Theupperpanelpicturestotalcost.Totalcostincreaseswithoutput.BetweenzeroandQ1,totalcostincreasesbutataTotalcostdecreasingrate(thecurveisconcave).Asshowninthelowerpanel,overthisrange,marginalcostdecreases.PastQ1,totalcostincreasesatanincreasingrate(thecurveisconvex)andmarginalcostincreases.Aver-agecostdeclineswheremarginalcostisbelowaverageTotalcosts(indollars)costandriseswheremarginalcostisaboveaveragecost.Thisrelationisageneralrule.Q$MarginalcostAveragecost(indollars)CostperunitofoutputQQ1Q2Quantityofoutputreturnstoscaleimplyconstantaveragecost.U-shapedcurves(aspicturedinFigure5.8)normallyareusedtoillustrateaveragecosts.Thisslopesuggestsaninitialregionofincreasingreturnstoscale,followedbydecreasingreturnstoscale.13Thereisalsoadirectlinkbetweenthemarginalcostcurveandtheunderlyingpro-ductionfunction.RecallfromEquation(5.8)thatcostminimizationrequirestheratioofthemarginalproducttopricetobeequalacrossallinputs.Forillustration,supposeattheoptimalinputmixtoproduce100autoparts,theratioofthemarginalproducttopriceforbothsteelandaluminumis2.Byexpending$1moreoneitherinput,outputincreasesby2units.Thereciprocalofthisratio(12)istheirmarginalcostofproduc-ingoneadditionalunitofoutput—if2unitsareproducedwith$1ofadditionalexpen-ditureoninputs,themarginalcostofproducingoneextraunitis$.50.Thisexamplein-dicatesthat,holdinginputpricesconstant,marginalcostisdeterminedbythemarginalproductivityoftheinputs:Thehighertheirmarginalproductivity,thelowerthemar-ginalcost.Ifthemarginalproductivitiesinourexampleweredoubled,theratioofthe13Someeconomistsarguethatthetypicallong-runaveragecostcurveisflattotherightofitsminimumefficientscale.Oncethatoutputisreached,additionaloutputcanbeproducedataconstantaveragecostbysimplyreplicatingtheprocess(theproductionfunctiondoesnotexperiencedecreasingreturnstoscale).Butthisargumentpresumesthatorganizationalcostsdonotincreasedisproportionallywithfirmsize.SeeP.McAfeeandJ.McMillan(1995),“OrganizationalDiseconomiesofScale,”JournalofEconomicsandManagementStrategy4:3,399–426. bri75829_ch05.qxd8/13/087:07PMPage157Chapter5ProductionandCost157MANAGERIALAPPLICATIONSIndustryRespondstoHigherMetalsPricesMetalspricesrosesubstantiallybetween2003and2004;forinstance,thepriceofhotrolledsteelincreasedbymorethan80percent.Manufacturingfirmslimitedtheimpactofthesehigherrawmaterialspricesthroughimprovedproductivityandswitchingtolessexpensivesubstitutes.Forexample,somestainlesssteelmakersbegantousemorechromiumandmanganeseandlessnickel.CraigYardeofYardeMetalsinSouthington,CT,saidthattherun-upinpriceshadbenefitedhiscompanybyincreasingthemarketvalueofthe40millionpoundsofmetalsinitsinventory,mostlyaluminumandstainlesssteel.Source:B.Simmon(2004),“SurgeinCostofMetalSqueezesPricingandProfits,”NewYorkTimes(February26),C.1.marginalproducttopricewouldbe4andthemarginalcostwouldbe$.25.Theinverserelationbetweenmarginalproductivityandmarginalcostmakesintuitivesense.Ifwithagivenincreaseininputsmoreoutputcanbeproduced,themarginalcostofproducingthatoutputislower.Inputpricesalsocanaffecttheshapesofthecostcurves.Forinstance,adecliningaveragecostcanbemotivatedbydiscountsonlargevolumepurchases.Similarly,ama-chinethatproduces20,000unitsmightnotbetwiceasexpensiveasamachinethatpro-ducesonly10,000units.Alternatively,ifthefirmbidsupthepriceofinputswithlargepurchases,averagecostcanrisewithincreasedoutput.Thus,thelong-runaveragecostcurvecanslopeupwardevenifthefirmdoesnotexperiencedecreasingreturnstoscale.OpportunityCostsManagersmustbecarefultousethecorrectsetofinputpricesinconstructingcostcurves.InChapter2,wedefinedopportunitycostasthevalueofaresourceinitsnextbestalterna-tiveuse.Currentmarketpricesforinputsmoreaccuratelyreflectopportunitycoststhanhistoricalcosts.Forinstance,ifanautosupplierpurchases1,000poundsofaluminumfor$600andsubsequentlythemarketpriceincreasesto$900,theopportunitycostofusingthealuminumis$900.Ifthecompanyusesthealuminum,itsreplacementcostis$900.Alternatively,thecurrentinventorycouldbesoldtoanotherfirmfor$900.Ineithercase,thefirmforgoes$900ifitusesthealuminuminitsproductionprocess.Therelevantcostsformanagerialdecisionmakingareopportunitycosts.Itisimportanttoincludetheopportunitycostsofallinputswhetherornottheyhaveactuallybeenpur-chasedinthemarketplace.Forinstance,ifanownerspendstimeworkinginthefirm,theopportunitycostisthevalueoftheowner’stimeinitsnextbestalternativeuse.ShortRunversusLongRunCostcurvescanbedepictedforboththeshortrunandthelongrun.Theshortrunistheoperatingperiodduringwhichatleastoneinput(typicallycapital)isfixedinsupply.Forinstance,intheshortrunitmightbeinfeasibletochangeplantsizeorchangethenum-berofmachines.Inthelongrun,thefirmhascompleteflexibility—noinputsarefixed.Thedefinitionsofshortrunandlongrunarenotbasedoncalendartime.Thelengthofeachperioddependsonhowlongittakesthefirmtovaryallinputs.Foracleaning-servicesfirmoperatingoutofrentedofficespace,theshortrunisarelativelybriefperiod—perhapsonlyafewdays.Foralargemanufacturingfirmwithheavyinvestmentsinlong-livedspecializedplantandequipment,theshortrunmightbearelativelylongtimeperiod—itmightbeamatterofyears. bri75829_ch05.qxd8/13/087:07PMPage158158Part2ManagerialEconomicsFigure5.9Short-RunCostCurves$Thisfiguredisplaystheshort-runcostcurvesTotalcostofahypotheticalfirm.Theupperpaneldepictstotalcost(TC)andtotalvariablecost(TVC).Fixedcostssimplyshiftthepositionofthevariablecostcurve.ThelowerpanelTotalvariablecostdepictsmarginalandaveragecosts.Averagefixedcostdeclineswithoutputsincethefixedcostisbeingspreadovermoreunits.Marginalcost(MC)declinestoQ1andTotalcosts(indollars)thenincreasesbeyondthatpointduetodiminishingreturns.MarginalcostdependsQonlyonthevariableinputfactorsandiscompletelyindependentofthefixedcost.$AverageAveragetotalcost(ATC)andAVCdeclinetotalcostaslongasmarginalcostislowerthantheMarginalaveragecostandincreasebeyondthatpoint.costAverageMarginalcostisequaltobothATCandAVCvariablecostattheirrespectiveminimumpoints.AveragetotalcostisalwayslargerthanAVC,sinceATCAFCAVC.However,thisdifferencebecomessmallerasoutputincreasesand(indollars)AFCdeclines.CostperunitofoutputAveragefixedcostQQ1Q2Q3QuantityofoutputShort-runcostcurvessometimesarecalledoperatingcurvesbecausetheyareusedinmakingnear-termproductionandpricingdecisions.Forthesedecisions,itoftenisap-propriatetotaketheplantsizeandcertainotherfactorsasgiven(sincethesefactorsarebeyondthecontrolofthemanagersintheshortterm).Long-runcostcurvesfrequentlyarereferredtoasplanningcurves,sincetheyplayakeyroleinlonger-runplanningdeci-sionsrelatingtoplantsizeandequipmentacquisitions.FixedandVariableCostsIntheshortrun,somecostsarefixedanddonotvarywithoutput.Thesefixedcostsareincurredevenifthefirmproducesnooutput.Forinstance,thefirmhastopaymanagers’salaries,interestonborrowedcapital,leasepayments,insurancepremiums,andpropertytaxeswhetherornotitproducesanyoutput.Variablecostschangewiththelevelofoutput.Thesecostsincludeitemslikerawmaterial,fuel,andcertainlaborcosts.Inthelongrun,allcostsarevariable.Short-RunCostCurvesFigure5.9displaystheshort-runcostcurvesfortheTAMCorporation.Forthisfirm,supposethatthebasicplantsizeisfixedandthatallotherinputsarevariable.Theupperpaneldepictstotalcost.Totalcostisthesumofthefixedcost(FC)andtotalvariablecost(TVC).Theshapeofthetotalcostcurveiscompletelydeterminedbytheshapeofthe