A Theory of Social Interactions
Author(s): Gary S. Becker
Source: The Journal of Political Economy, Vol. 82, No. 6 (Nov. - Dec., 1974), pp. 1063-1093
Published by: The University of Chicago Press
Stable URL: http://www.jstor.org/stable/1830662
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A Theoryof Social Interactions
GaryS. Becker
Research
ofChicagoand NationalBureauofEconomic
University
This essayuses simpletoolsof economictheoryto analyze interactions
characteristics
of
betweenthe behaviorof some personsand different
other persons. Although these interactionsare emphasized in the
contemporarysociological and anthropologicalliterature,and were
considered the cornerstoneof behavior by several prominentnineeconomists,theyhave beenlargelyignoredin themodern
teenth-century
economic literature.The central concept of the analysis is "social
income," the sum of a person's own income (his earnings,etc.) and
the monetaryvalue to him of the relevantcharacteristicsof others,
which I call his social environment.By using the concept of social
income,I can analyze the effecton these expendituresof changes in
prices,includingthe "price"
different
sourcesofincomeand in different
Interactionsamongmembersofthesame famofthesocial environment.
ily receive the greatestattention.The "head" of a familyis defined
not by sex or age, but as that member,if thereis one, who transfers
generalpurchasingpowerto all othermembersbecause he cares about
organitheirwelfare.A familywith a head is a highlyinterdependent
of income
zation that has the followingproperties:A redistribution
among membersdoes not affectthe consumptionor welfareof any
from
changesin transfers
memberbecause it simplyinduces offsetting
the head. Not only the head but othermemberstoo act "as if" they
in thesensethat
"loved" all members,even whentheyare reallyselfish,
theymaximizenottheirown incomealone but familyincome.Transfers
fromparentsto childrenin the form,say, of schooling,gifts,and bequests tend to be negativelyrelated to what the income of children
would be relativeto theirparentsin the absence of these transfers.
Therefore,the relativeincome of childreninclusiveof transferscould
Consequentbe unrelatedor even negativelyrelated to thesetransfers.
ly, one cannot inferanythingabout the stabilityacross generationsof
economicor social positionssimplyfromknowingthe relationbetween
parentalpositionand the amounttransferred.
[Journalof Political Economy,1974, vol. 82, no. 6]
C) 1974 by The University of Chicago. All rights reserved.
i063
Io64
JOURNAL OF POLITICAL
"No Man is an Island." [JOHN DONNE,
Emergent]
"Man is a social animal."
[SENECA,
ECONOMY
Devotions upon
De beneficiis]
1. Introduction
Before the theoryof consumer demand began to be formalized by Jevons,
Walras, Marshall, Menger, and others, economists frequently discussed
what they considered to be the basic determinantsof wants. For example,
Bentham (1789, chap. 5) discusses about 15 basic kinds of pleasures and
pains-all other pleasures and pains are presumed to be combinations of
the basic set-and Marshall (1962, bk. 3, chap. 2) briefly discusses a
few basic determinants of wants before moving on to his well-known
presentation of marginal utility theory. What is relevant and important
for present purposes is the prominence given to the interactions among
individuals.
Bentham mentions "the pleasures ... of being on good termswith him
or them," "the pleasures of a good name," "the pleasures resultingfrom
the view of any pleasures supposed to be possessed by the beings who
may be the objects of benevolence," and "the pleasures resultingfromthe
view of any pain supposed to be sufferedby the beings who may become
the objects of malevolence." Nassau Senior said that "the desire for distinction ...
is a feeling which if we consider its universality, and its
constancy, that it affectsall men and at all times, that it comes with us
from the cradle and never leaves us till we go into the grave, may be
pronounced to be the most powerful of all human passions" (quoted by
Marshall 1962, p. 87.) Marshall also stresses the desire for distinction
and illustratesits influence by discussing food, clothing, housing, and productive activities.1
Over the years I have received helpful commentson a succession of draftsfrom
numerouspersons,especiallymycolleaguesat theUniversityof Chicago and theNational
Bureau of Economic Research. I received veryusefulcommentson the draftprepared
forpublication fromRobert Barro, Isaac Ehrlich, Sam Peltzman, and George Stigler,
and valuable researchassistancefromWalter Wessels. My researchhas been supported
by a grant to the NBER from the National Instituteof Child Health and Human
Development,National Institutesof Health, U.S. Departmentof HEW; but the paper
is not an officialNBER publication since it has not been reviewedby the NBER Board
of Directors.
1 He limitshis discussionofconsumerdemand to the largelyformaltheoryofmarginal
theorybecause of the importance he attaches to the interactionbetween activities,
consumerbehavior and the basic wants: "Such a discussionof demand as is possibleat
this stage of our work must be confinedto an elementaryanalysis of an almost purely
formalkind" (1962, p. 90). He neverdeveloped the more complicated and less formal
analysis.
SOCIAL INTERACTIONS
I o65r
As greaterrigorpermeatedthe theoryof consumerdemand,variables
like distinction,
a good name, or benevolencewere pushed furtherand
further
out ofsight.Each individualor familygenerallyis assumedto have
a utilityfunctionthatdependsdirectlyon the goods and servicesit consumes.This is not to say thatinteractions
betweenindividualshave been
completelyignored.Pigou (1903), Fisher (1926, p. 102), and Panteleoni
(1898)2 includedattributes
ofothersin utilityfunctions(but did nothing
withthem). In recentliterature,"demonstration"and relativeincome"
effectson savings and consumption,3 "bandwagon" and "snob" influences
on ordinary consumption theory,4 and the economics of philanthropic
contributions5 have been discussed. But these effortshave not been unified
and, more significantly,have not captured the dominance attributed to
social interactions by nineteenth-centuryeconomists.
Of course, sociologists have fora long time emphasized the central role
of interactions and their importance in the basic structure of wants or
personality. Veblen's conspicuous consumption and conspicuous leisure
(if for this purpose he is classified as a sociologist) have entered ordinary
discourse. At one point he said: "But it is only when taken in a sense far
removed from its naive meaning that the consumption of goods can be
said to affordthe incentive fromwhich accumulation invariably proceeds.
The motive that lies at the root of ownership is emulation," and "the
usual basis of self-respectis the respect accorded by one's neighbors"
(Veblen 1934, pp. 25, 30). Interactions were also emphasized by
Durkheim, Simmel, Freud, and Weber, as well as in modern discussions
of "social exchange" and the "theory of action" (see Blau 1968; Parsons
1968).
My interestin interactionscan probably be traced to a study of discrimination and "prejudice" where I analyzed discriminatorybehavior by
incorporating the race, religion, sex, or other personal characteristics of
employees, fellow workers,customers, dealers, neighbors, etc., into utility
functions(Becker 1971 [1st ed., 1957]). Subsequently, in order to provide
a theoretical frameworkfor a study of philanthropy by the National Bureau of Economic Research, I incorporated the standard of living of
"poorer" persons into the utilityfunctionsof "richer" ones (Becker 1961).
Further reflectiongradually convinced me that the emphasis of earlier
economists deserved to be taken much more seriously because social
interactions had significance far transcending the special cases discussed
by myself6and others.
I owe thisreference
to George Stigler.
See, e.g., Bradyand Friedman (1947), Duesenbery(1949), or Johnson(1952).
4 See Leibenstein(1950).
5
See Vickery (1962), Schwartz (1970), Alchian and Allen (1967, pp. 135-42), and
Boulding (1973).
6
Other draftsthatwere also circulatedinclude Becker (1968).
2
3
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JOURNAL OF POLITICAL
ECONOMY
This essay incorporates a general treatment of interactions into the
modern theoryof consumer demand. In Section 2, various characteristics
of differentpersons are assumed to affect the utility functions of some
persons, and the behavioral implications are systematically explored.
Section 3 develops furtherimplications and applications in the context of
analyzing intrafamily relations, charitable behavior, merit goods and
multiperson interactions, and envy and hatred. The variety and significance of these applications is persuasive testimonynot only to the importance of social interactions but also the feasibilityof incorporating them
into a rigorous analysis.
2. Theoretical
Framework
A. Equilibrium
fora SinglePerson
According to the modern (and very old!) theory of household behavior,7
Ui = Ui(Zl, ..,Zm)
(2.1)
Zmare the basic wants
is the utilityfunctionof the ith person, and Z,, ...,
or commodities. As indicated earlier, Bentham mentions about 15 basic
wants, whereas Marshall and Senior stressan even smaller number. Each
person also has a set of production functions that determine how much
of these commodities can be produced with the market goods, time, and
other resources available to him:
Zj = f](xj tj Ei, R
Rj),
(2.2)
where xj are quantities of differentmarket goods and services; tj are
quantities of his own time, E' stands for his education, experience, and
are characteristics of other
R.
