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ECO 204, 2010-2011, Test 3 Solutions
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UniversityofToronto,DepartmentofEconomics,ECO2042010 2011AjazHussain
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Page1of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
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ECO 204, 2010-2011, Test 3 Solutions
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Question1[60Points.Allpartsworth10pointseach]
ThisquestionisbasedontheHBScase:ThePrestigeTelephoneCompany.Foryourconveniencehereis
exhibit1fromthecase(figuresbelowareforthePrestigeDataservicescompanyJanuaryMarch2003)
Exhibit1:PrestigeTelephoneCompany
January2003
February
2003
March
2003
IntercompanyHours 206 181 223
CommercialHours 123 135 138
TotalRevenueHours 329 316 361
Service Hours 32 32 40
AvailableHours 223 164 143
TotalHours 584 512 544
Inthecase,thecommercialpriceis
$800/hourandtheintercompanypriceis
$400/hour:
Pi=$400/hr.
PrestigeTelephone
Company
PrestigeData
Services
Commercial
CustomersPC=$800/hr
CommercialOther
Services
Data
D
a
t
a
Intercompany
ThePrestigeDataServicescos oursofdataservices):tfunctionwasestimatedtobe(here
ish
223,43628 ThePrestigeDataServicescommercialin e invers demandfunction March2003wasestimatedtobe:
1,4664.83 Page2of37
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ECO 204, 2010-2011, Test 3 Solutions
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(a)UnderthetermsofaregulationrulingPDSsintercompanybillingarecappedatanaverageof
$82,000/month.Whatdoesthisimplyfortheaverageintercompanyhoursthatcanbebilledper
month?IsPrestigeDataServicesabidingbyorviolatingthetermsoftheruling?Giveabriefexplanation.
Answer:
Ifintercompany
revenues
are
capped
at
$82,00 o nd
prices
are
$400/hr
then:
0/m nth
a
400 000 8 2 , 205
Thisimpliesthatintercompanyhoursshouldbe205hours/monthonaverage.IsPDSbilling205hours
onaverageeachmonth?Lookat:
Exhibit1:PrestigeTelephoneCompany
January2003
February
2003
March
2003
IntercompanyHours 206 181 223
CommercialHours 123 135 138
TotalRevenueHours 329 316 361
Service Hours 32 32 40
AvailableHours 223 164 143
TotalHours 584 512 544
Noticethataverageintercompany from 3were:hours JanMar200
2061812233 6103 203.33Thus,PDSisabidingbythetermsoftheagreement.
(b)WhatkindofreturnsdoesPDShaveforitsvariableinputs?Giveabriefexplanationbasedonthe
figuresabove(notbelow).
Answer:
ThePrestigeDataServicescos oursofdataservices):tfunctionwasestimatedtobe(here
ish
223,43628 SincethisisalinearcostfunctionPDSmusthav nt rns.Inparticular,noticethat:econsta retu
28 28Page3of37
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ECO 204, 2010-2011, Test 3 Solutions
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Sinceisconstant,PDShasconstantreturns.(c)RecallthatPDShasneverearnedprofits.Calculatethebreakevennumberofcommercialhoursand
theequationofthedemandcurveinthemonthwhenPDSbreakseven.Showallcalculations.
Answer
PDSsellsdataservicestointercompanyandcomm cial omers.Nowprofitsare:er cust
Breakevencommercialoutputiswhen:
0 Breakeven Breakeven Breakeven
Assuming 2 8 and 205 wehave:
Breakeven 223,436 400 28205
800 28191
Wecan
now
compute
the
demand
curve
in
the
month
when
PDS
breaks
even.
Assuming
the
other
factorsbesidespricearepushingthedemandcurverightweseethatinthebreakevenmonth,the
demandcurvehasthesameslopeastheMarch2003demandcurve:
Page4of37
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ECO 204, 2010-2011, Test 3 Solutions
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Commercial
Hours
CommercialPrice
$800
138
M
$1,466
135123
FJ
PDSCommercialDemandCurveinMarch2003
P=1,466 4.83Q
?
