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UNIVERSITYOFTORONTO

FacultyofArtsandSciences

AugustExaminations2010

ECO204

Y1Y

Duration:3hours TotalPoints:150 points

ExaminationAidsAllowed:Calculator.

Instructions:

Thisexamconsistsof3questionsin28pages,singlesided.

PleasegiveyournameasitappearsinROSI

LastName:____________________ FirstName:______________

StudentNumber:___________________________

Question Points Scores

1 50

2 55

3 45

TOTAL(150 Points)

YOUMUSTSTAYSEATEDDURINGTHELAST10MINUTESOFTHETESTWAITUNTILALLEXAMSARECOLLECTED

FORYOURCONVENIENCE,THEREISAWORKSHEETATTHEENDOFTHISTEST

KEEPANSWERSBRIEF.TOEARNCREDIT,SHOWCALCULATIONSANDGIVEARGUMENTSTOSUPPORTYOURANSWERS

Goodluck!

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Question1[50Points]

Aconsumerhasthefollowingutilityfunctionovergoods1and2:

Shehas

exogenously

given

income

$ 0 andisapricetaker.Assume 0 and

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0 .

(1)[5points]Whattypeofutilityfunctiondoesthisconsumerhave?Doesshehavemonotone

preferences?Giveabriefexplanationandshowallcalculations.

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(2)[5points]Sketchsomeindifferencecurvesinthegraphbelow.Dotheindifferencecurvescorrespond

toaddictivebehavior?Showallrelevantcalculationsneededtosketchtheindifferencecurves.

Q2

Q1

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(3)[5points]SupposetheconsumerisindifferentbetweenbundlesAandBwherebundleAis(1,1)and

bundleBis(2,

Q2

Q1

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).Doestheconsumerprefera25:75combinationofbundlesAandBtoeitherbundleA

orB?Ifso,whatsortofpreferencesdoesshehave?Ifnot,whatsortofpreferencesdoesshehave?

Showallcalculationsanddepictyouranswerinthegraphbelow.

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(4)[15points]Solveth :econsumersUMP

max,

s.t. , 0 , 0

Characterizetheconditionsforallinteriorandboundarysolutions.Showallcalculationsbelow.Hint:

Basedon

your

answer

to

part

(1)

is

one

of

the

constraints

an

equality

constraint?

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(5)[5points]Forthecaseofaninteriorsolution,calculatetheprice,crossprice,andincomeelasticities

ofgood2.Showallcalculationsbelow.

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(6) [5points]Forthecaseoftheboundarysolution 0,calculatetheprice,crossprice,andincomeelasticitiesofgood1.Showallcalculationsbelow.

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(7)[5points]Forthecaseoftheboundarysolution 0whatistheimpacton, andoptimalutilityfroma1%incometax?Showallcalculationsbelow.

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(8)[5points]Whatistheimpactontheconsumersutilityifthegovernmentmandates(requires)that

theconsumermustconsumeatleastoneunitofgood1?Showallcalculationsbelow.

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Question2[55Points]

AjaxCola,asoftdrinksmanufacturer,usesatechnologythatcombinesequalamountsofsweetener,

labor(),capital(),andmaterials()ascomplementaryinputstoproducesoftdrinks().Currently,AjaxColausessugar()asasweetener.

Ajaxpurchases/hires/leasesallinputsasapricetaker.Denotethepriceofsugarby , thewagerateby,thecapitalrentalrateby,andthepriceofmaterialsby

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.Inthisquestion,assumeallinputsare

variable.

(1)[5points]WritedownAjaxColasproductionfunctionandcharacterizeitsreturnstoscale.Showall

calculationsbelow.

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(2)[5points]Calculatetheoptimalinputsrequiredtoproducetargetoutput.Showallcalculationsbelow.

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(3)[5points]WhatisAjaxColascostfunction?Fromthiscalculatetheaverageandmarginalcost

functions.Showallcalculationsbelow.

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(4)[5points]Whatistheelasticityoftotalcostwithrespecttosugarprices?Showallcalculations

below.

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(5)[5points]Duetogreatervolatilityinsugarprices,AjaxColahasreconfigureditstechnologytoenable

theuseofsugar()and/orfructose()assweeteners,where2unitsoffructosecanbeperfectlysubstitutedforaunitofsugar.Denotethepriceoffructoseas

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.WritedownAjaxColasproduction

function.

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(6)[15points]Fortheproductionfunctioninpart(5),calculatetheoptimalinputsandcostfunctionof

producingtargetoutput.Showallcalculationsbelow.

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(7)[10points]Whatistheelasticityoftotalcostwithrespecttosugarpricesinthenewtechnology?

WasitagoodideaforAjaxColatohavereconfigureditstechnologytoallowtheuseofsugarand/or

fructoseassweeteners?Showallcalculationsbelow.

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(8)[5points]Suppose $5, $10, $5, $20 and $20 withprobability0.75and $40withprobability0.25.Whatistheexpectedcostofproducing 100 units?Showallcalculationsbelow.

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Question3[45Points]

ThePrestigiousAjaxCompany(PAC)consistsoftwodivisions1and2.Eachdivisionproducesthe

sameproductusinglabor()andfixedcapital()asinputsbutwithdifferenttechnologies.Division1producesoutputaccordingto:

Whiledivision2producesoutputaccordingto:

Assumebothdivisionshaveamplecapacityandproduceandselloutputindistinctmarkets.Currently

64, 16, $16 and $10.

(1)[5points]Characterizeeachdivisionsreturns(i.e.increasing,constant,ordecreasing).Showall

calculationsbelow.

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(2)[10points]CalculatetheoptimallaborrequiredtoproducetargetoutputinDivision1andtargetoutputinDivision2.Showallcalculationsbelow.

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(3)[5points]WhatareDivision1and2scostfunctions?Showallcalculationsbelow.

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(4)[5points]AssumingDivision1sdemandfunctionis 2,000 5andDivision2sdemandfunctionis 2,000 .WhataretheoptimalDivision1and2outputsandpricesiftherenopossibilityofarbitragebetweenthetwodivisionsmarkets?Showallcalculationsbelow.

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(5) [10points]AssumeDivision1sdemandfunctionis 2,000 5andDivision2sdemandfunctionis 2,000 .WhataretheoptimalDivision1and2outputsandpricesifthereisapossibilityofarbitragebetweenthetwodivisionsmarketsandthecostofarbitrageis$500?Showall

calculationsbelow.

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(6)[10points]AssumeDivision1sdemandfunctionis 2,000 5andDivision2sdemandfunctionis 2,000 .WhatareDivision1and2soptimal1

stdegreepricediscriminationoutputs

andpricesifthereisnopossibilityofarbitragebetweenthetwodivisionsmarkets?Showall

calculationsbelow.

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