Exercise and Solutions Manual to Accompany Foundations of Modern Macroeconomics, Second Edition

472 Pages·2009·2.81 MB·English

by  Ben J. Heijdra

FoundationsofModernMacroeconomics
Second Edition
ExerciseandSolutionsManual
This page intentionally left blank
Foundations of Modern
Macroeconomics
Second Edition
Exercise and Solutions Manual
BEN J. HEIJDRA
LAURIE S. M. REIJNDERS
and
WARD E. ROMP
1
3
GreatClarendonStreet,OxfordOX26DP
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Contents
Preface ix
1 Whoiswhoinmacroeconomics? 1
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 TheCobb-Douglasproductionfunction . . . . . . . . . . . . . . . . . . 1
3 TheAS-ADmodel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
4 Consumptiontax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5 Taxincidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
6 TheKeynesiancrossmodel . . . . . . . . . . . . . . . . . . . . . . . . . 4
7 Theimportleakage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
8 Theliquiditytrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
9 TheIS-LM-ASmodelwithinflation . . . . . . . . . . . . . . . . . . . . . 6
2 Dynamicsinaggregatedemandandsupply 25
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 TheKeynesiancrossmodel(continued) . . . . . . . . . . . . . . . . . . 25
3 TheIS-LMmodelwithcapitalaccumulation . . . . . . . . . . . . . . . 26
4 StabilityoftheIS-LMmodel . . . . . . . . . . . . . . . . . . . . . . . . . 26
5 TheBlinder-Solowmodel . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 RicardianequivalenceintheBlinder-Solowmodel . . . . . . . . . . . . 27
7 TheBlinder-Solowmodelwithcapitalaccumulation . . . . . . . . . . . 28
8 Adaptiveexpectationsinamonetaristmodel . . . . . . . . . . . . . . . 29
9 Moreonadaptiveexpectations . . . . . . . . . . . . . . . . . . . . . . . 29
10 Optimizationandcomputation . . . . . . . . . . . . . . . . . . . . . . . 30
11 Themultiplier-acceleratormodel . . . . . . . . . . . . . . . . . . . . . . 31
3 Rationalexpectationsandeconomicpolicy 65
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
2 Stabilizationofdemandshocks . . . . . . . . . . . . . . . . . . . . . . . 65
3 OverlappingwagecontractsandtheREH . . . . . . . . . . . . . . . . . 66
4 AvariationontheMuthmodel . . . . . . . . . . . . . . . . . . . . . . . 67
5 Expectationaldifferenceequations . . . . . . . . . . . . . . . . . . . . . 68
6 TheCaganmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7 Fiscalpolicyunderrationalexpectations . . . . . . . . . . . . . . . . . . 69
8 Thelabourmarket . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
9 Liquiditytrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
10 PIPmeetsthePigoueffect . . . . . . . . . . . . . . . . . . . . . . . . . . 71
11 PIPandtheoutputgap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
vi
12 Contemporaneousinformation . . . . . . . . . . . . . . . . . . . . . . . 72
13 Stickyprices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
14 Automaticstabilizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 Anticipationeffectsandeconomicpolicy 109
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2 TheIS-LMmodelwithstickyprices . . . . . . . . . . . . . . . . . . . . 110
3 Leaningagainstthewind . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4 Thetermstructureofinterestrates . . . . . . . . . . . . . . . . . . . . . 111
5 Fiscalpolicywithfixednominalwagesand
perfectforesight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5 Thegovernmentbudgetdeficit 143
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
2 Taxsmoothing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
3 Thetwo-periodmodelwithtaxsmoothing . . . . . . . . . . . . . . . . 144
4 Ricardianequivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5 Ricardianequivalenceinthetwo-periodmodel . . . . . . . . . . . . . . 145
6 Acloserlookatthelabourmarket 157
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
2 Two-sectormodelwithaskill-biasedproductivityshock . . . . . . . . 157
3 Progressivetaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4 Indivisiblelabour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5 Efficiencywages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7 Tradeunionsandthelabourmarket 173
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
2 Smalltalk... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
3 TheBlanchard-Summersmodel . . . . . . . . . . . . . . . . . . . . . . . 174
4 Variableunemploymentbenefits . . . . . . . . . . . . . . . . . . . . . . 174
5 Thetwo-sectorlabourmarketmodel . . . . . . . . . . . . . . . . . . . . 174
8 Searchinthelabourmarket 181
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
2 Searchunemployment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
3 ACESmatchingfunction . . . . . . . . . . . . . . . . . . . . . . . . . . 182
4 Downwardrealwagerigidity . . . . . . . . . . . . . . . . . . . . . . . . 183
5 Dynamicsofunemploymentandvacancies . . . . . . . . . . . . . . . . 183
9 Macroeconomicpolicy,credibility,andpolitics 199
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
2 Capitaltaxationandincomeinequality . . . . . . . . . . . . . . . . . . 199
3 Choiceofpolicyinstrument . . . . . . . . . . . . . . . . . . . . . . . . . 200
4 Rulesversusdiscretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
5 Politicalbusinesscycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
vii
10 Theopeneconomy 217
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
2 TheMundell-Flemingmodel . . . . . . . . . . . . . . . . . . . . . . . . 217
3 TheDornbuschmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
4 TheBuiter-Millermodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
5 Dynamicsofforeignreserves . . . . . . . . . . . . . . . . . . . . . . . . 220
6 PriceflexibilityintheMundell-Flemingmodel . . . . . . . . . . . . . . 221
11 Money 253
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
2 Optimalmoneygrowth. . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
3 Monetarysuperneutrality . . . . . . . . . . . . . . . . . . . . . . . . . . 255