Break
even
=
192
Thus,inthebreakevenmonth:
4.83 Since $800 and 192 wehave:
4.83 8004.83 192800 . 4 83 192
1,727.36Thecommercialdemandcurveinthebreakevenmonthis:
1,727.364.83
(d)In
general,
is
it
easier
for
the
commercial
division
to
breakeven
ifPDS
comprises
of
commercial
andintercompanydivisionsversusifPDScomprisesofjustacommercialdivision?Assumethetwo
scenarioshavethesametotalfixedcost.
Answer
Withtwodivisionswehad:
Page5of37
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ECO 204, 2010-2011, Test 3 Solutions
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Breakeven e outpriorpermission
Page6of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
Letscomparethisexpressionwiththecaseofasinglecommercialdivision:
Breakeven Noticethatsolongas (i.e.theother,intercompany,divisionhaspositivecontributionmargin),thenthecommercialbreakevenquantitywithanotherprofitabledivisionissmallerthanthe
breakevenquantityifthecommercialdivisionwasbyitself.
(e)[Thispartisindependentofallotherparts]SupposethatinMarch2003,thegovernmentimposesa
10%excisetaxoncommercialdataservices.Assumingallcommercialcustomerscanbemodeledbya
singlerepresentativeconsumerwithincome$ andutilityfunction, (wheregood1iscommercialdataservicesandgood2iseverythingelse)whatisthemarginalutilityduetotheexcise
tax
on
commercial
data
services?
Please
show
all
calculations
and
specifically
state
all
assumptions.
Answer:
Beforetheexcisehasbeenimposed,therepresentativeconsumer,withanunknownincome$,consumes138hoursofcommercialdataservicesandsomeunknownquantityofothergoods.Let
everythingelsebethebasegoodsothat 1 andassumetheconsumerhasaquasilinearutilityfunctionofthetype:
, Here
isanyfunctionofgood1suchthat
0 0.Inthiscase,thetotalutilityofabundleminus
theincome
is
the
consumer
surplus
of
good
1:
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ECO 204, 2010-2011, Test 3 Solutions
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Q2(EverythingElse)
Q1CommercialHours
Page7of37
Q2
138
U(Q1,Q2) Y
A
c
1,466 U(Q1,Q2) Y
Y/800
Y/1
A800
CommercialDemand
Q1CommercialHours138
ThatisatbundleA:
, 138, 121,466800138$45,954
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ECO 204, 2010-2011, Test 3 Solutions
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Q2(EverythingElse)
Q1CommercialHours
Page8of37
Q2
138
U(Q1,Q2) Y=$45,954
A
c
1,466 U(Q1,Q2) Y=$45,954
Y/800
Y/1
A800
CommercialDemand
Q1CommercialHours138
A10% excisetaxraisesthepriceofcommer 80andreducesdemandto:cialservicesto$8
1 ,4664.834 880 1,466 .83
4.8 8803 1,466 1,4668804.83 121.33
Thus,atbundleB:
, 121.33, 121,466880121.33$35,550
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ECO 204, 2010-2011, Test 3 Solutions
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Q2(EverythingElse)
Q1CommercialHours
Pc
Page9of37
Q2
138
U(Q1,Q2) Y=$45,954
Q2
121.33
U(Q1,Q2) Y =$35,550
Y/880
AB
Y/800
Y/1
138121.33
Q1CommercialHours
800
880
1,466 U(Q1,Q2) Y =$35,550
CommercialDemand
A
B
The refore,thechangeinutilityduetoa10%excisetaxoncommercialdataservicesis:
of a 10% excise tax on , , , , of a 10% excise tax on , , $35,550$45,954 $10,404
Noticethis
calculation
does
not
require
knowledge
of
the
actual
level
of
income,
the
exact
utility
function,ortheamountofgood2beingconsumed.
