西方经济学教学课件微观英文5

Chapter5

PRODUCTIONTopicstobeDiscussedTheTechnologyofProductionIsoquantsProductionwithOneVariableInput(Labor)ProductionwithTwoVariableInputsReturnstoScale5.1ProductionFunctionProductionFunction:Therelationshipbetweenthequantityofoutput(suchaswheat,steel,orautomobiles)andthequantitiesofinputs(oflabor,land,andcapital)iscalledtheproductionfunctionIndicatesthehighestoutputthatafirmcanproduceforeveryspecifiedcombinationofinputsgiventhestateoftechnology.Showswhatistechnicallyfeasiblewhenthefirmoperatesefficiently.Theproductionfunctionfortwoinputs: Q=F(K,L)Q=Output,K=Capital,L=LaborForagiventechnologyTP,APandMPTotalproductisthetotaloutputproduced.Averageproductequalstotaloutputdividedbythetotalquantityofinputs.Wecancalculatethemarginalproductofafactorastheextraoutputaddedforeachadditionalunitofinputwhileholdingallotherinputsconstant.ShortRunandLongRunShort-run:Periodoftimeinwhichquantitiesofoneormoreproductionfactorscannotbechanged.Theseinputsarecalledfixedinputs.Long-runAmountoftimeneededtomakeallproductioninputsvariable.5.2ProductionFunctioninShortRun Amount Amount Total Average Marginal ofLabor(L) ofCapital(K) Output(Q) Product ProductProductionwith

OneVariableInput(Labor) 0 10 0 --- --- 1 10 10 10 10 2 10 30 15 20 3 10 60 20 30 4 10 80 20 20 5 10 95 19 15 6 10 108 18 13 7 10 112 16 4 8 10 112 14 0 9 10 108 12 -4 10 10 100 10 -8TotalProductLaborperMonthOutputperMonth60112023456789101ABCDProductionwith

OneVariableInput(Labor)A:slopeoftangent=MP(20)B:slopeofOB=AP(20)C:slopeofOC=MP&APAverageProductProductionwith

OneVariableInput(Labor)81020OutputperMonth02345679101LaborperMonth30EMarginalProductObservations:LeftofE:MP>AP&APisincreasingRightofE:MP<AP&APisdecreasingE:MP=AP&APisatitsmaximumObservations:WhenMP=0,TPisatitsmaximumWhenMP>AP,APisincreasingWhenMP<AP,APisdecreasingWhenMP=AP,APisatitsmaximumProductionwith

OneVariableInput(Labor)Productionwith

OneVariableInput(Labor)LaborperMonthOutputperMonth60112023456789101ABCD81020E0234567910130OutputperMonthLaborperMonthAP=slopeoflinefromorigintoapointonTP,linesb,&c.MP=slopeofatangenttoanypointontheTPline,linesa&c.Astheuseofaninputincreasesinequalincrements,apointwillbereachedatwhichtheresultingadditionstooutputdecreases(i.e.MPdeclines).Productionwith

OneVariableInput(Labor)TheLawofDiminishingMarginalReturnsWhenthelaborinputissmall,MPincreasesduetospecialization.Whenthelaborinputislarge,MPdecreasesduetoinefficiencies.AssumesthequalityofthevariableinputisconstantAssumesaconstanttechnologyTheLawofDiminishingMarginalReturnsProductionwith

OneVariableInput(Labor)5.3ProductionFunctionintheLongRunProductionwithTwoVariableInputsThereisarelationshipbetweenproductionandproductivity.Long-runproductionK&Larevariable.IsoquantsanalyzeandcomparethedifferentcombinationsofK&LandoutputIsoquantsIsoquantsCurvesshowingallpossiblecombinationsofinputsthatyieldthesameoutputTheShapeofIsoquantsLaborperyear1234123455Inthelongrunbothlaborandcapitalarevariableandbothexperiencediminishingreturns.Q1=55Q2=75Q3=90CapitalperyearADBCEIsoquantsTheisoquantsemphasizehowdifferentinputcombinationscanbeusedtoproducethesameoutput.Thisinformationallowstheproducertorespondefficientlytochangesinthemarketsforinputs.ProductionwithTwoVariableInputs(L,K)Laborperyear1234123455Q1=55Theisoquantsarederivedfromtheproductionfunctionforoutputofof55,75,and90.ADBQ2=75Q3=90CECapitalperyearTheIsoquantMapMarginalRateof

