Eco204y Final 2009s

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  • UNIVERSITYOFTORONTO

    FacultyofArtsandSciences

    AugustExaminations2009

    ECO204Y1Y

    Duration:3hoursTotalPoints:300points

    ExaminationAid:OnlyRegularCalculators.

    Instructions:

    Thistestconsistsof8questionsin26pages,singlesided.

    Writetheanswersonlyintheprovidedspaceforeachpartofquestion.

    LastName:____________________FirstName:______________

    StudentNumber:_______________________________

    Question(Points)

    ScoresQuestion(Points)

    Scores

    1.10points 5.30points 2.20points 6.50points 3.20points 7.50points 4.90points 8.30points

    TOTAL(300Points) Allpartsareequallyweighted(10points)

    Foryourconvenience,therearetwoworksheetsattheendofthisexam

  • Question1Inthegraphbelow,depicttheconsumptionsetofaconsumerwho,duetophysicalconstraints,canconsumeanyamountofgood1andamaximumnumberof10unitsofgood2.Moreover,forthefirst20unitsofgood1,good2canbeconsumedinanyamount(uptoamaximumamountof10units);butformorethan20unitsofgood1,good2mustbeconsumedinintegeramounts.

    Question2Inamarketingsurvey,aconsumerwasaskedaboutherpreferencesovergoods1andgoods2.SheindicatesthatwhenQ1>Q2shehasdecreasingmarginalrateofsubstitutionandwhenQ1Q2shehasincreasingmarginalrateofsubstitution.

    (a)Graphherindifferencecurvesbelow.

    Page2of26

  • (b)Theconsumerindicatesshehasconvexpreferences.Whatcanyousayaboutthenatureofgoods1and2?Explainyouranswerusingthegraphinpart(a).

    Page3of26

  • Question3Supposeinvestorsonlycareaboutthe(expected)returnandriskoftheirportfolios.ThefollowingfiguredepictstheindifferencecurvesfortwoinvestorsAandB:

    (a)Whichinvestorismoreriskaverse?Explainbrieflywhy.

    (b)Whichinvestorwillallocateagreaterproportionoftheportfoliotoriskyassets?

    .

    Page4of26

  • Question4Gamsi,Laffont,andVuonginEconometricAnalysisofCollusiveBehaviorinaSoftDrinkMarket,JournalofEconomicsandManagementStrategy(Summer1992)estimatedthefollowingdemandequationsforCokeandPepsisyrup1.

    Qc=26.173.98Pc+2.25Pp+2.60Ac0.62Ap+9.58S+0.99I

    Qp=17.48+1.40Pc5.48Pp4.81Ac+2.83Ap+11.64S+1.92I

    Alldatawasquarterlyfrom19681986.Here:

    Q=quarterlyquantityofsyrupsold P=priceofsyrup(1986dollars) A=squarerootofquarterlyadvertisingexpenses(1986dollars) S=equals1ifspringorsummer,equals0ifwinterorfall I=realincome(1986dollars)

    Averagevaluesfromdataare:

    QC=30.22,QP=22.72,PC=12.96,PP=8.16,AC=5.89,AP=5.28,I=20.63.CokesTVCwasestimatedtobeTVCC=5QCandPepsisTVCwasestimatedtobeTVCp=4QP.

    (a)BrieflyexplainwhetherCokeandPepsihaveincreasing,constantordecreasingreturns.

    1CokeandPepsi,thecorporations,producesyruporconcentratewhichissoldto(typically)independentbottlers.Thebottlerscarbonatetheconcentrate,bottleanddistributethesoftdrinks.Thesedemandequationsarefortheconcentrate,i.e.bottlersdemand.

    Page5of26

  • (b)Attheaveragevalues,doesPepsisadvertisinghaveabiggerimpactonCokesalesordoesCokesadvertisinghaveabiggerimpactonPepsisales?Explainyouranswerandshowallsteps.

    (c)CalculateCokesrevenuemaximizingprice(s).Showallsteps.

    Page6of26

  • (d)AssumingPepsihasamplecapacitycalculatePepsisprofitmaximizingprice(s).Showallsteps.

    Page7of26

  • (e)Basedontheanswerinpart(d),calculatePepsisgrossmargin:revenueratio.Showallsteps.

    (f)CalculatePepsispriceelasticityattheoptimalprice.Showallsteps.

    Page8of26

  • (g)AssumingPepsihasacapacityofQp=20,calculatePepsisprofitmaximizingprice(s).Showallsteps.

    Page9of26

  • (h)AtthecurrentcapacityofQp=25,whatisthevalueofanadditionalunitofcapacity?HowmuchcapacityshouldPepsiadd?Showallsteps.

    Page10of26

  • (i)Trueorfalse:thevalueofadditionalcapacityisinverselyproportionaltocapacity;i.e.thelargerPepsiscapacity,thelowerthevalueofaddingmorecapacity.Showallsteps.

    Page11of26

  • Question5Considerafirmwhoseownershavehiredamanagertoruntheirfirm.Thefollowinggraphshowstherelationshipbetweenthefirmsprofitsandthenumberofemployeesthatthemanagerhires:

    SupposethemanagerhasutilityfunctionU=(Profits)(Employees).Ifnecessary,pleaseexplainyouranswerusinggraphs.(a)Trueorfalse:Becausesuchamanagerperceivesprofitsandemployeesasimperfectsubstitutes,themanagerwillneverchoosetheprofitmaximizingnumberofemployees.Brieflyexplain.

    Page12of26

  • (b)Supposeamanagerrunsthecompanyallbyherself.Someownersthinkhighlyofthishardworkingmanager.Aretheseownerscorrect?Brieflyexplain.

