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ECNM10069 Topics in Macroeconomics

Exam Date: From and To: Exam Diet:

09 May 2023 Exam: 13:00:00 – 15:00:00 May 2023

Please read full instructions before commencing writing

Exam paper information

•Total number of pages: 8 (including this page).

•This paper has 2 sections.

•Please answer question A1, and either A2 or A3 AND question B1, and either B2 or B3.

Special instructions

•Attach your personalised barcode to EACH script book.

•Complete each of the questions in Section B in a separate booklet (i.e., you should use a

total of four booklets), with the personalized barcode attached, and your personal

information filled in completely and correctly.

•You must complete the exa

m within the time specified at the top of this page.

•You must start EACH QUESTION on a separate page. Questions must be clearly

numbered in the left margin.

•Your answers must be clearly written.

•Your exam number (e.g., B123456) must be clearly written at the t

op of each

pa

ge.

•Answers may be subject to checks through TurnItIn.

•This examination will be marked anonymously.

•Students are allowed to keep the question sheet.

Special items

•Non- programmable calculators are permitted in this exam.

Examin

ers: Tim Worrall (Chair), Professor Nigar Hashimzade (External)

SectionA[50Marks]:GrowthandDevelopment

attention:answerquestionA1[15marks],and

eitherquestionA2or

A3[35marks].

[A1]Shortquestions[15marks].

Answereachsub-questionbasedontheconceptsthatwerecoveredinthecourse.The

argumentsshouldb eprimarilyverbal(thoughyoucanuseformulaeorgraphsifyouwish).

Beconcise.

ConsideraversionoftheCobb-Douglaspro ductionfunctionforcountryjinyeart:Y

jt

=

A

jt

K

α

jt

L

1−α

jt

,wherethetotalfactorpro ductivityA

jt

isdecomp osedasfollows:

A

jt

=X

t

×E

jt

X

t

istheworldtechnologyfrontier,andE

jt

istheinverseofthedistanceofcountryjtothe

frontier.

(a)Explaininwordswhatb othX

t

andE

jt

measure.Whichislikelytob emoreimp or-

tantforexplainingGDPgrowthintheUSoverthelast100years?Whichismore

imp ortantforexplainingdierencesinothercountries'GDPrelativetotheUS?[5

marks]

(b)Suggestap olicythegovernmentofacountrycouldusetoincreaseE

jt

,andexplain

howitcouldhelp.[5marks]

(c)Explaintwochannelsthroughwhichalargerp opulationcanhelpX

t

toincrease

faster.[5marks]

[A2]TheSolowMo del[35marks].

ConsideraSolowmo delindiscretetime.Thep opulationattimetisgivenbyL

t

=L

0

(1+n)

t

andtechnologyattimetisgivenbyA

t

=A

0

(1 +g)

t

.Thereisarepresentativehousehold

thatsavesaxedp ercentage,s,ofitsnetincomeineveryp erio d.

Arepresentativermpro ducesusingcapital,K

t

,lab our,L

t

,andanothernaturalresource

E

t

,whichitrentsfromtherepresentativehousehold.Therentalpriceofcapitalisdenoted

byR

t

,therentalpriceoflab our(thewage)isdenotedW

t

andtherentalpriceofthenatural

resourceisdenotedQ

t

.

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OutputisY

t

=K

α

t

E

γ

t

(A

t

L

t

)

1−α−γ

,withα≥0,γ≥0andα+γ <1.Capitalaccumu-

latesaccordingtoK

t+1

= (1−δ)K

t

+sY

t

.

(a)Writedowntherm'sprotmaximisationproblemandusetherm'srstorder

conditionstondtherentalpriceofthenaturalresource,Q

t

.[7marks]

(b)AssumethatE

t

representstheeconomy'sendowmentofland,whichisinxedsup-

ply,sothatE

t

=Eforallt.Findoutputp erworkerandshowthatitdep endsonthe

amountoflandavailablep erworker,E/L

t

.Explainwhythisisthecase.[7marks]

NowassumeinsteadthatE

t

representsnon-renewablesourcesofenergy(suchasoil,coaland

gas).Theinitialsto ckofnon-renewableenergywasZ

0

.Everyp erio d,aconstantfraction

oftheremainingsto ckofenergyisusedinpro duction,sothatE

t

=s

E

Z

t

,whereZ

t

isthe

remainingsto ckavailableinp erio dtand0< s

E

<1isaconstant.Thus,theamountof

energyusedinpro duction,E

t

,isdecreasingovertime.