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ECO 204, 2010-2011, Test 3 Solutions
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(f)RecallthatthePDSsvariableinputswerequasivariablepower(denoteby)andquasivariablelabor(denotebywhileitsfixedinputswerequasifixedpower,quasifixedlaborandallotherinputs.Denoteallfixedinputsascapital.SupposePDSsproductionfunctionis:
permission
Page10of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
Assume 1 and 0.Supposethepriceofpoweris$/hour,thepriceofquasivariablelaboris $30.25/hourandthepriceofcapitalis.Giventhat $4/hourand $24/hourwhatisthepriceofquasivariablepower?Hint:Solve theCMP
m s. t. ax, andusethefactthat $4/hourand $24/hour.Showallcalculationsbelow.Answer:
Wearetoldthat:
4Thismeansthat:
4Tofindweneedtoexpresstheoptimaldemandforpower intermsoftheparametersand(hopefully)solvefor.ThismeanswehavetosolvetheCMP.Thetotalcostof hoursofdataservices si : Wecouldsubstitutevaluesforsomeparametersnoworwecouldworkaslongaspossibleinparametric
formandthensubstitutenumbers.Welldothelattersothatyoucanseethealgebra.
TheCostMinimizationProblem(CMP)is:
min, s. t. , , 0Now: 1sothat:
min, s.t. , , 0
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ECO 204, 2010-2011, Test 3 Solutions
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SincetheproductionfunctionisoftheCobbDouglasformweknowthatfor 0 wemustusesomepowerandlaborsothat , 0.Assuch,wecandropthenonnegativityconstraints:
mission
Page11of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
min,
s.t. Now:
max, s.t. SetuptheLagrangian:
max, s.t.
max,
s. t.
max, L 0
TheFOCsare: L 7 0
L 6 7 0
L
0The1stFOCimplies:
L 7 0 7
7 The2ndFOCimplies:
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ECO 204, 2010-2011, Test 3 Solutions
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Page12of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
67 0 6
7
76 Equatingthesyieldsthefamiliartheoptimalinputbundleiswheretheisoquantistangenttotheisocostresult:
7 76
16 16
Thisallowsustoisolatepower(orforthatmatte lab intermsoflabor(power).Forinstance:r or)
16
6 Wecansubstitutethisinthe3rdFOC:
L 0
6
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ECO 204, 2010-2011, Test 3 Solutions
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6
6
6
6
Now,wearetoldthat
$4whichmeansthat:
4 Substitutetheexpressionfor toget:
4 4
6
Page13of37
4
1 6 1 4
1
6 1
4
4 6 1
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4 6 1
Substitute $30.25 toget: 4 6 1
Page14of37
30.25 0.9976$1
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ECO 204, 2010-2011, Test 3 Solutions
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Question2[40Points.Parts(d)&(e)worth5pointseach,allotherpartsworth10pointseach]
ThisquestionisbasedontheHBScaseTheAluminumIndustryin1994.Thefollowingtablecontainsthe
coststructureoftheaverageCISprimaryaluminumsmelter,theaveragestateprimaryaluminum
smelter,andtheaveragerationalprimaryaluminumsmelter(pleasenotethatcumulativecapacity
belowisthetotalcapacityofallsmelterswithinacategory(forexample,thetotalcumulativecapacityof
allCIS
smelters
is
1.788
million
tons
per
year):
Allcostfiguresare$/t
VariablecostsareinBOLD
Smelter
AverageCIS
Smelter
AverageState
Smelter
Average
Rational
Smelter
CountryCIS Allover Allover
Company CIS State Rational
AverageCapacity(000stpy)243.73 120.74 121.53
Totalelectricitycost148.62 454.49 292.29
Totalaluminacost382.13 407.27 348.49
Otherrawmaterials63.69 163.57 120.62
Plantpowerandfuel4.51 11.81 10.34
Consumables76.92 56.72 73.91
Maintenance39.57 46.45 53.84
Labor17.80 62.73 194.19
