MACRO ECONOMICS

1. UNIT7 CONSUMPTIONANDASSETPRICES
Structure
7.0 Objectives
7.1 Introduction
7.2 ~onsurn~tiohasIntertemporalChoice
,k
7.2.1 Life Cycle Hypothesis
72.2 Permanent Income Hypothesis
7.3 ConsumptionunderUncertainty:RandomWalkHypothesis
7.4 ConsumptionandRiskyAssets:Capital-AssetPricingModel
7.5 LetUsSumUp
7.6 Key Words
7.7 Some UsefulBooks
7.8 AnswerIHintsto CheckYourProgressExercises
7.0 OBJECTIVES
MergoingthroughthisUnityoushouldbeabletoexplain
e the Fisherianideaofconsumptionasanoutcomeof households' intertemporal
choices;
theLife-cyclehypothesisofModiglianiandBrumbergandthePermanentIncome
hypothesisof Friedman;
e the RandomWalkHypothesisofHall;and
e the asset price determinationthrough the ConsumptionAssetPricingModel
(CAPM).
7.1 INTRODUCTION
InEconomics,thereexistcloselinksbetweenthec w n teconomicvariablesandtheir
pastandfuturevalues.AsyouhaveseeninBlock2(onEconomicGrowth), paststate
oftendeterminesthecurrentstate,justasthecurrentstatedeterminesthefuture.But
there is also a link from futureto the present. Future of courseis oftenunknown.
However,expectationsaboutfuturevariablessometimesinfluencethecurrenteconomic
decisions.Inotherwords, thedecision makingprocessofaneconomicagentis often
'inter-temporal' in nature-involvingdifferentperiodsoftime.Consumptionand
savingsaretwoprimeexamplesofsuchinter-temporaldecisionmaking.
How doesa householddecide upon howmuchtoconsumetodayandhow much to
save?Keynesidentifiedcurrentincomeastheprimedetembntofc m tconsumption.
In its simplest form,aKeynesianconsumptionfunctioncanberepresentedby the
followinglinearequation:
C, = C + C I ; , ~ ? ~ O ,O<c<I:, ...(7.1)
d e r eC, iscurrent eonsumptionand I; iscurrentincome.Noticethatoneimportant

2. Intertemporal
Decision-Making f mofthisconsumptionfunctionisthattheuveragepmpmi~toconsume(C,1 )
fallsasincomerises.
Earlyempiricalstudiesusingcross-sectionalhouseholddatafoundevidenceinsupport
of decreasingaveragepropensitytoconsume:it wasfound that richer households
(withhigher Y,)indeedconsumedalowerfixtion oftheirincome.However,in1940s
Simon Kuznetsusinglongruntimeseriesdataonaggregateconsumptionandincome
foundthattheaveragepropensitytoconsumeremainedmoreor lessconstant,even
thoughaggregateincomeincreasedsubstantiallyovertheperiod underconsideration.
Thisapparentpuzzleledtothedevelopmentofanumberoftheoriesofhouseholds'
consumptionbehaviour,allofwhichfocusontheintertemporalnatureofconsumption
expenditure.Thefollowingsectiondiscussessomeoftheimportanttheoriesfromthis
literature.
7.2 CONSUMPTIONASINTERTEMPORALCHOICE
One of theearliest worksthat depictshouseholds' consumptionexpenditureas an
outcomeof households' intertemporaloptimizationexerciseisthatof Irving Fisher
(1930).The Fisherianideacan beeasilyexplainedintermsof a two period modelof
consumeroptimization.Letusassumethateachmemberofa householdlivesforexactly
two periods1
andletC, andC, denotehisconsumptionduringthefirstandthesecond
period okisliferespectively.Thepersonderivesutilityh mbothperiod's consumption
and hispreferencesarerepresentedbytheutilityfunction U(C,,C2).Let 1E; and Y,
betheincomeoftheindividualinthetwo periodsrespectively.Outofhisfirstperiod
income,the personconsumesC,andsavestherest( S, = Y, - C,) toearnan interest
income(1+ r)Sl inthenextperiod.InFisher's model,theonly purposeof savings is
future consumption.Accordingly,consumption duringsecond period is equal to
C2= Y, +(1 +r)S,.
C
y2 + S,.By re-arrangingthetermsin C, =Y2+(1+r)S,,we fmdthat =-
l + r l + r
c . 2 1 2
C2 =L+(Y;-c,)o r C l + - = ~ + - .Since S,= Y, -C,,we have-l + r l + r l + r l + r
Thusthe intertemporalbudgetconstrainisgivenby I
Thelefthandsideoftheintertemporalbudgetconstraintdenotesthepresentdiscounted
valueof thetotal consumption expenditureof theperson, whiletherighthand side
measuresthepresentdiscountedvalueof histotallife-timeincome (p).The person
decidesonthe levelsof C,and C2bymaximizinghis utilityU(C,,C2)subjecttohis
intertemporalbudgetconstraint.Noticethattheoptimizationexerciseofthehousehold
definesthecurrentconsumptionas a functionofthepresentdiscountedvalueof life
time income(f ) as wellasthe rateofinterest(r) onsaving2.
The timeperiods can be broadly defined so that the first time period covers his entire youth
and the second one covers his entire old age.
Strictlyspeaking,therate of interestqis the'expected' futurerate of interest(which isexpected
to prevail in period 2). We are assuminghere that future is certain and known.

