Eco204y Final 2009w
-
Upload
examkiller -
Category
Documents
-
view
222 -
download
0
Transcript of Eco204y Final 2009w
-
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