~nrcgidtc~ w c~dl recent NoA\ on t hc \toch-lh f d,ltlon4~lp, hhchold produc-

I1011. ‘IlKi cIlciogcIlolI\ ta\tc\ Sl‘ecIllc‘\lly, NC‘ mtroducc the concept ot ‘111 ‘lctl\ II\-

gc11e1 atiilp tunction to ~eprcwnt and dctermme a conwimcr’~ ncc& 7 hi\ function

gtwr ,Ihcc the propo5ItIon of Stigler and Becker (1977) about the relationship of the

flo\\ ot m\estmcnt to the stcch of cnp~tal, and IS ~omplen~entar~ to that of xt~\It!

production functtons Introduced b\ Laixxstrr (1971) The compleinentar!, concrots

ot actn~tv gener, tion and actt\Ity productml also pro\lde a has< for cwndinp the

concept of comnodlty productlon, Introduced h> hllchael and Beck (1972). mto

the production and requirement aspects The approach also facilitates the retinc-

ment ot both the theoretical foundation and methodological procedure for

econon~~c ~J>\I\ ol cntiogenou~ tastes on which Important contributionc h,l\c been

l~~c\~ousl\ made b! wllah (1976) aird Polidh and N’Je\ (1979)

!-he i1wcqx ol the c011w111pt1011 WI IRCIhlRte\ the IIW oi \0c10ec011 ‘IlllC nnd lN’lC1

IloIltwdgctaI~ tator\ to restrict the domain ot a11 IndI\ Idual’\ utiht~ ~Imc~ion This

met hodologI,al procrdul e has not been used In the con\ entional frCwworh The

_on;cIx proposed here \\ Ill therefore o\ ercome t hc problem :n the con\ cnt Iowl

t’~0110111Ic ,tndl\314 potnted out b\ Ferber (lQ?2). that ‘soc~oeco~w~~~~c \amblcs .11c

IntroctIIc~ti :I\ ‘the c\Ira. though essential Ingredient with no theclretical bds 5’

! urtheimoit, rhe ~on~eptuJ framworh Implies that there IS a distinct micro

Income-e\pe Iditure relationship for e\erk admissible set of socIoc;onomIc and

other tactors The aggregation of such micro Income-e\pendIture relationships

xroqs mdi~iduals ~Iil weld an aggregate con5umptIon t UIK~IOII 11 htch ~eflecr$ the

distribution ol conmnrr untt3 b! nofktdgetary fxtors, consistent ~tth the the

t OI mul,u!on ot frIedm,m ( 1957) ’ Thi, 15 also 111 line w Ith an empirical con\ump-

tIoIl tuncIIon pro\ lord b\ \gar\\ala and Drmh:\ater (197,)

\n 111dn ~dunl’s ~onwi~ption set restricts the domain ot his utiht~ function The

qucsi~on~ ol hou thrL restriction to the domain Is determined and ot Its relationship

to othei factors ha\e ne\er ha\e been a direct concern ot ezonomIxt$ HORCLC‘I, each wcioeconomic factor represents a dirtinct set ot human and nonhumm ~e~owct’~

%I& rezourws mwt be Itiarntamed m a >tate of ‘cquilibr~um The concept of a con-

\1111lpt1m set and It\ iu~~ctional relatIon5hIp can thus be developed under a

\toch-llo\\ trdmwoi h, along the proposition of Stigler and Becher (1977) that the

“~I:\c~tment reqL x3. 5Imply to maintain the capital stoch mtdct \\ould mcreaw d5

rhc \lPih lIlcle.3sed” In this ca\e, Stigler and Becher were concerned with mu\IcA

~~i\p~tdl Ho\%c\er, the Idea e\prewtl there can bc wtcndcd and generahred FIr\t,

mutic ~-dp&\l I\ only otle of the many wouIce4 which an Individual pow$se\ It

i”

fhc d11 tcrenccs depend on the nature and types ot H-NH re~ourcw and acti~Hte\;

I or ewmple, an lncrrase 111 the flow ot act~wt~es dssoclated with feedIng \\111 not

tn,reCisc the stoLA of one’s H-NH resources cncr an mth\ tdual has enough to nmn-

taln cqu~hbrmm rhus, 3R,‘&4 SO tor 4 >@ In contr,tst, an Increase 111 the Ho\% ot

‘tcrl\ Itw a~$ocmted wh lea~wng beyond those which are lequlred to mdmtain a

\trtte ot zqtnhbr~um m.,y add :o the <rock 01 one’s mtormatlon. shill, hnowledge,

.tncl othc‘r IIUIIKI~ resourcrc For such actI\ WS, aRG?+l > 0 for ,+I> 0 It follow F that