3. hFig.7.1wedepictthe optimalconsumptionchoices. WemeasureC2onx-axisand
C, on y-axis. The intertempora! budget constraint intersects the x-axis at
point(1+r)Y, +Y, becausewhenC,=0in(7.2)wehaveC, = (1+r)q +q.Similarly,
y2
wefind thatC, = Y,+-when C,=0.
l + r
Fig.7.1: IntertermporalUtilityMaximisation
It is noweasy to analyzethe impact ofa changein currentincome(Y,) oncurrent
consumption(C,).Undertheassumptionthatconsumptionin bothperiodsarenormal
goods(i.e.,associatedwithpositiveincomeeffects),anincreaseincurrentincome,
ceterisparibus,increasesthelife-timeincomeandhencebothC, andC, willincrease.
Theimpactofachangeintheintaestmte(r)oncurrentconsumptionismoreambiguous.
Notethatanincreaseinr impliesadeclineintherelativepriceoffutureconsumptionin
termsofcurrentcons~mption.~Suchachangeintherelativepriceistypicallyassociated
withtwoeffects: (i) an income efect, whichin thiscasewilllead toanincreasein
consumptioninboththeperiods(sinceadeclineinthepricelevelimpliesthechoiceset
of theconsumerbecomesbroader),and (ii)asubstitutionefect, whichinthiscase
will leadtoafallincurrentconsumption(sinceadeclineintherelativepriceoffuture
consumption implies that people will substitute current consumption by fiture
consumption).Theoveralleffectonanincreaseinroncurrentconsumptiondepends
ontherelative strengthofthetwoeffects.In ceterisparibusanincreaseinr leadsto
an increasein C, ifthe incomeeffectdominatesthesubstitutioneffect; ontheother
hand,anincreasein r leadstoa decreaseinC, ifthesubstitutioneffectdominatesthe
incomeeffect.Inthiscontextalsonotethatinsofaras S, = Y, -C,,anincreaseinthe
rateofinterest wouldalsoimplyhigheror lowersavingsdependingon therelative
sttengthoftheincomeandthesubstitutioneffect.
This Fisherianviewof lookingatconsumptionasan outcomeofanintertemporal
optimizationexercise onthepartofthe householdscame to playakeyroleinthe
' This is becauseforthe sameamountofcurrentconsumptionforegone(intheformofsavings),
one will now get higheramount of future consumption.
Consumptionand
Asset Prices