(c)Usingyouranswerfromparta),discusswhethertheequilibriumpriceQ

t

isincreas-

ingordecreasinginE

t

relativetothepriceoflab our,W

t

.Explainyouranswer.[7

marks]

Itcanb eshownthatthegrowthofaggregateoutput,Y

t

,onthebalancedgrowthpathis

approximately(youdonotneedtoshowthis)

g

Y

=

1

1−α

(

(1−α−γ)(n+g+ng)−γs

E

)

.

(d)Comparethistothebaselinemo del,wheretechnology,capitalandlab ourarethe

onlyinputs(i.e.γ= 0),withg

baseline

Y

=g+n+ng.Isg

Y

smallerorlargerthan

g

baseline

Y

?Explainwhyg

Y

dep endsnegativelyonγands

E

.[7marks]

(e)Considerthetwoversionsofthemo delab ove(theonewhereE

t

=Erepresentsthe

endowmentofland,andtheonewhereE

t

representsnon-renewablesourcesofen-

ergy).Dotheyalwaysconvergetoabalancedgrowthpathwheregrowthinaggregate

capital,outputandconsumptionisconstantandp ositive?Howdo esthiscompare

tothebaselinemo del?Explaintheintuitionforyouranswer.[7marks]

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[A3]TheRamseyMo del[35marks].

ConsideraRamseymo delindiscretetime,witharepresentativehouseholdandarep-

resentativerm.Thep opulationinp erio dtisgivenbyL

t

=L

0

(1 +n)

t

.Technologyin

p erio dtisgivenbyA

t

=A

0

(1 +g)

t

.

Thermpro ducesoutputusingthepro ductionfunctionF(K

t

,A

t

L

t

) =K

α

t

(A

t

L

t

)

1−α

.It

maximisesprotsbycho osingL

t

andK

t

ineveryp erio dt.

Theinnitely-livedrepresentativehouseholdmaximisesU=

∑

∞

t=0

β

t

logC

t

withβ∈(0,1),

whereC

t

representsconsumptioninp erio dt={0,1,2,3,...}.ThehouseholdsuppliesL

t

exogenousunitsoflab ourinelasticallyandK

t

unitsofcapitalforanendogenouswage,W

t

,

andanendogenousreturnoncapital,R

t

,resp ectively.

(a)Writedownthehousehold'sLagrangian.Explainwhichvariablesarethehousehold's

choicevariables,andwhichvariablesittakesasgiven.[7marks]

(b)TheEulerequationis

C

t+1

C

t

=β[1 +R

t+1

−δ](youdonotneedtoshowthis).Imag-

inetherearetwoeconomies,XandY,whichareidenticalexceptthatK

X

0

< K

Y

0

.In

b otheconomies,theinititallevelofcapitalinPerio d0isb elowitsbalancedgrowth

pathlevel.UsetheEulerequationtoexplainwhicheconomywillhavethefastest

rateofconsumptiongrowthb etweenPerio d0andPerio d1.[7marks]

(c)Findthecapitalshareofincome,x

K

t

=R

t

K

t

/Y

t

andexplainwhatitmeasuresinthis

mo del.Withoutdoinganymorecalculations,explainwhytherentalrateofcapital,

R

t

,mustb econstantonthebalancedgrowthpath.[7marks]

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(d)Thechartb elowshowsthelab ourshareofincome,x

L

t

=W

t

L

t

/Y

t

fortheUSAfrom

1970to2020.Commentonwhetherthepatterninthischartmatchesthepredictions

oftheRamseymo delab outthelab ourshare.[7marks]

(e)Nowassumethatthepro ductionfunctionisinsteadgivenbyF(K

t

,A

t

L

t

) =K

α

t

(A

t

L

t

)

φ

,

withα+φ <1.Findtherm'sprotsinthisversionofthemo del.Aretheyequal

tozero?Explainyouranswer.[7marks]

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SectionB[50Marks]:LabourEconomicsandMacroeconomics

attention:answerquestionB1[15marks],and

eitherquestionB2or

B3[35marks].

[B1]Shortquestions[15marks].

Answereachofthesequestionsinashortparagraphbasedonwhatwastaughtinthe

course.Questionsthatb eginwith"T/F/U"shouldb eansweredbyrstpickingoneofthe

threeoptions(True,FalseorUncertain)andthenjustifying.Yourgradewillb ebasedon

theexplanations.

(a)[T/F/U]Inthetwop erio dsneo classicalmo del,substitutioneects(regardinglab our

inresp onsetoawagechange)outweighincomeeectsintheshortrun,butinthe

longruneithereectcanb edominant.[5marks]

(b)[T/F/U]Intheeciencywagesmo del,ifitb ecomeseasierforrmstomonitor

worker'sp erformance,thatmakesiteasiertoinduceworkerstoexerthigheort

whichleadstohigherwages.[5marks]

(c)Inthesearchandmatchingmo del,explainintuitivelytheeectofanincreaseinthe

valueofunemploymentb enetsonthewagebargainingcurve.[5marks]

[B2]Parttimework[35marks].