"environmental" variables; and RJ,...,
persons that affecthis output of commodities. For example, ifZ1 measures
i's distinctionin his occupation, R,.. ., R1jcould be the opinions of i held
by other persons in the same occupation. Presumably, characteristics of
others affectthe production of a significantfractionof commodities.
If the Rj were completely outside i's control-that is, unaffectedby what
he does with his resources-i would maximize U taking the Rj as given.
This is one way to justify the usual neglect of interactions. They are
considered beyond the control of the persons being studied and are therefore taken as given when one is analyzing their reactions to changes in
resources and prices.
The point of departure of my approach is to assume the contrary,
namely, that i can change Rj by his own efforts.For example, he can
avoid social opprobrium and perhaps ostracism by not engaging in
criminal activities; achieve distinction by working diligently at his occu7
For an expositionof this theory,see Michael and Becker (1973).
io67
SOCIAL INTERACTIONS
pation, giving to charities, or having a beautiful house; or relieve his
envy and jealousy by talking meanly about or even physically harming
his neighbors. These effectscan be formalized in a production functionfor
the (RJ, ..., RJ) that depends partly on the effortsof i and partly on
other variables.
To simplifythe discussion,8 I follow Senior and assume only a single
commodity (distinction?) that is produced with a single good (the input of
time is ignored) and a single characteristic of others. Then maximizing
utilityis equivalent to maximizing the output of this commodity, and one
can write
(2.3)
Ui = Z(x, R).
I assume also (until Section 3C) that the effectofothervariables (including
the effortsof others) on this characteristic is not dependent on i's own
efforts.Therefore, R can be written as the additive function
R = Di + hA
(2.4)
where h measures the effectof i's efforts,and Di the level of R when i
makes no effort;that is, Di measures i's "social environment."
His budget constraintfor money income can be writtenas
PxX + PRh = Ii
(2.5)
where Ii is his money income, PRhis the amount he spends on R, and PRis
the price to him of a unit of R. Substitute R - Di forh in equation (2.5)
to get
Pax + PRR = Ii + PRDi = Si.
(2.6)
The right-hand side gives the sum of i's money income and the value to
him of his social environment, and will be called his social income. The
left-handside shows how his social income is "spent": partly on his "own"
goods (x) and partly on the characteristicsof others (R).'
If i maximizes the utility-output function given by equation (2.3)
subject to the constraint on social income given by equation (2.6), the
equilibrium condition is 10
aui
OUi = Px
PR
Ax / AR
(2.7)
8 I have also developedthe analysisassumingmany commoditiesand many characteristics.
9 Sociologistssometimesassertthat variables like social approval and respect"do not
have any materialvalue on whicha price can be put" (see Blau 1968). But pricesmeasure
onlyscarcityand have nothingintrinsicallyto do with"materialvalue"; PR,forexample,
only measuresthe resourcecost to i of changingsocial approval, respect,etc.
10 I assume forsimplicityin this formulathat PR measuresthe marginal as well as
average price of R.
Io68
JOURNAL OF POLITICAL
ECONOMY
x
U0
0
-e-
o
0
D~~~~~~~~~~~~~~~~~
D
SO
FIG.
SI
R
1
If I did not want to purchase any R, PR would be a "shadow" price,
measured by the monetary equivalent of the marginal utility(equal to the
marginal product) of R to i when R = Di (or when h = 0).
His equilibrium position is shown in figures 1 and 2. The firstfigure
assumes that R has a positive marginal product in the production of Z (a
positive marginal utility); that R refers, for example, to the respect
accorded i rather than to his envy of others. The quantity OD measures
his social environment,and Oxo his own income (measured in termsof x),
so that the "endowed" point E0 gives his utilitywhen he spends nothing
on R. If E0S0 measures the opportunities available for purchasing additional R," he would maximize his utilityby moving along E0S0to point
where the slope of this opportunity curve equaled the slope of his
eon
" If he can also reduce R by givingup own goods, the curve E,,S. would continuein
the southwestdirection(see ES, in the figure).However, thissectionwould be irrelevant
if R had positivemarginalutility.
I o69
SOCIAL INTERACTIONS
x
hlis
U 2.
UZ
F.
U1
U3
indifferencecurve. His equilibrium purchase of R is measured by the
line segment ho.
Figure 2 assumes that R has a negative marginal product (or utility)
because, say, it measures the income or prestige of persons that i envies.
The section of the opportunity curve to the southeast of point E0 is now
irrelevant,
and he movesalong thesouthwestsectionE0Soto pointe0. He
is willing to give up resources to reduce R because his utilityis raised by a
reductionin R; at pointe0, he spendsenoughresourcesto reduceR by how
Note that since the marginal (and average) price of R is negative in
figure2, i's social incomeis less thanhis own incomebecause thevalue of
his social environment is subtracted from his own income. That is, he is
made worse offby his social environmentif it is dominated by characteristics of others that are distastefulto him. Note too that as long as the
marginal utilityof R is not zero at the socially endowed position, his social
JOURNAL OF POLITICAL
I070
ECONOMY
fromhisown incomeevenifhe did notwantto spend
incomewould differ
anythingon R. He would add to (or subtractfrom)his own incomethe
productofD and the (monetaryequivalentof the) marginalutilityofR
at the endowedpositionEon In otherwords,the traditionalincomeconcept is incompleteeven when no resourcesare spenttryingto influence
the attitudesor situationof others.
The analysisdeveloped forsocial interactionsin thesefiguresand in
equations (2.3), (2.6), and (2.7) is also applicable wheneverthereis a
that eithercan be altereddirectlyor can have its
physicalenvironment
effectsaugmentedor diminished.For example, the human capital of a
personis the sum of the amount inheritedand that acquired through
moreover,the amountinvestedis partlydeterminedby the
investments;
in a houseis determinedby the weather
Or
inheritance. thetemperature
or offset
thenatand expenditures
on fuels,insulation,etc.,thatreinforce
ural environment.
A more general analysis,therefore,would assume that every term
enteringthe utilityfunctionhas both an environmentaland acquired
component.The generalanalysiscould readilybe developed,but I have
the discussionby ignoringthe nonsocialenvironment.
chosento simplify
withthosefromthe generalanalysisas long as
The resultsare consistent
the contribution
of the social environment
is, on the whole,significantly
Thisis assumedto
moreimportantthan thatof thephysicalenvironment.
be true. (I am indebtedto GilbertGhez and especiallyRobertBarrofor
stressing
thegeneralnatureof the analysis.)
B.
andPriceEffects
Income
An increasein i's own incomealone-without any changein pricesor the
social environment-wouldincreasebothx and R unlessone wereinferior.
The averagepercentageresponsein x and R per 1 percentchangein his
own incomeis notunity,but is lessby thefractiona, wherea is theshare
in hissocial income.12 Therefore,theeffectofa
ofthesocial environment
is smaller the more
change in his own income on his utility-output
is.
importanthis social environment
of his social environment
the greaterthe contribution
Put differently,
to his social income,the more his welfareis determinedby the attitudes
and behaviorofothersratherthanby hisownincome.Traditionalmodels
12 By differentiating
equation (2.6) withrespectto I, alone, i - wxn, + WRfR = 1-a,
where
dR Ii x =PRDI
dx I,
_ PRR pW x
d11 R
dI1 x
St
St
St
and I am assumingthatPR is given (not dependenton h, x, etc.). Of course,the weighted
average of income elasticitieswith respectto a change in Si mustequal unity,as in the
usual analysis.
1071
SOCIAL INTERACTIONS
of choice by economistsassume that own efforts
and access to property
income and transferpaymentsdeterminewelfare.On the otherhand,
its normativerequirements
thosewho stressthe social environment,
and
sanctionsforcomplianceand noncompliance,and the helplessnessof the
individualin the face of his environmentnaturallysee societydominatingindividualefforts
and, consequently,see littlescope forimportant
choicesby individuals.
The relativeimportanceof the social environment,as well as other
implicationsof the theoryof social interactions,can be empirically
estimatedfrominformationon expendituresmotivatedby these interactions.If i's social environmentdid not change when his own income
of others
changed, the induced absolute change in the characteristics
to thesecharacteristics.
would equal thechangein his contribution
Howwould differ
fromtherelative
ever,therelativechangein hiscontribution
because the level of the latteris partly
change in these characteristics
determinedby the social environment.