Freight68.76 53.17 37.82
Generalandadministrative67.11 52.48 86.58
Cumulativecapacity(000softons/year)
(allsmelters
in
acategory)
1,788.07
(AllCIS)
2,826.95
(Allstate)
16,962.17
(Allrational)
Totalvariablecostsperton($/ton)= 740.14 1,135.25 873.15
Page15of37
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ECO 204, 2010-2011, Test 3 Solutions
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(a)Solvetheprofitmaximizingproblemfortheaverage a ionalr t primaryaluminumsmelter:
max s. t. 0, Here
priceofaluminum/ton,
TotalfixedCost,
=Totalvariablecostand
capacity.Assume 0.Showallcalculations.Answer
Sincethecasereportscostfiguresin$pertonweassumethatallsmeltershaveconstantreturnsso
that:
constant constant
Thiswillbeusefulbelow.Now,asmeltersprofitmaximizationproblem(PMP)is:
max s. t. 0, Notethatsmeltersarepricetakerssothat isaconstant.Recallthatallinequalityconstraintsmustbeexpressedintheform .Therefore:
m a x s. t. 0, max s. t. 0,
Havingexpressedallconstraintsintermsof form heLagrangian:, tmax,, L 0
max,, L
L 0TheFOCis:
TheKuhnTuckerconditionsare:
0 , , 0Page16of37
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ECO 204, 2010-2011, Test 3 Solutions
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0 , 0 , 0Noticethereare4possiblecasesthatmustbechecked:
q=0
(Checkwhen2 0)
q=qc
(Checkwhen1 0 )
CaseA
1=0(Checkwhenqqc)
CaseB
2=0
(Checkwhenq0)
q=qc
(Checkwhen1 0 )
CaseC
1=0(Checkwhenqqc)
CaseD
CaseA 0 , Needtocheckif 0 , 0.
Thisrequiresthat 0 and >0.ThuscaseAisimpossible.CaseB 0 , 0
Needtocheckif
0, .
Since 0 theKTcondition isautom tisfied.Thusweneedtocheckif 0. StartwiththeFOC:
aticallysaL 0
Page17of37
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Page18of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
Substitute 0and 0: 0 0 0
Thus,for 0 weneed: 0 0
0 0
CaseB
is
the
solution
when
the
price
of
aluminum
is
lower
than
0.Thisisbecausethemarginalcostofproducingthe1stunitisgreaterthanorequaltotheprice,orthe,ofthe1stunit.
$
Qty
MC
qc
ConstantReturnsTechnology
PMR
B
Thus,anytime
0thecompetitivefirmssupplycurveis 0(thatsnotthesameastheMCcurve):
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ECO 204, 2010-2011, Test 3 Solutions
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$
Qty
MC
qc
ConstantReturnsTechnology
PMR
CaseBw n 0he 0 0 0
CaseC , 0tocheckif
0 , 0Need
Since 0 theKTcondition 0 isautomaticallysatisfied.Thusweneedtocheckif 0:L 0
0Substitute
and
0:
0
Thus,for 0 weneed:Page19of37
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Page20of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
CaseCwillbethesolutionifthealuminumprice,the
, isgreaterthan
themarginalcost
atfull
capacity:
$
Qty
MC
qc
ConstantReturnsTechnology
P
MR
C
Thus,anytime
thecompetitivefirmssupplycurveis
.Againnoticethatthe
competitive
firms
MC
curve
is
not
the
supply
curve:
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ECO 204, 2010-2011, Test 3 Solutions
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$
Qty
MC
Page21of37
qc
ConstantReturnsTechnology
PMR
Cas eCwhen 0 CaseD 1 , 0
Needtocheckif 0 , StartwiththeFOC:
L 0 0
Substitute
0 0
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ECO 204, 2010-2011, Test 3 Solutions
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ThisisthefamiliarECO100resultthatacompetitivefirmproduceswherepriceequalsmarginalcost.
TheonlyproblemisthatwedontknowwhencaseDwillbeasolutionforsure.Forthatweneedtothe
conditionsunderwhich 0 and .From:
Wehave:Thus:
0
0
0 ThisgivesusaconditionforcaseDtobeasolutionandfortheoutputsuppliedtobebetween0andfull
capacity.
