《管理经济学》第五章PPT课件.ppt

ProductionAnalysisandCompensationPolicy Chapter5 1 Chapter5OVERVIEW ProductionFunctionsTotal Marginal andAverageProductLawofDiminishingReturnstoaFactorInputCombinationChoiceMarginalRevenueProductandOptimalEmploymentOptimalCombinationofMultipleInputsOptimalLevelsofMultipleInputsReturnstoScaleProductionFunctionEstimationProductivityMeasurement 2 Chapter5KEYCONCEPTS productionfunctiondiscreteproductionfunctioncontinuousproductionfunctionreturnstoscalereturnstoafactortotalproductmarginalproductaverageproductlawofdiminishingreturnsisoquanttechnicalefficiencyinputsubstitutionmarginalrateoftechnical ridgelinesmarginalrevenueproducteconomicefficiencynetmarginalrevenueisocostcurve orbudgetline constantreturnstoscaleexpansionpathincreasingreturnstoscaledecreasingreturnstoscaleoutputelasticitypowerproductionfunctionproductivitygrowthlaborproductivitymultifactorproductivity 3 ProductionFunctions PropertiesofProductionFunctionsProductionfunctionsaredeterminedbytechnology equipmentandinputprices Discreteproductionfunctionsarelumpy Continuousproductionfunctionsemployinputsinsmallincrements 4 5 ReturnstoScaleandReturnstoaFactor Returnstoscalemeasureoutputeffectofincreasingallinputs Returnstoafactormeasureoutputeffectofincreasingoneinput 6 Total Marginal andAverageProduct TotalProductTotalproductistotaloutput 7 8 MarginalProduct Marginalproductisthechangeinoutputcausedbyincreasinginputuse IfMPX Q X 0 totalproductisrising IfMPX Q X 0 totalproductisfalling rare AverageproductAPX Q X 9 10 11 Total Marginal andAverageProduct Observations WhenMP 0 TPisatitsmaximumWhenMP AP APisincreasingWhenMP AP APisdecreasingWhenMP AP APisatitsmaximum 12 LawofDiminishingReturnstoaFactor DiminishingReturnstoaFactorConceptThelawofdiminishingreturns thelawofdiminishingmarginalreturns statesthatthemarginalproductofavariablefactormusteventuallydeclineasmoreofthevariablefactoriscombinedwithotherfixedresources 13 LawofDiminishingReturnstoaFactor IllustrationofDiminishingReturnstoaFactorTypically increasedspecializationandbetterutilizationofotherfactorsintheproductionprocessallowfactorproductivitytogrow Inpracticeitisveryraretoseeinputcombinationsthatexhibitincreasingreturnsforanyfactor Withincreasingreturnstoafactor anindustrywouldcometobedominatedbyoneverylargeproducer andthisisseldomthecase Inputcombinationsintherangeofdiminishingreturnsarecommonlyobserved 14 InputCombinationChoice ProductionIsoquantsIsoquantdenotesacurvethatrepresentsthedifferentcombinationsofinputsthatcanbeefficientlyusedtoproduceagivenlevelofoutput Technicalefficiencyisleast costproductionofatargetlevelofoutput 15 RepresentativeIsoquantsforTable5 1 16 InputCombinationChoice InputFactorSubstitutionIsoquantshapeshowsinputsubstitutability C shapedisoquantsarecommonandimplyimperfectsubstitutability 17 IsoquantsforInputswithVaryingDegreesofSubstitutability A ElectricPowerGeneration B BicycleProduction 18 IsoquantsforInputswithVaryingDegreesofSubstitution C DressProduction 19 MarginalRateofTechnicalSubstitution Themarginalrateoftechnicalsubstitution MRTS istheamountofoneinputfactorthatmustbesubstitutedforoneunitofanotherinputfactortomaintainaconstantlevelofoutput MRTS Y X SlopeofanIsoquantThemarginalrateoftechnicalsubstitutionusuallydiminishesastheamountofsubstitutionincreases Attheextremes isoquantsmayevenbecomepositivelysloped indicatingthattherangeoverwhichinputfactorscanbesubstitutedforeachotherislimited 20 MarginalRateofTechnicalSubstitution RationalLimitsofInputSubstitutionMPX 0orMPY 0areneverobserved becausethisimpliesthatoutputcouldbeincreasedbyusinglessofthatresource Therationallimitsofinputsubstitutionarewheretheisoquantsbecomepositivelysloped Ridgelinesgraphicboundsforpositivemarginalproducts Itisirrationaltouseanyinputcombinationoutsidethesetangents orridgelines Onlyforinputcombinationslyingbetweentheridgelineswillbothinputshavepositivemarginalproducts Itishereandalongthenegativelyslopedportionoftheisoquantthatoptimalinputcombinationsarefound 21 22 2020 1 27 23 MarginalRevenueProductandOptimalEmployment MarginalRevenueProductTheextrarevenueobtainedfromusingonemorefactorinputtoproduceandselladditionalunitsofoutput Marginalrevenueproductofafactorisgivenbythefactor smarginalproductmultipliedbythemarginalrevenueoftheproduct MRPL MPLxMRQ TR L 24 MarginalRevenueProductandOptimalEmployment OptimalLevelofaSingleInputProfitwillincreasesolongasthemarginalrevenuegeneratedbyaninput oritsmarginalrevenueproduct exceedsthemarginalcostofemployment Conversely whenmarginalrevenueproductislessthanthecostofemployment