,w IIKII\ IcIu,II’~ acts\ itw consist of those \\hxh arc Intended to mamtrw 1115

IC’WIICC’~ 111 cqmllbrlum dnd those ~hlch are mtended to c~lwnge his resources The

IUI mt’r cw ~eapond\ to the conventional concept of conwnptlon and the latter COI -

I cqmnd~ !o t ha o+ I~I txment (and dwivc~tment)

I o cicrl\c the consumption set function. the total quantity of the compo$lte com-

IIIOC]II\ .on\l\tc”ni ~\nh the cqmllbrlum tlcw of an .tctl\lty IS e\press<d as”

‘I - v [X, I(W)]. (6)

\\ hc~c IJ; I\ rltc COI~SUI~~IIOI~ set lxuanletcr and the function IS called a consumption

YL~ t uliLtlOl1 I he tunct~on slgmlles that the quantity of the composite commodlt]

,i<<ded depend\ on the le,ources, R, for which eqwhbrlum IS to mamtalned and

LOII~~I~~~IC~II c,ip~t~~l, A., \+ hlch txlhtates the flo\\ ot actl\ltles to satlsfb a COII-

~~~IIIWI‘~ ncctl~ For ewnple, if the parameter, IJI, represents the amount of food

\\h~ch nn mcf~\~dual need& to mdmtam the physical and r hyslologlcal resources of

III\ tC~mtl\ III d v~tt‘ ot equlhbrmm, then the lactors, R, that determlne the needs

\+t!t bc hi\ t,imllI wt‘ and composition The consmiiptlon capital, K, ~111 Include

hl\ cooh~np tx~ht~e~ and equ;pment as well as his coohmg hnowiedge and shills

I hc c\l<tcnic of ‘\hado\\ cost\’ to an mdl\idual’s resources when hrs needs are

noi ~ti\l cd In&catc\ that the actual flop of an acwity A cannot m general be

1~3. thCw @ This means that the actual commodity flow z cannot be less than w

I Is ~Jdttwn, the actunl flow of actwtles may or may not be greater than @ depending

w \\hrthtrr dR ‘~34 IS powlie or negatlbe for A <@ It follows that ; ma! or ma]

not be grtxtrr than w Specifxallq, for actwtles where aK&-l~O, for A<@, 4

ICING\ to be equal to Q, For actl\ltws of rhts type w=; For actl\ltles where

(+I? C{ 4 ‘0, tor 1 >O. 4 may eweed I$ mthcatmg that z may exceed I+U rhus, tlonl (3)

ws;=,(i,, \_‘, ) (7)

The Lonwniptlon set parameler w serw$ a$ a qwnttty constramt An mdl\ldual

ihouw> among \ub3tltutnblc tommodltles to satltfy \uch a con$trdmt That 15, the

” IZLJ (n) is obtamed as follows Bv applywg the lrnpliilt function theorem 10 (2). the composne con-

mcldlt\ : IS e\prebwd m terms of the consumptwn Lapual k and the flo\r of actw:\ A as z= u[k, -I] The

AIIXIIL pdrCtmelx Q, = f(R) tEq (1)) 1, the? wbwtuted lo- A by lettma A =O In (4) Smce an mdlvldual’s

resource.\ dre rcpre\cntcd b\ nonbudgetarp Iactors, thl\ eyuatlon also relates a consumption v‘r 10 wch

l‘klor\

~1 ~ch :P graphmll~ repicscnted h\ the lyric EE in FIB I on th2 ‘i ~~umpr~on th,ti

I// = 5 and p, = pJ -= I I2

For I~SCW~ pre\~ou+ noted, an mdl\ldwl \trl\ln, 0 Tut \atlsf\ hl\ nt‘<dc to n~,~ln-

taln 111s rewurccs m rqulhbr~um HIII not choo\e among the corrmodl:\ bundle\

represented III the atea to the left of the hnr EE’ Thl< area ~111 theretore not be

Included III the mdwtdual’s consumption set 4150, a cOn\UillL~tlOn et cannot

mclude :IIC area to the rrght of the hne EE’ if ewe,5 tn rn, tlw oi an actl\lt\,

A - @ > 0, causes dlsequlhbrlum (dlsproportlonaht> 1 In an Indl\ Idual’ rewurct‘t In

thlr case. a consumption set Includes onI> the commodlt\ bundk rcplcwltsd on

the line EE Ho\\e\er, If aR/c34: 0, for A<@, the con~umer’~ choose \t’[ is111

The cpee~f~cat~cw ot ‘i consumption set dc\cnbed above ImplIes that consumer

choice can be dl\lcied mto those 1% hxh ore to \atlsfv h~c needs and tbti>se \\h~h arc

to alter hrr resources The former m\ol\es choxe ot commodlt> burdlcs In 3 LOW

5umptton \et The latter m\ol\es choice of actnltlef that ~111 aitrl hts ~euc~~c’es ‘md

