课件大纲中级微观济学1101

北京大学国北京大学国家发展研究院2011年秋季学本科双学位课中级微观经济学(2第十四讲：成本曲TypesTypesofcostFixed,variableandtotalcostAveragefixed,averagevariableandaveragecostfunctionsMarginalcostMarginalandvariablecostMarginalandaveragecostShortrunandlongruncost2TypesofCostAtotalTypesofCostAtotalcostcurve总成本曲线isthegraphofafirm’stotalcostfunction.Avariablecostcurve可变成本曲线isthegraphofafirm’svariablecostfunction.Anaveragetotalcostcurve平均成本曲线isthegraphofafirm’saveragetotalcostfunction.Anaveragevariablecostcurve平均可变成本曲线isthegraphofafirm’saveragevariablecostfunction.Anaveragefixedcostcurve平均固定成本曲线isthegraphofafirm’saveragefixedcostfunction.Amarginalcostcurve边际成本曲线isthegraphofafirm’smarginalcostfunction.3TypesofTypesofCostHowarethesecostcurvesrelatedtoeachother?Howareafirm’slong-runandshort-runcostcurvesrelated?4Fixed,VariableFixed,Variable&TotalCostFisthetotalcostofshort-runfixedinputs固定投入fixedcostdoesnotvarywiththefirm’soutputlevel.cv(y)isthetotalofvariableinputs可变投whenproducingyoutputunits.cv(y)isthefirm’svariablecostfunctioncv(y)dependsuponthelevelsofthefixedinputs.5Fixed,Variable&Fixed,Variable&Totalc(y)isthetotalcostofallinputs,fixedandvariable,whenproducingyoutputunits.costfunction;c(y)isthefirm’sc(y)=F+cv(6$c(y)$c(y)=F+cv(y)FFy7Av.Fixed,Av.Variable&Av.Fixed,Av.Variable&TotalCostThefirm’stotalcostfunctionc(y)=F+cv(y).Fory>0,thefirm’saveragecostfunctionAC(y)=F+cv(yy=AFC(y)+AVC(8$/outputAFC(y)0$/outputAFC(y)0asy¥0y9Av.Fixed,Av.Fixed,Av.Variable&TotalCostInashort-runwithafixedamountofatleastoneinput,theLawofDiminishing(Marginal)Returnsmustapply,causingthefirm’saveragevariablecostofproductiontoincreaseeventually.$/output0$/output0y$/outputAFC(y)=ATC(y)$/outputAFC(y)=ATC(y)-0ySinceAFC(y)0asy¥SinceAFC(y)0asy¥,¥.$/outputATC(y)AVC(y)asyAndsinceshort-runAVC(y)musteventuallyincrease,ATC(y)musteventuallyincreaseinashort-0yMarginalCostMarginalcostisMarginalCostMarginalcostistherate-of-changeofvariableproductioncostastheoutputlevelThatMC(y)=¶cv(y)¶MarginalCostThefirm’stotalcostMarginalCostThefirm’stotalcostfunctionc(y)=F+cv(y)andthefixedcostFdoesnotwiththeoutputlevely,MC(y)=¶cv(y)=¶c(y)¶¶MCistheslopeofboththevariablecostandthetotalcostfunctions.MarginalandVariableSinceMC(y)MarginalandVariableSinceMC(y)isthederivativeofcv(y),cv(y)mustbetheintegralofMC(y).MC(y)=¶cv(That¶ycv(y)=MC(0MarginalandVariabley$/outputcMarginalandVariabley$/outputcv(y)MC(0Areaisthevariablecostofmakingy’units0yMarginal&AverageCostAVC(y)=cv(y)y¶AVC(y)=Marginal&AverageCostAVC(y)=cv(y)y¶AVC(y)=y·MC(y)-1·cv(y)¶>y·MC(y)=cv(<¶AVC(y)=<¶¶AVC(y)>cv(=<asMC(y)¶y<$/outputMC(y)$/outputMC(y)<AVC(y)¶AVC(y)<¶y$/outputMC(y)$/outputMC(y)>AVC(y)¶AVC(y)>¶y$/outputMC(y)=$/outputMC(y)=AVC(y)¶AVC(y)=¶Theshort-runMCcurveintersectstheshort-runAVCcurvefrombelowattheAVCcurve’syMarginal&AverageCostATC(y)=c(y)Similarly,y¶ATC(y)=y·Marginal&AverageCostATC(y)=c(y)Similarly,y¶ATC(y)=y·MC(y)-1·c(y)y2¶>y·MC(y)=c(<¶ATC(y)=<¶¶ATC(y)>c(=MC(y)=ATC(¶y<<$/output>MC(y)=$/output>MC(y)=ATC(<¶ATC(y)=<¶yShort-Run&Long-RunCostShort-Run&Long-RunCostAfirmhasadifferentshort-runtotalcostcurveforeachpossibleshort-runcircumstance.Supposethefirmcanbeinoneofjustthreeshort-runs;==x2=x2$s(y;2$s(y;2)F¢=w2x2¢F¢=w2x2Alargeramountoftheinputincreasesthefirm’sfixedcost.Whyalargeramountofthefixedinputreducetheslopeofthefirm’stotalcostyF0$s(y;2)F¢=w$s(y;2)F¢=wx F¢=w2x2F¢=w2x2cs2F¢F0yShort-Run&Short-Run&Long-RunCostThefirmhasthreeshort-runtotalcostcurves.Inthelong-runthefirmisfreetochooseamongstthesethreesinceitisfreetoselectx2equaltoanyofx2,x2,orx2.Howdoesthefirmmakethis$For0£y£,choose$For0£y£,choosex2=s(y;2)Fory¢£y£y,choose=x2=c(y),theruntotalcostcurve.F¢F0yyShort-Run&Long-RunShort-Run&Long-RunCostThefirm’slong-runtotalcostcurveconsistsofthelowestpartsoftheshort-runtotalcostlong-runtotalcostcurveisthelowerenvelopeoftheshort-runtotalcostShort-Run&Short-Run&Long-RunCostIfinput2isavailableincontinuousamountsthenthereisaninfinityofshort-runtotalcostcurvesbutthelong-runtotalcostcurveisstillthelowerenvelopeofalloftheshort-runtotalcostcurves.$s(y;2)$s(y;2)F¢F0yShort-Run&Short-Run&Long-RunTotalCostForanyoutputlevely,thelong-runtotalcostcurvealwaysgivesthelowestpossibletotalproductioncost.Therefore,thelong-runav.totalcostcurvemustalwaysgivethelowestpossibleav.totalproductioncost.Thelong-runav.totalcostcurvemustbethelowerenvelopeofallofthefirm’sshort-runav.totalcostcurves.Short-Run&Long-RunTotalCostShort-Run&Long-RunTotalCostE.g.supposeagainthatthefirmcanbeinoneofjustthreeshort-runs;x2=x2=x2x2= thenthefirm’sthreeshort-runaveragetotalcostcurvesare...Short-Run&Short-Run&Long-RunTotalCostThefirm’slong-runaveragetotalcostcurveisthelowerenvelopeoftheshort-runaveragetotalcostcurves...$/output$/outputACs(y;x2)ACs(y;x2Thelong-runav.totalcostcurveistheloweroftheshort-runav.totalcostyShort-Run&Long-RunShort-Run&Long-RunCostQ:Isthelong-runmarginalcostcurvethelowerenvelopeofthefirm’sshort-runmarginalcostThefirm’sthreeshort-runaveragetotalcostcurvesare...$/outputs(y;2)$/outputs(y;2)MCs(y;x2Cs(y;2)ACs(y;x2y$/outputs(y;2)MC$/outputs(y;2)MCs(y;x2Cs(y;2)ACs(y;x2y$/outputs(y;2$/outputs(y;2)MCs(y;x2Cs(y;2)ACs(y;x2MC(y),thelong-runmarginalcostcurve.yShort-Run&Short-Run&Long-RunCostlong-runmarginalcostisthemarginalcostfortheshort-runchosenb