Startwitha1-p erio dneo classicalmo deloflab oursupplyasseeninclass,whereindi-

vidualssupplylab ourforawageratew,andtheyreceivenon-lab ourincomev >0.Their

totaltimeendowmentisT,denominatedinweeklyhours.Imagineaworkerwithutility

functionU(c,l),thatsatisestheassumptionsoutlinedinclass.Thisindividualfacesthe

intro ductionofaparttimeworkp olicywherebythehourlywageratelowersfromwto0.5w

iftheworkerworkslessthan40hoursp erweek(theworkerearnsthefullwageifhoursare

atleast40).

(a)Writedowntheoptimisationproblemofthisindividualwiththenewp olicy.Illus-

trategraphicallythebudgetconstraintofthisproblemb eforeandafterthep olicy.

Hint:withthenewp olicy,thereisadiscontinuity(ajump)inthebudgetconstraint

at40hoursofwork.[7marks]

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(b)Whatwillhapp entothehoursworkedofanindividualwhoworkedexactly40hours

p erweekpriortotheintro ductionoftheparttimep enalty?Explain,usingagraph

toillustratetheanswer.[7marks]

(c)Takeanindividualwhoworkedlessthan40hourspriortotheparttimep olicy.Sup-

p osethatrmswanttoinducesuchindividualstoworkmorewithsuchap olicy.

Willthatp olicyb eeective?Howwouldthateectworker'swelfare?Illustrate

graphicallyyouranswerandexplain.[7marks]

Supp osethatpriortotheparttimep olicy,theindividualcouldonlywork40ormorehours,

orzerohours(i.e.workingb etween0and40hoursisnotanoption).

(d)Illustrategraphicallythecasewheretheindividualwasindierentb etweenworking

40hoursorzerohourspriortotheintro ductionoftheparttimep olicy.Wouldthis

individualprefertoworklessthan40hoursifgiventhechance?[7marks]

(e)Showgraphicallyhowtheintro ductionoftheparttimep olicydescrib edab ovewould

aecttheindividualdescrib edonitem(d).Istheindividualb etterorworseo ?

Explain[7marks]

[B3]Unionbargainingandbasicincome(35marks).ConsidertheRight-to-manage

mo delofunionsinwhichthermandunionbargainoverwages,andrmsdecidetheem-

ploymentlevelunilaterally.Weconsideraneconomywherethegovernmentpaysb enets

b >0toallindividuals(notjusttheunemployed)viaauniversalbasicincomeprogram.As-

sumethattheunionwishestomaximizeautilityfunctionoftheformU=N

γ

(

w+b−V

U

)

,

whereNisemployment,wistheaftertaxrealwage,V

U

isthevalueofunemployment,and

γ≥0.Firmswishtomaximizetheirprots,Π (w)andtheydecidethelevelofemployment

oncewagesarenegotiatedN

D

(w).Assumethatthermandtheunionnegotiateviathe

Nashbargaininggame,withunionbargainingp owerequaltoλ∈[0,1].Unemployedindi-

vidualsndjobsataratef.Similarlyasinclass,weassumethattheeconomyisinsteady

state,whichimpliesanegativerelationshipb etweenf(u)andtheunemploymentrateu:

f(u) =δ

1−u

u

,whereδ >0.Finally,weassumethatindividualssupplylab ourinelastically.

(a)Writedownthemaximisationproblemthatdescrib esthenegotiationb etweenthe

unionandtherm,b eingexplicitab outthechoicevariablesandp ossibleconstraints.

[7marks]

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Itcanb eshownthat(youdonotneedtoshowit)theoutcomeofthenegotiationisgiven

by

w=

[

λγε

N

+ (1−λ)ε

Π

λγε

N

+ (1−λ)ε

Π

−λ

]

[V

u

−b].

(b)DerivetheexpressionforV

u

asafunctionofw,uandmo delparameters.[5marks]

(c)Solveforthewagebargainingcondition(WBC),whichrelatesuandw.Showthat

theWBCisaverticallineonagraphwithwontheYaxisande= 1−uonthe

Xaxis.Finally,showthatthiscurveimpliesap ositivelevelofunemployment.[9

marks]

(d)DrawagraphwiththerealwagewontheYaxis,andemploymente= 1−uonthe

Xaxis.ShowonthegraphtheequilibriumwithoutUnionsandtheonewithUnions.

[7marks]

(e)Supp osethatthegovernmentincreasesthelevelofthebasicincome.Describ ehow

theequilibriumwouldchange.Explain,andcommentiftheseresultsarerealistic.[7

marks]

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