尼克尔森微观经济学课件中文版ch08

Chapter8第八章COSTFUNCTIONS成本函数1Copyright©2005bySouth-western,adivisionofThomsonlearning.Allrightsreserved.EconomicCost经济成本•Theeconomiccostofanyinputisthepaymentrequiredtokeepthatinputinitspresentemployment任何投入的经济成本是保持该投入处于现行使用状态所需支付的费用–theremunerationtheinputwouldreceiveinitsbestalternativeemployment该投入用于其他用途所能获得的最大报酬•注意与会计成本的区别–区别主要在资本成本、企业家才能的成本方面–在劳动力成本方面很一致2TwoSimplifyingAssumptions两个简化假设•Thereareonlytwoinputs仅有两种要素投入–homogeneouslabor(l),measuredinlabor-hours同质的劳动(l)，以劳动小时衡量–homogeneouscapital(k),measuredinmachine-hours同质的资本(k)，以机器小时衡量•entrepreneurialcostsareincludedincapitalcosts企业家的成本包括在资本成本内•Inputsarehiredinperfectlycompetitivemarkets投入来源于完全竞争市场–firmsarepricetakersininputmarkets厂商在投入市场上，为价格接受者3EconomicProfits经济利润•Totalcostsforthefirmaregivenby厂商的总成本为totalcosts=C=wl+vk•Totalrevenueforthefirmisgivenby厂商的总收入为totalrevenue=pq=pf(k,l)•Economicprofits()areequalto经济利润()为=totalrevenue-totalcost=pq-wl–vk=pf(k,l)-wl–vk4EconomicProfits经济利润•Economicprofitsareafunctionoftheamountofcapitalandlaboremployed经济利润是所使用的资本和劳动量的函数–wecouldexaminehowafirmwouldchoosekandltomaximizeprofit可以检验厂商如何选择k和l来最大化其利润•“deriveddemand”theoryoflaborandcapitalinputs劳动和资本投入的“引致需求”理论–fornow,wewillassumethatthefirmhasalreadychosenitsoutputlevel(q0)andwantstominimizeitscosts现在假定厂商已经选定其产出水平(q0)，并且想最小化其成本5Cost-MinimizingInputChoices成本最小化投入选择•Tominimizethecostofproducingagivenlevelofoutput,afirmshouldchooseapointontheisoquantatwhichtheRTSisequaltotheratiow/v在给定产出水平下，为了最小化其成本，厂商需要选择等产量线上的一点，在该点RTS等于比值w/v–itshouldequatetherateatwhichkcanbetradedforlintheproductiveprocesstotherateatwhichtheycanbetradedinthemarketplacek和l在生产过程的替代比率应该与它们在市场中交易价格的比值相等6Cost-MinimizingInputChoices成本最小化投入选择•Mathematically,weseektominimizetotalcostsgivenq=f(k,l)=q0数学上，我们在q=f(k,l)=q0的条件下最小化成本•SettinguptheLagrangian建立拉格朗日函数L=wl+vk+[q0-f(k,l)]•Firstorderconditionsare一阶条件为L/l=w-(f/l)=0L/k=v-(f/k)=0L/=q0-f(k,l)=07Cost-MinimizingInputChoices成本最小化投入选择•Dividingthefirsttwoconditionsweget前两个一阶条件相除，得到8)for(//kRTSkffvwll•Thecost-minimizingfirmshouldequatetheRTSforthetwoinputstotheratiooftheirprices成本最小化的厂商会使得两种投入的RTS与其价格比值相等Cost-MinimizingInputChoices成本最小化投入选择•Cross-multiplying,weget交叉相乘，我们得到9wfvfkl•Forcoststobeminimized,themarginalproductivityperdollarspentshouldbethesameforallinputs为了成本最小化，每美元的边际生产力对于所有投入应该是相同的Cost-MinimizingInputChoices成本最小化投入选择•Notethatthisequation’sinverseisalsoofinterest注意这一等式的倒数也是有意义的10kfvfwl•TheLagrangianmultipliershowshowmuchinextracostswouldbeincurredbyincreasingtheoutputconstraintslightly拉格朗日乘子表示如果稍微增加产出约束时，会产生的额外成本Cost-MinimizingInputChoices成本最小化投入选择11q0Givenoutputq0,wewishtofindtheleastcostlypointontheisoquant给定产出q0，我们希望在等产量线上，找到成本最少的点C1C2C3Costsarerepresentedbyparallellineswithaslopeof-w/v成本由斜率为-w/v的平行线表示lperperiodkperperiodC1C2C3Cost-MinimizingInputChoices成本最小化投入选择12C1C2C3q0Theminimumcostofproducingq0isC2生产q0的最小成本为C2lperperiodkperperiodk*l*Theoptimalchoiceisl*,k*最优选择为l*,k*Thisoccursatthetangencybetweentheisoquantandthetotalcostcurve在等产量线和总成本曲线的切点处取得ContingentDemandforInputs条件要素需求•InChapter4,weconsideredanindividual’sexpenditure-minimizationproblem在第四章中，我们考虑了个人支出最小化问题–weusedthistechniquetodevelopthecompensateddemandforagood我们使用这一方法提出商品的补偿需求•Canwedevelopafirm’sdemandforaninputinthesameway?我们可以用同样的方法提出厂商对一种投入的需求吗？•Inthepresentcase,costminimizationleadstoademandforcapitalandlaborthatiscontingentonthelevelofoutputbeingproduced在当前情况下，成本最小化所引起的资本和劳动的需求是视生产的产出水平而定的13TheFirm’sExpansionPath厂商的扩展线•Thefirmcandeterminethecost-minimizingcombinationsofkandlforeverylevelofoutput厂商可以对任意产出水平，决定成本最小的k和l的组合•Ifinputcosts（w，v)remainconstantforallamountsthefirmmaydemand,wecantracethelocusofcost-minimizingchoices如果厂商在任何产量下都有唯一确定的成本组合（w，v)，那么我们可以找到成本最小化选择的轨迹–calledthefirm’sexpansionpath叫做厂商的扩展线14TheFirm’sExpansionPath厂商的扩展线15lperperiodkperperiodq00Theexpansionpathisthelocusofcost-minimizingtangencies扩展线是成本最小化切点的轨迹q0q1EThecurveshowshowinputsincreaseasoutputincreases曲线显示了随着产出增加，投入如何增加TheFirm’sExpansionPath厂商的扩展线•Theexpansionpathdoesnothavetobeastraightline扩展线并不一定是直线–theuseofsomeinputsmayincreasefasterthanothersasoutputexpands随着产出扩张，某些投入的使用可能会比其他投入增加快•dependsontheshapeoftheisoquants取决于等产量线的形状•Theexpansionpathdoesnothavetobeupwardsloping扩展线并不一定是向上倾斜的–iftheuseofaninputfallsasoutputexpands,thatinputisaninferiorinput如果随着产出扩张某种投入的使用减少，该投入为劣等投入要素16CostMinimization成本最小化•SupposethattheproductionfunctionisCobb-Douglas假设生产函数为柯布道格拉斯q=kl•TheLagrangianexpressionforcostminimizationofproducingq0is生产q0的成本最小化的拉格朗日表示为L=vk+wl+(q0-kl)17CostMinimization成本最小化•Thefirst-orderconditionsforaminimumare最小值的一阶条件为L/k=v-k-1l=0L/l=w-kl-1=0L/=q0-kl=018CostMinimization成本最小化•Dividingthefirstequationbythesecondgivesus第二个等式除以第一个等式，得到19RTSkkkvwlll11•Thisproductionfunctionishomothetic生产函数是齐次的–theRTSdependsonlyontheratioofthetwoinputsRTS仅取决于两种投入的比值–theexpansionpathisastraightline扩展线为一条直线CostMinimization成本最小化•SupposethattheproductionfunctionisCES假设生产函数为CES：q=(k+l)/•TheLagrangianexpressionforcostminimizationofproducingq0is生产q0的成本最小化的拉格朗日表示为L=vk+wl+[q0-(k