con\umptton set. corlespondmg to the trddltlonat concepts ot 1 .\estment dnd

til5rnl c\tment

The coxept ot d consumptlosr set tunctlon prokldes a frdme\ioorh b> \\hlch SOCIO-

demographx and other tnctors can be Incorporated into a theor) of consumption

I‘ht~ requires that the proposltlon of an estabhshed consumption theory about non-

budgetarv factors be ekammed to determme the nature dnd types ot human and

nonhuman rcrources thdt these factors represent The relatIonshIp of these factors

to a consmlipt1on set c’dn then be determmed usmg mtormation on consumptnon

technolog>

In the case of relatl\e Income hypothesis, Duesenberrq (1949) has postulated the

mterdependr,nce of preferences HIS proposmon IS that people tend to emulate their

neighbors and to strive for a higher standard of hvmg As a result, people try to

mo\e to a higher level of consumption ahen Income increases but seek to mslntam

It \then mcome decreases For t!x reason, the propensity to corsume IS ~OSIKU to

depend on current mcomc relative to a reference incove This ob\ lously Implies that

z.1 mdl\Iduzl’s PI eferences are influenced by his referxce mcome However, a more

re‘lsonable mterpletatlon ~111 be that, tf the pattern of consumption m higher

mcome groups IS preferred oker that m tower income groups, the consumption

faclhtated ky a rise m income ~111 cause a systematic change m the stock of one’s

resources Thebe ~111 cause changes m what are required to mamtam equr!lbrmm,

whxh reprtssent changes m an mdlvldusl’s consumption set It fo!lows that the

concept of a consumprlon set and I<S relatIonship to nonbudgetary factors can be

used to represent the proposmons of the relative mcome hypothesis II; a micro-

economic fVameworh and to expiam its proposmon that people strive for a higher

standard ol hvmg hut resist downward adJustmerIt in the fete of declining income

To Illustrate ho\\ an mdlvldual’s mcome may affect his consumptton set, assume

that the mdtvldual concerned has a long-run utlht> function nlth respect to dctlvltles

of the forri represented III Fig 2 and that hts actnlty parameter 1s @(I) Also,

assume tha the mdlvldual ltds income of Y(t) whtch facthtates the rate of actlvlty

flow, A(t), to be equal to the actlvlty parameter, @(t) Th:s means that there 1s a

state of equlhbrmm m an mdlvldual’s resomxes His consumption set IS represented

on and to the right of the line EE’ m Fig 3 If the mdlvldual’s Income increases to

Y(r& 1) at (r+ l), faclhtatmg actlrlty flow at the rate A(t+ l)>A(t), then he will

‘2’

E\ 1,

\ \

\ a

0 E P \

expcrtence posttne dtseqmhbrtum to the extent tndtLated b\ the pLtp bctwxn c* ~11~1

@(r + 1) tn Ft*; 2 However, mcreased consumptton also leads 1c7 ,ut lnLregl\e III rhc

stocks of the mdrrtduat’s resource5, mcludmg con\umptton capt~~tl The 111~r ~.I\c II

one’s resources m turn causes an increase III the ielel of ,lctti ttte~ ~equt~:J to 1n~t111-

tam equlhbrtum As this occurs, there wrrll be changes m the xtlxtt\ parLmett~ I 2

dg>0, and ehe mdtvtduaf’s tong-run uttht\ functton sh~tts from [r(r) to q+ d 1)

When th+ adnistment is completed, the acttIn), par,nllcter become\ dtr - I) Ti L mdrvtduai’s consumption set wrll shift outward to the are.1 represented C>II anci ‘c$

the rght of the lme DD’ m Ftg 3 The tndt\tdua!‘c stan&nd ot h\tng 1s adtu~tcd

upward when hts mcome increases because h:s consumptton set 1s open on the up:vr

side If he expel Iewe a dccrca5e in mconit’ from }‘(I -t I). 111s doi\ mm1 adjustnwnt

I\ con+trauled bccau\c hr\ conwn~ption \et I\ no\\ bounded on ttlc IOMU wk by the

llilr III?’

In the per inanent-Income (Frwdman, 1957) and hte-cycle hypotheses (h4,~dlglw~~

