NAME121Consumption300
Blueindifference250
curve(7500)Black 200
budget line150
100
Blue indifference curve (4500)50
Blueindifferencecurve (3000)0
10
20
30
40
50
60Leisure
9.9(0)GeorgeJohnsonearns$5perhourinhisjobasatru?esnif-fer.Afterallowingtimeforalloftheactivitiesnecessaryforbodilyup-keep,Georgehas80hoursperweektoallocatebetweenleisureandlabor.SketchthebudgetconstraintsforGeorgeresultingfromthefollowinggovernmentprograms.
(a)Thereisnogovernmentsubsidyortaxationoflaborincome.(Useblueinkonthegraphbelow.)
Consumption400
Blue budget line300
Red budget line200
100
0204060
Leisure
80NAME123Consumption400
300
200
100
Blue budget line0204060
Leisure
809.10(0)IntheUnitedStates,realwageratesinmanufacturinghaverisensteadilyfrom1890tothepresent.Intheperiodfrom1890to1930,thelengthoftheworkweekwasreduceddramatically.Butafter1930,despitethecontinuinggrowthofrealwagerates,thelengthoftheworkweekhasstayedremarkablyconstantatabout40hoursperweek.HourlyWagesandLengthofWorkWeek
inU.S.Manufacturing,1890–1983
Sources:HandbookofLaborStatistics,1983andU.S.EconomicHistory,byAlbertNiemi(p.274).Wagesarein1983dollars.
YearWageHoursWorked18901.8959.019092.6351.019203.1147.419303.6942.119405.2738.119506.8640.519608.5639.719709.6639.8198310.7440.1122BUYINGANDSELLING(Ch.9)
(b)Allindividualsreceivealumpsumpaymentof$100perweekfromthegovernment.Thereisnotaxonthe?rst$100perweekoflaborincome.Butalllaborincomeabove$100perweekissubjecttoa50%incometax.(Useredinkonthegraphabove.)
(c)Ifanindividualisnotworking,hereceivesapaymentof$100.Ifheworkshedoesnotreceivethe$100,andallwagesaresubjecttoa50%incometax.(Useblueinkonthegraphbelow.)
Consumption
400
300
Red budget line200
100
Blue budget line0
20
40
60
Leisure
80(d)ThesameconditionsasinPart(c)apply,exceptthatthe?rst20hoursoflaborareexemptfromthetax.(Useredinkonthegraphabove.)
(e)Allwagesaretaxedat50%,butasanincentivetoencouragework,thegovernmentgivesapaymentof$100toanyonewhoworksmorethan20hoursaweek.(Useblueinkonthegraphbelow.)
124BUYINGANDSELLING(Ch.9)
(a)Usethesedatatoplota“laborsupplycurve”onthegraphbelow.
Hourly wage rate (in 1983 dollars)12
10
8
6
4
2
0
10
20
30
40
50
60
Hours of work per week
(b)Atwageratesbelow$4anhour,doestheworkweekgetlongeror
shorterasthewageraterises?
Shorter.
(c)Thedatainthistablecouldbeconsistentwithworkerschoosingvar-ioushoursaweektowork,giventhewagerate.Anincreaseinwageshasbothanendowmentincomee?ectandasubstitutione?ect.Thesubstitutione?ectalonewouldmakefora(longer,shorter)longerworkweek.Ifleisureisanormalgood,theendowmentincomee?ecttendstomakepeoplechoose(more,less)
more
leisureanda(longer,shorter)
shorter
workweek.Atwageratesbelow$4anhour,the(substi-
tution,endowmentincome)endowmentincomee?ectappearstodominate.Howwouldyouexplainwhathappensatwagesabove$4anhour?
Substitutionandendowmentincome
effectscanceleachother
out,sothe
workweekstaysroughlyconstant.
(d)Between1890and1909,wageratesroseby39
percent,but
weeklyearningsrosebyonly
20
percent.Forthisperiod,the
NAME125gaininearnings(overstates,understates)
understates
thegaininworkers’wealth,sincetheychosetotake(more,less)more
leisure
in1909thantheytookin1890.