4 Cash-in-advanceconstraintincontinuoustime . . . . . . . . . . . . . . 256
5 Cash-in-advancewithlaboursupply . . . . . . . . . . . . . . . . . . . . 257
12 NewKeynesianeconomics 279
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
2 CostfunctionforaDixit-Stiglitztechnology . . . . . . . . . . . . . . . . 279
3 Themultiplierwhentaxesaredistortionary . . . . . . . . . . . . . . . . 280
4 ConsumersintheNewKeynesianmodel . . . . . . . . . . . . . . . . . 280
5 ProducersintheNewKeynesianmodel . . . . . . . . . . . . . . . . . . 281
6 MonetarypolicyintheNewKeynesianmodel . . . . . . . . . . . . . . 283
13 Exogenouseconomicgrowth 305
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305
2 TheHarrod-Domarmodel . . . . . . . . . . . . . . . . . . . . . . . . . . 306
3 Theproductionfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
4 Thewage-rentalratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
5 TheSolow-Swanmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
6 ThePasinettimodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
7 TheSolow-Swanmodelwithpopulationgrowth . . . . . . . . . . . . . 308
8 Somemathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
9 Optimalinvestment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
10 Welfareoffuturegenerations . . . . . . . . . . . . . . . . . . . . . . . . 310
11 Thesavingsfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
12 ThesavingsratiointheRamseymodel. . . . . . . . . . . . . . . . . . . 311
13 Technologicalchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
14 Constantmarginalutility. . . . . . . . . . . . . . . . . . . . . . . . . . . 312
15 Intertemporalsubstitution . . . . . . . . . . . . . . . . . . . . . . . . . . 313
14 Endogenouseconomicgrowth 349
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
2 Endogenousgrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
3 Minimumconsumptionandendogenousgrowth . . . . . . . . . . . . . 350
4 Asymptoticendogenousgrowth . . . . . . . . . . . . . . . . . . . . . . 351
5 Externaleffectandendogenousgrowth . . . . . . . . . . . . . . . . . . 351
6 Asymptoticcapitalfundamentalistmodel . . . . . . . . . . . . . . . . . 352
viii
15 Realbusinesscycles 369
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
2 Smallopeneconomymodel . . . . . . . . . . . . . . . . . . . . . . . . . 369
3 Thenon-marketsector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
4 AgeneralRBCmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
5 Governmentspendingshocksintheunit-elasticmodel . . . . . . . . . 373
6 Nowealtheffectinlaboursupply . . . . . . . . . . . . . . . . . . . . . . 373
16 Overlappinggenerationsincontinuoustime 395
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
2 TheBuitermodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
3 Endogenousgrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
4 TheBlanchard-Yaarimodelwithoutinsurance . . . . . . . . . . . . . . 397
5 Technologicalchange . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397
6 Mandatoryretirement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
7 Publicinfrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400
17 Overlappinggenerationsindiscretetime 431
1 Shortquestions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
2 CapitalfundamentalisminanOLGmodel. . . . . . . . . . . . . . . . . 431
3 Welfareeffectsofdebt . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
4 Lifetimeuncertaintyinatwo-periodmodel . . . . . . . . . . . . . . . . 433
5 PensionsintheDiamond-Samuelsonmodel . . . . . . . . . . . . . . . . 434
6 Consumptiontaxationandredistribution . . . . . . . . . . . . . . . . . 434
Bibliography 457
Preface
About the manual
The first edition of Foundations of Modern Macroeconomics did not include any end-
of-chapter exercises, although I posted quite a few questions plus models answers
on the website for the book. Over the years, many teachers using the book have
approachedmeforsuchexercises. ThisExerciseandSolutionsManualismyresponse
totheirqueries. Inthismanualyoufindalargenumberofexercises(plusextensive
solutions) for each chapter. The aim of this manual is to allow the diligent student
to further develop his or her skills in model-based macroeconomics. The manual
includesthreetypesofexercises:
• Short questions. These questions often ask the student to comment on state-
ments regarding models discussed in the textbook. Typically, brief answers
aresufficientforthestudenttodemonstrateanunderstandingofthematerial
underconsideration. Sometimes,ashortquestionasksthestudenttoclarifya
conceptbyexplainingitverbally,orbygivingexamples.
• Relativelystraightforwardlongquestions.Thesequestionsareusuallycentered
aroundaparticularmodel. Studentsareaskedtodemonstrateanabilitytode-
riveconclusionsregardingmacroeconomicphenomenabysolvingthemodel.
Bylearningto“playwith”simplemodels,Iexpectthatthestudentwillbeable
toconstructhisorherownmodelsafterstudyingthismanual.
• Relatively difficult long questions which are a bit more challenging. To warn
(cid:1)
the student, such questions are marked with a star ( ). Other than that, the
objective behind these questions is the same as for the relatively easy ones.
Thestudentlearnshowtosolvemacroeconomicproblemsbyusingconsistent
andcoherentmacroeconomicmodels.
It must be stressed that the exercises and model solutions are not meant to em-
phasize a particular point of view about the field of macroeconomics or, for that
matter,themacro-economyitself. Theyaresimplyareflectionofthetypeofmodels
thathavebeenusedoverthelastfourdecadesorso.
I have adopted the following notational system in this manual. The prefix Q
is used to label information (equations, tables, figures) appearing in the questions
themselves. So, for example, equation (Q1.2) refers to equation (2) in the question
dealing with a topic from Chapter 1. In short, the syntax is Qx.y, where x is the
chapternumberandyistheobjectcounter. TheprefixAisusedtolabelinformation
appearingintheanswers,withthesimilarsyntaxAx.y. Informationfromthemain
textbookfeaturesthesyntaxx.y.