8/12/2019 Eco204y Final 2009w

1/30

UNIVERSITYOFTORONTO

FacultyofArtsandSciences

April MayExaminations2009

ECO204Y1Y

Duration:3hours

Total

Points:

200

points

ExaminationAid:OnlyRegularCalculators.

Instructions:

Thistestconsistsof12questionsin30pages,singlesided.

Thelastpageisaworksheet

Writeanswersonlyinthespaceprovidedforthatquestion

LastName:____________________ FirstName:______________

StudentNumber:_______________________________

Question(Points) Score Question(Points) Score

1. 20points 2. 10points

3. 25points 4. 10points

5. 15points 6. 20points

7. 25points 8. 30points

9. 5points 10. 5points

11. 20points 12. 15 points

TOTAL (200Points)

8/12/2019 Eco204y Final 2009w

2/30

Question1(20points)

Almaspreferencesovergoods1and2aregivenbytheutilityfunction:

U=Q1Q2

whereQ1andQ2areunitsofgoods1and2respectively.Suppose + =1.DenoteAlmasweekly

incomebyY. Denotethepriceofgood1byP1andthepriceofgood2byP2.

(a)(5points)DeriveAlmasdemandfunctionsforgoods1and2.Showyourcalculations.

Page2of30

8/12/2019 Eco204y Final 2009w

3/30

(b)(5points)Trueorfalse:foracompanysellinggood1toAlma,anypricewillmaximizerevenues.

Showyourreasoning.

(c)(5points)[This part can be answered without answering parts (a) & (b)].Trueorfalse:a10%increaseinallpricesandAlmasincomewillnotchangeheroptimalconsumptionofgoods1

and2.Brieflyexplainyourreasoning.

Page3of30

8/12/2019 Eco204y Final 2009w

4/30

(d)(5points)Suppose =0.25and =0.75.Evaluatethestatement:a100%increaseinAlmas

incomeleadstoa25%increaseintheconsumptionofgood1anda75%increaseinthe

consumptionofgood2.

Page4of30

8/12/2019 Eco204y Final 2009w

5/30

Question2(10points)

Yourutilityisafunctionofthreegoods:

U=min(Q1,Q2

,Q3)

DenoteincomebyYandthepriceofgood1byP1,thepriceofgood2byP2andthepriceofgood3

byP3.

(a)(5points)Derivethedemandequationsforgoods1,2and3.Explainyourreasoningandshow

allcalculations.

Page5of30

8/12/2019 Eco204y Final 2009w

6/30

(b)(5points)Whatistheincomeelasticityforgood1?Showyourcalculations.

Page6of30

8/12/2019 Eco204y Final 2009w

7/30

Question3(25points)

JennInc.isaperfectlycompetitivefirmwithacapacityof100units.Sheuseslabor(L)andcapital

(K)asvariableinputstoproduceoutput(q).Jennsproductionfunctionisgivenby:q=K1/2

L1/2

Supposethepriceoflaboris$160/workerandthepriceofcapitalis$10/machine.Denotetheprice

ofoutputbyP.

(a)(5points)DoesJennstechnologyhaveincreasing,constant,ordecreasingreturnstoscale?

Proveyouranswer.

Page7of30

8/12/2019 Eco204y Final 2009w

8/30

(b)(5points)DeriveJennscostfunctionandshowthatitexhibitsthereturnstoscalefromyour

answerinpart(a).Showyourcalculations.

Page8of30

8/12/2019 Eco204y Final 2009w

9/30

(c)(5points)IfJennisarationalproducer,whatistheequationofhersupplycurve?Showall

calculationsandgraphthesupplycurvebelow:

Page9of30

8/12/2019 Eco204y Final 2009w

10/30

(d)(5points)EttoreInc.isarationalproducerandhasthesametechnologyasJenn(i.e.q=K1/2

L1/2

).EttoreproposesamergerwithJennarguingthatthemergerwillbenefitfromeconomiesof

scope.IsEttorecorrect?

