eco204y final 2011w
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UNIVERSITYOFTORONTO
FacultyofArtsandSciences
AprilExaminations2011
ECO204Y1Y
Duration:3hours TotalPoints:150points
ExaminationAidsAllowed:Calculator.
Instructions:
Thisexamconsistsof3questionsin36pages,doublesided.
PleasegiveyournameandID#asitappearsinROSI
LastName:
First
Name:
StudentID#
___________________________________________________________________
Question Points Scores
1 60
2 45
3 45
Totalscore
(out
of
150 points) /
150
YOUMUSTSTAYSEATEDDURINGTHELAST10MINUTESOFTHEFINALEXAMWAITUNTILALLEXAMSARECOLLECTED
FORYOURCONVENIENCE,THEREARETWOWORKSHEETSATTHEENDOFTHISEXAM.
KEEPANSWERSBRIEF.TOEARNCREDIT,SHOWCALCULATIONSANDGIVEARGUMENTSTOSUPPORTYOURANSWERS
Goodluck!
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Question1[60Points]
Aconsumerhasthefollowingutilityfunctionovergoods1and2:
Shehasexogenouslygivenincome$ 0, isapricetakerwith$ 0 and$ 0,andhastheconsumptionset , : , 0.
(1)[5Points]Doesshehaveaquasilinearutilityfunction?Giveabriefexplanation.
(2)[5Points]Doesshehavemonotonepreferences?Ifshedoes(ordoesnot)havemonotonepreferencesthen
whatmustbetrueaboutherbudgetconstraint?Giveabriefexplanationandshowallcalculations.
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(3)[5Points]Showthattheconsumersindifferencecurveforanarbitraryutilitylevel lookslike:
Q2
Q1
Calculatethe and intercepts,theslopeatanybundle, andtheslopeatthe and intercepts.Showallcalculations.
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(4)[5Points]Giveagraphicalandalgebraicargumentforwhetherthisconsumerhasconvexpreferences.Show
allcalculations.Hint:Forthealgebraicproof,pickanytwobundlesonanindifferencecurveandusethe
definitionofconvexpreferences.
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(5)[10Points]SolvetheconsumersUtilityMaximizationProblem(UMP).Youareexpectedtousethe
appropriateoptimizationmethod(i.e.Lagrange/KuhnTucker).Showallcalculations.
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(6)[10Points]Supposetheconsumersbudgetsetisgivenby, , $10, $200, $100.FromtheUMPsolution,calculatetheoptimaldemands,priceelasticity,incomeelasticity,andcrosspriceelasticityofgoods1
and2aswellastheMUduetoasmalldecreaseinincome,asmallincreasein,asmalldecreasein, andrelaxingtheconstraintthat 0.Showallcalculationsandfillyouranswersinthetablebelow.
Summaryof
Answers:
please
fill
shaded
cells
below
Good1 Good2
Priceelasticity
Incomeelasticity
Crosspriceelasticity
M g tilityduetoar inalU
Asmalldecreaseinincome
Relaxingtheconstraint AsmallincreaseinAsmalldecreasein
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(7)[10Points]Supposetheconsumersbudgetsetisgivenby, , $10, $20, $100[Thisbudgetconstraintisdifferentfromthepreviouspart].FromtheUMPsolution,calculatetheoptimaldemands,price
elasticities,incomeelasticities,andcrosspriceelasticitiesforgoods1and2aswellastheMUduetoasmall
decreaseinincome,asmallincreasein,asmalldecreasein, andrelaxingtheconstraintthat 0.Showallcalculationsandfillyouranswersinthetablebelow.
SummaryofAnswers:pleasefillshadedcellsbelow
Good1 Good2
Priceelasticity
Incomeelasticity
Crosspriceelasticity
M g tilityduetoar inalU
Asmalldecreaseinincome
Relaxingtheconstraint AsmallincreaseinAsmalldecreasein
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(8)[10Points]Whatistheimpactontheconsumersutilityifthegovernmentmandates(requires)thatthe
consumermustconsumeatleast0.1unitsofgood2?AnswerthispartusingthegeneralUMPsolutioninpart(5)
above.Showallcalculationsbelow.
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S.AjazHussain,Dept.ofEconomics,UniversityofToronto
Question2[45Points]
Inthisquestionyouwillcalculatethecostofproducingtheproductsforthemixedbundlingprobleminquestion
3.Thatsaid,youdonthavetodoquestion2inordertoanswerquestion3sincequestion3givesyouthe
necessaryinformationfromquestion2.