and BrumbeIg. 1954, Ando and Modlgham, 1963) the propenslt\ to consume 15

po\tu!ated to bc dcternmed by lntcrcst r&e, nonhuman iesourcc~, total ,\eealth, and

the ‘uttltt! factor<’ Xlost ot these factors, ho\+e\er, are argument\ 111 an mdi\ldual’,

concuinptlon set tunctmi This IS obk~ous 111 the case of nonhuman resources and

total \\ealth because these, aslde from fmhtatlng ~01wm1pt~0r1. must dso be 111a111-

:.:lncd 111 a \tatt‘ ot cqurhbrlum the same IS also true of the ‘utll,ty factor5 such a~

,lgc md ldm~i\ i’ompowlon because these represent human and nonhuman

I~‘~OLIICC‘~ ot a qx~ftc nature and t!pe\ e\t‘q though the tr.ldltlonal tnt~*rplc;a*wl

I\ th,~t theje txtor< determine the ‘&pe 01 the Indltfcrencc CUILCT -ihc especial

cnlphn~~~ the life-cvck hvpothesls placc3 on lhc propwtloii that the piopcnslt! to

~on~umc‘ \arw nlth the age of a conwne~ umt can thu$ be Justlfxd because each

,ndl\Iduai po\\ews A dwmctne Set of human dnd nonhuman resources at each

ftagc ot 111s 6ft cycle The actl\nle\ and commodltleS required to malntCun

cqu~l~b~~ua~ thu% change as thew icsource5 change The Indnlduai‘s ,xtl\~t>

pxamctcr (and Con\umptlon set) ~111 thu\ undergo cystematlc change a\ he gee\

th~ouph cl11 tercnt stages ot 111s hfe cycle Thus IF lllustratcd m FIN 4

The 'IIIIIC' tactor emphwzed In the hfe-c\cle h!pothew 1s ako Important because

I( icpie\ent\ Consumption technolog! and wch other factors as ‘hfc stklr’ \\hlch

chnye weI t~wc ‘Time’ I$ therefore an Inclusl\e varlablr that represent5 change‘\

111 \\hdt are rcqwred to mauitam an mdl\lduA \ resources II: equlhwlum

The rlbo\c mdlcate\ that, to Incorporate soctoeconomlc factors in an aggregate

consrlmptlnn theor\, \\e must Identlt\ the relev,lnt barlables and then specify the

rcxttlitlon wocwed 1~1th thcw l&tor\ to the domaln of the Incil\ldual’q t,tllltk

Iullctloll It (1114 ploLedllIc I< .,pphcd, ‘1 1n1c1o 1ncnmc-~\l’cl~~lltilIc Icl‘lrloIi~hll~ cdl1

be de~~\d 011 tllc awIllpt1oIl that .l conwmer mdhc\ t ntwrul ~hwcc~ wbpxt 10 1114 budget culd nonbudgctm cl~nstralnts In tllc cclw ot the rd,lt~\ r‘ IIIC~~III~ h>jwthc\~\

the budget constiaint I\ an ~nd~~~dual’~ current ~nwme, \\h~lc II i< 1x1 mC~ncIit II~~PIW

III the UPC ot permanent-income and life-cycle h~~mhcse~

An lmpol tant ad\ antage of uc~ng ~oc~occonom~c txto~ 3 to restrict the ~OIIL~I,I 01

an lnd~~ldual’~ untlllty tunction 15 that such restriction\ cCm be nxx~~r~~pfull~ dct~ncd

and determined with intormatioti on con\.rnlptioIi tcchnolog~ It tollo\\\ that \:i~h

relation~hrp~ can be cnip~r~~~tll~ estimated C>nd explained \luch ot the cl,it,i about

a cnnwmer described a~ ~ocio-d~mograplli~ ta<tor\ cLlrl thu\ be used to dc\el~ (7

hypothesss about, dnd to :mpIi icallk ckplain. Iii\ bch,I\ Ior Thi\ o\ crLc)Iiic\ Ci iri,ilnt

dit ticulty o: not being able t(‘ niahc cttectI\c 11. ot the d‘il‘i <ibout tl1c con >11111c1

III the explanation ot hi\ hcha~~or when wch tactwc art‘ Intetplcted d\ reprexntln~

‘tastes’ and when the quest~o~l or ho\\ ~o~~oc.~nw~i~c txtor \ ~nt’lucn~c p~t‘tcIcn~c~

cannot be arccrtained

mdn ldual\ u nb higher mcome, and 1 t ~COIIIC ’ tncrea\es o\cl time, then L < 0 In

this case the slope of u*(t), da*(t) ‘dr, a111 be pos~tl\c. lero, OI neg~tl~e dqxm.~lnp

on whether Me’BS P’f or A+“# 19 dommnnt It t’<O, and rile” /“‘I = he , the

aggregate cxpcndnure-income ratio u 111 I emm constmt

L ettlne ‘7 C’; = C”, s l’ob = Y(;‘, and t L :l Ix = J- ‘I, the \\elghted a\eldge dgprepdte

Income ekpendlture relatlonshlp IS

C” zz y; + (y* I”’ (‘1)

I hl< aggregate of micro mcomr-expencltme rclatlopshlps CLW be cnn<ldeled a, the

