生产管理知识_生产函数决定成本函数

Landsburg PriceTheoryandApplication 6thedition 1 StevenLandsburg UniversityofRochester Chapter6ProductionandCosts Copyright 2005byThomsonSouth Western partoftheThomsonCorporation Allrightsreserved Landsburg PriceTheoryandApplication 6thedition 2 Introduction 生產函數決定成本函數 而 邊際 成本會影響供給函數 因此 本章先介紹生產函數 然後說明成本函數 生產函數在說明生產要素與產量之間的關係 生產要素分為兩類 一類是短期即可變動其使用的數量的 以勞工為代表 另一類是長期才可變動其使用的數量的 以資本為代表 產量受到生產技術與生產要素的影響WheredocostcurvescomefromDependsonfirm savailabletechnologyDeterminesproductionprocessProductionprocessdeterminesfirm scosts Landsburg PriceTheoryandApplication 6thedition 3 ProductionandCostsintheShortRun Limitedoptionsinshortrun SR InitialassumptionFirmcanhiremorelabor Landsburg PriceTheoryandApplication 6thedition 4 ProductionintheShortRun Totalproduct TP oflaborQuantityofoutputproducedbyfirminagivenamountoftimedependentonlaborhiredInformationgraphicallyrepresentedbyproductionfunctionProductionfunctionslopesupwardProductionfunctionisrulefordetermininghowmuchoutputcanbeproducedwithagivenbasketofinputs Landsburg PriceTheoryandApplication 6thedition 5 CalculatingMPandAP Marginalproductoflabor MPL IncreaseintotalproductbasedonhiringoneadditionalworkerAssumecapitalfixedSlopeofTPAverageproductoflabor APL Totalproductdividedbynumberofworkers Landsburg PriceTheoryandApplication 6thedition 6 RelationbetweenMPandAP N TP Landsburg PriceTheoryandApplication 6thedition 7 CalculatingMPandAP Landsburg PriceTheoryandApplication 6thedition 8 MPL APL Landsburg PriceTheoryandApplication 6thedition 9 EXHIBIT6 1Total MarginalandAverageProducts Landsburg PriceTheoryandApplication 6thedition 10 ShapeofMPandAPCurves APIfnumberofworkerslarge additionalworkerscauseaverageproductoflabortodecreaseInvertedU shapeMPInvertedU shapeAPandMPrelationshiptooneanotherIfMP AP MPliesaboveAPIfMP AP MPliesbelowAPIfMP AP APatmaximumorpeak Landsburg PriceTheoryandApplication 6thedition 11 EXHIBIT6 2TheStagesofProduction Landsburg PriceTheoryandApplication 6thedition 12 VariableCostsintheSR Constructingthefirm svariablecostcurveNeedtotalproductcurveNeedwageratePriceofhiringlaborMultiplynumberofworkersbywageratetogetvariablecostPL L VCCurverelatestotalproduct notnumberofworkers tovariablecost Landsburg PriceTheoryandApplication 6thedition 13 Exhibit6 3VCCurve Landsburg PriceTheoryandApplication 6thedition 14 EXHIBIT6 3VariableCostCurve Landsburg PriceTheoryandApplication 6thedition 15 FixedCostsintheSR CostsofcapitalPhysicalassets suchasmachineryandfactoriesEx handyman svan Landsburg PriceTheoryandApplication 6thedition 16 TotalCost TotalcostequaltosumoffixedandvariablecostsofproductionTC FC VC FC PL LAdditionalcostconsiderationsbesidetotals Landsburg PriceTheoryandApplication 6thedition 17 ComputingAverageandMarginalCosts Averagevariablecost AVC variablecostdividedbyquantityofoutputLaboronlyvariablefactorofproductionCalculateAVCbytakingthewagerateanddividingbyAPLAveragecost AC totalcostdividedbyquantityofoutputSometimescalledaveragetotalcostMarginalcost MC additionalcostattributabletothelastunitofoutputproducedLaboronlyvariablefactorofproductionCalculateMCbytakingthewagerateanddividingbyMPL