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ChapterProducerBehaviorChapterProducerBehavior2005北京大学经济学院ChapterFour北京大学经济学院ChapterFour北京大学经济学院4.14.2Production4.3Cost北京大学经济学院4.2.1Definition北京大学经济学院4.2.1DefinitionofProduct4.2.2TheShort-RunProduction4.2.3TheLong-RunProduction4.2.4OptimalInputsintheLong4.2.5Elastictiesof4.2ProductionReadingsaboutthisZhang:ChapterNicholson:ReadingsaboutthisZhang:ChapterNicholson:Chapter11,P267-北京大学经济学院ChapterFour北京大学经济学院ChapterFour北京大学经济学院4.14.2Production4.3Cost北京大学北京大学经济学院SymmetryBetweenConsumerandFirmUsesimilartoolsfromconsumertheorytoanalysethefirm.Ingeneral:SubjectSubjectconSymmetryBetweenConsumerandFirmUsesimilartoolsfromconsumertheorytoanalysethefirm.Ingeneral:SubjectSubjectcon大学济学北京大学经济学院北京大学经济学院ProductionTechnology(生产技术ProductionProcessbyProductionTechnology(生产技术ProductionProcessbywhichinputsareconvertedtoInputsalsocalled“factorsofproduction”(生产要素Input（1）:Labor(L)(skilled,Input（2）:Physicalcapital(K)（有形资本）(equipment,structuresinventories（存货）land),Mainissue:Whichtechnologyis北京大学经济学院Process（生产过程Labour,Goodsand北京大学经济学院Process（生产过程Labour,Goodsand北京大学经济学院DefinitionofProductionxi-theamountDefinitionofProductionxi-theamountused(level)ofinputInputbundle(投入组合)-vectorinputs(x1,x2,…qoutputlevel（产出水平Productionqf(1,L,xnThetechnology’sproductionfunctionstatesthemaximumamountofoutputpossiblefromaninputbundle.北京大学经济学院Productionfunctions–specificq=f(L,K)isageneralformoftheproductionfunctionwithProductionfunctions–specificq=f(L,K)isageneralformoftheproductionfunctionwithtwoOftenweneedtoworkwithmorespecificfunctionalforms.HerearefourcommononesLinear:Fixedproportions:q=min(aL,Cobb-qf(K,L)Ineachcaseq,L,Karevariablesanda,b,c,ρε(andA)北京大学经济学院ShortRunvsLongRun（短期与ShortRunvsLongRun（短期与长期Theshortrunisdefinedastheperiodoftimewhentheplantsizeisfixed.Intheshortrun,atleastonefactorofproductionisfixed(unchangeable)Thelongrunisdefinedasthetimeperiodnecessarytochangetheplantsize.Inthelongrun,allfactorsofproductioncanbechanged…are“variable”Thedurationofthelongrun(andthusthatoftheshortrun)dependsonthenatureoftheproduction北京大学经济学院北京大学经济学院北京大学经济学院ProductionWhenOnlyOneInputisThereareProductionWhenOnlyOneInputisTherearethreeimportantwaystomeasuretheproductivityofinputsinshort-run:TotalAverageMarginal北京大学经济学院TotalProduct(TP)（总产量TotalProductrepresentstherelationshipbetweenthenumberofworkers(orCapitals)andtheTOTALnumberofunitsofoutputproducedholdingallTotalProduct(TP)（总产量TotalProductrepresentstherelationshipbetweenthenumberofworkers(orCapitals)andtheTOTALnumberofunitsofoutputproducedholdingallotherfactorsofproduction(theplantsize)constant.TLTKf(L,Kf(L,K北京大学经济学院TheProductionFunction:TPincreaseswith81234Unitsof北京大学经济学院UnitsTheProductionFunction:TPincreaseswith81234Unitsof北京大学经济学院UnitsTotalProduct,QfVariable1,000dQ0d2Qd2Q0TotalProduct,QfVariable1,000dQ0d2Qd2Q00s北京大学经济InflectionPoint(拐点AverageProduct(AP)(平均产量 