Consideragain figures1 and 2, wherean increasein i's own income
withno changein the environment
is shownby a verticalincreasein the
endowedpositionfromE0 to E1. Since his equilibriumpositionchanges
fromeo to e1,thechangein R is exactlyequal to h1 - ho, thechangein i's
to R. The percentagechange in R in figure1 is clearlyless
contribution
thanthatin A,sinceR is thesumofh and (a fixed)D. Since thepercentage
change in R in figure2 is negative,it is also less than the percentage
changein A,whichis positive(sinceh is negative).However,ifR had been
increasedby theincreasein i's own income-if, say, the new equilibrium
positionwas at pointe'-the percentagechange in R would be positive
and would clearly exceed in algebraic value the negative percentage
changein h.
The own-incomeelasticityofdemandforcontributions
is relatedto the
ofdemandforcharacteristics
elasticity
by thefollowingformula:13
h
=
dh I,
-
nR__
_
(I~8
_
a
-2 n(
)
(2.8)
where0 < /3< 1 is thefractionofown incomethatis spenton contributionsto R. If a > 0, if the social environment
adds to i's social income,
13Since dh/dI =
dR/dIi,
nh
=
dh
Ii
j f * Ii jf=
dR Ii R
* R=
nR
*
R
R.
(2.8')
But
RPRR
h PRh
Since 1 - a=
1 + PRD
PRh
1
Si-I
/)Ii
(see n. 12 above), nh =
1 + 1/(1 (nRln)(C/I3 +
1
-1
-
a).
(1 -)
1
+ a/A
I072
then clearly nh
JOURNAL OF POLITICAL
>
1R.'4
Moreover if n
i
>
=
1
-
a
ECONOMY
1, necessarily
<
to the characteristics
of
1 even whennR < 1; thatis, contributions
otherscould have a "high" incomeelasticityevenwhenthecharacteristics
themselveshad a "low" elasticity.Of course,if nh > 1, the own-income
elasticityof demand forown consumption(ny)would be less than unity.
That is, social interactionimpliesa relativelylow income elasticityfor
own consumptionevenwithoutintroducing
transitory
changesin income,
errorsin variables,and the like.
Equation (2.8) further
impliesthatan increasein a, an increasein the
social environment,
with no change in the own-incomeelasticityof demand forcharacteristics
relativeto the averageelasticity(nR/A), 5 would
increase the own-incomeelasticityof demand for contributions.16 In
otherwords,themorethati's social incomewas determinedby his social
thegreaterwould be thepercentagechangein hiscontribuenvironment,
tionsto the characteristics
of othersas his own incomechanged.
If, on the otherhand, < 0-the social environment
subtractedfrom
i's social income-then equation (2.8) impliesthatnh < nR whennR > 0,
and nh > nR whennR < 0 (these different
cases are shownin fig.2). His
demand forcharacteristics
would probablybe reducedby an increasein
have a negative
his own income (i.e., nR < 0) if these characteristics
marginalutilityto him.Again, an increasein a, withnR/i held constant,
would raise nh (the argumentin n. 16 fullyapplies).
Since thesocial environment
to any personcannotbe readilyobserved,
an indirectmethodofestimatingat least itssignwould be useful.If nR/l
wereknown,thatis, ifthe relativeincomeelasticityof demand forcharacteristicswere known,thesignof x could be estimatedsimplyfrominformationon theown-incomeelasticityof demand forcontributions
to the
environment,and its magnitudefromadditional informationon the
fractionof own income spent on these contributions.Equation (2.8)
impliesthat
(2.9)
= h(f/'nR) - 1
nh >
a
1/Al-1
Therefore, a
j 0 as
nh( l/nR)
j 1, and information on
nh,
n/nR,
and /3
to estimatea.
would be sufficient
thatadds to i's socialincomewould
An increasein a socialenvironment
increasehisdemandforown goodsiftheyhad positiveincomeelasticities.
For [1 + a(1/1, - l)]/(l - a) > 1, since 1//3> 1, and 1 - a < 1.
An increasein a lowersh because the relativecontributionof own income to social
income is reduced.
1616
t
1\d_ nR f2
dnh(nR = constant
= nR (1
dnh*14
15
_1
da
n
n
,B
n
da
Both termsare greaterthan zero because /B< 1, and d/l/dx < 0 (thisis shownshortly);
> 0.
therefore,
dnhldcL
SOCIAL INTERACTIONS
1073
If his own income were unchanged,his increasedexpenditureon own
goods would have to be "financed" by reduced contributionsto the
characteristics
of others.Similarly,an increasein a social environment
thatsubtractsfromhis social income would increasehis expenditures
on
othersand reduce his expenditureson own goods. Consequently,the
effectofa changein theenvironment
is always (i.e., as long as own goods
are not inferior)partlyoffsetby induced changesin i's contributions
in
the oppositedirection,regardlessof whetherthe environment
adds to or
subtractsfromi's social income.
Geometrically,
a change in the social envirnment
is shownby a horizontalmovementoftheendowedposition.An increasein theenvironment
shiftsthe endowmentin figure1 frompoint E1 to E2; the equilibrium
positionis changedfrompointe1 to a pointon a higherindifference
curve
(e2), and i's contribution
declinesfromh1toh2.In figure2,theequilibrium
is changedfrompointe1 to a pointon a lowerindifference
curve (e2), and
i's contribution
increasesfromh1 to h2.17
Ifboththeownand environment
incomesofi changed,theeffect
would
be a combinationofthosewheneach alone changed.For example,ifboth
incomesincreased,the effecton his contributions
of the increasein the
environment
would at least partlyoffsetthe effectof the increasein his
own income.In particular,ifbothincomesincreasedbythesamepercentage, thepercentagechangein contributions
would be greaterthan,equal
to, or smaller than that percentageas his demand for characteristics
exceeded,equaled, or was less than unity.
Throughthe assumptionthatPRis constant,I have been assuming,in
effect,that expendituresand the social environmentare perfectsubstitutesin producingcharacteristics
ofothers.However,the qualitativeimplicationsofthisassumptioncan also be derivediftheyare simplybetter
substitutes
foreach otherthanforown consumption-ifPR risesas h rises,
but not "too" rapidly.For example, a rise in the environmentwould
reducecontributions,
and a risein own incomewould increasecontributionsby a relativelylargepercentageiftheenvironment
and expenditures
on thesecharacteristics
are simplyrelativelyclose directsubstitutes.
A risein the cost of changingthe characteristics
of others(PR) would
induce the usual substitution(and perhaps income) effectsaway from
thesecharacteristics.
If the environment
were given,the absolutechange
in contributions
would equal theabsolutechangein thesecharacteristics,
17 The endowment-income
elasticityof demand forcontributionscan easily be shown
to equal
Nh=
dD
.D =
h
(NR
1) (
1-a
1
+
+ 1
Clearly,when a > 0, Nh < 0 if NR < a = N, the average endowment-income
elasticity
of demand; and when a < 0, Nh > 0 if NR
a,.
I074
JOURNAL OF POLITICAL
ECONOMY
whilethepercentagechangeswould differaccordingto equation (2.8) in
thefollowingway:
Eh=
-
dhPRI=
1)1
)](2.10)
+l-x
ER [1 ?(l/f3
(same proofas in n. 13 above). Therefore,when a > 0, Eh would exceed
ER by an amountthatwould be greater,thegreatera and thesmallerf3.
Similarly,when a < 0, Eh would be less than E 18 by an amount that
would be greater,the greaterthe absolutevalue of a and the smallerfA
3. Applications
Three specificapplicationsofthegeneralanalysisofsocial interactionare
amongmembersofthesame family,charity,
now considered:interactions
and envyand hatred.These applicationsnot onlyprovideempiricalsupjust derived,but also bringout
portfortheincomeand priceimplications
a numberof otherimplicationsofsocial interaction.
A.
TheFamily
Assumethati caresabout his spouse in thesensethati's utilityfunction
dependsonj's welfare.'9I assume untilmuch laterin thissectionthatj
definethe
does not care positivelyor negativelyabout i. For simplicity,
variable measuringthisdependence,R., as follows:
R =
+ /ii
-
S. =
(3.1)
fromi toj, Sj isj's
whereIj isj's own income,hij are the contributions
social income,and xj are thegoods consumedbyj. The social incomeofi
equation (3.1) into equation (2.6):
can be derivedby substituting
PxXi+ PRRi = Si = Ii + pRt,
Px
(3.2)
resourcestoj. If i can transfer
wherePR is the price to i of transferring
resourcestoj withoutany "transactions"costs-presumably,these costs
are reducedby sharinga commonhousehold-and if i cares sufficiently
aboutj to have hij > 0, thenPR = px, and
Si = Pxi + p~x; = Ii + Ij
=
Iij
(3.3)
18 I assume that an increase in the absolute value of PR reduces the demand forR,
so thatEh > 0.