4. Intertemporat developmentofthesubsequentinfluentialtheoriesofconsumption,whichare: (a)the
Decision-Making lye-cycle hypothesisof Modigliani and Brumberg(1954), and (b) thepermanent
income hypothesisof Friedman(1957). Boththesetheoriesattempt to explainthe
empiricallyobserveddiscrepancybetweenthecross-sectionalandtimeseriesevidence
ontherelationshipbetweenthe averagepropensitytoconsumeand theincomelevel.
7.2.1 Life Cycle Hypothesis
Toexplain the life-cycleand permanentincomehypotheses,let usextend the two
period model that we have just discussed.toa T-periodmodel where each person
livesfor Tperiods(where T 2 2).Theutilityfunctionoftherepresentativemember
ofthehouseholdisagaingivenby U(C,,C,,C,,........,C, ).Forexpositionalsimplicity
letusassumeanadditiveutilityfimctionoftheform:
U(C,,C,,C, ,........,C,) =u(C,)+u(C,)+ ........+u(C,.)=Cu(c1). (7.3)
The utilityhction(7.3)is wellbehavedinthesensethatmar@ utilityispositive(in
symbols uf> 0)andincreasesata decreasingrate(impliesthat thesecondderivative
is negative, u" <0).Forsimplicityletusalsoassumethatthe rate ofinterest is zero4
sothat theintertemporalbudgetconstraintof thehouseholdnow becomes:
whereY,,Y,,,......,Y,.aretheincomesofthehouseholdinperiods 1,2,. ....,Trespectively
and A, istheamountofinitiallevelofwealthstockofthishousehold.Maximizationof
utilitysubjecttotheintertemporalbudgetconstraint willyieldaLagrangianfunctionof
theform:
where 2 is the associated Lagrangian multiplier. First order conditions for
optimizationyield:
ur(C,) = R for t = 1,2,....,T,whereur(Cl) isthemarginalutilityin period r.
The above condition implies that ur(CI)= u1(C2)= *..a. = ur(C,.) = A,and
therefore C, = C, =......=CT.Henceh m theintertemporalbudgetconstraint(7.4)
weobtain
q a v i n g a positive rate of interest will not have any effect on the subsequent analysis.
I

5. Theterm )?rithintheparenthesisintherighthandsideof(7.6)istheaveragevalueofthe
total life-time income of the individual.The optimizationexercise indicates that
consumptioninanyperiodisdeterminedtheindividual's totallife-timeincome.Letus
Consumptionand
Asset Prices
denotethelatterby f .Thenconsumptionatanypointoftimetisequalto (A, +f) /T .
Thisphenomenon,wherebytheindividualdivideshistotallife-timeresourcesequally
amongeachperiodandconsumptionatdifferentpointsof timearespreadevenlyover
theentire time horizoniscalled consumptionsmoothing.
Atanyparticularpointof timet,theactualincomeofthatperiodY, mayexceedorfall
short of the average life-time income(f / T ). Givcninitial wealth, since current
consumptiondependsonlyon theaveragelife-timeincome,thereforeanychangein
current income will haveaneffect on currentconsumptiononly to the extent that it
impacts upon the average lre-time income.To be moreprecise,suppose at some
time period, say 1 = j' ,current incomerises by anamountZfor some reason.The
correspondingincreasein averagelife-timeincomeisequal to z/ T andas a result,
consumptionat periodt = increasesonlyby theamount z/ T .Bythesametoken,
if thecurrent income at some period rises by an amount Zand the incomeatsome
subsequentperiodfallsbythesameamount, sothattheaveragelife-timeincomeremains
unchanged,thencurrentconsumptiondoesnotchangeinanyperiod.
Noticethatwhilechangesincurrentincomehavelimitedimpacton theconsumptionof
that period,current income playsa crucial rolein determinationofcurrent savings.
Recall thatsavingsatany timeperiod t isdefinedasS, = Y,-C,.
1 A,
By using the result obtained at (7.6) we get st =*[&?]-, . ..(7.7)
,=I
Aninterpretationof(7.7)isthatsavingsishighwhencurrentincomeishighrelativeto
the average life-time income. It is this idea which forms the basisof Modigliani-
Brumberg'slife-cyclehypothesis.
1 Accordingto Modiglianiand Brumberg, incomevariessystematicallyoverthelife-
timeofan individualand savingsallowpeopleto smoothenconsumptionovertheir
life-time,evenwhenincomesindifferentperiodsarenotequal.Inotherwords,people
maintainanevenstreamofconsumptionovertheirlife-timebysavingmoreduringhigh
incomeperiodsand savinglessduringthelowincomeperiods.
E
Thelife-cyclehypothesis postulatesthatan individualtypicallyhasanincomestream
whichislowduringthebeginningand towardstheendofone's life,andhighduringthe
middleyearsof one's life. This is because productivityof a personis typically low
duringtheearly and the lateyearsofhis life,and productivityisat thepeakduringthe
middleyears. On the other hand, consumptionatevery period remainsthe same at
of theindividualis representedbyFig. 7.2. WeobservefromFig.7.2, thatduringthe
earlyperiodsof one's life,anindividualdissaves(by runningdownhisinitialwealth,
1
and/orbyborrowing);hesavesduringthemiddleperiodsof hislifeanddissavesagain
duringthelateryearsbyrunningdownhis accumulated wealth.
i
I
)
' 2