TechnicalSubstitutionLaborpermonth1234123455CapitalperyearIsoquantsaredownwardslopingandconvexlikeindifferencecurves.1111212/31/3Q1=55Q2=75Q3=90SubstitutingAmongInputsManagerswanttodeterminewhatcombinationifinputstouse.Theymustdealwiththetrade-offbetweeninputs.Theslopeofeachisoquantgivesthetrade-offbetweentwoinputswhilekeepingoutputconstant.Productionwith

TwoVariableInputsSubstitutingAmongInputsThemarginalrateoftechnicalsubstitutionequals:Productionwith

TwoVariableInputsMRTSandMarginalProductivityIfoutputisconstantandlaborisincreased,then:Productionwith

TwoVariableInputsIsoquantsWhenInputsarePerfectlySubstitutableLaborpermonthCapitalpermonthQ1Q2Q3ABCObservationswheninputsareperfectlysubstitutable: 1) TheMRTSisconstantatallpointsontheisoquant. 2)Foragivenoutput,anycombinationofinputscanbechosen(A,B,orC)togeneratethesamelevelofoutputProductionwith

TwoVariableInputsPerfectSubstitutesFixed-Proportions

ProductionFunctionLaborpermonthCapitalpermonthL1K1Q1Q2Q3ABCObservationswheninputsmustbeinafixed-proportion: 1) Nosubstitutionispossible.Eachoutputrequiresaspecificamountofeachinput. 2) Toincreaseoutputrequiresmorelaborandcapital(i.e.movingfromA toBtoCwhichistechnicallyefficient).Fixed-ProportionsProductionFunctionProductionwith

TwoVariableInputsAProductionFunctionforWheatFarmersmustchoosebetweenacapitalintensiveorlaborintensivetechniqueofproduction.IsoquantDescribingthe

ProductionofWheatLabor(hoursperyear)Capital(machinehourperyear)2505007601000408012010090Output=13,800bushels peryearAB.PointAismorecapital-intensive,andBismorelabor-intensiveAssumptionsTwoInputs:Labor(L)&capital(K)Priceoflabor:wagerate(w)ThepriceofcapitalR=depreciationrate+interestrate5.4TheCostMinimizingInputChoiceTheIsocostLineTheIsocostLineC=wL+rKIsocost(Equal-CostLine):AlineshowingallcombinationsofL&KthatcanbepurchasedforthesamecostTheIsocostLineRewritingCaslinear:K=C/r-(w/r)LSlopeoftheisocost:istheratioofthewageratetorentalcostofcapital.Thisshowstherateatwhichcapitalcanbesubstitutedforlaborwithnochangeincost.ChoosingInputsWewilladdresshowtominimizecostforagivenlevelofoutput.WewilldosobycombiningisocostswithisoquantsProducingaGiven

OutputatMinimumCostLaborperyearCapitalperyearQ1C0C1C2AK1L1K3L3K2L2Q1isanisoquantforoutputQ1.IsocostcurveC0showsallcombinationsofKandLthatcanproduceQ1atthiscostlevel.IsocostC2showsquantityQ1canbeproducedwithcombinationK2L2orK3L3.However,bothofthesearehighercostcombinationsthanK1L1.COC1C2arethreeisocostlinesInputSubstitutionWhen

anInputPriceChangeC2K2L2BC1K1L1AQ1LaborperyearCapitalperyearIfthepriceoflaborchanges,theisocostcurveessteeperduetothechangeintheslope-(w/L).ThisyieldsanewcombinationofKandLtoproduceQ1.CombinationBisusedinplaceofcombinationA.Thenewcombinationrepresentsthehighercostoflaborrelativetocapitalandthereforecapitalissubstitutedforlabor.CostintheLongRunIsoquantsandIsocostsandtheProductionFunctionCostintheLongRunTheminimumcostcombinationcanthenbewrittenas:Minimumcostforagivenoutputwilloccurwheneachdollarofinputaddedtotheproductionprocesswilladdanequivalentamountofoutput.5.5ReturnstoScaleMeasuringtherelationshipbetweenthescale(size)ofafirmandoutput 1) Increasingreturnstoscale:output morethandoubleswhenallinputs aredoubledLargeroutputassociatedwithlowercost(autos)Onefirmismoreefficientthanmany(utilities)TheisoquantsgetclosertogetherReturnstoScaleLabor(hours)Capital(machinehours)102030IncreasingReturns:Theisoquantsmoveclosertogether510240AReturnstoScaleMeasuringtherelationshipbetweenthescale(size)ofafirmandoutput 2) Constantreturnstoscale:output doubleswhenallinputsaredoubledSizedoesnotaffectproductivityMayhavealargenumberofproducersIsoquantsareequidistantapartReturnstoScaleLabor(hours)Capital(machinehours)Constan