Intuitively,caseDsaysthatifthepriceoftheproductisbetween0andthefirmwillproduceanoutputbetweenzeroandfullcapacity:
$
Qty
MC
qc
Constant
Returns
Technology
PMR
Optimaloutput
anywhere
between
0
and
full
capacity
Page22of37
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ECO 204, 2010-2011, Test 3 Solutions
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Thus,anytime0 thecompetitivefirmssupplycurveisalsoitsMCcurve:ndmaynotbeusedforcommercial purposeswithoutpriorpermission
Page23of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
$
Qty
MC
qc
Constant
Returns
Technology
PMR
CaseDwhen 0 0 0 Puttingallcasestogetherwehaveacompetitivesmelterssupplycurve:
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ECO 204, 2010-2011, Test 3 Solutions
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$
Qty
Supply
Curve
qc
ConstantReturnsTechnology
Putanotherway,thequantitysuppliedis:
0, 0,0 ,
(b)Basedonyouranswertopart(a)whatistheimpactontheaveragerationalsmeltersoptimalprofits
from,holdingallelseconstant,a1%increasein:
Thepriceofaluminum?
Capacity?
Theminimumoutput?
Fixedcost?
Assumethat
$1,100/ton.Showallcalculations.
Answer:
Wearebeingaskedtoinvestigatetheimpactontheaveragerationalsmeltersprofitsduetoachange
inaparametertheeasiestwaytosolvethisisbytheenvelopetheorem.Todothis,wemustfirstfind
outtheaveragerationalsmeltersoutput.Recallthat:
Page24of37
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Allcostfiguresare$/t
VariablecostsareinBOLD
Smelter
AverageCIS
Smelter
AverageState
Smelter
Average
Rational
Smelter
CountryCIS Allover Allover
CompanyCIS State Rational
AverageCapacity(000stpy)243.73 120.74 121.53
Totalelectricitycost148.62 454.49 292.29
Totalaluminacost382.13 407.27 348.49
Otherrawmaterials 63.69 163.57 120.62
Plantpowerandfuel4.51 11.81 10.34
Consumables76.92 56.72 73.91
Maintenance39.57 46.45 53.84
Labor17.80 62.73 194.19
Freight68.76 53.17 37.82
Generalandadministrative67.11 52.48 86.58
Cumulativecapacity(000softons/year)
(allsmeltersinacategory)
1,788.07
(AllCIS)
2,826.95
(Allstate)
16,962.17
(Allrational)
Totalvariablecostsperton($/ton)= 740.14 1,135.25 873.15
Sinceweassumedallsmeltershaveconstantreturns,theaveragerationalsmelters $873.15for
0, 0,121.53]:
Page25of37
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$
Qty
Supply
Curve
Page26of37
qc =121.53
AverageRationalSmelter
MC=873.25
Currently,thepriceofaluminumis a d$1,100/ton n since:
$1,100 $873.15 Theaveragerationalsmelterwillproduceatfullcapacity(i.e.caseC):
$
Qty
Supply
Curve
qc =121.53
AverageRational
Smelter
P=$1,100 MR
MC=$873.25
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Page27of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
eCwhen 0Thus: 121.53and:
,1 873.25 226.751 0 0
0
Since873.25 then 873.25 873.25121.52 $106,117 .Moreover,addingupallaveragefixedcostitemswehave:
$345 345121.53 $41,928
Therefore:
1,100121.52 41,928 106,117
133,67241,928106,117 $14,373Noticethatproducingatfullcapacitymaximizesprofitsinthesensethatitminimizesloss.(Asastudy
question,you
should
check
that
operating
at
full
capacity
is
better
than
shutting
down,
confirming
the
rulethatarationalcompanyincurringlossesshouldshutdownwhen).Now,whatistheimpactontheaveragerationalsmeltersoptimalprofitsfrom,holdingallelseconstant,
a1%increasein:
Thepriceofaluminum?
Capacity?
Theminimumoutput?
Fixedcost?
Bytheenvelopetheorem,thechangeintheobjective(inthiscaseprofits)fromasmallchangeina
parameterisgottenbydifferentiatingtheLagrangianwithrespecttotheparameter,evaluatedatthe
initialsolution.