6. Fig.7.2: ConsumptionStreamoverLifetime
Giventhatconsumptionandsavingsarepostulatedtobehaveinthismanneroverthe
life-cycleofaperson,itisnoweasytoseehowthishypothesiscanexplaintheapparent
disparitybetweencross-sectionalandaggregatetimeseries dataon consumption
behaviour. Whenoneislookingatthecross-sectionaldatafora particularpointof
time, itislikelythatinarandomlyselectedsampleofhouseholds(whichareclassified
accordingtoincome),thehighincomecategorywillcontaina higher-than-average
proportionofpeoplebelongingtomiddlephawoftheirlifecycle,and thelowincome
categorywillcontaina higher-than-averageproportionofpeoplebelongingtoeither
theearlyorthelatephasesoftheir life.Sinceduringthemiddlephaseypeople havea
higheraveragepropensityto save (i.e.,ahigherS, / Y, ratio)and correspondinglya
loweraveragepropensitytoconsume(i.e.,a lowerC,/ Y, ratio), thecross-sectional
datawillreflectalowerpropensitytoconsumeforthehighincomecategorycompared
tothelowincomecategory.
4 1~t~~ohtitinim~rtantton~teherethat~urrent~~m~tion~~=-+-(A51T T ,=I
dependsnotonlyonthelife-timeincomeoftheindividual,butalsoontheinitialstock
/ Ct( ~ o n gRun)
Fig.73: Shortrunand LongrunConsumption

7. ofasset A,. Intheshort run(oratanyparticularpointof time)theassetstock remains
constant, In Fig. 7.3 we diagrammatically depictthe above relationshipbetweenC,
Consumptionand
Asset Prices
and Y,.Wemeasure C, along theverticalaxisand alongthehorizontalaxis.Weget
anupwardslopingline(slopelessthanunity)withapositiveintercept, as sho& inFig.
7.3.However, when wearelookingatthetimeseriesdatawhereincomeisincreasing
overalongperiod of time, then thestockofasset (whichispositivelycorrelatedtothe
level of income) id also increasing.Thus the intercept term on the line will keepon
increasing.In other words, the short run C, line will keepshiftingupwardovertime
(seethedotted line in Fig. 7.3).Henceif weareexaminingthelongrunconsumption
datatodetermine the longrun relationshipbetweenC, and Y,,wewillobservepoints
likeA,B,Calong successiveshortrunconsumptionlines.Inotherwords,thelongrun
consumption fictionwill besteeper,whereC, isproportionalto Y,,asshownin Fig.
7.3. Notethatalong the longrunconsumptionline,theaveragepropensitytoconsume
( C,/ Y,) remainsconstant.
7.2.2 Permanent Income Hypothesis
Friedman's permanent income hypothesisprovidesanalternativeexplanationto the
apparentdiscrepancy between cross-sectionaland timeseriesdataon consumption.
ThepeimanentincomehypothesisisalsofoundedontheFisheriantheoryofconsumption
asanintertemporalchoice. However, unlikethelife-cyclehypothesis, Friedrnandoes
not postulatethatincome followaregularpatternoverthelifecycleofanindividual;he
insteadarguesthat individualsexperiencemndomandtemporarychangesintheir income
fiomtimeto time.Accordingly, Friedmanviewsthecurrent incomeinanyperiod( Y,)
as consisting of two components:permanent income (Y,")and transitoryincome
(Y,").Permanent income is that part of the income which weexpect to prevail over
thelongrun. Friedman interpretsthisasthe longnm averageincomeof theindividual,
.Transitory income isany randomdeviation fmm thisaverage,
.Ap~iitivebansitory incomeimpliesthatthecurrenti n m e
exceedsthe permanent income; a negativetransitory incomeimpliesthatthecurrent
A 1
incomeis less than the permanent income. Since (;= + -
TT T ,=I
i.e.,current consumption of the household depends only on the permanent income,
my increasein the transitory part of thecurrent income, whichleavesthe permanent
incomeunchanged,will have no impacton the lcvelofcurrent consumption.
Let us now sce how Friedman's permanentincome hypothesissolves theapparent
puzzle in the consumption data.According to Friedman's hypothesis,the average
propensityto consume( C,/ Y,) dependsonthe ratioof permanenttocurrentincome
Y,"/ Y,.Thus when current incometemporarilyrisesabovethepermanentincomethe
average propensity to consume falls; the opposite happens when current income