Thisfunctionrepresentstheaverageamountof OutputperunitofAverageProduct(AP)(平均产量 Thisfunctionrepresentstheaverageamountof Outputperunitofqf(K,APLLLqf(K, KKK北京大学经济学院AP:slopeofrayfrom)=150e=AP:slopeofrayfrom)=150e=150/10=北京大学经济学院LAP:SlopeofrayfromAP(slopeofray)DecreasesafterL0AP(slopeofray)IncreasesuptoAP:SlopeofrayfromAP(slopeofray)DecreasesafterL0AP(slopeofray)IncreasesuptoL0北京大学经济学院AP:Increases,reachesamaximumandAP(slopeofray)IncreasesuptoLAP:Increases,reachesamaximumandAP(slopeofray)IncreasesuptoL0AP(slopeofray)DecreasesafterL0L北京大学经济学院MarginalProduct(MP)(边际产量 Theadditionaloutputthatcanbeproducedbyaddingonemoreunitoflabor(orCapital),holdingeverythingelseconstant.TheslopeMarginalProduct(MP)(边际产量 Theadditionaloutputthatcanbeproducedbyaddingonemoreunitoflabor(orCapital),holdingeverythingelseconstant.TheslopeoftheTotalProductMPfLLMPfKK北京大学经济学院MP:SlopeoftheProductionSlope=30/3=160130MP:SlopeoftheProductionSlope=30/3=1601309北京大学经济学院MP=TheRelationshipbetweenTPandLL北京大学经济学院TheRelationshipbetweenTPandLL北京大学经济学院TheLawofDiminishingReturnTheLawofDiminishingReturnWhathappenstooutputaswehiremoreandmoreworkers?RememberthattheplantsizeisThatmeansthatyouwillbehiringmoreworkerstoSHAREtheEXISTINGEQUIPMENTandtheEXISTINGSPACE.北京大学经济学院TheLawofDiminishingReturnTheLawofDiminishingReturnAsmoreofavariableinput(labor)isaddedtoafixedinput(plant),additionstooutputgetsmallerandNotethataddingworkersincreasesoutputbuttheincreasesbecomesmallerandsmallerasmoreworkersarehired.北京大学经济学院DiminishingMarginalDiminishingMPKfDiminishingMarginalDiminishingMPKfMPLf北京大学经济学院MarginalProducts:DiminishingMPqx1/3x2/12MPMP(2/MarginalProducts:DiminishingMPqx1/3x2/12MPMP(2/11M122122x5/3x2/129291/14/2xx2Bothmarginalproductsare北京大学经济学院TheReasonsofDiminishingIncreasingReturnsSpecialization（专业化TheReasonsofDiminishingIncreasingReturnsSpecialization（专业化DiminishingReturnsBeginsFeweropportunitiesforteamworkandspecializationL北京大学经济学院TheRelationshipbetweenAPandLL北京大学经济学院TheRelationshipbetweenAPandLL北京大学经济学院RelationshipbetweenMPandMPMP=APwhenAPisRelationshipbetweenMPandMPMP=APwhenAPisMPaboveMPbelow北京大学经济TheRelationshipbetweenAPand IfMPTheRelationshipbetweenAPand IfMP>AP,thentheAverageProductIfMP<thentheAPwillIfMP=AP,thentheAPisnotincreasingordecreasing:itisatthemaximumpoint.北京大学经济学院ProofofRelationshipsbetweenAPand,wecanqf(K,APProofofRelationshipsbetweenAPand,wecanqf(K,AP LLLdAPLLMPLSo,atamaximumL,L·MPL=qor北京大学经济学院ThreeStagesof（生产的三个阶段北京ThreeStagesof（生产的三个阶段北京大学经济学院ThreeStagesofProduction（生产的三个阶段qTotalProduct,qfVariable00qLqLAverageVariable001