19 Caringis notsimplya deusexmachina
introducedto derivethefollowingimplications,
since I have shown elsewhere(Becker 1974) that the marriagemarketis more likely to
pair a personwith someone he cares about than with an otherwisesimilar personthat
he does not care about.
SOCIAL
INTERACTIONS
I075
x
+ Vj
IjjupXl=j
l
slope-
P
R, =x1
FIG. 3
The social income of i equals the combined own incomes of i and j, or the
"family's" own income. Moreover, the equilibrium condition given by
equation (2.7) implies that
aU I/
au.
=
__
-
1,
(3.4)
or i would receive equal marginal utility from j's and his own
consumption.
Conditions (3.3) and (3.4) are shown in figure 3. Resources can be
transferredfrom i to j by moving along i's budget line in a southeast
direction fromthe endowed position at point Eo. The equilibrium position
is at point e, where the slope of i's indifferencecurves equals the slope of
his budget line ( = to -1 ). The vertical (or horizontal) interceptgives the
family's own income i's social income-deflated by the price of x.
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An important implication of this analysis is that a change in the distribution offamilyincome between i andj has no effectat all on the consumption or welfare of either, as long as i continues to transferresources to
j. A change in the distributionwould be on the same budget line as E if
total familyincome is unchanged: the change fromE0 to El is nominally
more favorable toj, whereas the change to E2 is nominally more favorable
to i. Since there is only one point of tangency between i's budget line and
an indifferencecurve, the equilibrium position must be unchanged at e.
A shiftin favor ofj's income to El simply induces an equal reduction in
i's contributionstoj (fromhM.to hbin the figure), whereas a shiftagainst
to
j's income to E2 induces an equal increase in his contributions(fromhM'j
htj)2
This discussion has assumed a two-person family but is equally applicable to larger families that include grandparents, parents, children,
uncles, aunts, or other kin. If one member, call him the "head," cares
sufficientlyabout all other members to transfer general resources to
them,2' redistributionof income among members would not affect the
consumption of any member, as long as the head continues to contribute
to all.
The head's concern about the welfare of other members provides each,
including the head, with some insurance against disasters. If a disaster
reduced the income of one member alone, k, by say 50 percent, the head
would increase his contributions to k, and thereby offsetto some extent
the decline in k's income. The head would "finance" his increased contribution to k by reducing his own consumption and his contributions to
other members; in effecteach member shares k's disaster by consuming
less. If k's share of familyincome were negligible, he would essentially be
fullyinsured against his own disasters because even a 50 percent decline
in his income would have a negligible effecton family income, and thus
on the consumption of each member. Since the share contributed by any
member would tend to be inversely related to family size, large families,
including the extended kinship family found in certain societies, can
provide self-insuranceespecially when old-age, health, and other kinds of
market insurance are not available or are very costly.22 Note that insurance is automatically provided when resources are voluntarilytransferred,
20 If the utilityof i also partlydepended directlyon the amountshe transferred
toj,
then
perhaps because i's "prestige" or "approval" partly depended on these transfers,
offamilyincomewouldhave a net effecton the consumptionofboth i andj.
redistribution
21 A somewhatweaker assumptionis that the familyis "fully connected" througha
between members; for example, a transfersresourcesto b because a
seriesof transfers
to the
to c because b cares about c, and so on untilm transfers
cares about b, b transfers
to no one (thisassumptionis made in an intergenerational
last member,n,and n transfers
contextby Barro 1974). Indirectly,a (or any othermemberbut n) would be transferring
to all membersbecause an increasein his contributionsto b would induce an increasein
the contributionsto all othermembers.
22 The interaction
betweenselfand marketinsuranceis analyzed in Ehrlich and Becker
(1972).
SOCIAL INTERACTIONS
1077
without the need for any member to have dictatorial control over the
family's allocation of resources.
The result on the unimportance of the distribution of income among
persons linked by transferscan also be used to understand the interaction
among generations.23 Suppose that the resources of the present generation
are changed at the expense of or to the benefitof the resources accruing to
future generations. For example, increased government debt or social
securitypayments are financed by increased taxes on futuregenerations,
or increased public investment,perhaps in schools, with benefitsaccruing
to future generations is financed by taxes on the present generation. If
present and future generations are fully connected by a series of intergenerational transfers,called "bequests," then each of these apparent
changes in the relative resources of present and futuregenerations would
tend to be offsetby equal but opposite changes in bequests. In particular,
increased public debt would not raise the real wealth or consumption of
the present generation or reduce that of future generations because increased taxes on future generations would be matched by increased
bequests to them. Similarly, increased public investment in education
would be matched by reduced private investmentin education.24
The budget constraintof the head is determined by total familyincome,
not his own income alone-equation (3.3) for a two-person family can
be readily generalized to many persons. Since the head maximizes his
utility subject to his budget constraint, anything that increased family
income would increase his utility.Therefore, the head would consider the
effecton total familyincome of his differentactions, and would forfeitown
income if the incomes of other familymembers were increased even more.
For example, he would not move to another city if his spouse's or children's income would be decreased by more than his own income would be
increased. Or, although children usually eventually set up their own
households and fullycontrol theirown incomes, the head would guide and
help finance their investmentsin education and other human capital to
maximize the present value of the real income yielded by these
investments.25
Put differently,the head automatically internalizes the "external"
effectsof his actions on other family members.26 Indeed, because the
This application is takenfromthe detailed discussionin Barro (1974).
The empiricalevidencedoes stronglysuggestthatmostof the investmentin higher
education by state governmentshas been offsetby reduced private investment(see
Peltzman 1973; McPherson,in preparation).
25 The incentivethat parentshave to investin their children is discussed in several
places (see, e.g., De Tray 1973; Parsons 1974).
26 The Coase Theorem proves that when "bargaining costs" are negligible, each
familymember could always be induced to maximize family opportunitiesthrough
bargaining with and side paymentsfromothermembers.I have proved that the head
(and, as shown later, other memberstoo) has this incentive and, in effect,makes or
receives "side payments" without bargaining with other members.The word "automatically" is used to distinguishthistheoremfromthe Coase Theorem.
23
24
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head maximizes familyincome, he fullyinternalizes these externalitiesnot
only when the income of differentmembers but also when their consumption, the other side of the budget constraint,is directlyaffected.He would
take an action directlyaffectingconsumption only when either the value
of any increase in his consumption exceeded the value (to him) of any
decrease in other members' consumption, or when any decrease in his
own was less valuable than the increase in theirs.2 7
For example, he would read in bed at night only if the value of reading
exceeded the value (to him) of the loss in sleep sufferedby his wife, or he
would eat with his fingersonly if its value exceeded the value (to him)
of the disgustexperienced by his family.The development of manners and
other personal behavior "rules" between family members well illustrates
how apparent "external" effectscan be internalized by social interaction
between members.
Note too that not only is the head better offwhen his utilityis raised,
but so too are other members of his family, even if his actions directly
reduce their consumption or increase their discomfortand disgust. For
if his utilityis raised and if their welfare has a positive income elasticity
to him, he would increase his contributionsto them by more than enough
to offsettheir initial losses. For example, if he benefitsfrom reading at
night, his wife does too because he more than compensates her for her
loss of sleep. 2 8
The head maximizes a utilityfunctionthat depends on the consumption
of all familymembers subject to a budget constraintdetermined by family
27 Although this is a rather immediate implication of his interestin maximizing
familyopportunities,a directproofmay be instructive.Suppose that a particularaction
changed the utilityof the head by
dUh
=
nmUhdxh +
E
j= 1, th
( 1)
muidxj,
where mzu= aUhI%, and dxj measuresthe change in consumptionof the jth family
member.If the head can transferresourcesto othermembersdollar fordollar, in equilibrium,
muO = 4hPj
(2')
allj,
wherei,, is the marginalutilityofincometo the head, and pj is the costofxj. Substitution
of eq. (2') into (1') gives
dUh
= Ah(phdXh
+
i=
E
1, 7 h
=
pjdXJ)
Since the head takes an action if and only if dUh
thathe takesan action if,and only if,
h
all
>
(3')
pidX3.
i
0, eq. (3') implies (since Ah
>
0)
E PfdxJ> O.
(4')
all j
which was to be proved.
28 Recall that I have been assuming that only a single good is consumed by each
person,althoughthisanalysispresupposesmany goods. The transitionto many goods is
ifthe head's utilitydependson a functionofthe variousgoods consumed
straightforward
by anothermemberthatis monotonicallyrelated to the utilityfunctionof that member
(see the discussionlater in thissection).