8. Intertemporal temporarilyfalls belowthepermanentincome.Nowwhen we are looking at cross-
Decision-Making sectionaldataof differenthouseholdsatanypointoftime, typicallythe high income
groupwillcontainsomepeoplewithahightransitoryincome,who willhave a lower
propensitytoconsumethantheaverage.Similarlythe low incomegroupwill contain
somepeoplewithalowmitoryincome,whowillhaveahigherpropensitytoconsume
thantheaverage.Asaresult,wewillobserveafallingaveragepropensityto consume
aswe move fiomthe lowertothe higherincomegroup.On theotherhand, whenwe
areconsideringlongruntimeseriesdata,therandom fluctuationstendto evenout so
thatanyincreasein incomeinthelogrunreflectsapermanentincreasein the average
incomelevel.Henceinthelogruntimeseriesdatawearelikely toobserveaconstant
averagepropensitytoconsume.
CheekYourProgress 1
1) Explainthe Fisherianideaofconsumptionasan intertemporalchoice. What
the impact of a change in incomeand a change in the interest rate on current
consumption?
2) What isthe puule in theconsumptiondatathat has been identified by Kuznets?
Howdo the Life-cyclehypothesisand permanent income hypothesissolvethis
puzzle?

9. 7.3 CONSUMPTIONUNDER UNCERTAI[NT'V:
RANDOM WALKHYPOTHESIS
In our discussionso far we have assumed that people know their averagelife-time
income(orthe permanentpartof theincome)withcertainty.What happensif there is
somedegreeof uncertaintywith the permanent incomeas well? Obviously. in the
presenceof uncertainty, people's expectationabout the fiiturebecomesimportant.
We can extend the logic of the permanent income hypothesis to argue that in the
presenceof uncertainty,individualsmaximize their expectedutilitysubject tothe
constraintthat thesumof total expectedconsurnptioncannotexceedthe totalvalueof
the expcctedlife-timeincome.In otherwords,theobjective fimctionof aconswneris
nowgivenby
whichhe maximizessubjectto iheconstraint
Note that since Futureis uncertain,theexpectationof peopleaboutfuturecomesto
play an importantrole,and thereforehowpeoplefornltheirexpectationalsobecomes
importantfor the decision making process.You haveearlierbeen introduced to the
rationalexpectationhypothesisin Block-3.Accordingtotherationalexpectationstheory
theoutcomesdo not differsystematicallyfromwhatpeopleexpectedthemtobe;.The
extensionofthepermanentincomehypothesisinthepresenceofuncertaintycombined
with the assumption of rational expectation led to the theory of 'random walk
consunlption", asexpounded by RobertHall (1978).
Hallarguedthat ifindividual'sconsumptionindeeddependedontheirexpectedaverage
life-timeincome,and ifpeoplehad rationalexpectations,thenchangesinconsumption
overtime will be unpredictable,i.e.,consumptionwill followa 'random walk7.The
intuition behind thisresultissimple:ifthelife-timeincome isexpected tochangeat
some futurepoint of time and people have thisinformation, then they will use this
informationoptimally(underrationalexpectation)andhillthereforeimmediatelyadjust
theirconsumptionoverdifferenttimeperiods(consumptionsmoothing)sothatcurrent
consumption wouldnotchangeatthetimewhentheactualincomechanges.Current
consumptioncanchangeonlyiftherearesurprisesinthelife-timeincome,whichwere
notanticipated.Toputitdifferently,currentconsumptioncanonlychangeduetoevents
which are unpredictable and as a result changes in consumption would also be
unpredictable.
Theoreticallyit iseasytoseehowthis hypothesisfollowsfiomtheaboveformulation
ofindividual's maximization problem,As wesawin (7.6) and (7.7) the individual
7' 7' 7'
maximizes E[u(cl11 subject to xE(Cl) = 4+ Sincetheindividualis
I=I r=l I=I
takinghis decisionat time t=1,underrationalexpectations,all hisexpectationsare
basedon theinformationavailableat period 1.Anoptimizingagent willequatehis
expected(as of period 1) marginal utilities in differentperiods. Nowin period 1,
Consumptionand
Asset Prices
consumptioninperiod1isa certainevent; hence E,[u'(C,)I =u'(C,).Ontheother