(e)(5points)[This part can be answered without answering parts (a) - (c)].AssumeJennisanirrationalproducer.Graphhersupplycurvebelowandbrieflyexplainyourreasoning.

Page10of30

8/12/2019 Eco204y Final 2009w

11/30

Question4(10points)

FuelledbyeasyaccesstodrugsfromtheUSA(UnitedStatesofAddicts)thecitizensoftheCanadian

townCrackotoaarefastbecomingdrugaddicts.ThemayorofCrackotoa,Ms.CindyBong,has

startedadrugtreatmentprogramwhichusespoliceofficers(P)anddrugcounselors(D)as

complementaryinputsin1:1ratiototreatdrugaddicts(A)astheoutput.

(a)(5points)Theprogramcurrentlyhas1,000policeofficersand1,000drugcounselors.IfCracko

toasgovernmentdoublesthebudgetforthedrugtreatmentprogram,howmanymorepolice

officersanddrugcounselorsshouldMs.CindyBonghire?Assumethepriceofpoliceofficersand

drugcounselorsisconstant.

Page11of30

8/12/2019 Eco204y Final 2009w

12/30

(b)(5points)Repeatpart(a)forthecasewherethepriceofpoliceofficersanddrugcounselors

alsodoubles.

Page12of30

8/12/2019 Eco204y Final 2009w

13/30

Question5(15points)

TheTablebelowreproducesTableBfromtheDHLcase:

InternationalAirExpressMarketSharesby$Revenues(1988)

Company MarketShare

DHL 44%

Fedex 7%

TNT 18%UPS 4%

Others 27%

Source:TableBinDHLcase.

(a)(5points)CalculatetheCR4intheinternationalairexpressmarket.Stateanyassumptions.

(b)(5points)EstimatetheHHIfromthedataintheTableabove.Briefexplainwhethertheestimate

overstatesorunderstatesthetrueHHI.

Page13of30

8/12/2019 Eco204y Final 2009w

14/30

(c)(5points)IfFedexandUPSmergewhatisthechangeintheglobalHHI?Showyourreasoning.

Page14of30

8/12/2019 Eco204y Final 2009w

15/30

Question6(20points)

ThefollowingtablereproducesportionsofExhibit11fromtheDHLcase.

Exhibit11RevenueandCostLaneExamples:DOXandWPX

U.K.toUnitedStates(1990) DOX WPX

Revenue $5,723,000 $2,342,000

OutboundCost 2,392,915 667,712

HubCost 596,608 490,436LineHaul

1 1,121,882 647,915

Delivery 1,376,953 386,049

GrossMargin 234,642 149,888

GrossMargin% 4.1 6.4

Shipments 231,139 68,580

Revenue/Shipment $24.76 $34.15

Note:Pleaseseefootnoteatthebottomofthispage.

(a)(10points)SupposeDHLsheadquartersinBrusselssetspricestomaximizeprofits.IfBrussels

raisesthepriceofadocumentfrom$24.76to$25.01howmanydocumentswillbesentfromthe

U.K.totheU.Sonthislane?Stateanyassumptions.

1Linehaulreferstotheairsegmentoftheshipment

Page15of30

8/12/2019 Eco204y Final 2009w

16/30

(b)(5points)ComputethepriceelasticityoftheWPXsegment.Showyourcalculations.

(c)(5points)SupposeDHLlowersthecostofshippingpackagesthroughlearningbydoing.

Assumingtheelasticityinpart(b)isconstant,whatmusttheMCofpackagesbeinorderforthe

priceofadocumenttobeequaltothepriceofapackageontheU.K.toU.S.lane?Showall

calculations.

Page16of30

8/12/2019 Eco204y Final 2009w

17/30

Question7(25points)

ProctorandGrumble(P&G),ariskneutraldecisionmaker,mustdecidewhethertodevelopand

releaseanewshampooShineonyoutargetedatbaldmen.IfP&Gdoesnotdevelopthe

shampootheoutcomeis$0m.IfP&Gdevelopstheshampoo,R&Dcostswillbe$100mandwhen

releasedintothemarketitwillbeasuccess(S)withprobability0.6orafailure(F)withprobability

0.4.