marginalprofitisnegative andthefirmwouldreduceusage TheMRPfunctionofoneinputisthisinput sdemandcurve SetMRPL PLtogetoptimalemployment Optimalemploymentandeconomicefficiencyisachievedintheoveralleconomywhenallfirmsemployresourcessoastoequateeachinput smarginalrevenueproductandmarginalcost IllustrationofOptimalEmployment 25 OptimalCombinationofMultipleInputs Underfixedinputscombination maximizeoutput Underconstantoutput minimumexpenditureofinputscombination Theoutputofmaximizationprofit 26 OptimalCombinationofMultipleInputs BudgetLines isocostcurve Abudgetlineismerelyastatementofthevariouscombinationsofinputsthatcanbepurchasedforagivendollaramount Least costproductionoccurswhenMPX PX MPY PYandPX PY MPX MPY 27 OptimalCombinationofMultipleInputs ExpansionPathShowsefficient oroptimal inputcombinationsasoutputgrows Atthepointofoptimalinputcombination isocostandisoquantcurvesaretangentandhaveequalslope Optimalinputproportionsareemploymentwhenanadditionaldollarspentonanyinputyieldsthesameincreaseinoutput Anyinputcombinationviolatingthisruleissuboptimal IllustrationofOptimalInputProportionsInputproportionsareoptimalwhennoadditionaloutputcouldbeproduceforthesamecost Optimalinputproportionsisanecessarybutnotsufficientconditionforprofitmaximization 28 29 OptimalLevelsofMultipleInputs OptimalEmploymentandProfitMaximizationProfitsaremaximizedwhenMRPX PXforallinputs Profitmaximizationrequiresoptimalinputproportionsplusanoptimallevelofoutput IllustrationofOptimalLevelsofMultipleInputs 30 ReturnstoScale EvaluatingReturnstoScaleReturnstoscaleshowtheoutputeffectofincreasingallinputs OutputElasticityandReturnstoScaleOutputelasticityis Q Q Q Xi XiwhereXiisallinputs labor capital etc Q 1impliesincreasingreturns Q 1impliesconstantreturns Q 1impliesdecreasingreturns ReturnstoScaleEstimation 31 32 ProductionFunctionEstimation CubicProductionFunctionsDisplayvariablereturnstoscale Firstincreasing thendecreasingreturnsarecommon PowerProductionFunctionsAllowmarginalproductivityofeachinputtovarywithemploymentofallinputs 33 ProductivityMeasurement HowIsProductivityMeasured ProductivitymeasurementistheresponsibilityoftheBureauofLaborStatistics since1800s Productivitygrowthistherateofchangeinoutputperunitofinput Laborproductivityisthechangeinoutputperworkerhour UsesandLimitationsofProductivityDataQualitychangesmakeproductivitymeasurementdifficult 34 35 Problems1 Determinewhetherthefollowingproductionfunctionsexhibitconstant increasing ordecreasingreturnstoscale Q 0 5X 2Y 40ZQ 3L 10K 500Q 4A 6B 8ABQ 7L2 5LK 2K2Q 10L0 5K0 3 36 Problems2 TheRoute66TruckStop Inc sellsgasolinetobothself serviceandfull servicecustomers Thosewhopumptheirowngasbenefitfromthelowerself servicepriceof 1 80pergallon Full servicecustomersenjoytheserviceofanattendant buttheypayahigherpriceof 1 90pergallon Thecompanyhasobservedthefollowingrelationbetweenthenumberofattendantsemployedperdayandfull serviceoutput 37 Route66TruckStop Inc 38 A Constructatableshowingthenetmarginalrevenueproductderivedfromattendantemployment B HowmanyattendantswouldRoute66employatadailywagerateof 160 includingwagesandbenefits C WhatisthehighestdailywagerateRoute66wouldpaytohirefourattendantsperday 39 Problems3 WillTruman Associates LLCisasuccessfulManhattan basedlawfirm Workerproductivityatthefirmismeasuredinbillablehours whichvarybetweenpartnersandassociates Partnertimeisbilledtoclientsatarateof 250perhour whereasassociatetimeisbilledatarateof 125perhour Onaverage eachpartnergenerates25billablehoursper40 hourworkweek with15hoursspentonpromotion administrative andsupervisoryresponsibilities Associatesgenerateanaverageof35billablehoursper40 hourworkweekandspend5hoursperweekinadministrativeandtrainingmeetings Variableoverheadcostsaverage50 ofrevenuesgeneratedbypartnersand givensupervisoryrequirements 60 ofrevenuesgeneratedbyassociates 40 A Calculatetheannual 50workweek netmarginalrevenueproductofpartnersandassociates B Ifpartnersearn 175 000andassociatesearn 70 000peryear doesthecompanyhaveanoptimalcombinationofpartnersandassociates Ifnot whynot Makeyouranswerexplicitandsupportanyrecommendationsforchange 41 Problems4 TicketServices Inc offersticketpromotionandhandlingservicesforconcertsandsportingevents TheShermanOaks California branchofficemakesheavyuseofspotradioadvertisingonWHAM AM witheach30 secondadcosting 100 Duringthepastyear thefollowingrelationbetweenadvertisingandticketsalespereventhasbeenobserved Sales units 5 000 100A 0 5A2 Sales units Advertising 100 AHere Arepresentsa30 secondradiospotad andsa