9.11(0)ProfessorMohamedElHodirioftheUniversityofKansas,inaclassictongue-in-cheekarticle“TheEconomicsofSleeping,”Manifold,17(1975),o?eredthefollowinganalysis.“Assumethereare24hoursinaday.Dailyconsumptionbeingxandhoursofsleeps,theconsumermaximizesautilityfunctionoftheformu=x2s,wherex=w(24?s),withwbeingthewagerate.”
(a)InElHodiri’smodel,doestheoptimalamountofsleepingincrease,decrease,orstaythesameaswagesincrease?
Staysthesame.
(b)HowmanyhoursofsleepperdayisbestinElHodiri’smodel?
8.9.12(0)WendyandMacworkinfastfoodrestaurants.Wendygets$4anhourforthe?rst40hoursthatsheworksand$6anhourforeveryhourbeyond40hoursaweek.Macgets$5anhournomatterhowmanyhoursheworks.Eachhas80hoursaweektoallocatebetweenworkandleisureandneitherhasanyincomefromsourcesotherthanlabor.EachhasautilityfunctionU=cr,wherecisconsumptionandrisleisure.Eachcanchoosethenumberofhourstowork.
(a)HowmanyhourswillMacchoosetowork?
40.
(b)Wendy’sbudget“line”hasakinkinitatthepointwherer=
40
andc=160.Useblueinkforthepartofherbudgetlinewhereshewouldbeifshedoesnotworkovertime.Useredinkforthepartwhereshewouldbeifsheworkedovertime.
NAME1279.13(1)WallyPiperisaplumber.Hecharges$10perhourforhisworkandhecanworkasmanyhoursashelikes.Wallyhasnosourceofincomeotherthanhislabor.Hehas168hoursperweektoallocatebetweenlaborandleisure.Onthegraphbelow,drawWally’sbudgetset,showingthevariouscombinationsofweeklyleisureandincomethatWallycana?ord.
Income2400
2000
Redbudgetline1600
1200
800
400
04080
120
128160200240Leisure
(a)WritedownWally’sbudgetequation.
I+10R=1,680.
(b)Whileself-employed,Wallychosetowork40hoursperweek.Theconstruction?rm,GlitzandDrywall,hadarushjobtocomplete.Theyo?eredWally$20anhourandsaidthathecouldworkasmanyhoursasheliked.Wallystillchosetoworkonly40hoursperweek.Onthegraphyoudrewabove,drawinWally’snewbudgetline.
(c)Wallyhasconvexpreferencesandnokinksinhisindi?erencecurves.Onthegraph,drawindi?erencecurvesthatareconsistentwithhischoiceofworkinghourswhenhewasself-employedandwhenheworkedforGlitzandDrywall.
(d)GlitzandDrywallwereinagreathurrytocompletetheirprojectandwantedWallytoworkmorethan40hours.Theydecidedthatinsteadofpayinghim$20perhour,theywouldpayhimonly$10anhourforthe?rst40hoursthatheworkedperweekand$20anhourforeveryhourof
126BUYINGANDSELLING(Ch.9)
Consumption400
Red part of line300
200
100
Blue part of line0204060
Leisure
80(c)Thebluelinesegmentthatyoudrewliesonalinewithequation
c+4r=320.
Theredlinethatyoudrewliesonalinewith
equationc+6r=400.(Hint:Fortheredline,youknowonepointonthelineandyouknowitsslope.)
(d)IfWendywaspaid$4anhournomatterhowmanyhourssheworked,shewouldwork40hoursandearnatotalof$160aweek.Onyourgraph,useblackinktodrawherindi?erencecurvethroughthispoint.
(e)WillWendychoosetoworkovertime?
Yes.
Whatisthebest
choiceforWendyfromtheredbudgetline?(c,r)=(200,33.3).
Howmanyhoursaweekwillshework?
46.6.