bri75829_ch05.qxd8/13/087:07PMPage159Chapter5ProductionandCost159MANAGERIALAPPLICATIONSDeLoreanAutomobilesThedifficultiesofcompetingwithplantsizessignificantlybelowtheminimumefficientscalearehighlightedbytheexperienceoftheDeLoreanMotorCompany.JohnZ.DeLoreanhadbeenahigh-rankingexecutiveatGeneralMotors.HeleftGMin1979toformhisownautomobilecompany,theDeLoreanMotorCompany.Thestrategyofthenewcompanywastospecializeinhigh-pricedluxurysportscars.Thecompany’sfirst(andonly)carwasthestainless-steelDMC12withalistpriceof$29,000—quiteahighcarpriceintheearly1980s.ThiscarsubsequentlywasfeaturedintheBacktotheFuturemovies.Althoughtheminimumefficientscaleisrelativelylargeinautoproduction,DeLoreanfelthecouldcompetebydesigninghigher-qualitysportscarsthanthelargeautocompanies.Plannedproductionfor1980was3,000cars.Thecompanysoonranintofinancialdifficulties.In1982,DeLoreanwasaccusedofconspiringtobuyanddistribute220poundsofcocainevaluedat$24million.FederalofficialsassertedthatDeLoreanwasenteringthedrugbusinesstohelpsavehisailingautomobilecompany.AlthoughDeLoreanwaslateracquittedonthesecharges,thecompanystillfacedinsurmountablefinancialdifficultiesandsoonwentoutofbusiness.totalvariablecostcurve.Fixedcostssimplyshiftupthelocationofthecurve.Between0andQ1,thetotalcostcurveisconcave.Overthisrange,themarginalproductivityofvariablefactorsincreases(assumingfixedinputprices).PastQ1,thetotalcostcurveisconvexandthemarginalproductivityofvariablefactorsdecreases.Thistypeofpatternisexpectedgiventhelawofdiminishingreturns.Atlowoutputlevels,fixedinputsarenotefficientlyutilized.Increasingthevariableinputsincreasesoutputmaterially.Overthisrange,totalcostincreases—butdoessoatadecreasingrate.Eventually,themarginalproductivityofthevariableinputsdeclinesanditbecomesincreasinglyexpensivetoproduceextraunitsofoutput.Thelowerpaneldepictsmarginalandaveragecosts.Averagefixedcost(AFC)istotalfixedcostdividedbyoutput.Averagefixedcostdeclineswithoutputsincethefixedcostisspreadovermoreunits.Marginalcost(MC)declinesuptoQ1andthenincreasesbe-yondthatpointduetodiminishingreturns.Notethatmarginalcostdependsonlyonthevariableinputfactorsandiscompletelyindependentofthefixedcost.Averagevariablecosts(AVC)aretotalvariablecostsdividedbyoutput.Bothaveragetotalcost(ATC)andaveragevariablecostdeclineaslongasmarginalcostislowerthanaveragecost;theyincreasebeyondthatpoint.Marginalcostisequaltobothaveragetotalcostandaveragevariablecostattheirrespectiveminimumpoints.Averagetotalcostisalwayslargerthanaveragevariablecost,sinceATCAFCAVC.However,thisdifferencebecomessmallerasaveragefixedcostdeclineswithhigheroutput.Long-RunCostCurvesIntheshortrun,firmsareunabletoadjusttheirplantsizes.Inthelongrun,however,ifafirmwantstoproducemoreoutput,itcanbuildalarger,moreefficientplant.Inthelongrun,theaveragecost(LRAC)ofproductionislessthanorequaltotheshort-runaveragecostofproduction.Indeed,theLRACcurvecanbethoughtofasanenvelopeoftheshort-runaveragecostcurves.Figure5.10(page160)illustratesthisconcept.Thefigureshowsfourpotentialplantsizes.Eachofthefourplantsprovidesthelow-costmethodofproductionoversomerangeofoutput,assumingthatonlythesefourplantsizesarefeasible.Forinstance,thesmallestplantprovidesthelowest-costmethodofpro-ducinganyoutputfromzerotoQ1,whilethenextlargestplantprovidesthelow-costmethodofproducingoutputsfromQ1toQ2,andsoon.Theheavyportionofeachcurveindicatestheminimumlong-runaveragecostforproducingeachlevelofoutput. bri75829_ch05.qxd8/13/087:07PMPage160160Part2ManagerialEconomicsFigure5.10Long-RunAverage$CostsasanEnvelopeofShort-RunAverageCostCurvesSRAC1SRAC2Inthelongrun,theaveragecost(LRAC)SRAC3SRAC4ofproductionislessthanorequaltotheshort-runaveragecost(SRAC)ofproduction.TheLRACcurvecanbethoughtofasanenvelopeoftheshort-runaveragecostcurves.Thefigureshowsfourpotentialplantsizes.Eachofthefourplantsprovidesthelow-cost(indollars)methodofproductionoversomerangeofoutput.Forinstance,thesmallestCostperunitofoutputplantprovidesthelowest-costmethodofproducinganyoutputfromzerotoQ1,whilethenextlargestplantprovidesthelow-costmethodofproducingoutputfromQ1toQ2,andsoon.TheheavyQportionofeachcurveindicatestheQ1Q2Q3minimumlong-runaveragecostforproducingeachlevelofoutput,Quantityofoutputassumingthatthereareonlythesefourpossibleplantsizes.Ifweextendthisanalysisbyassumingtherearemanydifferentfeasibleplantsizesthatvaryonlyslightlyinsize,theresultingLRACcurvewillberelativelysmooth,aspicturedinFigure5.11.Thisfigurealsopicturesthelong-runmarginalcostcurve(LRMC).Aswehavediscussed,themarginalcostisbelowaveragecostwhereaveragecostisfallingandaboveaveragecostwhereitisrising.Thetwoareequalattheminimumaveragecost.MinimumEfficientScaleMinimumefficientscaleisdefinedasthatplantsizeatwhichlong-runaveragecostfirstreachesitsminimumpoint.InFigure5.11,thisminimumoccursatQ*.Theminimumefficientscaleaffectsboththeoptimalplantsizeandthelevelofpotentialcompetition.MANAGERIALAPPLICATIONSPublicUtilitiesTheproductionofelectricpowertypicallyisassociatedwithlargeeconomiesofscale:Theaveragecostofproducingelectricitydecreaseswiththequantityproduced.Thisproductioncharacteristicimpliesthatitisgenerallymoreefficienttohaveonelargeplantthatproducespowerforanareathanseveralsmallerplants.Aproblemwithhavingoneproducerofelectricpowerinanarea,however,isthatthefirmhasthepotentialtooverchargeconsumersforelectricitysincetherearelimitedalternativesourcesofsupply.Concernsaboutthisproblemprovideonemotivationfortheformationofpublicutilitycommissionsthatregulatethepricesthatutilitycompaniescanchargeconsumers. bri75829_ch05.qxd8/13/087:07PMPage161Chapter5ProductionandCost161Figure5.11Long-RunAverage$andMarginalCostCurvesLong-runmarginalIftherearemanydifferentplantsizescostthatvaryonlyslightlyinsize,theresultinglong-runaveragecost(LRAC)Long-runaveragecurveisrelativelysmooth,aspicturedincostthisfigure.Thelong-runmarginalcost(LRMC)isbelowaveragecostwhereaveragecostisfallingandaboveaveragecostwhereitisrising.Thetwo(indollars)areequalattheminimumaveragecost.CostperunitofoutputTheminimumefficientscaleisdefinedastheplantsizeatwhichLRACsarefirstminimized(Q*inthisexample).QQ*QuantityofoutputAverageproductioncostisminimizedattheminimumefficientscale.Aswediscussinthenextchapter,competitionprovidesincentivesforfirmstoadoptthisplantsize.Iffirmsbuildplantsthatdepartmateriallyfromminimumefficientscale,theywillbeatacompetitivedisadvantageandcouldbeforcedoutofbusiness.Onecomplicatingfactoristransportationcosts.Iftransportationcostsarehigh,costdisadvantagesofsmallerre-gionalplantscanbemorethanoffsetbycostsavingsintransportingtheproducttocus-tomers.Inthiscase,whentotalproductionanddistributioncostsareconsidered,firmswithplantsthataresmallerthantheminimumefficientscalecansurviveinacompeti-tivemarketplace.Generally,thenumberofcompetitorswillbelargeandcompetitionmorevigorouswhentheminimumefficientscaleissmallrelativetototalindustrydemand.Forinstance,supposethatKatePolkisevaluatingthepossibilityofenteringanindustrywheresheseesestablishedfirmsreportingsubstantialprofits.Ifherfirmwouldhavetoproduce10per-centofthemarket’soutputtobecost-efficient,Kateshouldbeconcernedthatherentryislikelytodrivethepricedownandthusshewouldbelesslikelytoenterthemarketthanifsheneededtoproduceonly1percentofthemarket’soutputforefficientproduction.MANAGERIALAPPLICATIONSSizeDoesn’tAlwaysMatterRegisCorporationhas10,000beautysalons,buysshampoobythetrainload,spendsmillionsonadvertising,andusessophisticatedtechnologytotrackperformanceateachsalon.Nonetheless,the300,000independentsalonsintheUnitedStatesstillcompetequiteeffectivelywithRegischainslikeSupercuts.PaulFinkelstein,RegisCEOsays.