SOCIAL INTERACTIONS
I079
income and family consumption. Therefore, the effect of a change in
relative prices of goods, or in aggregate family income (as well as in its
distribution) on a family's consumption of differentgoods, could be predicted solely from the head's utilityfunction and a budget constraint on
family variables. The usual substitution and income effectsof demand
theorywould be fullyapplicable.
In this sense, then, a familywith a head can be said to maximize "its"
consistent and transitive utility function of the consumption of different
members subject to a budget constraint defined on family variables. The
"family's" utilityfunctionis identical with that of one member, the head,
because his concern for the welfare of other members, so to speak, integrates all the members' utility functions into one consistent "family"
function.
That is, a "family's" utility function is the same as that of one of its
members not because this member has dictatorial power over other
about all other memmembers, but because he (or she!) cares sufficiently
bers to transferresources voluntarily to them. Each member can have
complete freedom of action; indeed, the person making the transfers
would not change the consumption of any member even with dictatorial
power! For example, if i had dictatorial power, he could move the equilibrium position e in figure 3 to the vertical axis (or anywhere else), but
would not choose to move it because his utility partly depends on j's
consumption.291
Nothing much has yet been said about the preferencesof members who
29
It is difficultto contrastmy derivationof a "family" utilityfunctionwith a traditionalderivation,since explicitderivationsare rare. The mostexplicitappears to be in
curvesby Samuelson (1956). He considersthe
a well-knownarticleon social indifference
problemofrelatingindividualand familyutilityfunctions,but his discussionis briefand
elaboration,he refersto a
the argumentssometimesare notspelled out. Withoutsufficient
consistent"familywelfarefunction"being graftedonto the separate utilityfunctionsof
familymembers(p. 10). In addition, he says that a familymember's "predifferent
ferencesamong his own goods have the special propertyof being independentof the
othermembers'consumption.But since blood is thickerthan water, the preferencesof
membersare interrelatedby what mightbe called a 'consensus' or 'social
the different
welfarefunction'which takes into account the deservingnessor ethical worthsof the
consumptionlevels of each of the members."How are thesepreferencesinterrelatedby
a "consensus,"and should not the "deservingness"of the consumptionlevelsof different
(as in myapproach)?
members'preferences
memberssimplybe incorporatedintodifferent
Incidentally,at one point (p. 9), Samuelson appears to believe that if the familyutility
functionis the same as the head's, he musthave sovereignpower, which I have shown
is not necessary.He later (p. 20) says that "if withinthe familytherecan be assumed to
take place an optimalreallocationofincomeso as to keep each member'sdollar expenditureof equal ethical worth,thentherecan be derivedforthe whole familya set of wellcontoursrelatingthe totalsof what it consumes:the familycan be
behaved indifference
said to act as if it maximizes such a group preferencefunction" (italics in original).
In my analyses, the "optimal reallocation" results from interdependentpreferences
and the "group preferencefunction"is identical with that
and voluntarycontributions,
of the "head."
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JOURNAL OF POLITICAL
ECONOMY
are not heads. The major, and somewhat unexpected, conclusion is that if
to maximizefamily incomeand
also are motivated
a head exists, othermembers
alone. This is
evenif theirwelfaredependson theirown consumption
consumption,
the "rotten kid" theorem (I owe this name to the Barro family). For consider a selfishmember j who can take an action that would reduce his
income by b, but increase that of another member k by c. Initially,j would
be worse offby b, since the gain to k is of no direct concern to him. However, if c = b, the head would transferenough additional resources toj
fromk to leave him (and k) equally well off,since intrafamilyreallocations
of income do not affect the consumption of any member. Moreover, if
c > b iffamilyincome were raised byj's action-and ifj's welfare were
a superior "good" to the head, then he would transferenough additional
resources to j to make j better off. Consequently, even a selfishj would
only undertake actions that raised family income or consumption,
regardless of the initial impact on him.
In other words, when one member cares sufficientlyabout other members to be the head, all members have the same motivation as the head to
maximize family opportunities and to internalize fully all within-family
"externalities," regardless of how selfish (or, indeed, how envious) these
members are. Even a selfish child receiving transfersfrom his parents
consider the effectsof his actions on other siblings as
would automatically
well as on his parents. Put still differently,sufficient"love" by one member guarantees that all members act as if they loved other members as
much as themselves. As it were, the amount of "love" required in a
family is economized: sufficient"love" by one member leads all other
members by "an invisible hand" to act as if they too loved everyone.
Armed with this theorem, I do not need to dwell on the preferencesof
nonheads. Of course, just as there may be no head if all members are
sufficientlyselfish,so there may be none if they are all sufficientlyaltruistic. Each would want to transferresources to other members, but no
one would want to accept transfers.Aside from that, mutual interaction
or mutual interdependence of welfare raises no particular problems.30
30
oftheform
It frequently
has beenallegedto methatmutualinteraction
U1 = U[xt, gX(U)]
Ui = Ui[xi, gJAU)],
wherexiandxj aretheownconsumption
functions
ofi andj, andgiandgj aremonotonic
oftheutility
in instability
and unboundedutilitylevels.For
indexesU, and Up,results
whichraisesj'sutility
raisesi's utility,
it is argued,an increasein xi byoneunitdirectly
raisesi's utility,
and so on,untilUtand Uj approach
through
gj, whichin turnfurther
regress,
since,bysubstitution,
Mathematically,
thereis an infinite
infinity.
U, = U,[x,,g,{x, gj{x,,g, {xi, gj {...
}].
the
on the magnitudeof the interactions,
restrictions
However,withappropriate
infinite
has a finiteeffect,
and the"reducedforms"of U, and Uj on xi and Xj
regress
i o8 i
SOCIAL INTERACTIONS
By assuming in figure 3 and in the formal development given by equations (3.1)-(3.4) that only a single good is consumed by each person, I
eliminated any distinctionbetween transferringgeneral purchasing power and transferringparticular goods to another member. If each member
consumes many goods, the conclusions in this section about family
utilityfunctions,internalization of within-familyexternalities, and so on
fully hold only if the head is content to transfer general purchasing
power. He would transferin this form if his utility function depended
on the utility of other members-that is, if his utility function could be
writtenin the form
Uh =
Uh[Xh 1')
*,
Xhm5g1(X2 1, .. *X2m),
... * gnX(Xn,
* * )m)]
(3.5)
where xij is the quantity of theijth good consumed by the ith person, and
dgi = (E0 d=
implies that the utility of the ith person is unchanged. If he is concerned
not about the utility of other members but about their consumption of
particular "merit" goods, the conclusions can be quite different.The
systematicdiscussion of merit goods is postponed to Section 3C.
If parents are transferringresources to their children in the form,say,
of giftsand expenditures on education and other human capital or after
they die in the formof bequests, then an increase in the income of parents
by a given percentage would tend to increase contributionsto children by
a still larger percentage, certainly by one exceeding the increased welfare
of their children (see the discussion in Section 2). In other words, contributions to children can be very responsive to a change in parental income
without the welfare of children being so responsive.
Empirical evidence on bequests, gifts, and many other transfersto
children is seriously deficient. The general impression is, however, that
forexample,theCobbDouglasfunctions
Consider,
arewelldefined.
U,
=
XfaiUfb
=
XafUbf
are greaterthanzero,and bi and bj can eitherbe greater
whereal and aj presumably
thanorlessthanzero.Bysubstitution,
Us =
Xai/( 1-bjbj)XjajbL)/(1-bibj)
=
Xxfli
=
XgajbJ)/(1-bibj)Xjaj/( 1-bbj)
=
x1jxj,
sumto
on U, and Up.A finite
transformations
of monotonic
wherebibjis independent
or disutilities
thatthemarginalutilities
theregress
requiresthatIlbbjl< 1; essentially,
are lessthanunity.Notethatalthoughit is possibleforat = bi
due to interdependence
and thewelfareof theotherpersonto be equally
and aj = bj, forown consumption
or 1J1ji > lajl,
"important," the condition IbibJI< 1 implies that either jail > 1,8il,
hastobe moreimportant
ownconsumption
orboth;thatis,forat leastoneofthepersons,
in the"reducedforms."
thantheotherperson'sconsumption
io82
JOURNAL OF POLITICAL
ECONOMY
bequests have a very high income elasticity. Moreover, the elasticity of
expenditures on children's education with respect to parental income does
appear to be above unity (Schultz 1967, p. 9), which is consistentwith the
implications of the theory.