_____________________________________________________________________________________
Optionalnote:RecalltheLagrangianwas:
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max,, L 0right a
Page28of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
AnysolutiontothisproblemmustsatisfytheKTcondit s:ion
0 0
, , 0 , 0 , 0TheproducttermsintheKTconditionsimplythatattheoptimumthefollowingtermsarezero:
max,, L 0 ThisiswhydifferentiatingtheoptimalLagrangianisequivalenttodifferentiatingoptimalprofitswith
respecttotheparameter.
____________________________________________________________________________________
EnvelopeTheorem:themarginalprofitduetoa1%increaseinaluminumprice
TheLagrangianwas:
max,, L 0DifferentiatingtheLagrangianwithrespectt min mprice:oalu u
P L
Thisistheimpactonprofitsfroma$1increaseinaluminumprice.Tofindtheimpactduetoa1%
increaseinaluminumpricewehave:
% % P L L L Evaluateatoptimalsolution:
% % P
*
% % P 121.521,10014,373 9.3%% 9.3%% P% 9.3% 1 %
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S.AjazHussain,Dept.ofEconomics,UniversityofToronto
% New Initial Initial 100
New Initial
9.3%
Initial 0.093New Initial 0.093 Initial New Initial 0.093 Initial
New 14,37314,3730.093New $13,036
A1%increaseinaluminumpricesreducestheaveragerationalsmelterslossby9.3%orfromalossof
($14,373)toalossof($13,036).
EnvelopeTheorem:themarginalprofitduetoexpandingcapacityby1%
TheLagrangianwas:
max,, L 0DifferentiatingtheLagrangianwithrespectt capac y:o it
L
L
Thisistheimpactonprofitsfroma1unitincreaseincapacity.Tofindtheimpactduetoa1%increasein
capacitywehave:
% % L L L Evaluateatoptimalsolution:
% % *
% % 344.95 121.5214,373 2.92%% % 2.92% 1% 2.92%
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Page30of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
Initial 1New Initial Initial
00 2.92% 0.0292
N ew Initial 0.0292 Initial New Initial 0.0292 Initial New 14,37314,3730.0292
New $13,953.31A1%increaseincapacityreducestheaveragerationalsmelterslossby2.92%orfromalossof
($14,373)toalossof($13,953.31).
EnvelopeTheorem:themarginalprofitduetoraisingtheminimumoutputby1%
TheLagrangianwas:
max L 0,,
Wehadrequiredthat 0.Rewritingthisconstraintas wehave: max,, L
DifferentiatingtheLagrangianwithrespec
:tto
L Thisistheimpactonprofitsfroma1unitincreaseinminimumoutput.Tofindtheimpactduetoa1%
increaseinminimumout have:putwe
% % L L L 0 L 0Thereisnoimpactonoptimalprofitsfromraisingtheminimumoutputrequirementby1%.Why?
Becausetheoptimalsolutionisforthesmeltertoproducewellabovezero,sothattheminimumoutput
constraintdoesnotbindassuch,thereisnovalueinrelaxingtheconstraint.
EnvelopeTheorem:themarginalprofitof1%higherfixedcost
TheLagrangianwas:
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S.AjazHussain,Dept.ofEconomics,UniversityofToronto
DifferentiatingtheLagrangianwithrespec :tto
L
1
Thisistheimpactonprofitsfroma$1increaseinTFC.Tofindtheimpactduetoa1%increaseinTFCwe
have:
% % L L 1 L 1 Evaluateatoptimalsolution:
% % 1 *
% % 1 14,37341,928 2.% %
92% 2.92% 1
2.92%% New Initial Initial 1
New Initial Initial
00 2.92%
0.0292N ew Initial 0.0292 Initial New Initial 0.0292 Initial
New 14,37314,3730.0292 New $14,793
A1%increaseinTFCraisestheaveragerationalsmelterslossby2.92%orfromalossof($14,373)toa
lossof($14,793).
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(c)GraphtheprimaryaluminumindustrysupplycurveasifallCISsmeltersbehaveliketheaverageCIS
smelter,allstateownedsmeltersbehaveliketheaveragestatesmelter,andallrationalsmeltersbehave
liketheaveragerationalsmelter.