(f)Supposethatthejobsareequallyagreeableinallotherrespects.SinceWendyandMachavethesamepreferences,theywillbeabletoagreeaboutwhohasthebetterjob.Whohasthebetterjob?Mac.(Hint:CalculateWendy’sutilitywhenshemakesherbestchoice.CalculatewhatherutilitywouldbeifshehadMac’sjobandchosethebestamountoftimetowork.)
128BUYINGANDSELLING(Ch.9)
“overtime”thatheworkedbeyond40hoursperweek.Onthegraphthatyoudrewabove,useredinktosketchinWally’sbudgetlinewiththispayschedule.Drawtheindi?erencecurvethroughthepointthatWallychooseswiththispayschedule.WillWallyworkmorethan40hoursorlessthan40hoursperweekwiththispayschedule?
More.
9.14(1)Felicitylovesherjob.Sheispaid$10anhourandcanworkasmanyhoursadayasshewishes.Shechoosestoworkonly5hoursaday.Shesaysthejobissointerestingthatsheishappierworkingatthisjobthanshewouldbeifshemadethesameincomewithoutworkingatall.Askepticasks,“Ifyoulikethejobbetterthannotworkingatall,whydon’tyouworkmorehoursandearnmoremoney?”Felicity,whoisentirelyrational,patientlyexplainsthatworkmaybedesirableonaveragebutundesirableonthemargin.Theskepticinsiststhatsheshowhimherindi?erencecurvesandherbudgetline.
(a)Ontheaxesbelow,drawabudgetlineandindi?erencecurvesthatareconsistentwithFelicity’sbehaviorandherremarks.Putleisureonthehorizontalaxisandincomeontheverticalaxis.(Hint:Wheredoestheindi?erencecurvethroughheractualchoicehittheverticallinel=24?)
Income
240
50
24Leisure
9.15(2)Dudley’sutilityfunctionisU(C,R)=C?(12?R)2,whereRistheamountofleisurehehasperday.Hehas16hoursadaytodividebetweenworkandleisure.Hehasanincomeof$20adayfromnonlaborsources.Thepriceofconsumptiongoodsis$1perunit.
(a)IfDudleycanworkasmanyhoursadayashelikesbutgetszerowagesforhislabor,howmanyhoursofleisurewillhechoose?
12.
NAME129(b)IfDudleycanworkasmanyhoursadayashewishesforawagerateof$10anhour,howmanyhoursofleisurewillhechoose?
7.
Howmanyhourswillhework?9.(Hint:WritedownDudley’sbudgetconstraint.Solvefortheamountofleisurethatmaximizeshisutilitysubjecttothisconstraint.Rememberthattheamountoflaborhewishestosupplyis16minushisdemandforleisure.)
(c)IfDudley’snonlaborincomedecreasedto$5aday,whilehiswagerateremainedat$10,howmanyhourswouldhechoosetowork?
9.
(d)SupposethatDudleyhastopayanincometaxof20percentonallofhisincome,andsupposethathisbefore-taxwageremainedat$10anhourandhisbefore-taxnonlaborincomewas$20perday.Howmanyhourswouldhechoosetowork?
8.
Chapter10
NAME
IntertemporalChoice
Introduction.Thetheoryofconsumersavingusestechniquesthatyou
havealreadylearned.Inordertofocusattentiononconsumptionovertime,wewillusuallyconsiderexampleswherethereisonlyoneconsumergood,butthisgoodcanbeconsumedineitheroftwotimeperiods.Wewillbeusingtwo“tricks.”Onetrickistotreatconsumptioninperiod1andconsumptioninperiod2astwodistinctcommodities.Ifyoumakeperiod-1consumptionthenumeraire,thenthe“price”ofperiod-2con-sumptionistheamountofperiod-1consumptionthatyouhavetogiveuptogetanextraunitofperiod-2consumption.Thispriceturnsouttobe1/(1+r),whereristheinterestrate.