“Wedon’trunabigbusiness.Werun10,000$300,000businesses.”Hesaysit’ssalonlocationfirst,andqualityofstylistssecondthatmakethebusinessgo.Thosearefactorsthatanindependentsalonalsocanoffer.Source:F.Bailey(2003),“InSomeBusinesses,SizeIsIrrelevanttoSuccess,”TheWallStreetJournal(November11),B13. bri75829_ch05.qxd8/13/087:07PMPage162162Part2ManagerialEconomicsANALYZINGMANAGERIALDECISIONS:DevelopingEconomiesofScaleforMalaysia’sProtonHoldingsProtonHoldingsBhdisanationalcarmakerinsporteditionofSavvy,andSatriaNeowererelativeMalaysia.Inlate2007,theMalaysiangovernmentsuccesses.Themanagementalsoimplementedstrin-owned43percentofthecompany.Theremaininggentcostcontrols.Nonetheless,analystsconcludedstockofthecompanytradedonpublicstockex-thatProton’slong-runabilitytosurvivedependsonchanges.ProtonwasamongMalaysia’sworstper-whetheritcanachieveincreasedproductionvolumeformingcompaniesin2005,aftercompetitionfromandeconomiesofscale.Withoutsufficientscaleitisforeigncarmakersandalackofnewmodelscosttheunlikelythatthecompanywillsurvivetheintensefirmsignificantmarketshareandprofits.Ithassincelocalandworldwidecompetition.Theanalystsasserthiredanewchiefexecutive,solditsloss-makingthatbyitself,ProtonwouldfindithardtoachieveMVAgustamotorbikefirm,andpledgedtofindeconomiesofscaleandtodevelopnewtechnologies.anewtechnologypartner.ThecompanyhasbeenSupposethatyouarehiredasaconsultanttoundersubstantialpressure,withitsshareofdomesticadviseProton’smanagement.Whatdotheanalystssalesfallingto44percentfrom75percentoverthemeanwhentheysaythatProtonneedstoachievepastdecade.economiesofscaletobecompetitive?DiscussataAnalystspolledinlate2007notedthatthecom-generallevelthetypesofactionsthatthecompanypany’snewmanagementhadmadeseveralmovesmightwanttoconsidertoachievethenecessaryscale.torevampthecompanyandthattheseeffortswerebearingfruitintermsofincreasedsalesvolumeandSOURCE:KathyFong(2007),“NoEconomiesofScaleforProtonmarketshare.NewmodelssuchasthePersona,awithoutGlobalPartner,”StarBiz,thestaronline(November21).Industrieswhereaveragecostdeclinesoverabroadrangeofoutputarecharacterizedashavingeconomiesofscale.Significanteconomiesofscalelimitthenumberoffirmsintheindustry.Forinstance,iftheminimumefficientscaleis25percentoftotalindustrysales,thereisroomforonlyfourfirmstoproduceatthatvolume.Thelevelofcompeti-tionamongexistingfirmscanvarysignificantly,evenifthereareonlyafewfirmsintheindustry.However,threatofentryislesspressingthaninindustrieswherescaleeconomiesarelow.Thethreatofpotentialnewcompetitorsisoftenanimportantconsiderationinafirm’sstrategicplanning.Insubsequentchapters,weexaminehowafirm’smarketstruc-tureaffectsmanagerialdecisionmaking.LearningCurvesForsomefirms,thelong-runaveragecostofproducingagivenlevelofoutputdeclinesasthefirmgainsproductionexperience.Forexample,withmoreoutput,employeesmightgainimportantinformationonhowtoimproveproductionprocesses.Theyalsobecomemoreproficientastheygainexperienceonthejob.14Alearningcurvedisplaystherelationbetweenaveragecostandcumulativeproductionvolume.Cumulativeproductionisthetotalamountoftheproductproducedbythefirmacrossallprevious14A.Alchian(1959),“CostsandOutputs,”inTheAllocationofEconomicResources,byM.Abramovitzandothers(StanfordUniversityPress:PaloAlto,CA),23–40. bri75829_ch05.qxd8/13/087:07PMPage163Chapter5ProductionandCost163Figure5.12LearningCurve$AveragecostAlearningcurvedisplaystheofproducingrelationbetweenaveragecostforQ*unitsagivenoutputperiod,Q*,andcumulativepastproduction.Inthisexample,therearesignificantlearningeffectsintheearlystagesofproduction.Theseeffectsbecomeminimalasthefirmcontinuestoproducetheproduct.(indollars)CostperunitofoutputLearningcurve∑QCumulativequantityofoutputproducedproductionperiods.Figure5.12presentsanexamplewheretherearesignificantlearn-ingeffectsintheearlystagesofproduction.Eventually,however,theseeffectsfrequentlybecomeminimalasthefirmcontinuestoproducetheproduct.Figure5.13illustratesthedifferencebetweeneconomiesofscaleandlearningeffects.Economiesofscaleimplyreductionsinaveragecostasthequantitybeingproducedwithintheproductionperiodincreases.Learningeffectsimplyashiftintheentireaver-agecostcurve:TheaveragecostforproducingagivenquantityinaproductionperiodFigure5.13EconomiesofScale$versusLearningEffectsThisfigureshowstheaveragecostcurvesforafirmwhenithasexperiencedhighandlowcumulativevolume.Inbothcases,thereareeconomiesofscale(averagecostdeclineswithoutput).Theaveragecostforeachlevelofoutput,however,islowerLearningeffectwherethefirmhasexperiencedhighAveragecostwithlowcumulativevolumebecauseoflearning(indollars)cumulativevolumeeffects.CostperunitofoutputAveragecostwithhighcumulativevolumeQQuantityofoutput bri75829_ch05.qxd8/13/087:07PMPage164164Part2ManagerialEconomicsACADEMICAPPLICATIONSEconomiesofScaleandLearningEffectsintheChemicalProcessingIndustryMarvinLiebermanstudiedeconomiesofscaleandlearningeffectsinthechemicalprocessingindustry.Hefoundthatforeachdoublinginplantsize,averageproductioncostsfellbyabout11percent.Foreachdoublingofcumulativevolume,theaveragecostofproductionfellbyabout27percent.Thus,thereisevidenceofbotheconomiesofscaleandlearningeffectsinthechemicalprocessingindustry.Thesizeoftheestimatessuggeststhatlearningeffectsaremoreimportantthaneconomiesofscaleinexplainingtheobserveddeclineincostswithintheindustryfromthe1950stothe1970s.Source:M.Lieberman(1984),“TheLearningCurveandPricingintheChemicalProcessingIndustries,”RandJournal15,213–288.decreaseswithcumulativevolume.Learningeffectssometimescanprovideexistingfirmsinanindustryacompetitiveadvantageoverpotentialentrants;itdependsonthenatureoftheinformation(Chapter3)andthedistributionofthatinformationacrossemployees.WediscussthisissueinmoredetailinChapter8.EconomiesofScopeThusfar,wehavefocusedontheproductionofasingleproduct.Mostfirms,however,producemultipleproducts.Economiesofscopeexistwhenthecostofproducingasetofproductsjointlywithinonefirmislessthanthecostofproducingtheproductssepa-ratelyacrossindependentfirms.Jointproductioncanproducecostsavingsforavarietyofreasons.Efficienciescanresultfromcommonuseofproductionfacilities,coordinatedmarketingprograms,andsharingmanagementsystems.Also,theproductionofsomeproductsprovidesunavoidableby-productsthatarevaluabletothefirm.Forinstance,asheeprancherjointlyproducesbothmuttonandwool.Economiesofscopehelpexplainwhyfirmsproducemultipleproducts.Forinstance,PepsiCoisamajorproducerofsoftdrinks;yetitalsoproducesawiderangeofsnackfoods(forexample,cornchipsandcookies).ThesemultipleproductsallowPepsiCotoleverageitsproductdevelopment,distribution,andmarketingsystems.TheseissuesarediscussedingreaterdetailinChapter8.Economiesofscopeandeconomiesofscalearedifferentconcepts.Economiesofscopeinvolvecostsavingsthatresultfromjointproduction,whereaseconomiesofscaleinvolveefficienciesfromproducinghighervolumesofagivenproduct.Itispossibletohaveeconomiesofscopewithouthavingeconomiesofscaleandviceversa.MANAGERIALAPPLICATIONSEconomiesofScaleandScopeinApartmentManagementHomePropertiesofNewYorkisarealestateinvestmenttrustspecializinginapartmentcommunitiesinselectNortheast,Midwest,andMid-Atlanticmarkets.BoardChairmanNormanLeenhoutsnoted:“Sincethebeginningoflastyear,wehavemorethandoubledthesizeofourownedportfolio.Byconcentratingourgrowthinourcoremarkets,wearerealizingmaterialscaleeconomies—especiallyinadvertisingandpersonnelcosts.Moreover,weexploitscopeeconomiesbyidentifyingbestpracticesinourdifferentmarketsandexportingthosepracticestopropertiesthroughoutourportfolio.”Source:“HomePropertiesReportsRecordSecondQuarter1999Results”(August5,1999),PRNewswire. bri75829_ch05.qxd8/13/087:07PMPage165Chapter5ProductionandCost165MANAGERIALAPPLICATIONSEconomiesofScaleandScopeinDSPProductionIn1999,TexasInstrumentswastheleadingproducerofDSPs(digitalsignalprocessors).ItsDSPspoweredroughlytwoofeverythreedigitalphones,mosthigh-performancediskdrives,andathirdofallmodems.Theyalsoareusedinamyriadofotherproductsincludingdigitalcameras,Internetaudio,digitalspeakers,handheldinformationappliances,printers,electric-motorcontrols,andwirelessnetworkingequipment.DSPsareprogrammable.Theyareespeciallygoodatperformingsuperfastreal-timecalculations,whichcomeinhandywhenyouwanttocompress,decompress,encrypt,orfiltersignalsandimages.ProgrammabilityhelpskeepDSPsinexpensivetoproduce.ThemajordifferencebetweenaDSPinacellphoneandaDSPinadigitalcameraisthesoftwarethattellsitwhattodo.ThusTIgainssubstantialeconomiesofscaleinDSPproductioneventhoughthechipsareusedinavarietyofproducts.Italsoenjoyseconomiesofscope.Forinstance,itisabletoleveragetechnologicaldevelopmentsacrossitsvariousproducts.WhileTIwasnotablyslowintechnologydevelopmentafewyearsago,itisnowaworldleader.Forexample,itmakesacell-phonechipwhosecircuitsarejust0.18micron(millionthofameter)apart.ThisdistanceissimilartoIntel’sandIBM’smostadvancedchips.Source:E.Schonefeld(1999),“HotterThanIntel,”Fortune(October11),179–184.ProfitMaximizationThusfar,wehavefocusedonthecostsofproducingdifferentlevelsofoutput.However,whatoutputlevelshouldamanagerchoosetomaximizefirmprofits?Toanswerthisquestion,wereturntotheconceptofmarginalanalysisthatweinitiallyintroducedinChapter2.Marginalcostsandbenefitsaretheincrementalcostsandbenefitsthatareassociatedwithaparticulardecision.Itistheseincrementalcostsandbenefitsthatareimportantineconomicdecisionmaking.Anactionshouldbetakenwhenevertheincrementalbenefitsofthatactionexceeditsincrementalcosts.Indecidingwhetherornottopro-duceonemoreunitofaproduct,theincrementalbenefitismarginalrevenue(seeChapter4),whiletheincrementalcostisequaltomarginalproductioncost(includinganydistributioncosts)—fixedcostsdonotaffectthedecision.Thereforethefirmshouldproduceextraunitssolongasmarginalrevenueexceedsmarginalcost;thefirmshouldnotproduceextraunitsifmarginalrevenueislessthanmarginalcost.Attheprofit-maximizinglevelofproduction,thefollowingconditionholds15:MRMC(5.9)AswesawinChapter4,marginalrevenuedependsonthedemandcurvefortheprod-uct.Theeffectivedemandcurvethatthefirmfaceswillbeaffectedbythedegreeofcom-petitionintheproductmarket.InChapter6,weexaminehowtheoutputdecisionsoffirmsvaryacrossdifferentmarketsettings.Thechangesinmetalpricesthroughoutthe1990schangedthetotalcostofautomo-bilemanufacturing.Typically,suchchangesareaccompaniedbychangesinthemarginalcostofproduction.Forexample,areductioninsteelpriceswouldmeannotonlyasubstitutiontowardsteelfromotherinputsbutalsoanincreaseinoutput.Figure5.14(page166)illustratesthiseffect.Notethatthisanalysisholdsotherfactorsconstant.Ifthe15Technicalnote:Sinceprofitsequaltotalrevenuesminustotalcosts,Equation(5.9)isthefirst-orderconditionforprofitmaximization.Thisconditionholdsatbothminimumandmaximumprofits.Atthemaximum,themarginalcostcurvecutsthemarginalrevenuecurvefrombelow—thesecond-ordercondition. bri75829_ch05.qxd8/13/087:07PMPage166166Part2ManagerialEconomicsFigure5.14OptimalOutputand$ChangesinMarginalCostMC0ThisfigureillustratesthatadecreaseinMC1marginalcost(fromMC0toMC1)raisestheoptimaloutputofthefirm(fromQ*0toQ*1).(indollars)Cost/revenueperunitMRQQ*Q*01Quantityofoutputdemandforautomobilesisfallingatthesametime(thusshiftingmarginalrevenuedown-ward),theneteffectcouldbeanincreaseinoutput.However,theincreaseinoutputwouldbelessthanifsteelpriceswereconstant.FactorDemandCurvesIndiscussingtheoptimalinputmix,wenotedthatthefollowingconditionmustholdforefficientproduction:MPiPiMPjPj(5.10)forallinputsiandj.Theratiosofmarginalproducttopricereflecttheincrementalout-putfromaninputassociatedwithanadditionaldollarexpenditureonthatinput.Therec-iprocalsoftheseratiosreflectthedollarcostforincrementaloutputorthemarginalcost:PiMPiPjMPjMC(5.11)Attheprofit-maximizingoutputlevel,MRMC.Therefore,attheoptimaloutputlevelthefollowingconditionmusthold:PiMPiMR(5.12)orequivalently,PiMRMPi(5.13)Equation(5.13)isthefirm’sdemandcurveforinputi.16Ithasastraightforwardinter-pretation.Theright-handsideoftheequationrepresentstheincrementalrevenuethat16Technicalnote:Themarginalproductofinputicandependonthelevelsofotherinputsusedintheproductionprocess.Thus,thedemandcurveforaninputmustallowotherinputstoadjusttotheiroptimallevelsasthepriceofinputichanges.Thisadjustmentisnotimportantifthemarginalproductofinputiisnotaffectedbythelevelsoftheotherinputs. bri75829_ch05.qxd8/13/087:07PMPage167Chapter5ProductionandCost167MANAGERIALAPPLICATIONSChinaBecomesthe“World’sSmokestack”Thischapterfocusesonhowfirmschooseamongalternativeinputmixes.Anotherimportantproductiondecisioniswheretolocatetheplant.Costscanvarydramaticallyacrosslocationsduetodifferencesinthepricesforlabor,land,transportationandotherinputs,taxes,environmentalandsafetyregulations,threatofterrorism,andpoliticalrisk.Thesteelindustryprovidesagoodexampleofhowchangesincostscanmotivatesignificantchangesinthelocationofproduction.Duringthe1950stheRuhrValleyinGermanyhadtheworld’shighestgrowthrateinsteelproduction.Initsheyday,Germanyproduced10percentoftheworld’ssteelsupply.In2006,Germanyproducedonly3.8percentoftheworld’ssupply,rankingseventhbehindChina,Japan,theUnitedStates,Russia,India,andSouthKorea.China,whichhasdisplayedmeteoricgrowthinsteelproduction,supplied34percent.Germansteelproductionslowedinthe1960sasminershadtodigdeeperforcoalandtaxesandlaborcostscontinuedtoincrease.Anotherimportantfactorwasnewenvironmentalregulation.TheemissionsfromsteelplantshadmadetheRuhrValleyoneofthemostpollutedplacesintheworld.Theairwasdarkandgrimy.Theresidentssufferedfromaninordinateincidenceoflungandotherpollution-relateddiseases.ThewhiteshirtsthatmenworetochurchonSundayturnedtogreybythetimetheycamehome.Inaneffortto“greenthecountry,”thegovernmentimposedcostlypollutioncontrolrequirementsonthesteelcompanies.DifferencesinlaborcostsandenvironmentalstandardsmotivatedashiftinsteelproductionfromGermanytoChinaas“smoke-spewingplants”weredisassembledintheRuhrValleyandmoved5,000milesawaytoChina.ThePhoenixsteelmillsinDortmundhadbeenamongGermany’slargestsincebeforeWorldWarII.Inthelate1990stheywereslatedforclosureandwerelikelyheadedforthescrapheap.TheChineserealizedthattheycouldbuyarelativelysophisticatedGermanblastfurnaceforasmallfractionofwhatanewonewouldcost.AChinesecompanysentworkerstoDortmundwholabeledeverypartoftheseven-storyblastfurnace,disassembledit,andpackeditintowoodencratesforthevoyagetoChina.TheyworkeddayandnighttoaccomplishthistaskinamuchshortertimethanitwouldhavetakenGermanworkers,whoweregovernedbystrictunionandgovernmentworkrules.TheHebeiProvinceis“China’snewRuhrValley.”Itsairisheavilypollutedanditscitizenssufferfromavarietyofassociatedhealthproblems.Meanwhile,theRuhrValley’spollutionlevelhassubstantiallyimproved.Thisimprovement,however,hascomeatacost.Dortmund,whichin1960had30,000residentsworkinginthesteelindustry,nowhaslessthan3,000.WhileDortmundcontinuestohavehighunemployment,thedeclineinsteeljobshasbeenoffsettosomeextentbynewjobsinotherless-pollutingindustries.Source:JosephKahnandMarkLandler(2007),“ChinaGrabsWest’sSmoke-SpewingFactories,”nytimes.com(December21).thefirmobtainsfromemployingonemoreunitoftheinput(theincrementaloutputtimestheincrementalrevenue).Wecallthisincrementalrevenuethemarginalrevenueproduct(MRPi)ofinputi.Figure5.15(page168)illustratesthedemandcurveforaninput.17AtthecurrentinputpriceofP*,thefirmoptimallyusesQ*unitsoftheinput.iiThefirmoptimallyemploysadditionalunitsoftheinputuptothepointwherethemar-ginalcostoftheinput(itspricewithconstantinputprices)isequaltothemarginalrev-enueproductoftheinput.Intuitively,ifthemarginalrevenueproductisgreaterthantheinputprice,thefirmincreasesitsprofitabilitybyusingmoreoftheinput.Ifthemar-ginalrevenueproductislessthanthepriceoftheinput,thefirmincreasesprofitabilitybyreducingtheuseoftheinput.Profitsaremaximizedwhenthetwoareequal.Ourdiscussionoftheprofit-maximizingoutputlevelandtheoptimaluseofaninputmightappeartosuggestthatthesedecisionsaretwodistinctchoices.Thetwo17Technicalnote:Thesecond-orderconditionformaximumprofitsensuresthatthedemandcurvefortheinputisthedownward-slopingportionofthemarginalrevenueproductcurve.Thus,Figure5.15displaysonlythedownward-slopingportionofthecurve. bri75829_ch05.qxd8/13/087:07PMPage168168Part2ManagerialEconomicsFigure5.15FactorDemandCurve$Thedemandcurveforafactorofproductionisthemarginalrevenueproductcurve(MRP)fortheinput.Themarginalrevenueproductisdefinedasthemarginalproductoftheinputtimesthemarginalrevenue.Itrepresentstheadditionalrevenuethatcomesfromusingonemoreunitofinput.ThefirmP*imaximizesprofitswhereitpurchasesinputsuptothepointwherethepriceof(indollars)theinputequalsitsmarginalrevenueMRPiproduct.Cost/revenueperunitofinputQiQi*QuantityofinputiMANAGERIALAPPLICATIONSHogProducersReacttoIncreaseinCornPricesPorkisthemostwidelyeatenmeatintheworld,providingabout38percentofdailymeatproteinworldwide(despitethefactthatitisnotconsumedbysomepeopleduetoreligiousrestrictions).TheUnitedStatesDepartmentofAgriculturereportsthatin2006thepercapitaconsumptionofporkwas43.9kg.,40kg.,and29kg.inChina,Europe,andtheUnitedStates,respectively.IronicallyinChina’s“YearofthePig”(2007),therewasacrisisthatincreasedporkpricesby50percent.Thedramaticpriceincreasecausedbothsocialunrestandgovernmentinterventionto“helpkeepporkaffordable.”Feedcostistypicallyabout50to60percentofthetotalcostofproducingpork.IntheUnitedStates,cornaccountsforabout80percentofthetypicalhogfeed.Risingfuelpricesandgovernmentpoliciespromotingtheuseofcorn-basedethanolasanalternativetogasolinecausedU.S.cornpricesnearlytodoubleinthesummerandfallof2006.Thispricechangesignificantlyincreasedthecostoffeedinghogs.U.S.hogproducerswereabletolessentheeffectsoftheincreaseincornpricesbyswitchingtofeedmixesthatuselesscornandmoredistilledgrainandsolubles(DDGS).DDGSisaby-productofthecorn-basedethanolproductionprocess.ScientistsfoundthatDDGScouldbesubstitutedforcornata10percentinclusionratewithouthavingasignificanteffectontheefficiency,growth,orcarcasstraitsofthehogs.CornandDDGS,however,arenotperfectsubstitutesinthehogproductionprocess.FeedmixeswithhigherDDGSinclusionrates(e.g.,20percentand30percent)producedsmallerpigsthatoffsettheadvantagesoflowerfeedcosts.Thisexamplehighlightsageneralpointaboutproductioncosts.Increasesininputpricesincreaseproductioncosts.Theeffectofthepriceincreaseoftencanbemitigatedbyshiftingtheinputmixtowardrelativelylessexpensiveinputs.Theabilitytoreducecostsinthismannerdependsonthedegreeofsubstitutabilityamongtheinputs.Source:JohnLawrence(2006),“ImpactonHogFeedCostofCornandDDGSPrices,”IowaFarmOutlook(November15,2006),1–4. bri75829_ch05.qxd8/13/087:07PMPage169Chapter5ProductionandCost169MANAGERIALAPPLICATIONSDemandforLaborFallsFollowing9/11TerroristAttacksOrganizedlaborwasparticularlyhardhitbytheterroristattacksfollowing9/11.Ofthe760,000jobcutsinthethreemonthsfollowingtheattack,roughly50percentwereunionmembers—nearlyfourtimesorganizedlabor’s13.5percentoftheU.S.workforce.Thereasonforthishigher-than-averagejoblossisbecauseunionsaredisproportionatelyrepresentedinthehard-hittravelandtourismindustries.Unionsrepresentingpublicemployeesalsoareseeinglargejobcutsasstateandlocalbudgetsarecut.September11significantlyshiftedconsumers’demandfortravelandtourismservicestotheleft.Whendemandshiftstotheleft,sodoesthefirm’smarginalrevenuecurve.Hence,labor’smarginalrevenueproduct—theproductofmarginalrevenueandthefactor’smarginalproduct(holdingconstantlabor’smarginalproduct)—alsoshiftstotheleft.Source:A.Bernstein(2001),“ASockintheEyeforLabor,”BusinessWeek(December17),44.decisions,however,arelinkeddirectly.Oncethefirmchoosesthequantitiesofinputs,outputisdeterminedbytheproductionfunction.Thus,profit-maximizingfirmschoosetheoutputwheremarginalrevenueequalsmarginalcostandproducethatout-putsothatthepriceofeachinputisequaltoitsmarginalrevenueproduct.Inourautoexample,anincreaseinsteelpriceswouldbeexpectedtomotivatesimultaneousadjustmentsinboththenumberofautomobilesproducedandthemethodsusedtoproducethem.CostEstimationOurdiscussionindicatesthatadetailedknowledgeofcostsisimportantformanagerialdecisionmaking.Short-runcostsplayanextremelyimportantroleinoperatingdeci-sions.Forinstance,whenthemarginalrevenuefromincreasedoutputisabovetheshort-runmarginalcostofproduction,profitsincreasebyexpandingproduction.Alter-natively,ifmarginalrevenueisbelowshort-runmarginalcost,reducingoutputincreasesprofits.Long-runcosts,inturn,provideimportantinformationfordecisionsonoptimalplantsizeandlocation.Forinstance,ifeconomiesofscaleareimportant,onelargeplantismorelikelyoptimalwiththeproducttransportedtoregionalmarkets.Alternatively,ifscaleeconomiesaresmall,smallerregionalplants,whichreducetransportationcosts,aremorelikelyoptimal.Ifmanagersaretoincorporatecostsintheiranalysesinthismanner,theymusthaveaccurateestimatesofhowshort-runandlong-runcostsarerelatedtovariousfactorsbothwithinandbeyondthecontrolofthefirm.18Amongthemostcommonlyusedstatisticaltechniquesforestimatingcostcurvesisregressionanalysis.Aregressionesti-matestherelationbetweencostsandoutput(possiblycontrollingforotherfactors,suchastheproductmixortheweather,whichaffectcosts).Thedataforthisanalysiscanbeeithertime-seriesdataoncosts,output,andothervariables,orcross-sectional18