Answer:
Fromthe
case
we
know
that
CIS
and
state
owned
smelters
most
likely
behave
as
irrational
smelters,
i.e.
theyproducealuminumevenifthepricefallsbelow.Putanotherway,irrationalsmeltersproducealuminumregardlessoftheprice.Recallthat:
Allcostfiguresare$/t
VariablecostsareinBOLD
Smelter
AverageCIS
Smelter
AverageState
Smelter
Average
Rational
Smelter
CountryCIS Allover Allover
CompanyCIS State Rational
AverageCapacity(000stpy)243.73 120.74 121.53
Totalelectricitycost148.62 454.49 292.29
Totalaluminacost382.13 407.27 348.49
Otherrawmaterials63.69 163.57 120.62
Plantpowerandfuel4.51 11.81 10.34
Consumables76.92 56.72 73.91
Maintenance39.57 46.45 53.84
Labor17.80 62.73 194.19
Freight68.76 53.17 37.82
Generalandadministrative67.11 52.48 86.58
Cumulativecapacity(000softons/year)
(allsmeltersinacategory)
1,788.07
(AllCIS)
2,826.95
(Allstate)
16,962.17
(Allrational)
Totalvariablecostsperton($/ton)= 740.14 1,135.25 873.15Page32of37
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
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Assumingconstantreturnsandthatsmeltersproduceatfullcapacity(forcasesCandD)weseethat
together,thestateandCISsmelterswillproduceacumulativeoutputof1,788.07+2,826.95=4,615.02
000stonsatanypricewhiletherationalsmelterswillproduce16,962.17000softonssolongas 873.15:
$
Qty
(mtons)
PrimaryAluminumIndustry
Supply
Curve
Page33of37
CIS&Statesmelters
Rational
smelters
873.25
4.61m 21.588m
(d)[Thispartisindependentofallpartsbelow]Graphtheprimaryaluminumindustrysupplycurvefrom
part(c)belowandthenshowtheimpactofallrationalsmeltersexperiencinglearningbydoing
(assumelearning
by
doing
has
asmall
effect).
Answer
Withlearningbydoingtherewillbeadecreaseineverysmelters. However,sincethestateandCISsmeltersproduceatanyprice,therewillbenochangeinthetheirsupplycurvewhilstlearningby
doingpushestherationalsmelterssupplycurvedown:
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$
Qty
(mtons)
PrimaryAluminumIndustry
Supply
Curve
Page34of37
CIS&Statesmelters
Rational
smelters
873.25
4.61m 21.588m
(e)Usetheprimaryaluminumsupplymodelinpart(c)topredictthedemandforprimaryaluminumfor
thecaseforthecaseswhen(i) $ 8 0 0/ton,(ii)$1,100/ton.Pleaseshowallgraphsbelowandexplainyourreasoning.
Answer:
Case(i):$800/.Inthiscase:
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
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$
Qty
(mtons)
PrimaryAluminumIndustry
Supply
Curve
Page35of37
CIS&Statesmelters
Rational
smelters873.25
P=800
4.61m 21.588m
NoticethatallCISandstatesmelterswillproducealuminumwhileallrationalsmelterswillshutdown.
Thetotaloutputwillbe4.61mtons.Assumingnoinventorybuildupsorrundowns,demandforprimary
aluminum w l ns.i lbe4.61mto
Case(ii):$1,100/.Inthiscase:
$
Qty
(mtons)
PrimaryAluminumIndustry
Supply
Curve
P=1,100
CIS&
State
smelters
Rational
smelters873.25
4.61m 21.588m
S.AjazHussain,Dept.ofEconomics,UniversityofToronto
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Noticethatallsmelterswillproducealuminum.Thetotaloutputwillbe21.588mtons.Assumingno
inventorybuildupsorrundowns,demandforprimaryaluminumwillbe21.588mtons..
TheEnd
WORKSHEETS
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S.AjazHussain,Dept.ofEconomics,UniversityofToronto
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ECO 204, 2010-2011, Test 3 Solutions
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