eco204y final 2010s
TRANSCRIPT
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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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WORKSHEET