The responsiveness of expenditures on children's education and other
trainingand skills to parental income has oftenbeen noted, and lamented
as evidence of immobility and rigid "class" structure. Yet my analysis
implies that the welfare of children-a measure of their "class"-rises by
a smaller percentage than parent expenditures on them, and possibly
even by a smaller percentage than parental income. Put differently,considerable regression toward the mean across generations-that is, the
expected income or other measure of the position of children would be
much closer to the average position than is that of their parents-can be
observed at the same time that contributionsto children are very responsive to parental income. 31
The crucial point is that considerable regression toward the mean
across generations would occur partly because of genetic factorsand luck
if all parents spent an equal amount on their children. As a result of this,
and given interdependent preferences, higher-income parents tend to
spend considerably more on their children than lower-income ones. However, these expenditures would only tend to dampen but not eliminate the
31
In one study,the elasticityof children'syearsof schoolingwith respectto parental
with
income is a sizeable + 1.2, at the same time that the elasticityof children'sincome
respect to parental income is only +0.3, or a 70 percentregressiontoward the mean
(unpublished calculations by Jacob Mincer fromthe Eckland Sample). Note in this
regard,however,that parentscannot easily preventconsiderableregressiontoward the
mean by investingin their children. For let the relation between the human capital
investedin childrenand parentalincome be
SC = a + b log IP + u,
whereb is the elasticityof parentalresponse,and u representsother determinantsof SC.
According to the theoryof investmentin human capital (Mincer 1974; Becker 1975
[in press]),
log IC = a + rSc + v,
where r is the rate of returnon human capital, and v representsotherdeterminantsof
log IC. Then by substitution,
log IC = (a + ra) + rblog I, + (ru + v).
Even if r were as large as 0.2, and b as large as 2.0, rbwould only be 0.4: the regression
toward the mean would be 60 percent.If v = c log Ip + v', where 1 - c measuresthe
degree of "intrinsic"regressionto the mean, thenby substitution,
log IC = (a + ra) + (rb + c) log Ip + (ru + tv').
Since the analysis in the text implies that b would be positivelyrelated to 1 - c as
parentstryto offsetthe "intrinsic"regression,the "observed" regressionto the mean,
1 - y = 1 - (c + rb) = ( 1 - c) - rb,
may be only weakly related to and also is less than the "intrinsic" regression1 - c.
I am indebted to discussionswithJacob Mincer on the issues sketchilycovered in this
footnote.
SOCIAL
I o83
INTERACTIONS
regression toward the mean. Therefore, the elastic response of contributions to children can give a very biased picture of the degree of immobility
or inheritance of "class" position. Indeed, contributions would be more
responsive to parental income the strongerare the basic forcesproducing
mobility because parents attempt to offsetthese forces. In other words,
an elastic response of contributions to parental income may be evidence
!3 2
of sizeable mobility
B.
Charity
If someone makes contributionsof time or goods to unrelated persons or
to organizations, he is said to be "charitable" or "philanthropic." The
discussion of contributions within a family indicates that charitable
behavior can be motivated by a desire to improve the general well-being
of recipients.33 Apparent "charitable" behavior can also be motivated by
a desire to avoid the scorn of others or to receive social acclaim. Not much
generality is sacrificed, however, by only considering charity motivated
by a desire to improve well-being.34
The numerous implications about family behavior developed in the
previous section fullyapply to the synthetic"family" consistingof a charitable person i and all recipients of his charity. For example, no member's
well-being would be affectedby a redistributionofincome among them, as
32 It is generallybelieved that the United States has a more mobile "open" society
than European countries do; yet (admittedly crude) comparisons of occupational
mobilitybetween fathersand sons do not reveal large differencesbetween the United
States and several Western European countries (Lipset and Bendix 1959). Since the
analysis in this paper suggeststhat parents' contributionsto theirchildren'seducation
and other trainingis more responsiveto parental position in "open" societies,more
responsiveparental contributionsare probably offsettingthe greater "openness" of
Americansociety.
3 3The Random
HouseDictionary
oftheEnglishLanguage(unabridged,1967) definescharity
as "the benevolentfeeling,especiallytowardthosein need or in disfavor."
34 The utilityfunctionof a charitablepersonwho desiresto improvethe generalwellbeing of recipientscan be writtenas
Ui = Uixi
Xj
(
-
Pi- )]
whereh is his charitalbegiving,xj measuresthe well-beingof recipients,and aU/lIj =
aUjIah > 0; that is, a unit increasein the own income of recipientshas the same effect
on the utilityof a charitablepersonas a unit increasein his giving.The utilityfunction
ofa personwho makes"charitable" contributionsto win social acclaim can be writtenas
U.
U, xi IJ A
where still aUjiah > O-an increase in his contributionswould increase his acclaimbut now the sign of aU1/Ij is not so obvious. If, however,contributionsand the income
of recipientswere much closer substitutesforeach otherthan forthe own consumption
ofthecontributor,
whichis plausible,thentheseutilityfunctions
have similarimplications.
Not much generalityis sacrificed,therefore,
by only consideringcharitymotivatedby a
desireto improvethe well-beingof recipients.
Io84
JOURNAL OF POLITICAL
ECONOMY
long as i continued to give to all of them. For he would simply redistribute his giving until everyone losing income was fully compensated and
everyone gaining was fully"taxed." Moreover, all members, not simply i,
would tryto maximize "family" opportunitiesand "family" consumption,
instead of their own income or consumption alone. In addition, each
member of a synthetic "family" is at least partly "insured" against
catastrophes because all other members, in effect,would increase their
giving to him until at least part of his loss were replaced. Therefore,
charityis a formof self-insurancethat is a substituteformarket insurance
and government transfers.Presumably, the rapid growth of these latter
during the last 100 years discouraged the growth of charity.
According to the analysis in Section 2, an increase in the income of a
charitable person would increase his charitable giving by a greater
percentage than the increase in the well-being of recipients. Indeed, his
income elasticityof demand for giving would exceed unity, possibly by a
substantial amount, as long as his elasticityof demand fortheirwell-being
(which I will call his demand forcharity) was not much below his average
income elasticity. The available evidence on charitable giving clearly
supports this implication of the theory: income elasticities estimated by
Taussig (1965) fromgiving in differentincome classes in 1962 are all well
above unity, ranging from a low of + 1.3 in the under $25,000 class to a
high of +3.1 in the $100,000-$200,000 class.35
A crucial implication of charitable giving in terms of social interaction
between the giver and others is that an increase in the incomes of recipients would reduce giving. Therefore, an increase in the incomes of both
recipientsand givers should not increase giving by as much as an increase
in the incomes ofgiversalone. These implications are tested and confirmed
by Schwartz (1970), who analyzes aggregate time series on incomes and
charitable giving in the United States between 1929 and 1966 and also
compares his findingswith the cross-sectional findingsof Taussig (1965)
reported above. 3 6
The usual theory of consumer choice ignores social interactions, and
would consider charitable giving simply as a "good" that enters the
3 Theseestimates
thatcharitable
in tax rates.Note,however,
are netofdifferences
Sinceonly
in personalincometaxreturns.
fromitemizeddeductions
givingis estimated
sincemanytaxand notto individuals
can be deducted,
givingto (certain)institutions
and sinceothers
withlowerincomes,do notitemizetheirdeductions,
payers,especially
describe
oftax-reported
givingmaynotaccurately
theresponse
theirdeductions,
inflate
ofactualgiving.
theresponse
Bothstudies
incometaxreturns.
likeTaussig's,is basedonpersonal
36 Schwartz's
study,
ofgiving,wherepriceis measuredby one minusthe
also estimatethepriceelasticity
generally
responseto price,elasticities
marginaltax rate.Schwartzfindsconsiderable
ofthetheory
ofsocialinterwiththeimplications
exceeding- 0.5, whichis consistent
to price;but Schwartz
actions.Taussig,on theotherhand,findsonlya weakresponse
are biaseddownward.
arguesthatTaussig'sfindings
SOCIAL
I o85
INTERACTIONS
giver's utilityfunctionalong with his other goods:
Uj =
Ui(xi, A) ,
(3.6)
where h measures the amount given by i, and xi are the other goods that
he consumes. This "conventional" approach does not imply that an
increase in i's income would increase his giving by a particularly large
percentage, or that an increase in the incomes of recipients would lower
his giving. Therefore, considerable ad hocery would be required if the
"conventional" approach were to explain the evidence on charitable
giving that is more readily explained by an approach that incorporates
social interactions.
These findingscan be used to make very crude, but instructive,calculations of the share of recipient's own incomes in the social incomes of
contributors. If the own-income elasticity of demand for giving is taken
from Taussig as +2.0, the share of own income spent on giving as 0.04
(see Schwartz 1970, p. 1278), and the income elasticity of demand for
charity as equal to the average income elasticity (actually, Schwartz's
findingssuggest that it may be lower than the average), then, according
to equation (2.9), charity's share in social income would be (2 - 1)/(1/
0.4. If the own-income elasticity of giving were taken as
0.04 - 1)
+ 3.0 rather than + 2.0, charity's share would double to 0.08; if, in
addition, the income elasticity of charity were only four-fifthsof the
average elasticity,its share would increase furtherto 0.1 1 (a tithe?).