Iftheshampooisasuccess,grossrevenues(beforeR&Dcosts)areestimatedtobe$500m.Onthe

otherhand,iftheshampooisafailure,grossrevenues(beforeR&Dcosts)areestimatetobe$0m.

(a)(5points)DrawP&Gsdecisiontreeandindicatewhethertheshampooshouldbedeveloped.

Page17of30

8/12/2019 Eco204y Final 2009w

18/30

(b)(5points)P&Gsstatisticsconsultantthinkstheprobabilityofsuccessmaynotbeaccurate: i.e.

thereisamarginoferrorintheprobabilityofsuccess.Theconsultantworriesthatwithinthe

marginoferror,thedecisioninpart(a)maybechange.Forwhatrangeoftheprobabilityofsuccess

willP&Gmakethedecisioninpart(a)?

(c)(5points)[This part can be answered without answering parts (a) - (b)].Supposeamarketingcompanyhasdevelopedaperfect(100%accurate)testfornewproducts.Thetest

resultscanbepositive(+)ornegative().Fillintheentriesinthetwowayclassificationtablebelow.

S F Total

+

Total 100

Brieflyexplainyouranswerbelow.

Page18of30

8/12/2019 Eco204y Final 2009w

19/30

(d)(5points)DrawP&Gsdecisiontreeifitmakesthedecisionwiththeperfecttestinpart(c).

WhatisP&Gsdecisionwiththeperfecttest?

(e)(5points)Whatisthevalueofaperfecttest?Showyourcalculations.

Page19of30

8/12/2019 Eco204y Final 2009w

20/30

Question8(30points)

LeeHao,aprivateinvestor,hasatT=0purchasedaperpetualannuity(bond)issuedbytheBMO

(BankofManyOdors).Thepurchasepriceis$500andtheannuitywill,startingatT=0,payan

annualcouponpaymentof$100forever.

(a)(5points)CalculatetheyieldtomaturityoftheBMObond.WhatcanyousayaboutLeeHaos

opportunitycostofcapital?Incaseyouneedit,thesumofaninfiniteseries[1+x+x2+x

3+..]is

1/(1 x).

Page20of30

8/12/2019 Eco204y Final 2009w

21/30

LeeHaoisariskaverseinvestorwithutilityfunctionU=X

.Therecenteconomicdownturnhasled

LeeHaotobelievethatthereisachanceBMOwilldefaultonthebond:heexpectstheannual

couponpaymenttobe$40.

(b)(5points)WhatdoesLeeHaothinktheprobabilityofBMOdefaultingis?Showyourreasoning.

(c)(5points)WhatisLeeHaosexpectedutilityfromfacingtheuncertaintythatBMOmight

default?

Page21of30

8/12/2019 Eco204y Final 2009w

22/30

(d)(5points)ExpressLeeHaosutilityfromfacingtheuncertaintyofadefaultasanequivalentrisk

offacingtheuncertaintyofreceivingeither$10,000or$0.Showyourcalculations.

Page22of30

8/12/2019 Eco204y Final 2009w

23/30

(e)(5points)HowcanLeeHaousecreditdefaultswapstohedgeagainsttheriskofBMO

defaulting?Pleasedescribehowthecreditdefaultswapcontractwillbestructuredandhowthe

counterpartyexpectstoprofitfromtheswap.

(f)(5points)[This part can be answered without answering parts (a) - (e)].Whyhavecreditdefaultswapsbecomeaproblemrecently?

Page23of30

8/12/2019 Eco204y Final 2009w

24/30

Question9(5points)

AsyouwalkthroughTorontosPearsonairporttocatchaflighttoParis,youseeaboothselling

flightinsurancefor$12.Ifyoudieontheflight,theinsurancecompanywillpayyourfamily

$200,000.Asof2009theprobabilityofdyingflyingwas1in1.1million.Shouldyoubuythepolicy?

Stateanyassumptions.Hint:Whatisthepriceperdollarofinsurance?

