PROFITMAXIMIZATION(利润最大化)尼科尔森中级微观

1,Chapter9,PROFITMAXIMIZATION,Copyright2005bySouth-Western,adivisionofThomsonLearning.Allrightsreserved.,2,TheNatureofFirms,AfirmisanassociationofindividualswhohaveorganizedthemselvesforthepurposeofturninginputsintooutputsDifferentindividualswillprovidedifferenttypesofinputsthenatureofthecontractualrelationshipbetweentheprovidersofinputstoafirmmaybequitecomplicated,3,ContractualRelationships,Somecontractsbetweenprovidersofinputsmaybeexplicitmayspecifyhours,workdetails,orcompensationOtherarrangementswillbemoreimplicitinnaturedecision-makingauthorityorsharingoftasks,4,ModelingFirmsBehavior,Mosteconomiststreatthefirmasasingledecision-makingunitthedecisionsaremadebyasingledictatorialmanagerwhorationallypursuessomegoalusuallyprofit-maximization,5,ProfitMaximization,Aprofit-maximizingfirmchoosesbothitsinputsanditsoutputswiththesolegoalofachievingmaximumeconomicprofitsseekstomaximizethedifferencebetweentotalrevenueandtotaleconomiccosts,6,ProfitMaximization,Iffirmsarestrictlyprofitmaximizers,theywillmakedecisionsina“marginal”wayexaminethemarginalprofitobtainablefromproducingonemoreunitofhiringoneadditionallaborer,7,OutputChoice,TotalrevenueforafirmisgivenbyR(q)=p(q)qIntheproductionofq,certaineconomiccostsareincurredC(q)Economicprofits()arethedifferencebetweentotalrevenueandtotalcosts(q)=R(q)C(q)=p(q)qC(q),8,OutputChoice,Thenecessaryconditionforchoosingthelevelofqthatmaximizesprofitscanbefoundbysettingthederivativeofthefunctionwithrespecttoqequaltozero,9,OutputChoice,Tomaximizeeconomicprofits,thefirmshouldchoosetheoutputforwhichmarginalrevenueisequaltomarginalcost,10,Second-OrderConditions,MR=MCisonlyanecessaryconditionforprofitmaximizationForsufficiency,itisalsorequiredthat,“marginal”profitmustbedecreasingattheoptimallevelofq,11,ProfitMaximization,output,revenues&costs,R,C,12,MarginalRevenue,Ifafirmcansellallitwisheswithouthavinganyeffectonmarketprice,marginalrevenuewillbeequaltopriceIfafirmfacesadownward-slopingdemandcurve,moreoutputcanonlybesoldifthefirmreducesthegoodsprice,13,MarginalRevenue,Ifafirmfacesadownward-slopingdemandcurve,marginalrevenuewillbeafunctionofoutputIfpricefallsasafirmincreasesoutput,marginalrevenuewillbelessthanprice,14,MarginalRevenue,Supposethatthedemandcurveforasubsandwichisq=10010pSolvingforprice,wegetp=-q/10+10ThismeansthattotalrevenueisR=pq=-q2/10+10qMarginalrevenuewillbegivenbyMR=dR/dq=-q/5+10,15,ProfitMaximization,Todeterminetheprofit-maximizingoutput,wemustknowthefirmscostsIfsubscanbeproducedataconstantaverageandmarginalcostof$4,thenMR=MC-q/5+10=4q=30,16,MarginalRevenueandElasticity,TheconceptofmarginalrevenueisdirectlyrelatedtotheelasticityofthedemandcurvefacingthefirmThepriceelasticityofdemandisequaltothepercentagechangeinquantitythatresultsfromaonepercentchangeinprice,17,MarginalRevenueandElasticity,Thismeansthat,ifthedemandcurveslopesdownward,eq,p0andMRpifthedemandiselastic,eq,p-1,MC0,Asoutputincreasesbeyondq1,totalrevenuedecreasessoMR0,24,MarginalRevenueCurve,Whenthedemandcurveshifts,itsassociatedmarginalrevenuecurveshiftsaswellamarginalrevenuecurvecannotbecalculatedwithoutreferringtoaspecificdemandcurve,25,TheConstantElasticityCase,Weshowed(inChapter5)thatademandfunctionoftheformq=apbhasaconstantpriceelasticityofdemandequaltobSolvingthisequationforp,wegetp=(1/a)1/bq1/b=kq1/bwherek=(1/a)1/b,26,TheConstantElasticityCase,ThismeansthatR=pq=kq(1+b)/bandMR=dr/dq=(1+b)/bkq1/b=(1+b)/bpThisimpliesthatMRisproportionaltoprice,27,Short-RunSupplybyaPrice-TakingFirm,output,price,SMC,SAC,SAVC,28,Short-RunSupplybyaPrice-TakingFirm,output,price,SMC,SAC,SAVC,p*=MR,q*,29,Short-RunSupplybyaPrice-TakingFirm,output,price,SMC,SAC,SAVC,p*=MR,q*,30,Short-RunSupplybyaPrice-TakingFirm,output,price,SMC,SAC,SAVC,p*=MR,q*,Profitmaximizationrequiresthatp=SMCandthatSMCisupward-sloping,0,31,Short-RunSupplybyaPrice-TakingFirm,Thepositively-slopedportionoftheshort-runmarginalcostcurveistheshort-runsupplycurveforaprice-takingfirmitshowshowmuchthefirmwillproduceateverypossiblemarketpricefirmswillonlyoperateintheshortrunaslongastotalrevenuecoversvariablecostthefirmwillproducenooutputifpSAVC,32,Short-RunSupplybyaPrice-TakingFirm,Thus,theprice-takingfirmsshort-runsupplycurveisthepositively-slopedportionofthefirmsshort-runmarginalcostcurveabovethepointofminimumaveragevariablecostforpricesbelowthislevel,thefirmsprofit-maximizingdecisionistoshutdownandproducenooutput,33,Short-RunSupplybyaPrice-TakingFirm,output,price,SMC,SAC,SAVC,34,Short-RunSupply,Supposethatthefirmsshort-runtotalcostcurveisSC(v,w,q,k)=vk1+wq1/k1-/wherek1isthelevelofcapitalheldconstantintheshortrunShort-runmarginalcostis,35,Short-RunSupply,Theprice-takingfirmwillmaximizeprofitwherep=SMC,Therefore,quantitysuppliedwillbe,36,Short-RunSupply,Tofindthefirmsshut-downprice,weneedtosolveforSAVCSVC=wq1/k1-/SAVC=SVC/q=wq(1-)/k1-/SAVCSMCforallvaluesofp1(p2,)(p1,)Thewelfaregaintothefirmofthispriceincreasecanbemeasuredbywelfaregain=(p2,)-(p1,),45,ProducerSurplusintheShortRun,output,price,SMC,46,ProducerSurplusintheShortRun,output,price,SMC,p1,q1,p2,q2,47,ProducerSurplusintheShortRun,Mathematically,wecanusetheenvelopetheoremresults,48,ProducerSurplusintheShortRun,Wecanmeasurehowmuchthefirmvaluestherighttoproduceattheprevailingpricerelativetoasituationwhereitwouldproducenooutput,49,ProducerSurplusintheShortRun,output,price,SMC,p1,q1,50,ProducerSurplusintheShortRun,Theextraprofitsavailablefromfacingapriceofp1aredefinedtobeproducersurplus,51,ProducerSurplusintheShortRun,output,price,SMC,p1,q1,p0,52,ProducerSurplusintheShortRun,Producersurplusistheextrareturnthatproducersmakebymakingtransactionsatthemarketpriceoverandabovewhattheywouldearnifnothingwasproducedtheareabelowthemarketpriceandabovethesupplycurve,53,ProducerSurplusintheShortRun,Becausethefirmproducesnooutputattheshutdownprice,(p0,)=-vk1profitsattheshutdownpriceareequaltothefirmsfixedcostsThisimpliesthatproducersurplus=(p1,)-(p0,)=(p1,)(-vk1)=(p1,)+vk1producersurplusisequaltocurrentprofitsplusshort-runfixedcosts,54,ProfitMaximizationandInputDemand,AfirmsoutputisdeterminedbytheamountofinputsitchoosestoemploytherelationshipbetweeninputsandoutputsissummarizedbytheproductionfunctionAfirmseconomicprofitcanalsobeexpressedasafunctionofinputs(k,l)=pqC(q)=pf(k,l)(vk+wl),55,ProfitMaximizationandInputDemand,Thefirst-orderconditionsforamaximumare/k=pf/kv=0/l=pf/lw=0Aprofit-maximizingfirmshouldhireanyinputuptothepointatwhichitsmarginalcontributiontorevenuesisequaltothemarginalcostofhiringtheinput,56,ProfitMaximizationandInputDemand,Thesefirst-orderconditionsforprofitmaximizationalsoimplycostminimizationtheyimplythatRTS=w/v,57,ProfitMaximizationandInputDemand,Toensureatruemaximum,second-orderconditionsrequirethatkk=fkk0capitalandlabormustexhibitsufficientlydiminishingmarginalproductivitiessothatmarginalcostsriseasoutputexpands,58,InputDemandFunctions,Inprinciple,thefirst-orderconditionscanbesolvedtoyieldinputdemandfunctionsCapitalDemand=k(p,v,w)LaborDemand=l(p,v,w)Thesedemandfunctionsareunconditionaltheyimplicitlyallowthefirmtoadjustitsoutputtochangingprices,59,Single-InputCase,Weexpectl/w0diminishingmarginalproductivityoflaborThefirstorderconditionforprofitmaximizationwas/l=pf/lw=0Takingthetotaldifferential,weget,60,Single-InputCase,Thisreducesto,Solvingfurther,weget,Sincefll0,l/w0,61,Two-InputCase,Forthecaseoftwo(ormoreinputs),thestoryismorecomplexifthereisadecreaseinw,therewillnotonlybeachangeinlbutalsoachangeinkasanewcost-minimizingcombinationofinputsischosenwhenkchanges,theentireflfunctionchangesBut,eveninthiscase,l/w0,62,Two-InputCase,Whenwfalls,twoeffectsoccursubstitutioneffectifoutputisheldconstant,therewillbeatendencyforthefirmtowanttosubstitutelforkintheproductionprocessoutputeffectachangeinwwillshiftthefirmsexpansionpaththefirmscostcurveswillshiftandadifferentoutputlevelwillbechosen,63,SubstitutionEffect,q0,lperperiod,kperperiod,BecauseofdiminishingRTSalonganisoquant,thesubstitutioneffectwillalwaysbenegative,64,OutputEffect,Output,Price,65,OutputEffect,q0,lperperiod,kperperiod,Thus,theoutputeffectalsoimpliesanegativerelationshipbetweenlandw,66,Cross-PriceEffects,Nodefinitestatementcanbemadeabouthowcapitalusagerespondstoawagechangeafallinthewagewillleadthefirmtosubstituteawayfromcapitaltheoutputeffectwillcausemorecapitaltobedemandedasthefirmexpandsproduction,67,SubstitutionandOutputEffects,Wehavetwoconceptsofdemandforanyinputtheconditionaldemandforlabor,lc(v,w,q)theunconditionaldemandforlabor,l(p,v,w)Attheprofit-maximizinglevelofoutputlc(v,w,q)=l(p,v,w),68,SubstitutionandOutputEffects,Differentiationwithrespecttowyields,69,ImportantPointstoNote:,Inordertomaximizeprofits,thefirmshouldchoosetoproducethatoutputlevelforwhichthemarginalrevenueisequaltothemarginalcost,70,ImportantPointstoNote:,Ifafirmisapricetaker,itsoutputdecisionsdonotaffectthepriceofitsoutputmarginalrevenueisequaltopriceIfthefirmfacesadownward-slopingdemandforitsoutput,marginalrevenuewillbelessthanprice,71,ImportantPointstoNote:,Marginalrevenueandthepriceelasticityofdemandarerelatedbytheformula,72,ImportantPointstoNote:,Thesupplycurveforaprice-taking,profit-maximizingfirmisgivenbythepositivelyslopedportionofitsmarginalcostcurveabovethepointofminimumaveragevariablecost(AVC)ifpricefallsbelowminimumAVC,thefirmsprofit-maximizingchoic