EC102EconomicsB Class2
Week3/LT 28.01.2016
SamiraBarzin
[email protected]
samirabarzin.jimdo.com
OfficeHoursEC102:Mon10:30–11.30
(32L1.30)
EC102
Class2:Q1
SamiraBarzin
Increaseincapital_____outputand_____the
amountofoutputusedtoreplacedepreciaQng
capital.
a)  increase;increase
b)  increase;decrease
c)  decrease;increase
d)  decrease;decrease
EC102
Class2:Q1
SamiraBarzin
Someofthetermsofthemodel:
k:capitalperworker
!
:depreciaQonrate
f(k):outputperworkerisafuncQonthatincreases
incapital(i.e.ifcapitalincreases,outputperworker
willincrease)
Soincreasesink:
! ↑ → !! ↑ ! ↑ → ! ! ↑ and
EC102 SamiraBarzin
Class2:Q1
Increaseincapital_____outputand_____the
amountofoutputusedtoreplacedepreciaQng
capital.
a)  increase;increase✔
b)  increase;decrease✖
c)  decrease;increase✖
d)  decrease;decrease✖
EC102
Class2:Q2
SamiraBarzin
IftwoeconomiesareidenQcal(includinghavingthesame
investmentrate),butoneeconomyhasasmallercapital
stock.Then:
a)  thehighcapitaleconomywillbeatahighersteadystate
b)  thelowcapitaleconomywillbeatahighersteadystate
c)  thetwoeconomieswillbeatthesamesteadystate
d)  thelowcapitaleconomywillgrowfasterduring
transiQon
e)  thehighcapitaleconomywillgrowfasterduring
transiQon
EC102
current
capitalstock
forlow
capital
economy
Class2:Q2
SamiraBarzin
current
capitalstock
forhigh
capital
economy
Ifbotheconomiesonlydifferinthecapitalstock,thentheinvestmentanddepreciaQon
curvesarethesameforbothcountries.TheintersecQonofthedepreciaQonand
investmentcurvesarethesameforbothcountries,sobothcountrieshavethesame
steadystate.Capitalincreasesoutputatadecreasingrate,i.e.thelessabsolutecapital
stockthereexiststhehigherthereturnfromeachaddiQonalunitofcapital(herethe
returnofcapitalis(output)growth.Thecountrywithalowercapitalstockwilltherefore
exhibitahighergrowthrate.
EC102
Class2:Q2
SamiraBarzin
IftwoeconomiesareidenQcal(includinghavingthesame
investmentrate),butoneeconomyhasasmallercapital
stock.Then:
a)  thehighcapitaleconomywillbeatahighersteadystate
✖
b)  thelowcapitaleconomywillbeatahighersteadystate
✖
c)  thetwoeconomieswillbeatthesamesteadystate✔
d)  thelowcapitaleconomywillgrowfasterduringtransiQon
✔
e)  thehighcapitaleconomywillgrowfasterduring
transiQon✖
EC102
Class2:Q3
SamiraBarzin
Whichofthefollowingwouldincreasethesteady
statelevelofoutput:
a)  adropintheconsumpQonrate
b)  lowergovernmentspending
c)  anincreaseinimportsoradecreaseinexports
d)  anincreaseinthecapitaldepreciaQonrate
e)  adecreaseinthecapitaldepreciaQonrate
EC102
Class2:Q3
SamiraBarzin
a)  adropintheconsumpQonrate✔
AllconsumersspendtheirincomeonconsumpQonand
savingsy=(c+s)ywherecistheconsumpQonrate,i.e.the
relaQveamountofyourincomeyouspendonconsumpQon
andsisthesavingsrate,i.e.therelaQveamountofyour
incomeyouspendonsavingswithforbothcands:0<c<
1,0<s<1.Sinceconsumersspendalltheirincomeon
eitherconsumpQonorsavings:c+s=1<=>s=1–c.
Hence,
! ↓ → 1 − ! ↑= ! ↑ → !" ! ↑ = !" ↑→ ! ↑
EC102
Class2:Q3
SamiraBarzin
b)  lowergovernmentspending -  seedocument“TheSolowModel(withandwithoutgovernment)”
c)  anincreaseinimportsoradecreaseinexports✔
GDPisdefinedas:GDP=Y=C+I+G+NX
whereNX=Exports–Imports
Reformulatetogetanexpressionofinvestments:
I=Y-C–G-NXandinperworkertermsi=y–c–g–nx
alsowehave:sy=isothatsy=y–c–g–nx=y–c–g–ex+im
Ifimportsareincreased,thensincreases,samefordecreasing
exports.Eitherofthesewillresultsinahigherinvestmentsofsyand
henceahighersteadystatelevelofoutput.