C.
Merit Goodsand MultipersonInteractions
Contributors are content to transfergeneral purchasing power to recipients if they are concerned about the general welfare or utility of recipients-as seen by recipients. They want to restrict or earmark their
transfers,on the other hand, if they are concerned about particular
"merit" goods consumed by recipients. For example, parents may want
transfersto their children spent on education or housing, or only the
money incomes rather than "full" incomes of children may be of concernto
parents, or contributors to beggars may not want their giving spent on
liquor or gambling.
Assume, therefore,that i transfersresources toj that are earmarked for
particular goods consumed by j because the utilityfunction of i depends
not only on his own goods but also on these goods ofj. Ifj were permitted
to spend his own income as he wished, an assumption modified shortly,he
would spend less on these goods as a result of the earmarked transfersfrom
i. Clearly, the reduction in his own spending would be greater, the
greater the transfer,the smaller the fractionof his social income spent on
these goods, and the smaller their income elasticity. For example, if they
Io86
JOURNAL OF POLITICAL
ECONOMY
take 20 percentof his social incomeand have an incomeelasticityequal
to 2.0, he would reduce his own spendingby $0.60 for each dollar
earmarkedby i.37
As longasj continuesto spendon themeritgoods,earmarkedtransfers
are worthas much toj as a transferof general purchasingpower with
equal monetaryvalue. Moreover,i would not have a greatereffectonj's
than withgeneral
consumptionof thesegoods withearmarkedtransfers
transfers.
Therefore,as long as j continuesto spend on thesegoods,earmarked transfersare equivalent to general transfers;and the results
derivedforthelatterfullyhold fortheformer.For example,a redistributionofincomebetweeni and j would have no effecton the consumption
ofeitheras longas bothcontinueto spendon themeritgoods,orbothi and
j wantto maximizetheircombinedincomes,nottheirown incomesalone.
On the otherhand, ifj did not want to spend anythingon the merit
large,such transfers
were sufficiently
goods because earmarkedtransfers
with
would be worthless toj and moreto i thanwould generaltransfers
equal moneyvalue. Moreover,variousresultsderivedforgeneraltransfers
ofincometoj and away from
no longerhold: forexample,a redistribution
merit
of
goods and increasehis consumpi would reducej's consumption
tionofothergoods.
If i wereaware thatj reducedhis spendingon meritgoods whentransfersincreased,i would be discouragedfromgivingbecausej's reaction
raisesi's privatepriceof meritgoods to
PM=
=
PM1
1
1
rj
38
Vmfnm
(3.7)
wherePmis the marketprice of meritgoods, and the other termsare
definedin note 37. Similarly,ifj were aware thati reducedhis transfers
whenj increasedhisspendingon meritgoods,j would also be discouraged
fromspendingbecause i's reactionraisesthepricetoj. Indeed,j could end
up consumingfewermeritgoods than he would ifi were not concerned!
or alwaysminor
That theseinducedreactionsare notsimplyhypothetical
is persuasivelyshown in a recentstudyof highereducation (Peltzman
to highereducationmainlythroughhighly
1973). Statesearmarktransfers
Privatespendingwas apparentlyreduced
subsidizedpublic institutions.
by (at least) $0.75 per dollar of public spendingin 1966-67; private
spendingmay have been reducedby morethan $1.00 per dollarofpublic
spendingin 1959-60, so that totalspendingon highereducationin that
yearwould have been reducedby public spending.
3 It is easily
onmerit
goods;
thatrj = 1 - Vmnm,
where
is thesharespent
shown
Urn
inj's ownspendingperunitincrease
and rj, thereduction
nm,theirincomeelasticity;
in i's contribution.
ifvm= 0.2, and nm= 2.0,rj = 0.6.
Therefore,
38 For example,
ifj spent$0.60 lessforeach dollartransferred
by i, the price to i
wouldbe p_ =pm(1/0.4)= 2.5Pm' ormorethantwicethemarket
price.
SOCIAL INTERACTIONS
Io87
Both i and j want to limitthe induced reactionsof the otherbecause
such reactionsreflectthe incentiveto "underreveal"preferences
about
meritgoods and "free-ride"in theirconsumption.Since equation (3.7)
showsthatthesereactionsraisethepriceofmeritgoodsto i andj, in effect,
bothwant to lowertheseprices.Indeed, it is well knownfromthetheory
of public goods,and a meritgood is a particularkindof "public" good,
thatefficient
pricesto i andj would be lessthanthemarketprice; indeed,
theseefficient
priceswould sumto the marketprice of the meritgood.39
Efficient
pricesmightbe achieved,forexample,by i andj matchingeach
other's spending in specifiedproportions,or each might be given a
spendingquota.
I intentionally
say "might"be achievedbecause any agreementhas to
be "policed" to insurethat each lives up to his commitment.Policing
is relativelyeasy forthe consumerof the meritgoods,j, since he usually
automaticallyknowshow much is spentby i, but is much moredifficult
fori, since he does not automaticallyknow how much is spentbyj.40
Parentsmay use theirchildren'sgradesin schoolto measuretheinputof
timeand effort
by childrenthatpresumably"matches" the moneycontributionby theparents.4'Or parentsmay save a largepartoftheirtotal
transfer
to childrenfora bequest when theydie in orderto providean
incentivefor children to spend "appropriately,"at least while their
parentsare alive.42This mayexplainwhytheinheritancetax on bequests
apparently has induced relativelylittle substitutiontoward gifts to
children(see Shoup 1966; Adams 1974).
The "underrevealing,""free-riding,"coordinationof efforts,and
"policing"discussedformeritgoods are commonto all multiperson
interactions-that is, all situationswheretwo or morepersonsare affectedby
the consumption,attitudes,or otherbehaviorof the same person.The
analyticalissues formultipersoninteractionsare the same as forother
"public" goods: is public interventiondesirable-for example, should
charitablegivingbe deductiblefrompersonalincome in arrivingat tax
liabilitiesin order to lower the privateprice of giving-and do private
equilibria withoutgovernmentinterventionmore closely approximate
joint maximization,a Nash noncooperativegame solution,or something
Since space is limited,I refrainfromdiscussingfurther
quite different?
theseand relatedissues.
3 A proofof thiswell-knownsummationformulacan be foundin Samuelson (1954).
The difficulty
of policing "merit" goods is shown amusinglyin a recentWizard of
Id cartoon. Two drunksmeet, and one says, "Could you spare a buck fora bottle of
wine?" The otheranswers,"How do I knowyou won't buy food with it?"
41 I owe thisexample to Lisa Landes.
42 This conclusionabout the incentivesprovidedby large bequestsis a special case of
a more general result proven elsewhere (see Becker and Stigler 1974) that relatively
largepensionsdiscourageemployeesfromactingcontraryto theinterests
oftheiremployers
(a bequest servesthe same purpose as a pension).
40
Io88
D.
JOURNAL OF POLITICAL
ECONOMY
EnvyandHatred
An enviousor maliciouspersonpresumablywould feelbetteroffifsome
otherpersonsbecome worse offin certainrespects.He could "harm"
himself(i.e., spendhisown resources)in orderto harmothers:in figure2,
he givesup *o unitsof his own consumptionin orderto harm othersby
hounits.The termsof trade between his own harm and the harm to
others,given by the curve EOSl in figure 2, is partly determined
by his skill at "predatory"behavior and partlyby public and private
to preventcrime,libeling,maliciousacts,trespass,and other
expenditures
predatorybehavior. Since an increasein these expenditureswould increase the cost to him of harmingothers,he would be discouragedfrom
harmingthem.The limitedevidenceavailable on predatoryexpenditures
supportsthisimplicationof the theory.Crimesagainst personsprovide
some evidenceon predatorybehavior,since most assaultsand murders
probably are motivatedby the harm to victims.43The frequencyof
assaults and murder (and also crimesagainst property)apparentlyis
stronglynegativelyrelatedto the probabilityof conviction,punishment,
and othermeasuresof the cost of committingthesecrimes(see Ehrlich
1973).
Section 2 suggeststhat a rise in own income would tend to reduce
on the
predatoryexpenditures.An increasein the social environment,44
other hand, would necessarilyincrease these expenditures,unless own
a risein thesocialenvironwerean inferior
consumption
good. Therefore,
mentand own incomeby the same percentagewould reduce predatory
expenditures
by less than would a rise in own income alone, and might
even increasethem.