BillyBobBuggins(BBB)restaurantinSudburyOntariospecializesinSurfandTurfcuisine1.BBBoffers
customersthechoiceofhavingsurfandturf(forexample,alobstertailandsteak),orjustsurf(forexample,a
lobstertail),
or
just
turf
(for
example,
asteak).
Letting
surf
(seafood)
be
good
1and
turf
(red
meat)
be
good
2.BBBsmenuis:
Billy Bob Buggins Surf and Turf RestaurantBringing you the finest fishy and mystery meat cuisine since January 2011
9 Accolades Avenue, Sudbuy, OntarioCall 416 555 9999 for reservations
Surf and Turf plate PriceBundleSurf plate Price1Turf plate Price2
We use the finest canned seafood and blend of mystery red meats
BBBpreparesatargetoutput platesbyusinglabor andseafood as surf complementsina1:1ratio.
BBBpreparesatargetoutputofturfplatesbyusinglabor andmeatascomplementsaccordingtotheproductionfunction:
min2 Meat,
Inturn,meatconsistsofbeef()andmutton()combinedasperfectsubstituteswhereaunitofbeefisperfectlysubstitutablefortwounitsofmutton.
BBBpurchases/hires/leasesallinputsasapricetaker.Denotethepriceofseafoodas , thelaborwagerateby,thepriceofbeefby,andthepriceofmuttonby.Inthisquestion,assumeallinputsarevariable.
1SurfandTurfreferstoseafoodandmeatdishes.Surfisseafood(namedforoceansurf)andturfisredmeat(namedforgrass,or
turf,uponwhichcattle/animalsgraze).
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S.AjazHussain,Dept.ofEconomics,UniversityofToronto
S
(Seafood)
L
(Labor)
(1)[5Points]WritedownBBBsproductionfunctionforsurf(seafood)usinglabor andseafoodas
complementsina1:1ratio,characterizeitsreturnstoscale,andgraphsomeisoquantsbelow.Showall
calculationsbelow.
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(2)[10Points]WritedownBBBsproductionfunctionforturfusinglabor withmeatascomplementsaccordingto min2 Meat, , characterizeitsreturnstoscale,andgraphsomeisoquantsbelow.Also,writedownBBBsproductionfunctionforMeatusingbeefandmuttonasperfectsubstitutes(whereaunitof
beefisperfectlysubstitutablefortwounitsofmutton),characterizeitsreturnstoscale,andgraphsomeiso
quantsbelow.Showallcalculationsbelow.
TurfPayattentiontowhichinputsareonthe, axes
Meat
L(Labor)
MeatPayattentiontowhichinputsareonthe, axes
M
(Mutton)
B (Beef)
Ifnecessary
use
the
next
page
for
additional
calculations
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(3)[5Points]Derivethecostfunctionofsurfplatesandfromthischaracterizethereturnstoscale.Showallcalculations.
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(4)[10Points]Derivethecostfunctionofturfplatesandfromthischaracterizethereturnstoscale.Showallcalculations.
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(5)[5Points]WhatisBBBstotalcostfunctionofproducing platesofsurfandturf?Isittruethatthecostof surfandturfplatesisthesumofthecostofsurfplatesandthecostofturfplates?Thatis:is ?Showallcalculations.
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(6)[10Points]Suppose:
$1, $0.50, $2, $2
Showthatthecostofasurfplateis$1.50and f lateis$1.50:thecosto a turfp
$1.50, $1.50
Showall
calculations.
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Question3[45Points]
NOTE:Ifyoucantsolveaparticularpart,thentryansweringlaterpartswhichcontainallrequiredinformation
Fromquestion2(independentofthisquestion)recallthatBillyBobBuggins(BBB)restaurantinSudburyOntario
specializesinsurfandturfcuisine2.BBBofferscustomersthechoiceofhavingsurfandturf(forexample,a
lobstertailandsteak),orjustsurf(forexample,alobstertail),orjustturf(forexample,asteak).Lettingsurf
(seafood)begood1andturf(redmeat)begood2,BBBsmenuis:
Billy Bob Buggins Surf and Turf RestaurantBringing you the finest fishy and mystery meat cuisine since January 2011
9 Accolade Avenue, Sudbuy, OntarioCall 416 555 9999 for reservations
Surf and Turf plate PriceBundleSurf plate Price1Turf plate Price2
We use the finest canned seafood and blend of mystery red meats
Suppose
that:
S $1.50;T $1.50
BBBsowner,Mr.BillBugginshastopriceamixedbundleofasurfplate,aturfplate,andasurfandturfbundle.
Assumecustomersalwayspurchaseeitheraplateofsurf,oraplateofturf,oraplateofsurfandturfbundle.