EC102
Class2:Q3
SamiraBarzin
d)  anincreaseinthecapitaldepreciaQonrate✖
e)  adecreaseinthecapitaldepreciaQonrate✔
AnincreaseinthedepreciaQonrate,shijsthecapital
depreciaQon()upwards,assumingtheinvestmentrateis
!!
unaffected,theintersecQon(SS)willnowbeclosertothe
originandtheSS-capitalperworkerstockislower.Alower
capitalstockisassociatedwithaloweroutputinSS(asoutput
isanincreasingfuncQonofcapital).
Theoppositeappliesforthecaseofadecreaseinthe
depreciaQonrate
EC102
Class2:Q3
SamiraBarzin
Whichofthefollowingwouldincreasethesteady
statelevelofoutput:
a)  adropintheconsumpQonrate✔
b)  lowergovernmentspending✔
c)  anincreaseinimportsoradecreaseinexports
✔
d)  anincreaseinthecapitaldepreciaQonrate✖
e)  adecreaseinthecapitaldepreciaQonrate✔
EC102
Class2:Q4
SamiraBarzin
Assumethatawarreducesacountry’slabourforce
butdoesnotdirectlyaffectitscapitalstock.Thethe
immediateimpactwillbethat:
a)  totaloutputwillfall
b)  totaloutputwillrise
c)  outputperworkerwillfall
d)  outputperworkerwillrise
EC102
Class2:Q4
SamiraBarzin
Thewarresultsin: ! ↓butconstant
!
(Denotepost-warlabourforceL’andpre-warlabourforceL
sothatL’<L.
a)  totaloutputwillfall✔vs.b)totaloutputwillrise✖
TotaloutputisafuncQonthatincreasesinbothcapitaland
labourF(K,L).Pre-waroutputF(K,L)andpost-waroutput
F(K,L’),asL’<LthenF(K,L)>F(K,L’).
c)  outputperworkerwillfall✖vs.d)outputperworkerwill
rise✔
Outputperworkerisy=f(k)=F(K/L).WithL’<Lthenpre-war
outputperworkerF(K/L)<F(K/L’)<=>y<y’.
EC102
Class2:Q4
SamiraBarzin
Assumethatawarreducesacountry’slabourforce
butdoesnotdirectlyaffectitscapitalstock.Thethe
immediateimpactwillbethat:
a)  totaloutputwillfall✔
b)  totaloutputwillrise✖
c)  outputperworkerwillfall✖
d)  outputperworkerwillrise✔
EC102
Class2:Q5
SamiraBarzin
Considertwoeconomieswiththesameinvestmentrate(andthe
samedepreciaQonrate).Imagineinoneofthetwoeconomies
populaQonispermanentlygrowingfasterthanintheother–for
exampleinoneeconomypopulaQonisforevergrowingatarateof
2%peryearandintheotherat3%.Whichofthefollowingdoyou
thinkistrue?
a)  theeconomywithfasterpopulaQongrowthwillhaveahigher
steadystateincomepercapita
b)  theeconomywithfasterpopulaQongrowthwillhavealower
steadystateincomepercapita
c)  thetwoeconomieswillhavethesamesteadystateincomeper
capita
d)  ifpopulaQonisgrowingtherecannotbeasteadystatelevelof
incomepercapita
EC102
Class2:Q5
SamiraBarzin
ThemajorityofthevariablesofinterestintheSolowmodel
areinperworkerterms.Forexample,capitalperworkerisk=
K/L,acountrywithalargepopulaQongrowthratewill
undoubtedlyeventuallyhavealargerL,sothatkwillbe
smallerwithincreasesinL.Incomepercapita(equivalentto
outputpercapita)isy=Y/L,soasLincreasesydecreases.
Thiscanalsobewrisenasy=f(k),withincreasingL,k
decreasessothatymustalsodecrease.
(TheSolowmodelwithpopulaQongrowthhasthepopulaQon
growthratenenterwithcapitaldepreciaQon.Capital
depreciaQonwouldbecome ! + !.Increasesinnresultsin
!
anupwardsshijofthecurve,soSSmovestothelej(thisis
associatedwithlowerpercapitacapitalstockandoutput).