Landsburg PriceTheoryandApplication 6thedition 18 ComputingAverageandMarginalCosts Landsburg PriceTheoryandApplication 6thedition 19 EXHIBIT6 4DerivingtheAverageandMarginalCostCurves Landsburg PriceTheoryandApplication 6thedition 20 MC AC Landsburg PriceTheoryandApplication 6thedition 21 ShapesofCostCurves VCcurvealwaysincreasingMoreoutputrequiresmorelaborHighercostsTCcurvedeterminedbysumofFCandVCFCconstantHassameshapeasVCcurveMC AC andAVCcurvesareU shaped Landsburg PriceTheoryandApplication 6thedition 22 EXHIBIT6 5TheGeometryofProductCurvesandCostCurves Landsburg PriceTheoryandApplication 6thedition 23 CostCurvesRelations MCrelationshiptoAVCandACMCbelowAVC AVCfallingMCaboveAVC AVCrisingMCequalsAVC AVCatminimumCanreplaceAVCwithAC sameholdstrueShapesofcostcurvesrelatedtoshapesofproductcurves Landsburg PriceTheoryandApplication 6thedition 24 ProductionandCostsintheLongRun Inlongrun LR firmcanadjustemploymentofcapitalandlaborAttemptstoachievetheleastcostmethodofproducingagivenquantityofoutput Landsburg PriceTheoryandApplication 6thedition 25 Isoquants GeometryofLRproductionLabelverticalaxiswithK standsforcapitalLabelhorizontalaxiswithL whichstandsforlaborFixedperiodoftimeWanttouseleastcostlymethodAvoidtechnologicallyinefficientpointswhichareoutsidetheboundaryGeneralobservationsSlopedownwardFilltheplaneNevercrossConvex Landsburg PriceTheoryandApplication 6thedition 26 MarginalRateofTechnicalSubstitution AbsolutevalueofslopeofisoquantMPLdividedbyMPKAmountofcapitalnecessarytoreplaceoneunitoflaborwhilemaintainingaconstantlevelofoutputIfmuchlaborandlittlecapitalemployedtoproduceaunitofoutput MRTSLKissmallGeometricallyisoquantisconvex Landsburg PriceTheoryandApplication 6thedition 27 EXHIBIT6 8TheProductionFunction Landsburg PriceTheoryandApplication 6thedition 28 ChoosingaProductionProcess MinimizingcostimportantpartofmaximizingprofitIsocostallowtokeeptrackofcostsSetofallbasketsofinputsthatcanbeemployedatagivencostSlope PL PKMinimizingcostandmaximizingoutputrequiresfirmchoosetangencypointbetweenanisocostandanisoquantMeansthatMRTS PL PKTangenciesliealongcurvecalledthefirm sexpansionpath Landsburg PriceTheoryandApplication 6thedition 29 EXHIBIT6 9CostMinimization Landsburg PriceTheoryandApplication 6thedition 30 Long RunCostCurves InformationneededProductionfunctionorisoquantsInputpricesFirm slong runtotalcostCostofproducingagivenamountofoutputwhenthefirmisabletooperateonitsexpansionpathLong runaveragecostLong runtotalcostdividedbyquantityLong runmarginalcostPartoflong runtotalcostattributabletothelastunitproduced Landsburg PriceTheoryandApplication 6thedition 31 EXHIBIT6 11DerivingLong RunTotalCost Landsburg PriceTheoryandApplication 6thedition 32 EXHIBIT6 12Long RunTotal Marginal andAverageCosts Landsburg PriceTheoryandApplication 6thedition 33 ReturnstoScale Whenallinputquantitiesareincreasedby1 doesoutputgoupby morethan1 IncreasingreturnstoscaleOccursatlowlevelsofoutputLong runaveragecostcurveisdecreasing exactly1 Constantreturnstoscale Whatafirmcandoone itcandotwice Long runaveragecostcurveisflat lessthan1 DecreasingreturnstoscaleOccursatsufficientlyhighlevelsofoutputLong run