Page24of30

8/12/2019 Eco204y Final 2009w

25/30

Question10(5points)

WhenbookingaonewayflightonAirCanada,youhavetheoptionofpurchasingatravelinsurance

policyOnMyWayfor$25.HereisthedescriptiononAirCanadaswebsite:

Getextraprotectionincaseofflightdelaysordisruptionsthatarebeyondtheairline's

responsibilityorcontrol.OnMyWayoffersaroundtheclockpriorityrebookingservice,

ahotelifneeded,andmuchmoreforonlyasmallfee.

Underactuariallyfairinsurance,whatisthebenefitoftheOn

My

Waytravelinsuranceprogram

forapassengertravelingonewayfromTorontotoNYC?AccordingtoFlightstats.com,86%of

flightsfromTorontotoNYCareontime.

Page25of30

8/12/2019 Eco204y Final 2009w

26/30

Question11(20points)

Lb.CakeCorporationisacakefranchisor.Underthetermsofthecurrentcontractwitharestaurant

ontheUTorontocampus,Lb.Caketakesafraction oftherestaurantsrevenues(R)andincursa

fraction oftherestaurantstotalcost(C).

Lb.CakesuppliesingredientstotherestaurantwithamarkupoverAC:assumeACisconstantand

therestauranthasnoothercostsbesidesthecostofingredients.

Supposetherestauranthasacapacityof700cakesaday.Dailydemandisgivenbytheequation:

P=100 10Q

PisindollarspercakeandQisinhundredsofcakes.

Suppose =0.2, =0.25,AC=$8perhundredcakes,and,Lb.Cakechargestherestauranta100%

markupoverAC.

(a)(10points)IfLb.CakechoosesthepriceandquantityattheUTlocation,solvefortheoptimalP

andQ.Showallcalculations.

Page26of30

8/12/2019 Eco204y Final 2009w

27/30

(b)(10points)Lb.Cakehasanopportunitytorenegotiatethecontract:itcanchangeeither by

0.1orby0.1orthemarkupby10%.(i.e.Lb.Cakecanonlychangeoneofthese).Whatdoyou

thinktheyshoulddo?Showyourreasoningbelow.

Page27of30

8/12/2019 Eco204y Final 2009w

28/30

Question12(15points)

CapitalNone,acreditcardcompany,hastodecidetoday(T=0)whethertomakeacreditcard

offertoaparticularconsumer.Thereisnocostofmakingthisunsolicitedoffer.IfCapitalNone

doesnotmakeanoffer,thevalueofthisdecisionis$0.Ifitmakesanoffer,assumetheconsumer

alwaysaccepts.

ThetermsoftheCapitalNonecreditcardare:

Issuedfortwoperiodsonly(T=1,2)

Maximumlimitof$1,000ineachperiod2(The2hereisafootnote,notsquared).

LetidenotetheinterestratechargedbyCapitalNoneontheendingbalanceineachperiod.

Inanyperiodtheconsumerhasthecreditcard,shealwaysmaxesoutitout:i.e.,shechargesthe

maximumlimitof$1,000.

Inanyperiod,theconsumercandefaultonthecreditcardwithprobabilityp.Iftheconsumer

defaultsinT=1,CapitalNoneswallowsthelossandcancelshercreditcardinT=2.Ifthe

consumerdefaultsinT=2,CapitalNoneagainswallowstheloss.

Inanyperiod,iftheconsumerdoesnotdefaultCapitalNoneprofitsfrominterestratechargeson

thebalance:i*(balance).Denotetheopportunitycostofcapitalbyr.

ShowthatforCapitalNonetomakeacreditcardoffertothisconsumer,theinterestrateonthe

balancemustbeatleasttheoddsofdefault:i.e.i p/(1 p).Hint:discountallfigurestoT=0.

2Thatis,$1,000limitinT=1and$1,000limitinT=2.

Page28of30

8/12/2019 Eco204y Final 2009w

29/30

Page29of30

8/12/2019 Eco204y Final 2009w

30/30

WORKSHEET