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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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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