平狄克和鲁宾费尔德微观经济学microeconomics-rubinfeld-pindyck-tex

Chapter11:Appendix185CHAPTER11APPENDIXTRANSFERPRICINGINTHEINTEGRATEDFIRMEXERCISES1.ReviewthenumericalexampleaboutRaceCarMotors.Calculatetheprofitearnedbytheupstreamdivision,thedownstreamdivision,andthefirmasawholeineachofthethreecasesexamined:(a)nooutsidemarketforengines;(b)acompetitivemarketforenginesinwhichthemarketpriceis$6,000;and(c)thefirmisamonopolysupplierofenginestoanoutsidemarket.InwhichcasedoesRaceCarMotorsearnthemostprofit?Inwhichcasedoestheupstreamdivisionearnthemost?thedownstreamdivision?Weshallexamineeachcase,thencompareprofits.WearegiventhefollowinginformationaboutRaceCarMotors:ThedemandforitsautomobilesisP=20,000-Q.ThereforeitsmarginalrevenueisMR=20,000-2Q.Thedownstreamdivision’scostofassemblingcarsisCA(Q)=8,000Q,sothedivision’smarginalcostisMCA=8,000.Theupstreamdivision’scostofproducingenginesisCEQE2QE2,sodivision’smarginalcostisMCE(QE)=4QE.Case(a):Todeterminetheprofit-maximizingquantityofoutput,setthenetmarginalrevenueforenginesequaltothemarginalcostofproducingengines.Becauseeachcarhasoneengine,QEequalsQ,andthenetmarginalrevenueofenginesisNMRE=MR-MCA,orNMRE=(20,000-2Q)-8,000=12,000-2QE.SettingNMREequaltoMCE:12,000-2QE=4QE,orQE=2,000.Thefirmshouldproduce2,000enginesand2,000cars.Theoptimaltransferpriceisthemarginalcostofthe2,000engines:MCE=4QE=(4)(2,000)=$8,000.Theprofit-maximizingpriceofthecarsisfoundbysubstitutingtheprofit-maximizingquantityintothedemandfunction:P=20,000-Q,orP-20,000-2,000=$18,000.TheprofitsforeachdivisionareequaltoE=(8,000)(2,000)-(2)(2,000)2=$8,000,000,andC=(18,000)(2,000)-((8,000)(2,000)+16,000,000)=$4,000,000.TotalprofitsareequaltoE+C=$12,000,000.Chapter11:Appendix186Case(b):Todeterminetheprofit-maximizinglevelofoutputwhenanoutsidemarketforenginesexists,firstnotethatthecompetitivepriceforenginesontheoutsidemarketis$6,000,whichislessthanthetransferpriceof$8,000.Withthemarketpricelessthanthetransferprice,thismeansthatthefirmwillbuysomeofitsenginesontheoutsidemarket.Todeterminehowmanycarsthefirmshouldproduce,setthemarketpriceofenginesequaltonetmarginalrevenue.Weusethemarketprice,sinceitisnowthemarginalcostofengines,andtheoptimaltransferprice6,000=12,000-2QE,orQE=3,000.Thetotalquantityofenginesandautomobilesis3,000.ThepriceofthecarsisdeterminedbysubstitutingQEintothedemandfunctionforcars:P=20,000-3,000,orP=$17,000.Thecompanynowproducesmorecarsandsellsthematalowerprice.Todeterminethenumberofenginesthatthefirmwillproduceandhowmanythefirmwillbuyonthemarket,setthemarginalcostofengineproductionequalto6,000,solveforQE,andthenfindthedifferencebetweenthisnumberandthe3,000carstobeproduced:MCE=4QE=6,000,orQE=1,500.Thus,1,500engineswillbeboughtontheexternalmarket.Fortheengine-buildingdivision,profitsarefoundbysubtractingtotalcostsfromtotalrevenue:E=TRE-TCE=($6,000)(1,500)-(2)(1,500)2=$4,500,000.Fortheautomobile-assemblydivision,profitsarefoundbysubtractingtotalcostsfromtotalrevenue:A=TRA-TCA=($17,000)(3,000)-(8,000+6,000)(3,000)=$9,000,000.Totalprofitsforthefirmarethesumofthetwodivisions,T=$13,500,000.Case(c):Inthecasewherethefirmisamonopolysupplierofenginestotheoutsidemarket,thedemandintheoutsidemarketforenginesis:PE,M=10,000-QE,whichmeansthatthemarginalrevenuecurveforenginesintheoutsidemarketis:MRE,M=10,000-2QE.Todeterminetheoptimaltransferprice,findthetotalnetmarginalrevenuebyhorizontallysummingMRE,Mwiththenetmarginalrevenuefrom“sales”tothedownstreamdivision,12,000-2QE.ForoutputofQEgreaterthan1,000,thisis:NMRE,Total=11,000-QE.SetNMRE,Totalequaltothemarginalcostofproducingenginestodeterminetheoptimalquantityofengines:11,000-QE=4QE,orQE=2,200.Nowwemustdeterminehowmanyofthe2,200enginesproducedwillbesoldtothedownstreamdivisionandhowmaywillbesoldontheexternalmarket.First,notethatthemarginalcostofproducingthese2,200engines,andthereforetheoptimaltransferprice,is4QE=$8,800.Settheoptimaltransferpriceequaltothemarginalrevenuefromsalesintheoutsidemarket:8,800=10,000-2QE,orQE=600.Chapter11:Appendix187Therefore,600enginesshouldbesoldintheexternalmarket.Todeterminethepriceatwhichtheseenginesshouldbesold,substitute600intodemandintheoutsidemarketforenginesandsolveforP:PE,M=10,000-600=$9,400.Finally,setthe$8,800transferpriceequaltothenetmarginalrevenuefromthe“sales”tothedownstreamdivision:8,800=12,000-2QE,orQE=1,600.Thus,1,600enginesshouldbesoldtothedownstreamdivisionforuseintheproductionof1,600cars.Todeterminethesalepriceofthecars,substitute1,600intothedemandcurveforautomobiles:P=20,000-1,600=$18,400.Todeterminethelevelofprofitsforeachdivision,subtracttotalcostsfromtotalrevenue:E={($8,800)(1,600)+($9,400)(600)}-(2)(2,200)2=$10,040,000,andA=($18,400)(1,600)-[(8,000+8,800)(1,600)]=$2,560,000.Totalprofitsareequaltothesumoftheprofitsfromthetwodivisions,orT=$12,600,000.Thetablegivesprofitsearnedbyeachdivisionandthefirmforeachcase.ProfitswithUpstreamDivisionDownstreamDivisionTotal(a)Nooutsidemarket8,000,0004,000,00012,000,000(b)Competitivemarket4,500,0009,000,00013,500,000(c)Monopolizedmarket10,000,0002,600,00012,600,000Theupstreamdivision,buildingengines,earnsthemostprofitwhenithasamonopo