EC102
Class2:Q5
SamiraBarzin
Considertwoeconomieswiththesameinvestmentrate(andthe
samedepreciaQonrate).Imagineinoneofthetwoeconomies
populaQonispermanentlygrowingfasterthanintheother–for
exampleinoneeconomypopulaQonisforevergrowingatarateof
2%peryearandintheotherat3%.Whichofthefollowingdoyou
thinkistrue?
a)  theeconomywithfasterpopulaQongrowthwillhaveahigher
steadystateincomepercapita✖
b)  theeconomywithfasterpopulaQongrowthwillhavealower
steadystateincomepercapita✔
c)  thetwoeconomieswillhavethesamesteadystateincomeper
capita✖
d)  ifpopulaQonisgrowingtherecannotbeasteadystatelevelof
incomepercapita✖
EC102
SamiraBarzin
Class2:EssayQuesQon
Consideraneconomywithagovernment,
consumers,andfirms,butnoforeignsector(no
exportsandimports)
EC102
a) 
SamiraBarzin
Class2:EssayQuesQon
WritedownanexpressionforGDPintermsof
expenditures
Therearethreeagentsintheeconomy:households,
firmsandthegovernment.
Householdsconsume,firmsinvestandthegovernment
hasexpendituressothattheGDPisasumofthe
expenditures:
Y=C+I+G
(savingsarenotanexpenditures,theyareanintertemporalshijin
consumpQonfromtodaytothefuture,e.g.whatyousaveyougetpaidout
nextyearandthenyoucanbuyyourselfanewcar(=consumpQon))
EC102
b) 
SamiraBarzin
Class2:EssayQuesQon
Usetheexpressionina)toderiveanexpression
forinvestment
Fromthepreviousexpressionwecanderive
investment
Y=C+I+G
<=> I=Y–C-G
EC102
SamiraBarzin
Class2:EssayQuesQon
SupposethatconsumpQonisafracQon(1s)ofGDP,whilethegovernmentspenda
fracQontofGDPongovernmentpurchases
EC102
c) 
SamiraBarzin
Class2:EssayQuesQon
Rewritetheexpressionforinvestmentintermsofs
andt
ConsumpQoncannowbeexpressedas:C=(1-s)Y
Governmentexpenditurescanbeexpressedas:G=tY
SubsQtuteintotheinvestmentequaQon:
I=Y–C–G=Y–(1-s)Y–tY=(s-t)Y
inperworkerterms: i=(s-t)y
EC102
SamiraBarzin
Class2:EssayQuesQon
Assumes>tandnopopulaQongrowth
EC102
SamiraBarzin
Class2:EssayQuesQon
d)  WhatisthelawofmoQonofcapitalperworker?
Eachperiodnewcapitalentersthecapitalstockthrough
investmentsi=(s-t)y(aslongass>ttheni>0)
Eachperiodcapitalleavesthecapitalstockdueto
depreciaQon !!
Aslongasnewinvestmentsoutweighthecapitallostdueto
depreciaQon,capitalstockwillgrow(thechangeinthe
capitalstockisposiQve),viceversaforthecasewhennew
investmentsarelessthancapitaldepreciated.
∆! = ! − !! = ! − ! ! − !! = ! − ! ! ! − !!
EC102
e) 
SamiraBarzin
Class2:EssayQuesQon
DrawadiagramthatillustratesthelawofmoQonin
(d)andusethediagramtodescribethegrowth
process
-seedocument“TheSolowModel(withandwithout
government)”(SecQon:SpecialCase:Governmentspending)
EC102
f) 
SamiraBarzin
Class2:EssayQuesQon
Supposethattheeconomyisatthepointofzero
growth(steadystate),andthegovernmentreducest
tot’<t,whathappenstothegrowthrateintheshort
andinthelongrun?
-seedocument“TheSolowModel(withandwithout government)”(SecQon:Achangeingovernment spending)
(ShortrunreferstothetransiQonperiodbetweentheold
andthenewSS,Longrunreferstothestateinthenew
steadystate)
EC102
SamiraBarzin
Class2:EssayQuesQon
g)  ExplaintheeconomicintuiQonforthe
resultin(f)
-seedocument“TheSolowModel(withandwithout government)”(SecQon:Achangeingovernment spending)
EC102
h) 
SamiraBarzin
Class2:EssayQuesQon
Considertwoeconomiesoutsidethesteadystate.Thetwo
economieshavethesamecapitalperworker,whichisless
thaneithercountry’ssteadystatelevel.Country1hasa
highert1>t2.Whicheconomydoyouexpecttosee
growingfaster?
Thisisthesameascomparingthesamecountrybeforeandajer
achangeingovernmentexpenditures,thisisillustratedinthe
SolowModeldocument.Ahighert(c.p.),resultsinalowerSS,
hencecountry1hasalowerSSthancountry2.Sinceboth
countrieshavecurrentlythesamecapitalperworker,but
country2hasahigherSS,country2isfurtherawayfromtheSS
capitalperworkeramountandwillhenceexperiencealarger
growthrate.