Prestige Telecom-Economics Case

8/10/2019 Prestige Telecom-Economics Case

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ECO 204, 2010-2011, Test 3 Solutions

Thistestiscopyrightmaterialandmaynotbeusedforcommercialpurposeswithoutpriorpermission

UniversityofToronto,DepartmentofEconomics,ECO2042010 2011AjazHussain

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Page1of37

S.AjazHussain,Dept.ofEconomics,UniversityofToronto
http://www.economics.utoronto.ca/index.php/index/index/homehttp://www.economics.utoronto.ca/index.php/index/index/homehttp://www.economics.utoronto.ca/index.php/index/index/homehttp://www.economics.utoronto.ca/index.php/index/index/homehttp://www.economics.utoronto.ca/index.php/index/index/homehttp://www.economics.utoronto.ca/ahussain/http://www.economics.utoronto.ca/ahussain/http://www.economics.utoronto.ca/ahussain/http://www.economics.utoronto.ca/ahussain/http://www.economics.utoronto.ca/index.php/index/index/homehttp://www.utoronto.ca/


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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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(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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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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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:

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Thistestiscopyrightmaterialandmaynotbeusedforcomm rcialpurposeswith

Breakeven e outpriorpermission

Page6of37


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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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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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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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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Thistestiscopyrightmaterialandmaynotbeusedforcommercialpurposeswithoutprior

(f)RecallthatthePDSsvariableinputswerequasivariablepower(denoteby)andquasivariablelabor(denotebywhileitsfixedinputswerequasifixedpower,quasifixedlaborandallotherinputs.Denoteallfixedinputsascapital.SupposePDSsproductionfunctionis:

permission

Page10of37


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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Thistestiscopyrightmaterialandmaynotbeusedforcommercialpurposeswithoutpriorper

SincetheproductionfunctionisoftheCobbDouglasformweknowthatfor 0 wemustusesomepowerandlaborsothat , 0.Assuch,wecandropthenonnegativityconstraints:

mission

Page11of37


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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Thistestiscopyrightmaterialan fo

Ldmaynotbeused rcommercial purposeswithoutpriorpermission

Page12of37


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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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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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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(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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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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Thistestiscopyrightmaterialandmaynotbeusedfor mmer alpurp

0co ci oseswithoutpriorpermission

Page18of37


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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$

Qty

MC

qc


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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Thistestiscopyrightmaterialandm notbeusedforcommercial p

0ay urposeswithoutpriorpermission

Page20of37


CaseCwillbethesolutionifthealuminumprice,the

, isgreaterthan

themarginalcost

atfull

capacity:

$

Qty

MC

qc


P

MR

C

Thus,anytime

thecompetitivefirmssupplycurveis

.Againnoticethatthe

competitive

firms

MC

curve

is

not

the

supply

curve:


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$

Qty

MC

Page21of37

qc


PMR

Cas eCwhen 0 CaseD 1 , 0

Needtocheckif 0 , StartwiththeFOC:

L 0 0

Substitute

0 0



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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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Thistestiscopyrightmateriala

Thus,anytime0 thecompetitivefirmssupplycurveisalsoitsMCcurve:ndmaynotbeusedforcommercial purposeswithoutpriorpermission

Page23of37


$

Qty

MC

qc

Constant

Returns

Technology

PMR

CaseDwhen 0 0 0 Puttingallcasestogetherwehaveacompetitivesmelterssupplycurve:


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$

Qty

Supply

Curve

qc


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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Smelter

AverageCIS

Smelter

AverageState

Smelter

Average

Rational

Smelter


CompanyCIS State Rational




Otherrawmaterials 63.69 163.57 120.62


Consumables76.92 56.72 73.91

Maintenance39.57 46.45 53.84

Labor17.80 62.73 194.19

Freight68.76 53.17 37.82



(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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Thistestiscopyrightmaterialandmaynotbeusedforcommercial pu

Cas rposeswithoutpriorpermission

Page27of37


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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Thistestiscopy materi landmay notbeusedforcommercial purposeswithoutprior permission

max,, L 0right a

Page28of37


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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Thistestiscopyrightmaterialandmaynotbeus forcommer

9.3%ed cialpurposeswithoutpriorpermission

Page29of37


% 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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Thistestiscopyrightmaterialandmay notbeused

New Initial forcommercial purposeswithoutpriorpermission

Page30of37


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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Thistestiscopy materi landmay notbeusedforcommercial purposeswithoutprior permission

max,, L 0right a

Page31of37


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:



Smelter

AverageCIS

Smelter

AverageState

Smelter

Average

Rational

Smelter


CompanyCIS State Rational




Otherrawmaterials63.69 163.57 120.62


Consumables76.92 56.72 73.91

Maintenance39.57 46.45 53.84

Labor17.80 62.73 194.19

Freight68.76 53.17 37.82



(allsmeltersinacategory)

1,788.07

(AllCIS)

2,826.95

(Allstate)

16,962.17

(Allrational)

Totalvariablecostsperton($/ton)= 740.14 1,135.25 873.15Page32of37



33/37



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)


Supply

Curve

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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:



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$

Qty

(mtons)


Supply

Curve

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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)


Supply

Curve

P=1,100

CIS&

State

smelters

Rational

smelters873.25

4.61m 21.588m



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Noticethatallsmelterswillproducealuminum.Thetotaloutputwillbe21.588mtons.Assumingno

inventorybuildupsorrundowns,demandforprimaryaluminumwillbe21.588mtons..

TheEnd

WORKSHEETS

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