Thesecondtrickisinthewayyoutreatincomeinthetwodi?erentperiods.Supposethataconsumerhasanincomeofm1inperiod1andm2inperiod2andthatthereisnoin?ation.Thetotalamountofperiod-1consumptionthatthisconsumercouldbuy,ifheborrowedasmuch
moneyashecouldpossiblyrepayinperiod2,ism1+m1+2
r.Asyouworktheexercisesandstudythetext,itshouldbecomeclearthattheconsumer’sbudgetequationforchoosingconsumptioninthetwoperiodsisalways
cc2m1+1+r=m1+2
1+r.
Thisbudgetconstraintlooksjustlikethestandardbudgetconstraintthat
youstudiedinpreviouschapters,wherethepriceof“good1”is1,the
priceof“good2”is1/(1+r),and“income”ism1+maregivenaconsumer’sutilityfunction,theinterest(1+2
rrate,).Thereforeifyouandtheconsumer’sincomeineachperiod,youcan?ndhisdemandforconsump-tioninperiods1and2usingthemethodsyoualreadyknow.Havingsolvedforconsumptionineachperiod,youcanalso?ndsaving,sincetheconsumer’ssavingisjustthedi?erencebetweenhisperiod-1incomeandhisperiod-1consumption.
Example:AconsumerhastheutilityfunctionU(c1,c2)=c1c2.Thereis
noin?ation,theinterestrateis10%,andtheconsumerhasincome100inperiod1and121inperiod2.Thentheconsumer’sbudgetconstraintc1+c2/1.1=100+121/1.1=210.Theratioofthepriceofgood1tothepriceofgood2is1+r=1.1.TheconsumerwillchooseaconsumptionbundlesothatMU1/MU2=1.1.ButMU1=c2andMU2=c1,sotheconsumermustchooseabundlesuchthatc2/c1=1.1.Takethisequationtogetherwiththebudgetequationtosolveforc1andc2.Thesolutionisc1=105andc2=115.50.Sincetheconsumer’speriod-1incomeisonly100,hemustborrow5inordertoconsume105inperiod1.Topaybackprincipalandinterestinperiod2,hemustpay5.50outofhisperiod-2incomeof121.Thisleaveshimwith115.50toconsume.
Youwillalsobeaskedtodeterminethee?ectsofin?ationoncon-
130BUYINGANDSELLING(Ch.9)
132INTERTEMPORALCHOICE(Ch.10)
sumerbehavior.Thekeytounderstandingthee?ectsofin?ationistoseewhathappenstothebudgetconstraint.
Example:Supposethatinthepreviousexample,therehappenedtobe
anin?ationrateof6%,andsupposethatthepriceofperiod-1goodsis1.Thenifyousave$1inperiod1andgetitbackwith10%interest,youwillgetback$1.10inperiod2.Butbecauseofthein?ation,goodsinperiod2cost1.06dollarsperunit.Thereforetheamountofperiod-1consumptionthatyouhavetogiveuptogetaunitofperiod-2consump-tionis1.06/1.10=.964unitsofperiod-2consumption.Iftheconsumer’smoneyincomeineachperiodisunchanged,thenhisbudgetequationisc1+.964c2=210.Thisbudgetconstraintisthesameasthebudgetconstraintwouldbeiftherewerenoin?ationandtheinterestratewerer,where.964=1/(1+r).Thevalueofrthatsolvesthisequationisknownastherealrateofinterest.Inthiscasetherealrateofinterestisabout.038.Whentheinterestrateandin?ationratearebothsmall,therealrateofinterestiscloselyapproximatedbythedi?erencebetweenthenominalinterestrate,(10%inthiscase)andthein?ationrate(6%inthiscase),thatis,.038～.10?.06.Asyouwillsee,thisisnotsuchagoodapproximationifin?ationratesandinterestratesarelarge.10.1(0)PeregrinePickleconsumes(c1,c2)andearns(m1,m2)inperiods1and2respectively.Supposetheinterestrateisr.
(a)WritedownPeregrine’sintertemporalbudgetconstraintinpresentvalueterms.
c1+
c2=mm1+2
(1+r)
(1+r).
(b)IfPeregrinedoesnotconsumeanythinginperiod1,whatisthemosthecanconsumeinperiod2?
m1(1+r)+m2.
Thisisthe(future
value,presentvalue)ofhisendowment.
