PROFITMAXIMIZATION(利润最大化)尼科尔森中级微观

1Chapter9PROFITMAXIMIZATIONCopyright©2005bySouth-Western,adivisionofThomsonLearning.Allrightsreserved.2TheNatureofFirms•Afirmisanassociationofindividualswhohaveorganizedthemselvesforthepurposeofturninginputsintooutputs•Differentindividualswillprovidedifferenttypesofinputs–thenatureofthecontractualrelationshipbetweentheprovidersofinputstoafirmmaybequitecomplicated3ContractualRelationships•Somecontractsbetweenprovidersofinputsmaybeexplicit–mayspecifyhours,workdetails,orcompensation•Otherarrangementswillbemoreimplicitinnature–decision-makingauthorityorsharingoftasks4ModelingFirms’Behavior•Mosteconomiststreatthefirmasasingledecision-makingunit–thedecisionsaremadebyasingledictatorialmanagerwhorationallypursuessomegoal•usuallyprofit-maximization5ProfitMaximization•Aprofit-maximizingfirmchoosesbothitsinputsanditsoutputswiththesolegoalofachievingmaximumeconomicprofits–seekstomaximizethedifferencebetweentotalrevenueandtotaleconomiccosts6ProfitMaximization•Iffirmsarestrictlyprofitmaximizers,theywillmakedecisionsina“marginal”way–examinethemarginalprofitobtainablefromproducingonemoreunitofhiringoneadditionallaborer7OutputChoice•TotalrevenueforafirmisgivenbyR(q)=p(q)q•Intheproductionofq,certaineconomiccostsareincurred[C(q)]•Economicprofits()arethedifferencebetweentotalrevenueandtotalcosts(q)=R(q)–C(q)=p(q)q–C(q)8OutputChoice•Thenecessaryconditionforchoosingthelevelofqthatmaximizesprofitscanbefoundbysettingthederivativeofthefunctionwithrespecttoqequaltozero0)('dqdCdqdRqdqddqdCdqdR9OutputChoice•Tomaximizeeconomicprofits,thefirmshouldchoosetheoutputforwhichmarginalrevenueisequaltomarginalcostMCdqdCdqdRMR10Second-OrderConditions•MR=MCisonlyanecessaryconditionforprofitmaximization•Forsufficiency,itisalsorequiredthat0)('**22qqqqdqqddqd•“marginal”profitmustbedecreasingattheoptimallevelofq11ProfitMaximizationoutputrevenues&costsRCq*ProfitsaremaximizedwhentheslopeoftherevenuefunctionisequaltotheslopeofthecostfunctionThesecond-orderconditionpreventsusfrommistakingq0asamaximumq012MarginalRevenue•Ifafirmcansellallitwisheswithouthavinganyeffectonmarketprice,marginalrevenuewillbeequaltoprice•Ifafirmfacesadownward-slopingdemandcurve,moreoutputcanonlybesoldifthefirmreducesthegood’spricedqdpqpdqqqpddqdRqMR])([)(revenuemarginal13MarginalRevenue•Ifafirmfacesadownward-slopingdemandcurve,marginalrevenuewillbeafunctionofoutput•Ifpricefallsasafirmincreasesoutput,marginalrevenuewillbelessthanprice14MarginalRevenue•Supposethatthedemandcurveforasubsandwichisq=100–10p•Solvingforprice,wegetp=-q/10+10•ThismeansthattotalrevenueisR=pq=-q2/10+10q•MarginalrevenuewillbegivenbyMR=dR/dq=-q/5+1015ProfitMaximization•Todeterminetheprofit-maximizingoutput,wemustknowthefirm’scosts•Ifsubscanbeproducedataconstantaverageandmarginalcostof$4,thenMR=MC-q/5+10=4q=3016MarginalRevenueandElasticity•Theconceptofmarginalrevenueisdirectlyrelatedtotheelasticityofthedemandcurvefacingthefirm•Thepriceelasticityofdemandisequaltothepercentagechangeinquantitythatresultsfromaonepercentchangeinpriceqpdpdqpdpqdqepq//,17MarginalRevenueandElasticity•ThismeansthatpqepdqdppqpdqdpqpMR,111–ifthedemandcurveslopesdownward,eq,p0andMRp–ifthedemandiselastic,eq,p-1andmarginalrevenuewillbepositive•ifthedemandisinfinitelyelastic,eq,p=-andmarginalrevenuewillequalprice18MarginalRevenueandElasticityeq,p-1MR0eq,p=-1MR=0eq,p-1MR019TheInverseElasticityRule•BecauseMR=MCwhenthefirmmaximizesprofit,wecanseethatpqepMC,11pqepMCp,1•Thegapbetweenpriceandmarginalcostwillfallasthedemandcurvefacingthefirmbecomesmoreelastic20TheInverseElasticityRulepqepMCp,1•Ifeq,p-1,MC0•Thismeansthatfirmswillchoosetooperateonlyatpointsonthedemandcurvewheredemandiselastic21AverageRevenueCurve•Ifweassumethatthefirmmustsellallitsoutputatoneprice,wecanthinkofthedemandcurvefacingthefirmasitsaveragerevenuecurve–showstherevenueperunityieldedbyalternativeoutputchoices22MarginalRevenueCurve•Themarginalrevenuecurveshowstheextrarevenueprovidedbythelastunitsold•Inthecaseofadownward-slopingdemandcurve,themarginalrevenuecurvewillliebelowthedemandcurve23MarginalRevenueCurveoutputpriceD(averagerevenue)MRq1p1Asoutputincreasesfrom0toq1,totalrevenueincreasessoMR0Asoutputincreasesbeyondq1,totalrevenuedecreasessoMR024MarginalRevenueCurve•Whenthedemandcurveshifts,itsassociatedmarginalrevenuecurveshiftsaswell–amarginalrevenuecurvecannotbecalculatedwithoutreferringtoaspecificdemandcurve25TheConstantElasticityCase•Weshowed(inChapter5)thatademandfunctionoftheformq=apbhasaconstantpriceelasticityofdemandequaltob•Solvingthisequationforp,wegetp=(1/a)1/bq1/b=kq1/bwherek=(1/a)1/b26TheConstantElasticityCase•ThismeansthatR=pq=kq(1+b)/bandMR=dr/dq=[(1+b)/b]kq1/b=[(1+b)/b]p•ThisimpliesthatMRisproportionaltoprice27Short-RunSupplybyaPrice-TakingFirmoutputpriceSMCSACSAVCp*=MRq*Maximumprofitoccurswherep=SMC28Short-RunSupplybyaPrice-TakingFirmoutputpriceSMCSACSAVCp*=MRq*SincepSAC,profit029Short-RunSupplybyaPrice-TakingFirmoutputpriceSMCSACSAVCp*=MRq*Ifthepricerisestop**,thefirmwillprodu