10. Intertemporal
Decision-Making
hand, expected (as of period 1 ) marginal utility at any subsequent period is given
by: El[u'(C,)] ;t= 2,3,....,T.Thusthe optimalityconditionimplies:
u'(C,) = E,[u'(C,)]= El[u'(C,)] = -... = El[u'(C,.)] ...(7.10)
In order to explain (7.10) -further let us take a quadratic utility function of the
a
form:u(Cl) = C,--C: for t = 1,2,....., T .Thenthemarginal utility fimctionislinear
2
in C,, i.e., ul(Cl) = 1-aC, forall I. Therefore,
Usingthisin the optimalityconditionweget:
Onsimplification,
The above condition implies thatexpectationas of period 1 about C', equals C,.ln
more general termsif expectations areformed atany period t about afuture period
t+ 1,thenoptimalityconditionrequiresthatexpectationasofperiod I aboutC',,, equals
Cl,i.e., Cl = El[C,,,1.Sinceunderrationalexpectationstheactual valueofa variable
candifferfromitsexpected valueonlybya random term,this would imply
=CI+ el+,, ...(7.12)
whereel,, isarandomternwhoseexpectedvalueiszero.Ifyoulook carefully,equation
(7.12)says thatconsumption fromperiod t to period t+l would remain unchanged,
exceptforan unpredictablerandomterm.Thisispreciselytheconclusionoftherandom
walk hypothesis. The hypothesis says that changes is consumption over time is
unpredictable, because they canonly change due to the presence of unpredictable I
randomevents.
The random walk hypothesishasimportant implications from the point of viewof
policyeffectiveness.It impliesthatanygovernmentpolicyto influenceconsumption
(for example, a tax cut) can work only to the extent that it is not anticipated. For
example,ifthegovernmentannouncesataxcutpolicytoday,whichwillbeimplemented
h mnextyear,thenmnsurnerswithrationalexpectationswilladjusttheirconsumption
todayitself,sothatconsumptionwouldremainunchangedwhenthetax policyactually
becomesoperativenext year.
7.4 CONSUMPTIONANDRISKYASSETS: 1
CAPITAL-ASSETPRICINGMODEL
whileanalysingconsumptionunderuncertaintyinthepreviousSection,wehadimplicitly

11. assumed thatthesourceof uncertaintyisthehouseholds' income.Inotherwords,we
hadassumedthattherewasno uncertaintyasfarastheassetreturnisconcerned:the
returntoasset(r) wastreatedasgiven.(Infact,forsimplicitywehadassumedthatit
hasa valueequal to zero). If the returnto asset is non-zero,but theexactreturn is
uncertainthentheoptimalityconditionoftheindividual's utilitymaximirationwillinclude
anexpectedreturn termasshownbelow:
wheret isthetime period whenexpectationsareformed.
Weh o wfrom the theoremfor statisticalexpectation(operatorE)fortwoeventsA
and Bthat E(AB) = E(A).E(B)+Cov(AB) (where Cov(AB) is the co-variance
between the two events Aand B). We can visualize (7.13) as a case of two joint
eventsand writetheoptirnalityconditionas:
Nowsuppose there are two assets: i)one with a certain(risk-free)return givenby
-
if+,,and ii)anotherwith an uncertainriskyreturnwithanexpectedreturnvalueequal
to El(r,,, ).Fortherisky asset applicationofthecondition(7.14) impliesthat
1+ El [r,,, I =
w")- cov,[(I + r,,, ,ul(C,+,)I
i.e.,
El [uf(C,+,)I
For the risk-freeasset,the returniscertain and thereforeis uncorrelatedto C,,, .In
otherwords, for the risk-freeasset Cov,[(I+<+,,u'(C,,,)] = 0. Hencefor therisk-
freeasset,thecondition(7.14) impliesthat
Coinparing(7.15)and (7.16) weget:
Thecondition(7.17)givesusawayofdeterminingtheoptimal(orequilibrium)expected
returnofariskyasset. Notethata highervalueofC',,, impliesalowervalueof ur(C,,,).
Thereforea positiveco-variancebetweenr,,, andC,,, impliesanegativeco-variance
betweenr,,, and ur(C',,,) . Hence (7.17) implies that the higher is the correlation
betweenr,,, and C,,,,the greater is the required expected retunlon arisky asset
comparedtothe returnfrom therisk-freeasset.To put it differently,thegreateristhe
covariancebetween r,,, and C,,,,the higher isthepremiumthatanasset mustoffer
Consumptionand
Asset Pricea

12. htertemporal
Decision-Making
relativetotherisk-freerate.This modelofdeterminationof expectedreturn ofrisky
assetsisknownastheConsumptionCapitalAssetPricingModel(CAPM).
CheckYourProgress 2
1) Describethe RandomWalkHypothesisofconsumption.Whatistheimplication
ofthis hypothesisfromtheperspectiveofgovernment policy?
2) ExplaintheConsumptionCapitalAssetPricing rilleforariskyasset.
7.5 LETUSSUM UP
The presentunitviewed consumptionin adynamicset up and introducedyou lothe
problemofintertemporalutilitymaximization.Inthiscontextit discussedthe issueof
consumptionandsavingswhenmorethanonetimeperiodsareconsidered.TheFishexian
ideathatconsumptionisanoutcomeofhousehold'sintertempomloptimizationcxercise
hasbeenexplainedintheunit.
Empirical studiesinvolvingcross-sectiondatafindthat richerhouseholdsconsumea
smaller fiactionof their incomecomparedto poorerl~ouseholds.However,studies
based on timeseries datashow that the proportion of consumption in incomehas
remained moreor lessthe samealthough household incomehas increasedmanifold,
This apparent discrepancy has been attempted to be resolved through life-cycle
hypothesisandpermanentincomehypothesis.According tothe lifecycle hypothesis
theshortrunconsumption fkction showsa decliningaveragepropensitytoconsume
(APC)whilethelongrunconsumptionfunctionexhibitsconstantAPCduetoincrease
in asset base. On the other hand, the permanent income hypothesis explains the
discrepancyintermsofpermanentincomea dtransitoryincome.
Inthepresenceof unertaintyactualconsumptionbehaviourmaybedificult to predict.
Inthissituationconsumptionmayfollowarandompattern.Thistheoryofconsumption,
knownas the Random Walk Hypothesis, has been explained here. Finally, in the
presenceofuncertaintythepriceoftheriskyassetmayfollowa specific patternwhich
16 hasbeenexplainedinthediscussionontheCAPM model. I
.8'
~

13. 7.6 KEYWORDS
AveragePropensity to Consume
Ceteris Paribus
ConsumptionSmoothing
Expected Utility
Intertemporal Decision
PermanentIncome
RationalExpectations
TransitoryIncome
It isdefinedastheratiooftotal consumption
C
(C) tototal income(Y). ThusAPC =-
Y
It means'every thingelse.remainingthessu:neY.
Even though the income of an individual
changesacross time periods, he divid,eshis
lifetimeresourcesequallyamongeachperiod
and consumption atdifferent pointsof time
arespread evenly.
The totalutilityexpected to bederived from
thefutureincomestream.
Adecisionwhich involvedmorethanonetime
period.
That part of the current income that is
expectedto remainstableoverthelong run.
The hypothesisthatexpectationssf people
on thewholeisunbiased.
That part of the current income which is a
deviationfiompermanent iticome;.
7.7 SOME USEFUL BOOKS
Branson,William H.,1989,MacroeconomicTheoryandPolicy(3rdEdition),Harper
and Row, chapter 12.
Romer, David, 2001, Advanced Macroeconomics (2nd Edition), McGraw-Hill,
chapter7.
b
I
-
7.8 ANSWERS/HINTSTOCHECKYOUR
1 PROGRESSEXERCISES -
CheckYourProgress1
1) Read Section 7.2and writeyouranswer.
2) Read Section 7.2and writeyouranswer.
CheckYourProgress2
*
1) Read section 7.3 and writeyouranswer.
2) Readsection 7.4 and writeyouranswer.
Consumptionand
Asset Prices