complete macroeconomics theory for spring

UCLAiDepartmentiofiEconomics



Springi2022iPhD.iQualifyingiExamiiniMacroeconomiciTheory




Instructions:iThisiexamiconsistsiofithreeiparts,iandiyouiareitoianswerialli questions.i Al
lithreeipartsiwillireceiveiequaliweightiiniyourigradeiindependentiofitheinumberiofiquesti
onsicontainediinithatipart.
Youi havei fouri hoursi toi completei thisi exam.

, Part I i




This part consists of two questions both of which are required.
i i i i i i i i i i




Questioni1
Consideriaione-sectorigrowthieconomyiwithitwoitypesioficonsumptionigoods,i c1
(nondurablesiandiservices)iandi c2i (durableigoods).iDurableiconsumptionipurchasesimade
iniperiodit,i xti ,icontributeitoiaistock,i c2t1i,itheiservicesifromiwhichiprovidediutilityiin
perioditi+i1.i Alliquantitiesiareiexpressediinipericapitaitermsianditheipopulation,igro N i ,
t
wsiatitheirateii1i.
Aisocialiplannerisolvesitheifollowingiproblem:

maxiiitiNi[ilogici i(1ii)ilogici iAilog(1ihi)]
t 2t t

1t
ti0

subjectito
ci ixi iii iit k  ih1i,i i i1
1t t t ti i t

Nti1c2ti1i i(1i D i)Ntic2ti iNtixti
Nti1kti1i i(1ii)Ntikti iNtiit
Nti1i i N t i,i i i i1
N0i=1,ic2,0i andik0i given.

A. Transformithisiproblemiintoiaistationaryidynamiciprogram.

B. Fullyicharacterizeitheisteadyistateigrowthipathiforithisieconomy.i Beisureithatiyouihav
eisufficientiequationsitoidetermineitheisteadyistateigrowthipathiofi c1ti ,i c2ti ,i iti ,ikti ,iandi x ,
ti
hti .

C. Defineiairecursiveicompetitiveiequilibriumiforitheistationaryiversioniofithisieconomy.iBe
isureitoistateitheiproblemsisolvedibyihouseholdsiandifirmsiiniyouridecentralizedieconomy

.

D. Giveniinitialivaluesiforitheistateivariables,iareitheiallocationsithatiwouldibeichosenibyithei
socialiplannerithatisameiasithoseithatisatisfyiyouriequilibriumidefinition?i Explain.