Futurevalue.
(c)IfPeregrinedoesnotconsumeanythinginperiod2,whatisthemost
hecanconsumeinperiod1?m1+m
(1+2
r).Thisisthe(futurevalue,presentvalue)ofhisendowment.Presentvalue.Whatisthe
slopeofPeregrine’sbudgetline?
?(1+r).
10.2(0)MollyhasaCobb-DouglasutilityfunctionU(c1,c2)=ca1?a
where0
xa1?aandthebudgetconstraintisofthe“standard”formp1x1m1x+p2x2=,2
thenthedemandfunctionsforthegoodsarex1=am/p1andx2=(1?a)m/p2.
NAME133(a)SupposethatMolly’sincomeism1inperiod1andm2inperiod2.Writedownherbudgetconstraintintermsofpresentvalues.
c1+
c2/(1+r)=m1+m2/(1+r).
(b)Wewanttocomparethisbudgetconstrainttooneofthestandardform.IntermsofMolly’sbudgetconstraint,whatisp1?1.
What
isp2?
1/(1+r).
Whatism?
m1+m2/(1+r).
(c)Ifa=.2,solveforMolly’sdemandfunctionsforconsumptionineachperiodasafunctionofm1,m2,andr.Herdemandfunctionforconsumptioninperiod1isc1=
.2m1+.2m2/(1+r).
Her
demandfunctionforconsumptioninperiod2isc2=
.8(1+r)m1+
.8m2.
(d)Anincreaseintheinterestratewilldecrease
herperiod-1
consumption.Itwill
increase
herperiod-2consumptionand
increase
hersavingsinperiod1.
10.3(0)Nicklebyhasanincomeof$2,000thisyear,andheexpectsanincomeof$1,100nextyear.Hecanborrowandlendmoneyataninterestrateof10%.Consumptiongoodscost$1perunitthisyearandthereisnoin?ation.
NAME135(e)Willheborroworsaveinthe?rstperiod?
Save.
Howmuch?
500.
(f)OnyourgraphuseredinktoshowwhatNickleby’sbudgetlinewouldbeiftheinterestrateroseto20%.KnowingthatNicklebychosethepointAata10%interestrate,evenwithoutknowinghisutilityfunction,youcandeterminethathisnewchoicecannotbeoncertainpartsofhisnewbudgetline.Drawasquigglymarkoverthepartofhisnewbudgetlinewherethatchoicecannotbe.(Hint:CloseyoureyesandthinkofWARP.)
(g)SolveforNickleby’soptimalchoicewhentheinterestrateis20%.Nicklebywillconsume1,458.3
unitsinperiod1and
1,750
unitsinperiod2.
(h)Willheborroworsaveinthe?rstperiod?
Save.
Howmuch?
541.7.
10.4(0)Decidewhethereachofthefollowingstatementsistrueorfalse.Thenexplainwhyyouransweriscorrect,basedontheSlutskydecompositionintoincomeandsubstitutione?ects.
(a)“Ifbothcurrentandfutureconsumptionarenormalgoods,anincreaseintheinterestratewillnecessarilymakeasaversavemore.”
False.
Substitutioneffectmakeshimconsumelessinperiod1andsavemore.Forasaver,incomeeffectworksinoppositedirection.Eithereffectcoulddominate.
(b)“Ifbothcurrentandfutureconsumptionarenormalgoods,anin-creaseintheinterestratewillnecessarilymakeasaverchoosemoreconsumptioninthesecondperiod.”
True.Theincome
andsubstitutioneffectsbothleadtomoreconsumptioninthesecondperiod.
10.5(1)Laerteshasanendowmentof$20eachperiod.Hecanborrowmoneyataninterestrateof200%,andhecanlendmoneyatarateof0%.(Note:Iftheinterestrateis0%,foreverydollarthatyousave,yougetback$1inthenextperiod.Iftheinterestrateis200%,thenforeverydollaryouborrow,youhavetopayback$3inthenextperiod.)