Again, the implicationsof the theorycan be testedwithevidenceon
crimes against persons. Since assaults and murdershave been more
frequentat lowerincomelevels,45an increasein own incomeappears to
in own income alone are
reduce crimesagainst persons,if differences
in theincomesofindividualsat a momentin time
measuredby differences
(as in thediscussionofcharityin Section3B). As predictedby thetheory,
an increasein own income that is accompanied by an increasein the
social environment
(as measuredby the incomeof others)does not have
such a negativeeffecton thesecrimes.Indeed, the frequencyof assaults
and murdershas not been reduced by the sizeable growthin aggregate
statespresently
incomesduringthe last 40 years,nor do higher-income
have fewercrimesagainstpersonsthan otherstates.46
43Most robberies,burglaries,and larcenies,on theotherhand, probablyare motivated
by the prospectsof materialgain.
44 That is, in thatpartofthesocial environment
thatmotivatespredatoryexpenditures.
45
Persons committingcrimes against other personsas well as against propertyare
much more likely to live in low income areas (see Crime Commission 1967a, table 9).
46 The rate of assaultsgrewsignificantly
from1933 to 1965 in the United States, and
the murderrate remainedabout the same (Crime Commission1967b,figs.3, 4). Higher-
SOCIAL INTERACTIONS
Io89
Over theyears,evenacute observersofsocietyhave differed
radicallyin
theirassessmentof the importanceof envy and hatred. Two hundred
years ago, for example, Adam Smith recognizedthese "passions" but
shuntedthemaside withthecomment:"Envy,malice,or resentment,
are
the only passionswhich can promptone man to injure anotherin his
personor reputation.But thegreater
partofmenarenotvery
under
frequently
theinfluence
ofthose
passions,
and theveryworstmenare so onlyoccasionally.
As theirgratification
too, how agreeable soever it may be to certain
characters,is not attendedwithany real or permanentadvantageit is in
thegreaterpartofmencommonlyrestrained
byprudentialconsiderations.
Men may live togetherin societywithsome tolerabledegreeof security,
thoughthereis no civil magistrateto protect
them
fromtheinjustice
of those
passions"(Smith 1937; my italics)."' To ThorsteinVeblen, on the other
hand,writingmanyyearslater,theremotivesare theverystuff
oflifethat
dominateeverything
else: "The desireforwealthcan scarcelybe satiated
in any individualinstance,and evidentlya satiationof the average or
general desire for wealth is out of the question. However widely, or
equally,or 'fouly,'it may be distributed,
no generalincreaseof the community'swealth can make any approach to satiating this need, the
groundof which is the desireof everyoneto excel everyoneelse in the
accumulationofgoods" (Veblen 1934,p.32).4 8
In principle,theimportanceofenvyand hatredcan be measuredusing
equation (2.9) by the contribution
of the relevantsocial environment
to
social income; this is done in a crude way in Section 2B for charity.
Unfortunately,
not enough information
is available eitheron the ownincomeelasticityof demand or on the fractionof own income spenton
"predatory" behavior to make even crude estimatesof the relative
contribution
ofenvyand hatred.
Still,it may be usefulto noteseveralimplicationsofthediffering
views
about the significance
of envyand hatred.For example,Veblen's belief
that the welfareof a typicalperson primarilydepends on his relative
income positionimpliesthat social income essentiallyis zero: that the
value of the social environmentcausing envy would exactly offsetthe
value of own income.49 For then,and only then,would a rise in this
income states do not have fewercrimes against personseven when the probabilityof
conviction,the punishment,and several other variables are held constant (Ehrlich
1973, tables 2-5). Note that Ehrlich's study,unlike the evidence fromthe Crime Commission,holds the "price" of crime constantwhen estimatingthe effectsof income (and
holds income constantwhen estimatingthe effectsof price).
"4 Not much later, JeremyBentham reached a similar conclusion: "The pleasure
derivable by any person fromthe contemplationof pain sufferedby another,is in no
instanceso great as the pain so suffered"(Bentham 1952-54).
48 Similarly,
a sociologistrecentlyhas arguedthatenvyis a powerfulmotivein primitive
as well as advanced societies,communistas well as capitalist ones, and is critical in
determiningeconomicprogressand public policy (see Schoeck 1966).
41 "Own" income here includes the value of other
aspects of the social environment.
I090
JOURNAL OF POLITICAL
ECONOMY
social environment
and own incomeby the same percentage,pricesheld
constant, not affectsocial income or welfare. That is, a rise in all incomes
in a community by the same percentage would not improve anyone's
welfare in Veblen's world. 50
If social income were negative, if the environment causing envy were
more important than own income, a rise in the environment and
own income by the same percentage would lower social income and
welfare. That is, a general rise in incomes in a more extreme Veblenian
world would actually lower welfare! 5
On the other hand, Smith's belief that envy is a relativelyminor determinant of welfare implies that social income is positive: the environment
causing envy is less important than own income. A rise in the environment
and own income by the same percentage would then raise social income
and welfare. That is, Veblen's general rise in the community's income
would raise the welfare of the typical person.
4. Summary
This essay uses simple tools of economic theory to analyze interactions
between the behavior of some persons and differentcharacteristicsof other
persons. Although these interactionsare emphasized in the contemporary
sociological and anthropological literature, and were considered the
cornerstone of behavior by several prominent nineteenth-centuryeconomists, they have been largely ignored in the modern economic literature.
The central concept of the analysis is "social income," the sum of a
person's own income (his earnings, etc.) and the monetary value to him
of the relevant characteristics of others, which I call his social environment. The optimal expenditure of his own income to alter these characteristics is given by the usual marginal conditions. By using the concept of
social income, I can analyze the effecton these expenditures of changes in
differentsources of income and in differentprices, including the "price"
of the social environment. Perhaps the most important implication is
that a change in own income alone would tend to cause a relatively
large change in these expenditures; in other words, the own-income
elasticity of demand for these expenditures would tend to be "large,"
certainlylarger than the elasticityresultingfromequal percentage changes
in own income and the social environment.
50
If U1 = Ui(Ii/I), where I is the average communityincome, then Si = Ii- pI,
whereSi is i's social income, and p, is the price of fin termsof Ii. If i did not engage in
curve: slope =
predatorybehavior,p, would simplyequal the slope of his indifference
dI/dI = Ii/ = pr. Hence Si = Ii -I/I* I = 0.
51 When envyis so important,economicdevelopmentis undesirablebecause it lowers
ofthedeveloping
welfare.See Schoeck's(1966) discussionofwhathe calls "the envy-barrier
countries."
SOCIAL
INTERACTIONS
IO9I
Interactions among members of the same family receive the greatest
attention. The "head" of a familyis defined not by sex or age, but as that
member, if there is one, who transfersgeneral purchasing power to all
other members because he cares about their welfare. A family with a
head is a highly interdependent organization that has the following
properties:
A redistributionofincome among members does not affectthe consumption or welfareof any member because it simply induces offsettingchanges
in transfersfrom the head. As a result, each member is at least partially
insured against disasters that may strikehim.
Not only the head but other members too act "as if " they "loved" all
members, even when they are really selfish,in the sense that they maximize not their own income alone but family income. As it were, the
existence of a head economizes on the amount of true love required in a
family.
A family acts "as if " it maximized a consistent and transitive utility
function subject to a budget constraint that depended only on family
variables. This utilityfunctionis the same as the head's not because he has
dictatorial power,but because his concern forthe welfareofother members
integratesall their utilityfunctionsinto one consistent"family" function.
Transfersfrom parents to children in the form,say, of schooling, gifts,
and bequests tend to be negatively related to what the income of children
would be relative to their parents in the absence of these transfers.
Therefore, the relative income of children inclusiveof transferscould be
unrelated or even negatively related to these transfers.Consequently, one
cannot inferanything about the stability across generations of economic
or social positions simply from knowing the relation between parental
position and the amount transferred.
More brieflytreated are charity and envy, with special attention to
the effectsof differentkinds of income change on charitable contributions and expenditures to alleviate envy. For example, the much higher
income elasticity of demand for charitable contributions estimated from
differencesin individual incomes at a moment in time than fromaggregate
changes in incomes over time is shown to be implied by this theory of
social interactions,but not readily by the traditional theory of choice.
From a methodological viewpoint, the aim of the paper is to show how
another relation considered important in the sociological and anthropological literature can be usefully analyzed when incorporated into the
frameworkprovided by economic theory. Probably the main explanation
for the neglect of social interactions by economists is neither analytical
intractability nor a preoccupation with more important concepts, but
excessive attention to formal developments during the last 70 years. As a
consequence, even concepts considered to be important by earlier
economists, such as social interactions,have been shunted aside.
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JOURNAL OF POLITICAL
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