利润最大化范里安英文

ChapterNineteen,Profit-Maximization,EconomicProfit,Afirmusesinputsj=1,mtomakeproductsi=1,n.Outputlevelsarey1,yn.Inputlevelsarex1,xm.Productpricesarep1,pn.Inputpricesarew1,wm.,TheCompetitiveFirm,Thecompetitivefirmtakesalloutputpricesp1,pnandallinputpricesw1,wmasgivenconstants.,EconomicProfit,Theeconomicprofitgeneratedbytheproductionplan(x1,xm,y1,yn)is,EconomicProfit,Outputandinputlevelsaretypicallyflows.(流量）E.g.x1mightbethenumberoflaborunitsusedperhour.（每小时劳动投入量）Andy3mightbethenumberofcarsproducedperhour.（每小时产出量）Consequently,profitistypicallyaflowalso;e.g.thenumberofdollarsofprofitearnedperhour.,EconomicProfit,Howdowevalueafirm?如何为一个公司订价？SupposethefirmsstreamofperiodiceconomicprofitsisP0,P1,P2,andristherateofinterest.Thenthepresent-valueofthefirmseconomicprofitstreamis,EconomicProfit,Acompetitivefirmseekstomaximizeitspresent-value.一个竞争性企业为最大化利润流现值。How?,EconomicProfit,Supposethefirmisinashort-runcircumstanceinwhich（假定公司处于短期的生产环境）Itsshort-runproductionfunctionis,EconomicProfit,Supposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionisThefirmsfixedcostisanditsprofitfunctionis,Short-RunIso-ProfitLines短期等利润线,A$Piso-profitline（等利润线）containsalltheproductionplansthatprovideaprofitlevel$P.A$Piso-profitlinesequationis,Short-RunIso-ProfitLines,A$Piso-profitlinecontainsalltheproductionplansthatyieldaprofitlevelof$P.Theequationofa$Piso-profitlineisI.e.,Short-RunIso-ProfitLines短期等利润线,hasaslopeof,andaverticalinterceptof,Short-RunIso-ProfitLines,Increasingprofit,y,x1,Short-RunProfit-Maximization短期公司利润最大化,Thefirmsproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirmsconstraintonchoicesofproductionplans.（给定公司的生产计划约束，使生产计划尽可能地达到最高的等利润线上。）Q:Whatisthisconstraint?（生产计划约束？）,Short-RunProfit-Maximization,Thefirmsproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirmsconstraintonchoicesofproductionplans.（生产计划的选择约束）Q:Whatisthisconstraint?（技术约束）A:Theproductionfunction.（生产函数）,Short-RunProfit-Maximization,x1,Technicallyinefficientplans,y,Theshort-runproductionfunctionandtechnologysetfor,Short-RunProfit-Maximization,x1,Increasingprofit,y,Short-RunProfit-Maximization,x1,y,Short-RunProfit-Maximization,x1,y,Givenp,w1andtheshort-runprofit-maximizingplanis,Short-RunProfit-Maximization,x1,y,Givenp,w1andtheshort-runprofit-maximizingplanisAndthemaximumpossibleprofitis,Short-RunProfit-Maximization,x1,y,Attheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximaliso-profitlineareequal.,Short-RunProfit-Maximization,x1,y,Attheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximaliso-profitlineareequal.,Short-RunProfit-Maximization,isthemarginalrevenueproductofinput1,therateatwhichrevenueincreaseswiththeamountusedofinput1（要素1的边际产品收益）.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.,Short-RunProfit-Maximization;ACobb-DouglasExample,Supposetheshort-runproductionfunctionis,Themarginalproductofthevariableinput1is,Theprofit-maximizingconditionis,Short-RunProfit-Maximization;ACobb-DouglasExample,Solving,forx1gives,Short-RunProfit-Maximization;ACobb-DouglasExample,Solving,forx1gives,Thatis,Short-RunProfit-Maximization;ACobb-DouglasExample,Solving,forx1gives,Thatis,so,Short-RunProfit-Maximization;ACobb-DouglasExample,isthefirmsshort-rundemand,forinput1whenthelevelofinput2isfixedatunits.,Short-RunProfit-Maximization;ACobb-DouglasExample,isthefirmsshort-rundemand,forinput1whenthelevelofinput2isfixedatunits.,Thefirmsshort-runoutputlevelisthus,ComparativeStaticsofShort-RunProfit-Maximization,比较静态分析Whathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?,ComparativeStaticsofShort-RunProfit-Maximization,Theequationofashort-runiso-profitlineis,soanincreaseinpcauses-areductionintheslope,and-areductionintheverticalintercept.,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,Anincreaseinp,thepriceofthefirmsoutput,causesanincreaseinthefirmsoutputlevel(thefirmssupplycurveslopesupward),andanincreaseinthelevelofthefirmsvariableinput(thefirmsdemandcurveforitsvariableinputshiftsoutward).,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,anditsshort-runsupplyis,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,increasesaspincreases.,anditsshort-runsupplyis,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,increasesaspincreases.,anditsshort-runsupplyis,increasesaspincreases.,ComparativeStaticsofShort-RunProfit-Maximization,Whathappenstotheshort-runprofit-maximizingproductionplanasthevariableinputpricew1changes?,ComparativeStaticsofShort-RunProfit-Maximization,Theequationofashort-runiso-profitlineis,soanincreaseinw1causes-anincreaseintheslope,and-nochangetotheverticalintercept.,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,x1,y,ComparativeStaticsofShort-RunProfit-Maximization,Anincreaseinw1,thepriceofthefirmsvariableinput,causesadecreaseinthefirmsoutputlevel(thefirmssupplycurveshiftsinward),andadecreaseinthelevelofthefirmsvariableinput(thefirmsdemandcurveforitsvariableinputslopesdownward).,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,anditsshort-runsupplyis,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,decreasesasw1increases.,anditsshort-runsupplyis,ComparativeStaticsofShort-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,decreasesasw1increases.,decreasesasw1increases.,anditsshort-runsupplyis,Long-RunProfit-Maximization长期利润最大化,Nowallowthefirmtovarybothinputlevels.Sincenoinputlevelisfixed,therearenofixedcosts.,Long-RunProfit-Maximization,Bothx1andx2arevariable.Thinkofthefirmaschoosingtheproductionplanthatmaximizesprofitsforagivenvalueofx2,andthenvaryingx2tofindthelargestpossibleprofitlevel.,Long-RunProfit-Maximization,Theequationofalong-runiso-profitlineis,soanincreaseinx2causes-nochangetotheslope,and-anincreaseintheverticalintercept.,Long-RunProfit-Maximization,x1,y,Long-RunProfit-Maximization,x1,y,Largerlevelsofinput2increasetheproductivityofinput1.,Long-RunProfit-Maximization,x1,y,Largerlevelsofinput2increasetheproductivityofinput1.,Themarginalproductofinput2isdiminishing.,Long-RunProfit-Maximization,x1,y,Largerlevelsofinput2increasetheproductivityofinput1.,Themarginalproductofinput2isdiminishing.,Long-RunProfit-Maximization,x1,y,foreachshort-runproductionplan.,Long-RunProfit-Maximization,x1,y,Themarginalproductofinput2isdiminishingso.,foreachshort-runproductionplan.,Long-RunProfit-Maximization,x1,y,themarginalprofitofinput2isdiminishing.,foreachshort-runproductionplan.,Long-RunProfit-Maximization,Profitwillincreaseasx2increasessolongasthemarginalprofitofinput2Theprofit-maximizinglevelofinput2thereforesatisfies,Long-RunProfit-Maximization,Profitwillincreaseasx2increasessolongasthemarginalprofitofinput2Theprofit-maximizinglevelofinput2thereforesatisfiesAndissatisfiedinanyshort-run,so.,Long-RunProfit-Maximization,Theinputlevelsofthelong-runprofit-maximizingplansatisfyThatis,marginalrevenueequalsmarginalcostforallinputs.,and,Long-RunProfit-Maximization,TheCobb-Douglasexample:When,thenthefirmsshort-rundemandforitsvariableinput1is,anditsshort-runsupplyis,Short-runprofitistherefore,Long-RunProfit-Maximization,Long-RunProfit-Maximization,Long-RunProfit-Maximization,Long-RunProfit-Maximization,Long-RunProfit-Maximization,Whatisthelong-runprofit-maximizinglevelofinput2?Solve,toget,Long-RunProfit-Maximization,Whatisthelong-runprofit-maximizinginput1level?Substitute,into,toget,Long-RunProfit-Maximization,Whatisthelong-runprofit-maximizinginput1level?Substitute,into,toget,Long-RunProfit-Maximization,Whatisthelong-runprofit-maximizingoutputlevel?Substitute,into,toget,Long-RunProfit-Maximization,Whatisthelong-runprofit-maximizingoutputlevel?Substitute,into,toget,Long-RunProfit-Maximization,Sogiventhepricesp,w1andw2,andtheproductionfunction,thelong-runprofit-maximizingproductionplanis,Returns-to-ScaleandProfit-Maximization,Ifacompetitivefirmstechnologyexhibitsdecreasingreturns-to-scalethenthefirmhasasinglelong-runprofit-maximizingproductionplan.（该竞争性企业若存在规模报酬递减的技术，则会存在唯一一个长期利润最大化的产出计划）,Returns-toScaleandProfit-Maximization,x,y,y*,x*,Decreasingreturns-to-scale,Returns-to-ScaleandProfit-Maximization,Ifacompetitivefirmstechnologyexhibitsexhibitsincreasingreturns-to-scalethenthefirmdoesnothaveaprofit-maximizingplan.,Returns-toScaleandProfit-Maximization,x,y,y”,x,Increasingreturns-to-scale,y,x”,Increasingprofit,Returns-to-ScaleandProfit-Maximization,Soanincreasingreturns-to-scaletechnologyisinconsistentwithfirmsbeingperfectlycompetitive.（因此，规模报酬递增的技术假设与竞争性企业假定是矛盾的）,Returns-to-ScaleandProfit-Maximization,Whatifthecompetitivefirmstechnologyexhibitsconstantreturns-to-scale?,Returns-toScaleandProfit-Maximization,x,y,y”,x,Constantreturns-to-scale,y,x”,Increasingprofit,Returns-toScaleandProfit-Maximization,Soifanyproductionplanearnsapositiveprofit,thefirmcandoubleupallinputstoproducetwicetheoriginaloutputandearntwicetheoriginalprofit.,Returns-toScaleandProfit-Maximization,Therefore,whenafirmstechnologyexhibitsconstantreturns-to-scale,earningapositiveeconomicprofitisinconsistentwithfirmsbeingperfectlycompetitive.Henceconstantreturns-to-scalerequiresthatcompetitivefirmsearneconomicprofitsofzero.,Returns-toScaleandProfit-Maximization,x,y,y”,x,Constantreturns-to-scale,y,x”,P=0,RevealedProfitability显示利润,Consideracompetitivefirmwithatechnologythatexhibitsdecreasingreturns-to-scale.Foravarietyofoutputandinputpricesweobservethefirmschoicesofproductionplans.Whatcanwelearnfromourobservations?,RevealedProfitability,Ifaproductionplan(x,y)ischosenatprices(w,p)wededucethattheplan(x,y)isrevealedtobeprofit-maximizingfortheprices(w,p).,RevealedProfitability,x,y,ischosenatprices,RevealedProfitability,x,y,ischosenatpricessoisprofit-maximizingattheseprices.,RevealedProfitability,x,y,ischosenatpricessoisprofit-maximizingattheseprices.,wouldgivehigherprofits,sowhyisitnotchosen?,RevealedProfitability,x,y,ischosenatpricessoisprofit-maximizingattheseprices.,wouldgivehigherprofits,sowhyisitnotchosen?Becauseitisnotafeasibleplan.,RevealedProfitability,x,y,ischosenatpricessoisprofit-maximizingattheseprices.,wouldgivehigherprofits,sowhyisitnotchosen?Becauseitisnotafeasibleplan.,Sothefirmstechnologysetmustlieundertheiso-profitline.,RevealedProfitability,x,y,ischosenatpricessoisprofit-maximizingattheseprices.,Sothefirmstechnologysetmustlieundertheiso-profitline.,Thetechnologysetissomewhereinhere,RevealedProfitability,x,y,ischosenatpricessomaximizesprofitattheseprices.,wouldprovidehigherprofitbutitisnotchosen,RevealedProfitability,x,y,ischosenatpricessomaximizesprofitattheseprices.,wouldprovidehigherprofitbutitisnotchosenbecauseitisnotfeasible,RevealedProfitability,x,y,ischosenatpricessomaximizesprofitattheseprices.,wouldprovidehigherprofitbutitisnotchosenbecauseitisnotfeasiblesothetechnologysetliesundertheiso-profitline.,RevealedProfitability,x,y,ischosenatpricessomaximizesprofitattheseprices.,Thetechnologysetisalsosomewhereinhere.,RevealedProfitability,x,y,Thefirmstechnologysetmustlieunderbothiso-profitlines,RevealedProfitability,x,y,Thefir