管理经济学（原书第14版） 课件 第10章　生产与成本估计

Chapter10ProductionandCostEstimationMANAGERIALECONOMICSFoundationsofBusinessAnalysisandStrategyFourteenthEditionCHRISTOPHERR.THOMAS©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.LearningObjectives10.1Specifyandexplainthepropertiesofashort‐runcubicproductionfunction.10.2Employregressionanalysistoestimateashort‐runproductionfunction.10.3Discusstwoimportantproblemsconcerningthepropermeasurementofcost:correctingforinflationandmeasuringeconomic(opportunity)costs.10.4Specifyandestimateashort‐runcostfunctionusingacubicspecification.2EmpiricalProductionFunctionAnempiricalproductionfunctionisthemathematicalformoftheproductionfunctiontobeestimated.Along-runproductionfunctionisaproductionfunctioninwhichallinputsarevariable.Ashort-runproductionfunctionisaproductionfunctioninwhichatleastoneinputisfixed.3EmpiricalProductionFunctionSpecificationAsuitablefunctionalformforestimatingeitheralong-runorashort-runproductionfunctionisthecubicproductionfunction,expressedas:4Short-RunCubicProductionFunctionHoldingcapitalconstant,theshort-runcubicproductionfunctionisderivedasfollows:5PropertiesofaShort-RunCubicProductionFunction1Theaverageandmarginalproductsoflaborare,respectively:6PropertiesofaShort-RunCubicProductionFunction2Marginalproductoflaborbeginstodiminishbeyondunitsoflabor.Averageproductoflaborbeginstodiminishbeyondunitsoflabor.7Figure10.1MarginalandAverageProductCurvesfortheShort-RunCubicProductionFunctionQ=AL3+BL2Accessthetextalternativeforslideimages.8Short-RunCubicProductionFunctionParameterRestrictionsTohavenecessarypropertiesofaproductionfunction,parametersmustsatisfythefollowingrestrictions:A<0andB>09Table10.1SummaryofaShort-RunCubicProductionFunctionShort-RunCubicProductionFunctionTotalproductAverageproductMarginalproductDiminishingmarginalreturnsDiminishingaverageproductRestrictionsonparametersA<0B>010Figure10.2ScatterDiagramforaCubicProductionFunctionAccessthetextalternativeforslideimages.11EstimationofaShort-RunProductionFunction1Touselinearregressionanalysis,thecubicequationmustbetransformedintolinearform:Q=AX+BWEstimatedregressionlinemustpassthroughtheorigin.Regressionthroughtheoriginisaregressioninwhichtheintercepttermisforcedtoequalzero.Estimateusingdataforwhichthelevelofusageofoneormoreinputsisfixed(usuallytime-seriesdataareused).12EstimationofaShort-RunProductionFunction2Datacollectionmaybecomplicatedbythefactthataccountingdatadonotincludefirm’sopportunitycosts,knownastheusercostofcapital.Capitalcostsshouldreflectnotonlyacquisitioncostbutanyforegonerentalincome,depreciation,andcapitalgains/losses.NominalcostdataDatathathavenotbeencorrectedfortheeffectsofinflation.Musteliminateeffectsofinflationbydeflating

nominalcostdata.Correctfortheinfluenceofinflationbydividingnominalcostdatabyanappropriatepriceindex(orimplicitpricedeflator).13Figure10.3TheProblemofInflationAccessthetextalternativeforslideimages.14Figure10.4TypicalShort-RunCostCurvesAccessthetextalternativeforslideimages.15Short-RunCubicCostFunctionAveragevariablecostandmarginalcostfunctionsare,respectively:CubicspecificationproducesS-shapedTVCcurveandU-shapedAVCandSMCcurves.16PropertiesofaShort-RunCubicCostFunctionAveragevariablecostreachesitsminimumvalueat:Toconformtotheoreticalproperties,parametersmustsatisfythefollowingrestrictions:

a>0,b<0,and

c>017Table10.2SummaryofaCubicSpecificationforTotalVariableCostCubicTotalVariableCostFunctionTotalvariablecostAveragevariablecostMarginalcostAVCreachesminimumpointRestrictionsonparametersa>0b<0c>018Figure10.5APotentialDataProblemAccessthetextalternativeforslideimages.19SummaryThefirststepinestimatingaproductionfunctionistospecifytheempiricalproductionfunction,whichistheexactmathematicalformoftheequationtobeestimated.Toestimateacubicshort-runproductionfunctionusinglinearregression,transformthecubicequationintolinearform;theestimatedregressionlinemustpassthroughtheorigin.Amanagertypicallyusestime-seriesobservationsoncost,output,andinputpricestoestimatetheshort-runcostfunction.Theeffectsofinflationmustbeeliminated.Becauseallthreecostcurves(TVC,AVC,andSMC)employthesameparameters,onecanestimateanyoneofthemtoobtainestimatesofallthreecurves.20EndofMainContent©McGrawHillLLC.Allrightsreserved.NoreproductionordistributionwithoutthepriorwrittenconsentofMcGrawHillLLC.AccessibilityContent:TextAlternativesforImages22Figure10.1MarginalandAverageProductCurvesfortheShort-RunCubicProductionFunctionQ=AL3+BL2

-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledastheaverageandmarginalproductoflabor.Thehorizontalx-axisislabeledaslabor.Aconcave-downwardincreasingcurve,labeledMP,beginsatapointclosetotheverticalaxisatacertainheight,risesfromlefttotheright,andreachesahighpointmdirectlyabovethepointLsubscriptmequalsnegativeBover3A.Thecurvethenfallsfromlefttoright,passesthroughpointa,andendsclosetothex-axis.Anotherconcave-downwardincreasingcurve,labeledAP,beginsatapointclosetotheverticalaxisandbelowthestartingpointofthefirstcurve,risesfromlefttotheright,intersectsthefirstcurveatapointa,directlyabovethepointLsubscriptaequalsnegativeBover2A.Thecurvethenfallsfromthelefttotherightandendsabovethefirstcurve.Notethatthevaluesareapproximate.Returntoparent-slidecontainingimages.23Figure10.2ScatterDiagramforaCubicProductionFunction-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledasoutputandrangesfrom0to140inincrementsof20.Thehorizontalx-axisislabeledaslaborandrangesfrom0to45inincrementsof5.40datapointsfollowanincreasingtrendandarearrangedinanSshape.AcurvelabeledTPbeginsattheorigin,passesthroughsomedatapoints,initiallyconcaveupward,thenriseslinearlyfromthelefttotheright,andendsatthetopright.Averticaldashedlinesegmentconnectsadatapointat(20.78,0).ThepointislabeledLcapsubscriptmequals20.78.Anotherverticaldashedlinesegmentconnectsadatapointonthecurvewith(31.16,0).ThepointislabeledLcapsubscriptaequals31.16.Notethatthevaluesareapproximate.Returntoparent-slidecontainingimages.24Figure10.3TheProblemofInflation-TextAlternativeReturntoparent-slidecontainingimages.Theverticaly-axisislabeledascostinnominaldollars.Thehorizontalx-axisislabeledasoutputinphysicalunits.AdashedverticallinesegmentisplotteddirectlyaboveapointQnaughtonthex-axis.Thedashedlinehasfourdotsatregularintervals.MovingfromtoptobottomthedotsarelabeledasOctober2023,July2023,April2023,andJanuary2023.Notethatthevaluesareapproximate.Returntoparent-slidecontainingimages.25Figure10.4TypicalShort-RunCostCurves-TextAlternativeReturntoparent-slidecontainingimages.Inthefirstgraph,theverticaly-axisislabeledasthetotalvariablecostindollars.Thehorizontalx-axisislabeledquantity.AcurvelabeledTVCbeginsattheorigin,initiallyconcavedown,risesfromlefttoright,thenbecomesconcaveupandextendsupfromlefttoright.Inthesecondgraph,theverticaly-axisislabeledasmarginalandaveragevariablecostindollars,andthehorizontalaxisislabeledasquantity.AcurvelabeledAVC,concaveupward,beginsatapointnearthey-axis,slightlyfallsfromthelefttotheright,thenstartstoriseaftera