134INTERTEMPORALCHOICE(Ch.10)
Consumption next year in 1,000s4
3
Red line2
Bluelinea1
eSquigglyline0
1234Consumption this year in 1,000s
(a)WhatisthepresentvalueofNickleby’sendowment?
$3,000.
Whatisthefuturevalueofhisendowment?$3,300.Withblueink,showthecombinationsofconsumptionthisyearandconsumptionnextyearthathecana?ord.LabelNickelby’sendowmentwiththeletterE.
(b)SupposethatNicklebyhastheutilityfunctionU(C1,C2)=C1C2.WriteanexpressionforNickleby’smarginalrateofsubstitutionbetweenconsumptionthisyearandconsumptionnextyear.(YouranswerwillbeafunctionofthevariablesC1,C2.)
MRS=?C2/C1.
(c)WhatistheslopeofNickleby’sbudgetline??1.1.WriteanequationthatstatesthattheslopeofNickleby’sindi?erencecurveisequaltotheslopeofhisbudgetlinewhentheinterestrateis10%.
1.1=C2/C1.
AlsowritedownNickleby’sbudgetequation.
C1+
C2/1.1=3,000.
(d)Solvethesetwoequations.Nicklebywillconsume1,500
units
inperiod1and1,650
unitsinperiod2.LabelthispointAonyour
diagram.
136INTERTEMPORALCHOICE(Ch.10)
(a)Useblueinktoillustratehisbudgetsetinthegraphbelow.(Hint:Theboundaryofthebudgetsetisnotasinglestraightline.)
C240
30
Red line20
Blue line10
Black line0
10
20
30
40C1
(b)Laertescouldinvestinaprojectthatwouldleavehimwithm1=30andm2=15.Besidesinvestingintheproject,hecanstillborrowat200%interestorlendat0%interest.Useredinktodrawthenewbudgetsetinthegraphabove.WouldLaertesbebettero?orworseo?byinvestinginthisprojectgivenhispossibilitiesforborrowingorlending?Orcan’tonetellwithoutknowingsomethingabouthispreferences?Explain.
Betteroff.Ifheinvestsintheproject,hecanborroworlendtogetanybundlehecouldaffordwithoutinvesting.
(c)ConsideranalternativeprojectthatwouldleaveLaerteswiththeendowmentm1=15,m2=30.Againsupposehecanborrowandlendasabove.Butifhechoosesthisproject,hecan’tdothe?rstproject.UsepencilorblackinktodrawthebudgetsetavailabletoLaertesifhechoosesthisproject.IsLaertesbettero?orworseo?bychoosingthisprojectthanifhedidn’tchooseeitherproject?Orcan’tonetellwithoutknowingmoreabouthispreferences?Explain.
Can’ttell.He
canaffordsomethingshecouldn’taffordoriginally.Butsomethingshecouldaffordbefore,hecan’taffordifheinvestsinthisproject.
10.6(0)Thetablebelowreportsthein?ationrateandtheannualrateofreturnontreasurybillsinseveralcountriesfortheyears1984and1985.
NAME137In?ationRateandInterestRateforSelectedCountries
%In?ation%In?ation%Interest%InterestCountryRate,1984
Rate,1985
Rate,1984
Rate,1985
UnitedStates3.61.99.67.5Israel304.648.1217.3210.1Switzerland3.10.83.64.1W.Germany2.2?0.25.34.2Italy9.25.815.313.9Argentina90.0672.2NANAJapan0.62.0NANA(a)Inthetablebelow,usetheformulathatyourtextbookgivesfortheexactrealrateofinteresttocomputetheexactrealratesofinterest.
(b)WhatwouldthenominalrateofreturnonabondinArgentinahavetobetogivearealrateofreturnof5%in1985?710.8%.WhatwouldthenominalrateofreturnonabondinJapanhavetobetogivearealrateofreturnof5%in1985?
7.1%.
(c)Subtractingthein?ationratefromthenominalrateofreturngivesagoodapproximationtotherealrateforcountrieswithalowrateofin?ation.FortheUnitedStatesin1984,theapproximationgivesyou
6%
whilethemoreexactmethodsuggestedbythetextgivesyou
5.79%.