Inaddition,somefirmsestimatecostcurvestoobtaininsightsintotheirunderlyingproductionfunctions.Recallthattheshapesofcostcurvesdependontheunderlyingproductionfunctions.Thus,itoftenispossibletoinferthecharacteristicsofaproductionfunctionfromtheshapeofthecorrespondingcostcurves.Typically,thedataforestimatingcostcurvesismorereadilyavailablethanthenecessarydataforestimatingproductionfunctions. bri75829_ch05.qxd8/13/087:07PMPage170170Part2ManagerialEconomicsdata,whichincludesobservationsonvariablesacrossfirmsorplantsatapointintime.Forinstance,inmanyapplications,itisassumedthatshort-runtotalcostsareapprox-imatelylinear19:VCabQ(5.14)whereVCistotalvariablecostsfortheperiodandQisthequantityofoutputproduced.Adetaileddiscussionofcostestimationisbeyondthescopeofthisbook.Sufficeittosaythatsimilarproblemsariseincostestimationasariseinthecaseofdemandesti-mation(forexample,omitted-variablesproblems).Amongthemostcommonproblemsincostestimationaredifficultiesinobtainingdataonrelevantcosts.Costestimatesoftenarebasedonaccountingreports,whichrecordhistoricalcosts.Aswehaveindi-cated,thesehistoricalcostsdonotnecessarilyreflecttheopportunitycostsofusingresources.Moreover,thereistheissueofchoosingtheappropriatefunctionalform.Equation(5.14)presumesalinearmodel.However,costcurvesneednotbelinear.Forinstance,itmightbeappropriatetouseaquadraticmodel,whichwouldincludeanadditionalQ2term.Oneofthemoreseriousproblemscomplicatingcostestimationisthefactthatmostplantsproducemultipleproducts.Multipleproductsareproducedinthesameplantbecausethereareeconomiesofscope.Ratherthanproducetwodifferenttypesofcerealsintwoseparateplants,ittypicallyischeapertoproducetheminoneplant;fixedresourcescanbeusedmoreefficiently.Ifaplantproducesmultipleproducts,totalandaveragecostsforeachproductcanbecalculatedonlybyallocatingfixedcostsacrosstheproducts.ThisallocationoftenisarbitraryandcomplicatedfurtherbytheexistenceofANALYZINGMANAGERIALDECISIONS:RichManufacturingGinaPicarettoisproductionmanagerattheRichBhagathasannounceda$3priceincreaseforitsManufacturingCompany.Eachyearherunitbuysmachineparts.Thisfigurerepresentstheprojectedupto100,000machinepartsfromBhagatIncorpo-$3increaseinlaborcostsduetoitsnewunionrated.ThecontractspecifiesthatRichwillpaycontract.ItisGina’sresponsibilitytoevaluatethisBhagatitsproductioncostsplusa$5markup(cost-announcement.pluspricing).Currently,Bhagat’scostsperpartare$10forlaborand$10forothercosts.Thusthe1.Whydomanyfirmsusecost-pluspricingforcurrentpriceis$25perpart.Thecontractprovidessupplycontracts?anoptiontoRichtobuyupto100,000partsatthis2.Whatpotentialproblemsdoyouenvisionwithprice.Itmustpurchaseaminimumvolumeofcost-pluspricing?50,000parts.3.ShouldGinacontestthepriceincrease?Bhagat’sworkforceisheavilyunionized.DuringExplain.recentcontractnegotiations,Bhagatagreedtoa4.Istheincreasemorelikelytobejustifiedinthe30percentraiseforworkers.Inthislaborcontract,shortrunorthelongrun?Explain.wagesandbenefitsarespecified.However,Bhagatis5.Howwilla$3increaseinthepriceofmachinefreetochoosethequantityoflaboritemploys.partsaffectGina’sownproductiondecisions?19Variablecostsarenormallyestimatedwithanintercept.Althoughvariablecostsundoubtedlyarezerowhenoutputiszero,mostcostcurvesarenonlinear.Forcingtheintercepttobezeroyieldsalesspreciseestimateofthisslope—thechangeincostsassociatedwithachangeinoutput. bri75829_ch05.qxd8/13/087:07PMPage171Chapter5ProductionandCost171jointcosts.Costaccountantsuseaccountingrecordstotrackcostsofindividualprod-ucts.Fixedandvariableresourcesusedbyeachproductarerecorded.Theseproductcosts,calculatedbythecostaccountants,typicallyareusedtoestimateshort-runandlong-runaverageandmarginalcosts.Despitetheseestimationproblems,costcurvesplayanimportantroleinmanagerialdecisionmaking.Nonetheless,itisimportantthatmanagersmaintainahealthyskepti-cismwhenusingtheseestimates.Forinstance,inmakingmajordecisions,itgenerallyisinstructiveformanagerstoexaminewhetheraproposeddecisionisstillattractivewithreasonablevariationintheestimatedparametersofthecostfunction—thatis,toconductsensitivityanalysis.SummaryAproductionfunctionisadescriptiverelationthatconnectsinputswithoutputs.Itspec-ifiesthemaximumpossibleoutputthatcanbeproducedforgivenamountsofinputs.Returnstoscalereferstotherelationbetweenoutputandaproportionalvariationinallinputstakentogether.Aproductionfunctiondisplaysconstantreturnstoscalewhena1percentchangeinallinputsresultsina1percentchangeinoutput.Withincreasingreturnstoscale,a1percentchangeinallinputsresultsinagreaterthan1percentchangeinoutput.Finally,withdecreasingreturnstoscale,a1percentchangeinallinputsresultsinalessthan1percentchangeinoutput.Returnstoafactorreferstotherelationbe-tweenoutputandthevariationinonlyoneinput,holdingotherinputsfixed.Returnstoafactorcanbeexpressedastotal,marginal,oraveragequantities.Thelawofdiminish-ingreturnsstatesthatthemarginalproductofavariablefactorwilleventuallydeclineastheuseoftheinputisincreased.Mostproductionfunctionsallowsomesubstitutionofinputs.Anisoquantdisplaysallcombinationsofinputsthatproducethesamequantityofoutput.Theoptimalinputmixtoproduceanygivenoutputdependsonthecostsoftheinputs.Anisocostlinedis-playsallcombinationsofinputsthatcostthesame.Costminimizationforagivenout-putoccurswheretheisoquantistangenttotheisocostline.Changesininputpriceschangetheslopeoftheisocostlineandthepointoftangency.Whenthepriceofaninputincreases,thefirmwillreduceitsuseofthisinputandincreaseitsuseofotherin-puts(substitutioneffect).Costcurvescanbederivedfromtheisoquant/isocostanalysis.Thetotalcostcurvedepictstherelationbetweentotalcostsandoutput.Marginalcostisthechangeintotalcostassociatedwithaone-unitchangeinoutput.Averagecostistotalcostdividedbytotaloutput.Averagecostfallswhenmarginalcostisbelowaveragecost;averagecostriseswhenmarginalcostisaboveaveragecost.Averageandmarginalcostsareequalwhenaveragecostisataminimum.Thereisadirectlinkbetweentheproductionfunc-tionandcostcurves.Holdinginputpricesconstant,theslopesofcostcurvesaredeter-minedbytheunderlyingproductiontechnology.Opportunitycostisthevalueofaresourceinitsnextbestalternativeuse.Currentmar-ketpricesmorecloselyreflecttheopportunitycostsofinputsthanhistoricalcosts.Therelevantcostsformanagerialdecisionmakingaretheopportunitycosts.Costcurvescanbedepictedforboththeshortrunandthelongrun.Theshortrunistheoperatingperiodduringwhichatleastoneinput(typicallycapital)isfixedinsupply.Duringthisperiod,fixedcostscanbeincurredevenifthefirmproducesnooutput.Inthelongrun,therearenofixedcosts—allinputsandcostsarevariable.Short-runcostcurvesaresometimescalledoperatingcurvesbecausetheyareusedinmakingnear-termproductionandpricingdecisions.Fixedcostsareirrelevantforthesedecisions.Long-runcostcurvesarereferredtoasplanningcurves,sincetheyplayakeyroleinlonger-runplanningdecisionsrelatingtoplantsizeandequipmentacquisitions. bri75829_ch05.qxd8/13/087:07PMPage172172Part2ManagerialEconomicsTheminimumefficientscaleisdefinedasthatplantsizeatwhichlong-runaveragecostisfirstminimized.Theminimumefficientscaleaffectsboththeoptimalplantsizeandthelevelofpotentialcompetition.Industrieswheretheaveragecostdeclinesoverabroadrangeofoutputarecharacterizedashavingeconomiesofscale.Alearningcurvedisplaystherelationbetweenaveragecostandthecumulativevol-umeofproduction.Forsomefirms,thelong-runaveragecostforproducingagivenlevelofoutputdeclinesasthefirmgainsexperiencefromproducingtheoutput(thatis,therearesignificantlearningeffects).Economiesofscopeexistwhenthecostofproducingajointsetofproductsinonefirmislessthanthecostofproducingtheproductsseparatelyacrossindependentfirms.Economiesofscopehelpexplainwhyfirmsoftenproducemultipleproducts.Theprofit-maximizingoutputleveloccursatthepointwheremarginalrevenueequalsmarginalcost.Atthispoint,themarginalbenefitsofincreasingoutputareoffsetexactlybythemarginalcosts.Themarginalrevenueproductofinputi(MRPi)equalsthemarginalproductoftheinputtimesmarginalrevenue.Profit-maximizingfirmsuseaninputuptothepointwheretheMRPoftheinputequalstheinputprice.Atthispoint,themarginalbenefitofemployingmoreoftheinputisoffsetexactlybyitsmarginalcost.Managersoftenuseestimatesofcostcurvesindecisionmaking.Acommonstatisticaltoolforestimatingthesecurvesisregressionanalysis.Onecommonprobleminstatisticalestimationisthedifficultyofobtaininggoodinformationontheopportunitycostsofre-sources.Anotherproblemwithestimatingcostcurvesinvolvesallocatingfixedcostsinamultiproductplant.Costaccountantstrackthecostsandestimateproductcosts.AppendixTheFactor-BalanceEquation20Thisappendixderivesthefactor-balanceequation—Equation(5.9)inthetext:MPiPiMPjPj(5.15)Thisconditionmustholdifthefirmisproducingoutputinamannerthatminimizescosts(assuminganinteriorsolution).Recallthatatthecost-minimizingmethodofproduction,theisoquantcurveandisocostlinearetangent.Thus,theymusthaveequalslopes.Thefactor-balanceequationisfoundbysettingtheslopeoftheisoquantequaltotheslopeoftheisocostlineandrearrangingtheexpression.Inthetext,weshowedthattheslopeoftheisocostlineisPjPi.Wenowderivetheslopeofanisoquant.SlopeofanIsoquantTheproductionfunctioninthetwo-inputcasetakesthefollowinggeneralform:Qf(xi,xj)(5.16)Tofindtheslopeofanisoquant,wetotallydifferentiateEquation(5.16).Wesetthisdif-ferentialequaltozero,sincequantitydoesnotchangealonganisoquant:dQ[Qxidxi][Qxjdxj]0(5.17)Theslopeoftheisoquantisdefinedbydxidxj.Thus,Slopeofanisoquant(Qxj)(Qxi)(5.18)MPjMPi(5.19)20Thisappendixrequiresabasicknowledgeofcalculus. bri75829_ch05.qxd8/13/087:07PMPage173Chapter5ProductionandCost173Thisexpressionhasastraightforwardinterpretation.Forillustration,assumethatatsomefixedcombinationofxiandxj,themarginalproductofiis1andthemarginalproductofjis2.Atthispoint,theslopeoftheisoquantis2.Thismeansthat2unitsoficanbegivenupfor1unitofjandoutputwillstaythesame.Thisistruebydefinitionsincejhastwicethemarginalproductofi.Factor-BalanceEquationWhenemployingthecost-minimizingproductionmethod,theslopeoftheisoquantisthesameastheslopeoftheisocostline:MPjMPiPjPi(5.20)Rearrangingthisexpressiongivesusthefactor-balanceequation:MPiPiMPjPj(5.21)Thisexpressionimmediatelygeneralizestoproductionfunctionswithmorethantwoinputs.SuggestedG.Stigler(1987),TheTheoryofPrice(Macmillan:NewYork),Chapters6–10.ReadingSelf-Evaluation5–1.TheZimmermanCompanydigsditches.Itfacestheproductionfunction,QL12K,whereProblemsQisthenumberofditchesdug,Lishoursoflabor,andKisthenumberofdiggingtools.a.Completethefollowingtable:K0K1K2K3L0L1L2L3b.Doestheproductionfunctiondisplayincreasing,decreasing,orconstantreturnstoscale?Explain.c.ArethemarginalproductsofKandLincreasing,decreasing,orconstant?Explain.d.Assumeconstantinputprices.Drawthegeneralshapesofthefollowing:(1)long-runaveragecost;(2)short-runmarginalcost,assumingLisfixed;(3)short-runmarginalcost,assumingKisfixed.5–2.21Aproductisproducedusingtwoinputsxandxcostingw$10andw$5perunit,1212respectively.Theproductionfunctionisy5x1.5x2whereyisthequantityofoutput,and12x1,x2arethequantitiesofthetwoinputs.Themarginalproductsofinputs1and2forthisproductionfunctionare:MP7.5x0.5x2112MP10x1.5x212a.Whatinputquantities(x1*,x2*)minimizethecostofproducing10,000unitsofoutput?b.Whatisthetotalcostofproducingthe10,000units?21Thisproblemrequiresslightlyhigherskillsinalgebrathanmostoftheotherproblemsinthebook.Readerswhocannotworktheproblemontheirownshouldstudythegeneralapproachusedinthesolutiontoobtainabetterunderstandingoftheconditionsforcostminimization. bri75829_ch05.qxd8/13/087:07PMPage174174Part2ManagerialEconomicsSolutionstoSelf-EvaluationProblems5–1.a.K0K1K2K3L00000L10123L201.412.834.24L301.733.465.19b.Theproductionfunctionshowsincreasingreturnstoscale.Asyouincreasebothinputsbythesameproportion,outputgoesupbyahigherproportion(e.g.,ifyoudoublebothinputsoutputgoesupbymorethandouble).Thiscanbeseenalongthediagonalofthetable.c.ThemarginalproductofKisconstant.IfyouholdLfixedandincreaseK,themarginalin-creaseinoutputisconstantasyouaddmoreandmoreK.Youcanseethisalongtherowsofthetable.ThemarginalproductofLisdecreasing.IfyouholdKfixedandincreaseL,themarginalincreaseinoutputdeclinesasyouaddmoreandmoreL.Thiscanbeseenalongthecolumnsofthetable.d.IncreasingreturnstoscaleimpliesthatLRACdeclinesasoutputisincreased(thereareeconomiesofscale).ThemarginalproductofKisconstant.ThusSRMCisconstantwhenKisthevariableinput.Forexample,whenL1,eachadditionalunitofKproducesoneextraunitofoutput(seethesecondrowofthetable).Inthiscase,SRMC(thecostofproducinganadditionalunitofoutput)issimplythepriceofK.ThemarginalproductofLisdecreasing.ThusSRMCisincreasingwhenListhevariableinput.Thegeneralshapesofthegraphsare:$/unit$/unit$/unitQQQLRACSRMC(Lfixed)SRMC(Kfixed)5–2.a.Thecost-minimizingcombinationofinputsisfoundbyequatingtheirmarginalproducttopriceratios:MP1P1MP2P2.Thisconditioncanbeexpressedas:MP1w1=MP2w2So,wegetMPw7.5*x0.5*x2111210=Q=MPw1.552210*x1*x23-1x28Qx1x2=2Q=4x13Thus:x1(38)x2(i)Usetherelationinequation(i)toexpresstheproductionfunctionfory10,000unitsasafunctionofonlyx2.Younowhaveasolvableequationwithoneunknownvariable,x2:3x1.531.51.52223.5y=5x1x2Q10,000=5ab(x2)=5abx288 bri75829_ch05.qxd8/13/087:07PMPage175Chapter5ProductionandCost175Solvingforx2andobtainingx1fromequation(i):x2*13.357x1*5.01b.Thetotalcostofproducingthe10,000unitsissimplythesumoftheexpendituresmadetoacquireeachoftheinputs:TCw1x1w2x2105.01513.357$116.87Review5–1.Distinguishbetweenreturnstoscaleandreturnstoafactor.Questions5–2.Yourcompanycurrentlyusessteelandaluminuminaproductionprocess.Steelcosts$.50perpound,andaluminumcosts$1.00perpound.Supposethegovernmentimposesataxof$.25perpoundonallmetals.Whataffectwillthishaveonyouroptimalinputmix?Showusingisoquantsandisocostlines.5–3.Yourcompanycurrentlyusessteelandaluminuminaproductionprocess.Steelcosts$.50perpound,andaluminumcosts$1.00perpound.Supposethatinflationdoublesthepriceofbothinputs.Whataffectwillthishaveonyouroptimalinputmix?Showusingisoquantsandisocostlines.5–4.Isthe“longrun”thesamecalendartimeforallfirms?Explain.5–5.Youwanttoestimatethecostofmaterialsusedtoproduceaparticularproduct.Accordingtoaccountingreports,youinitiallypaid$50forthematerialsthatarenecessarytoproduceeachunit.Is$50agoodestimateofyourcurrentproductioncosts?Explain.5–6.Supposethataveragecostisminimizedat50unitsandequals$1.Whatismarginalcostatthisoutputlevel?5–7.Whatisthedifferencebetweeneconomiesofscaleandeconomiesofscope?5–8.Whatisthedifferencebetweeneconomiesofscaleandlearningeffects?5–9.Supposethatyoucansellasmuchofaproductasyouwantat$100perunit.Yourmarginalcostis:MC2Q.Yourfixedcostis$50.Whatistheoptimaloutputlevel?Whatistheoptimaloutput,ifyourfixedcostis$60?5–10.Discusstwoproblemsthatariseinestimatingcostcurves.5–11.Supposethatthemarginalproductoflaboris:MP100L,whereListhenumberofwork-ershired.Youcanselltheproductinthemarketplacefor$50perunit,andthewagerateforlaboris$100.Howmanyworkersshouldyouhire?5–12.Textbookauthorstypicallyreceiveasimplepercentageoftotalrevenuegeneratedfrombooksales.Thepublisherbearsalltheproductioncostsandchoosestheoutputlevel.Supposetheretailpriceofabookisfixedat$50.Theauthorreceives$10percopy,andthefirmreceives$40percopy.Thefirmisinterestedinmaximizingitsownprofits.Willtheauthorbehappywiththebookcompany’soutputchoice?Doestheselectedoutputmaximizethejointprofits(forboththeauthorandcompany)fromthebook?5–13.Supposeyourcompanyproducesoneproductandthatyouarecurrentlyatanoutputlevelwhereyourpriceelasticityis0.5.Areyouattheoptimaloutputlevelforprofitmaximization?Howcanyoutell?5–14.Semiconductorchipsareusedtostoreinformationinelectronicproducts,suchaspersonalcom-puters.OneoftheearlyleadersintheproductionofthesechipswasTexasInstruments(TI).Duringtheearlyperiodinthedevelopmentofthisindustry,TImadethedecisiontopriceitssemiconductorssubstantiallybelowitsproductioncosts.Thisdecisionincreasedsales,butresultedinnear-termreductionsinprofits.ExplainwhyTImighthavemadethisdecision.5–15.TheAFL-CIOhasbeenasteadfastproponentofincreasingtheminimumwage.Offeratleasttworeasonswhytheymightlobbyforsuchincreases. bri75829_ch05.qxd8/13/087:07PMPage176176Part2ManagerialEconomics5–16.MountainSpringsWaterCompanyproducesbottledwater.Internalconsultantsestimatethecompany’sproductionfunctiontobeQ300L2K,whereQisthenumberofbottlesofwaterproducedeachweek,Listhehoursoflaborperweek,andKisthenumberofmachinehoursperweek.Eachmachinecanoperate100hoursaweek.Laborcosts$20perhour,andeachmachinecosts$1,000perweek.a.Supposethefirmhas20machinesandisproducingitscurrentoutputusinganoptimalKLratio.HowmanypeopledoesMountainSpringsemploy?Assumeeachpersonworks40hoursaweek.b.Recenttechnologicaladvancementshavecausedmachinepricestodrop.MountainSpringscannowleaseeachmachinefor$800aweek.HowwillthisaffecttheoptimalKLratio(i.e.,willtheoptimalKLratiobesmallerorlarger)?Showwhy.5–17.TheWorkerbeeCompanyemploys100highschoolgraduatesand50collegegraduatesatre-spectivewagesof$10and$20.Thetotalproductforhighschoolgraduatesis1,000100QH,whereasthetotalproductforcollegegraduatesis5,00050QC.QHthenumberofhighschoolgraduates,whileQCthenumberofcollegegraduates.Isthecompanyhiringtheoptimalamountofeachtypeofworker?Ifnot,hasithiredtoomanyhighschoolortoomanycollegegraduates?Explain.5–18.QTCTFCTVCMCACAFCAVC0150080260350460575695712081509185a.Completetheabovetable.b.GraphTC,TFC,TVC,MC,AC,AFC,andAVCagainstQ.5–19.SupposetheJonesManufacturingCompanyproducesasingleproduct.Atitscurrentinputmixthemarginalproductoflaboris10andthemarginalproductofcapitalis20.Theperunitpriceoflaborandcapitalare$5and$10,respectively.IstheJonesCompanyusinganoptimalmixoflaborandcapitaltoproduceitscurrentoutput?Ifnot,shoulditusemorecapitalorlabor?Explain.5–20.SupposetheproductionfunctionofPowerGunsCo.isgivenbyQ25LKwhereQisthequantityofgunsproducedinthemonth,Listhenumberofworkersemployed,andKisthenumberofmachinesusedintheproduction.Themonthlywagerateis$3,000perworkerandthemonthlyrentalrateforamachineis$6,000.CurrentlyPowerGunsCo.employs25workersand40machines.Assumeperfectdivisibilityoflaborandmachines.a.WhatisthecurrentaverageproductoflaborforPowerGunsCo.?Whatisthecurrentmarginalproductofmachines?(Assume1unitincreaseinmachines.)b.DoesPowerGuns’productionfunctiondisplayincreasing,decreasing,orconstantreturnstoscale?Explain.c.WhatisthetotalcostofthecurrentproductionofPowerGunsinamonth?Whatistheaveragecosttoproduceashootinggun?Assumingthenumberofmachinesdoesnotchange,whatisthemarginalcostofproducingoneadditionalgun?d.Whatisthelawofdiminishingreturns?Doesthisproductiondisplaythischaracteristic?Explain. bri75829_ch05.qxd8/13/087:07PMPage177Chapter5ProductionandCost1775–21.AssumeKodak’sproductionfunctionfordigitalcamerasisgivenbyQ100(L0.7K0.3),whereLandKarethenumberofworkersandmachinesemployedinamonth,respectively,andQisthemonthlyoutput.Moreover,assumethemonthlywageperworkeris$3,000andthemonthlyrentalratepermachineis$2,000.Note:Giventheproductionfunction,themarginalproductfunctionsareMP70(L0.3K0.3)andMP30(L0.7K0.7).LKa.IfKodakneedstosupply60,000unitsofcameraspermonth,howmanyworkersandmachinesshoulditoptimallyemploy?b.Whatarethetotalcostandaveragecostofproducingthequantitygivenin(a)?5–22.Forsimplicity,throughoutthisproblem,assumelabor(L),capital(K),andquantityproduced(Q)canbeinfinitelydivided—thatis,itisfinetohire3.3workers,rent4.7machines,and/orproduce134.2units.Answerthefollowingquestions,assumingtheproductionfunctionforDurableTiresCorp.isQL13K12,whereQisthequantityoftiresproduced,Listhenum-berofworkersemployed,andKisthenumberofmachinesrented.a.Whatisthequantityoftiresproducedwhenthecompanyemploys64workersand36machines?b.Whataretheaverageproductoflabor(L)andtheaverageproductofmachines(K)whentheinputmixistheonegivenabove?Clearlyandconcisely,pleaseexplainhowyouwouldinterpretthesenumbers.c.Continuetoassumetheinputmixgivenabove:Whatisthemarginalproductoflabor(L),ifthenumberofworkersisincreasedby1unit?Whatisthemarginalproductofcapital(K),ifthenumberofmachinesisincreasedby1unit,instead?Clearlyandconcisely,pleaseexplainhowyouwouldinterpretthesenumbers.d.DoesDurableTires’productionfunctiondisplayincreasing,decreasing,orconstantreturnstoscale?Explain.Wouldyouranswerchange,iftheproductionfunctionwereQL12K12?How?Explain.e.DoesDurableTires’productionfunctiondisplayincreasing,decreasing,orconstantreturnstolabor?Explain.Wouldyouranswerchange,iftheproductionfunctionwereQL12K12?How?Explain.5–23.Answerthefollowingquestions,continuingtoassumetheproductionfunctionforDurableTiresCorp.isQL13K12,whereQisthequantityoftiresproduced,Listhenumberofworkersemployed,andKisthenumberofmachinesrented.Moreover,assumethewageperunitoflabor(WL)is$50andtherentalpricepermachineis$200(WK).a.Whatisthetotalcostofproducingthequantityoftiresyoufoundinyouranswertoquestion5–23(a)?Andtheaveragecost?Assumingthenumberofmachinesrenteddoesnotchange,whatisthemarginalcostofproducingoneadditionaltire?b.Giventheproductionfunctionabove,themarginalproductoflaborandthemarginalprod-uctofcapitalareMP13(L23K12)andMP12(L13K12),respectively.GivenLKthewageandrentalrateabove,isDurableTiresCorp.adoptinganoptimalinputmixtopro-ducethequantityoftiresfoundinquestion5–23(a)?Ifyes,why?Ifnot,whynot,andhowcouldDurableTiresCorp.savemoneyproducingthatsamequantityoftires?Explain.c.Whathappenstotheoptimalinputmixyoufoundinquestion5–23,ifthegovernmentintroducesataxthatraisesthecostoflaborto$150perworker?Explain.5–24.AssumeDurableTiresCorp.facesthefollowingdemandcurve,P2500.1Q.IfDurableTires’marginalcostisconstantat$35,howmanytiresshoulditproduceinordertomaximizeitsprofits?What’sDurableTires’profitinthiscase?Shouldtheelasticityofdemandbegreater,equal,orlessthan1attheprofit-maximizingpriceandquantity?Explain(hint:youmayuseagraphtosupportyourargument).