    (c)Whatsortofmanagerwouldbeidealfortheowners?Whatistheutilityfunctionofsuchamanager?Brieflexplain.

    Page13of26

  • Question6Foryourconvenienceherearesomeusefulequations:

    E[Rp]=(1)RF+E[RM]

    E[Var(x)]=i=1:npi(xiEV[x])2

    E[cov(x,y)]=i=1:npi(xiEV[x])(yiEV[y])

    E[ax+by]=aE[x]+bE[y](aandbareconstants)

    Var(ax+by)=a2Var(x)+b2Var(y)+2abcov(x,y)(aandbareconstants)

    ConsiderthefollowingtableofreturnsandprobabilitiesfortworiskyassetsAandB:

    State RateofReturnA RateofReturnB Probability

    Strong 10% 5% 0.3

    Normal 5% 20% 0.4

    Weak 10% 5%

    (a)CalculatetheexpectedreturnandriskofassetA.

    (b)CalculatetheexpectedreturnandriskofassetB.

    Page14of26

  • (c)CalculatetheexpectedcovarianceofassetAandassetBreturns.

    (d)SupposeyouwanttoconstructaportfolioconsistingofassetsAandBthatminimizestheexpectedrisk.SupposeaproportionoftheportfolioisinassetAandproportion(1)isinassetB.CalculatethetheproportionofportfolioinassetAwhichminimizesriskofaportfolioofassetsAandB.

    Page15of26

  • (e)Giventheallocationinpart(c),willportfolioriskbeimpactedmorebyhigherriskinessofassetAorassetB?Showallcalculations.

    Page16of26

  • Question7Supposeweanalyzeamarketconsistingoftwogoods,good1andgood2.Thecompanysellinggood1hasidentifiedtwosegmentsofconsumers:segmentAandsegmentB.AllconsumersarepricetakersandhaveincomeY.AssumeP2=1.ExtensivemarketresearchshowsthatasegmentAconsumerhastheutilityfunction:

    U=q2+(q18)2/2(0.1),

    WhileasegmentBconsumerhastheutilityfunction:

    U=q2+(q110)2/2(0.1)

    (a)WhatistheindividualdemandequationofasegmentAandsegmentBconsumer?Showallsteps.Hint:Theutilityfunctionsarespecialcasesof:U=(q1)

    2/2+q2.DontforgetthatP2=1.

    Page17of26

  • (b)Thecompanyproducinggood1producesoutputaccordingtotheproductionfunction:Q1=Lk

    1/2wherecapitalisfixedatk=100,Lislabor,andQ1istheoutputproduced.Ifthecompanyhastotalfixedcostof$1,000andMC=$20,whatisthepriceofcapitalandlabor?

    Page18of26

  • (c)Supposethereare15consumersinsegmentAand15consumersinsegmentB.CalculateaggregatedemandforsegmentsAandB.Ifyoucouldntsolvetheindividualdemandequationsinpart(a)thenuse:TypeA:q1=abP1TypeB:q1=cdP1

    Page19of26

  • (d)Ifthecompanyproducinggood1hasnocapacityconstraintsandhaszeroopportunitycost,whataretheprofitmaximizingoutputsandpricesifitpractices3rddegreepricediscriminationwithnopossibilityofarbitrage?Showallsteps.

    Page20of26

  • (e)Ifthecompanyproducinggood1hasacapacityconstraintof100andhaszeroopportunitycost,whataretheprofitmaximizingoutputsandpricesifitpractices3rddegreepricediscriminationwithnopossibilityofarbitrage?Showallsteps.

    Page21of26

  • Question8ThefollowingtablereproducesportionsofExhibit11fromtheHarvardBusinessSchoolDHLcase.

    Exhibit11RevenueandCostLaneExamples:DOXandWPXU.K.toUnitedStates(1990) DOX WPXRevenue $5,723,000 $2,342,000OutboundCost 2,392,915 667,712HubCost 596,608 490,436LineHaul2 1,121,882 647,915Delivery 1,376,953 386,049GrossMargin 234,642 149,888GrossMargin% 4.1 6.4Shipments 231,139 68,580Revenue/Shipment $24.76 $34.15Note:Pleaseseefootnoteatthebottomofthispage.

    (a)SupposeDHLsmanagementbelievesthata$5increaseinthepriceofDOXwillresultina75%dropinDOXshipmentsandthata$5decreaseinpriceofDOXwillresultina75%increaseinDOXshipments.WhatistherevenuemaximizingDOXprice?Showallcalculations.

    2Linehaulreferstotheairsegmentoftheshipment

    Page22of26

  • Page23of26

  • (b)TheDHLcasearguedthatmanagersincentiveswerewarped(distorted).AssumeDHLsolvesthewarped(distortedincentives)problem,calculatetheprofitmaximizingpriceofDOXbetweentheU.K.andU.S.(c)Anotherexpresscarrier,UsPoorSouls(UPS)offerstoleasespaceonDHLaircrafts.UPSoffersDHL$2forthespaceoccupiedbyaDOX.AssumingDHLcarriesallDOXfromU.K.toU.S.(andviceversa)onitsownaircraft,whatshouldDHLdo?

    Page24of26

  • WORKSHEET

    Page25of26

  • Page26of26

    WORKSHEET

    Question (Points)ScoresQuestion (Points)Scores1. 10 points5. 30 points2. 20 points6. 50 points3. 20 points7. 50 points4. 90 points8. 30 pointsTOTAL (300 Points)All parts are equally weighted (10 points)For your convenience, there are two worksheets at the end of this exam