Butforcountrieswithveryhighin?ationthisisapoor
approximation.Theapproximationgivesyou
?87.3%
forIsrael
in1984,whilethemoreexactformulagivesyou?21.57%.ForArgentinain1985,theapproximationwouldtellusthatabondyieldinganominalrateof
677.7%
wouldyieldarealinterestrateof5%.This
contrastswiththeanswer
710.8%
thatyoufoundabove.
NAME139Ambrosia next period100
75
50
25
0
25
50Ambrosia this period
75100(b)IfJaneplannedtospendnoredincomeinthenextperiodandtoborrowasmuchredcurrencyasitcanpaybackwithinterestwithnextperiod’sredincome,howmuchredcurrencycoulditborrow?
80.
(c)The(exact)realrateofinterestonbluemoneyis?25%.
The
realrateofinterestonredmoneyis
25%.
(d)Ontheaxesbelow,drawJane’sbluebudgetlineanditsredbudgetline.ShadeinallofthosecombinationsofcurrentandfutureambrosiaconsumptionthatJanecana?ordgiventhatithastopaywithbothcurrencies.
138INTERTEMPORALCHOICE(Ch.10)
RealRatesofInterestin1984and1985
Country1984
1985
UnitedStates
5.75.5Israel?21.57109.4Switzerland0.53.33W.Germany
3.04.4Italy
5.6
7.6
10.7(0)WereturntotheplanetMungo.OnMungo,macroeconomistsandbankersarejolly,clevercreatures,andtherearetwokindsofmoney,redmoneyandbluemoney.RecallthattobuysomethinginMungoyouhavetopayforittwice,oncewithbluemoneyandoncewithredmoney.Everythinghasablue-moneypriceandared-moneyprice,andnobodyiseverallowedtotradeonekindofmoneyfortheother.Thereisablue-moneybankwhereyoucanborrowandlendbluemoneyata50%annualinterestrate.Thereisared-moneybankwhereyoucanborrowandlendredmoneyata25%annualinterestrate.
AMungoannamedJaneconsumesonlyonecommodity,ambrosia,butitmustdecidehowtoallocateitsconsumptionbetweenthisyearandnextyear.Jane’sincomethisyearis100bluecurrencyunitsandnoredcurrencyunits.Nextyear,itsincomewillbe100redcurrencyunitsandnobluecurrencyunits.Thebluecurrencypriceofambrosiaisoneb.c.u.per?agonthisyearandwillbetwob.c.u.’sper?agonnextyear.Theredcurrencypriceofambrosiaisoner.c.u.per?agonthisyearandwillbethesamenextyear.
(a)IfJanespentallofitsblueincomeinthe?rstperiod,itwouldbeenoughtopaythebluepricefor100?agonsofambrosia.IfJane
savedallofthisyear’sblueincomeattheblue-moneybank,itwouldhave
150
b.c.u.’snextyear.Thiswouldgiveitenoughbluecurrency
topaythebluepricefor75?agonsofambrosia.Onthegraphbelow,drawJane’sbluebudgetline,depictingallofthosecombinationsofcurrentandnextperiod’sconsumptionthatithasenoughblueincometobuy.
140INTERTEMPORALCHOICE(Ch.10)
Ambrosia next period100
75
Red linec50
25
Blue line025
5075100Ambrosia this period
(e)ItturnsoutthatJane?ndsitoptimaltooperateonitsbluebudgetlineandbeneathitsredbudgetline.FindsuchapointonyourgraphandmarkitwithaC.
(f)Onthefollowinggraph,showwhathappenstoJane’soriginalbudgetsetiftheblueinterestraterisesandtheredinterestratedoesnotchange.Onyourgraph,shadeinthepartofthenewbudgetlinewhereJane’snewdemandcouldpossiblybe.(Hint:Applytheprincipleofrevealedpreference.ThinkaboutwhatbundleswereavailablebutrejectedwhenJanechosetoconsumeatCbeforethechangeinblueinterestrates.)