Themarketingfirm3Cs,4Ps&7Mshasidentifiedthreesegmentsofcustomers:
Segment Incom o a omere f cust
A $100
B
$150C $200
Supposeeachsegmenthasthefollowingtypeofutilityfunctionoversurf(good1)andeverythingelse
(toothpaste,shampoo,clubbingetc):
,
Ignoreturfbeingacomponentofeverythingelse.Theparameter, , , variesbysegment(willbegivenbelow).
Suppose
each
segment
has
the
following
type
of
utility
function
over
turf
(good
2)
and
everything
else
(toothpaste,shampoo,clubbingetc):
2SurfandTurfreferstoseafoodandredmeat.Surfisseafood(namedforoceansurf)andturfisredmeat(namedforgrass,turf,on
whichcattle/animalsgraze).
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, 2
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Ignoresurfbeingacomponentofeverythingelse.Theparameter , , , variesbysegment(willbegivenbelow).
(1)[5Points]Supposethatsurfandeverythingelseandturfandeverythingelsecanbeconsumedininteger
amountsonly.Graphtheintegerconsumptionsetsbelow:
Integerconsumptionsetofsurfandeverythingelse
Everything
Else
Q1(Surf)
Integerconsumptionsetofturfandeverythingelse
EverythingElse
Q2(Turf)
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(2)[5Points]Graphanindifferencecurveforsurfandeverythingelseandturfandeverythingdefinedover
anintegerconsumptionset.Youneedonlygivearoughsketchoftheindifferencecurves.Hint:Whatdoesthe
indifferencecurveof, looklikeinthestandardconsumptionset?
Indifferencecurveofsurfandeverythingelse
(Integer
consumption
set)
Everything
Else
Q1(Surf)
Indifferencecurveofturfandeverythingelse
(Integer
consumption
set)
EverythingElse
Q2(Turf)
Explainhowyougotyouranswersbelow:
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(3)[5Points]Letting priceofasurfplateand priceofaunitofeverythingelse,calculatethereservationprice(i.e.willingnesstopay)ofonesurfplate
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forasurfcustomerwithincome andutilityfunction:
,
Doesthereservationpricedependonincome?Showallcalculationsbelowandifnecessaryusethegraph
below:
EverythingElse
Q1(Surf)
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(3)[5Points]Letting priceofaturfplateand priceofaunitofeverythingelse,calculatethereservationprice(i.e.willingnesstopay)ofoneturfplate
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ofaturfcustomerwithincome andutilityfunction:
, 2
Doesthereservationpricedependonincome?Showallcalculationsbelowandifnecessaryusethegraph
below:
Everything
Else
Q2(Turf)
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(4)[5Points]Treateverythingelseasthebasegoodsothat priceofaunitofeverythingelse=$1.SupposeasurfcustomerinsegmentsA,BandCrespectivelyhasthefollowingutilityfunctionoversurfand
everythingelse:
,
1 , 2 , 4
SupposeaturfcustomerinsegmentsA,BandCrespectivelyhasthefollowingutilityfunctionoverturfand
everythingelse:
, 2
3, 2, 12
Basedonyouranswersaboveshowthatthereservationprice(i.e.willingnesstopay)forasurfplate(good1)
andturfplate(good2)are:
Segment
Cus m me
to erInco
A $100 $1 $6 B $150 $2 $4 C $200 $4 $1
Costofaplateof: $1.50 $1.50
Calculatethereservationpriceforabundleofsurfandturf.Besuretostateanyassumptionsaboutreservation
priceofasurfandturfbundleandindicatewhetheryourassumptionisalwaystrue.
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(5)[5Points]Iftheoptimalpriceofasurfplatesoldindividuallyequalsthereservationpriceofacustomerin
segmentC(i.e. showtheremustbe 3 (roundedup) stomersinsegmentC.cu
Segment #custom r gmente sinse Cus m meto erInco A 20 $100 $1 $6 B 10 $150 $2 $4
CShowthat
(roundedup)
$200 $4 $1
Costofaplateof: $1.50 $1.50
Showallcalculationsbelow:
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(6)[20Points]Calculatetheoptimalmixedbundlepricesofasurfplate,aturfplate,andasurfandturfbundle
plateforthefollowingdata.Showallcalculationsbelowandsummarizeyouranswerbelow.
Segment #custom r gmente sinse Cus m meto erInco A 20 $100 $1 $6 B 10 $150 $2 $4C 8 $200 $4 $1
Costof
aplate
of: $1.50 $1.50
OptimalPrice Whichsegment(s)willpurchase?
Good1,SurfPlate
Good2,TurfPlate
BundleofGoods1&2,SurfandTurfplate
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WORKSHEET
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WORKSHEET
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