aggregate consumption function It reflects thr clistI:bution of consumer units bv

nonbudgctary factors consistent with Friedman’s (!%7) lormulatlon This means

thal the aggregate parameter ~111 change over time if the mlcr*J parameter or Income

ccmposltlon changes

The presence of micro-parameter and mclJme-compo,ltlon effects IJJ the aggre-

gate parameter 1s miportant for the understanding of the dynamic behavior of the

aggregate savmg+mcome ratlo, for two reasons First, If the propensity to consume

1s lower for rndlblduals ~;th higher income, and if income Increases oker tmie, then

the mcome-Lomposltlon effect on the aggregate parameter 1s negative Second, past

consumption faclhtated bq pa$t Income and changes in consumptlo? technology

have the effects of contnbutmg to accumlllatlon of consumption capital, lmplymg

that the consumption ser parameter IS an rrldlrect (posmve) functron of pa<t mcome

and direct (positive) function of time This IS partially rmphed ln the previously

noted proposItIon of the relat:ve income hypothesis that people tend to adopt the

pattern of corlsumptlon m higher income groups and current consumption 1s

influenced bc prei lous!y attamed highest level of income It IS also partially ImplIed

in the proposltlons of the permanent-income and life-cycle hypotheses that the pro-

penslty to consume depends OII the stock of one’s resources and time, ard that pe;-

manent Income on which one’s current consumption depends 1s measured m terms

of tht weigh-ed al erage of past mccame These two aspects mdlcate that the dynamic

behavior of the aggre};ate sa\mgs-Income ratio depends directly on whether charlges

In income composltlon or micro-parameter effect IS .nore dominant

To illustrate this, consider three Income levels, $5000, $10000, and $15 000, with

the respectl\e propensmes to expend of 0 8, 0 7, and 0 6 If at time t the composl-

lion of mcc?le Y/z Y IS respectivel- 0 2, 0 6, and 0 2, then the propensity to con-

sume m agtregatc 1s 0 7, as shown III row t of Table 1 ”

if at (t+ 1) the propensltg to consu.me remam\ at 0 8, 0 7, and 0 6 at each of the

three Income levels, the aggregate parameter ~111 undergo changes as the composl-

tlon of Income changes If, for example, Income Increases m (t + 1) so that the com-

posltlon of income for the three levels 1s 0 1,O 5, and 0 4, the propensity to consunie

” The rew~ that Y/r Y 15 nor a umplc propxtlon of 55000, $10000 dud 51.5 000 15 th,u the number

of mdi\idudls anb different let& of mcome IS dltlerent

111 aggregate, ulll decrease to 0 57 Thrs 15 \ho\\n 111 IOU (I L ! b of Pahlc I in ttll\

ewmplc ‘ne Let rease in the aggregate pardmetcr from 0 - in f to 0 ii- III (i - 1; ,

attrlbutabk en,~:ol> :o the InCor~~e-Co~~~p~~~lt~~~n et tc~t PhlL c’\dlllpk rf_9IKt~ “71‘

baw ptopo$ltlcli ot the dbstslute-income h\potht\l\ l-he abwjutt’-~xomi’

hypothesis ~111 prollde an adequate e\planatlon ot the beha\lor of the ag:rqz,:~~

parameter If the micro jxrameters In tact remdin conYtClnt o\er time Hcvs~\~r *i

Instead of rem,umng conctJnt, the micro parameter in t’~h lncomt’ lc~ei ~nc‘reaw

o\el time, we can no longer say that the aggregdtc pardmetcr \\]I1 Areaw beiL~~l~i‘

of the rl,e 111 income For cxnmj>le, in tt,e lllu\trrtlon prcxnted III Table I I it th,,

parameter tor each income level ha, InLrea\ed (to 0 83, 0 ‘3 and U 6: re<pzLt.L<I\ ) as sho\bn 11~ rev+ (I c I)‘, :hen the micro-parameter eftect \\1!1 r’\~:l\ klft\ct the

Income-composltlon effect, dnd the propen\lt\ tg con~umc 111 ng~repLite \\~ii IX (1 _

5. Concludmg remarks

Heferences