Exploitation, altruism, and social welfare

17 Pages·2013·0.19 MB·English

Article
Politics,Philosophy&Economics
12(4)375–391
Exploitation, altruism,
ªTheAuthor(s)2013
Reprintsandpermissions:
and social welfare: sagepub.co.uk/journalsPermissions.nav
DOI:10.1177/1470594X13496066
An economic exploration ppe.sagepub.com
Matthias Doepke
Northwestern University, USA
Abstract
Child labor is often condemned as a form of exploitation. I explore how the notion of
exploitation, as used in everyday language, can be made precise in economic models of
childlabor.Exploitationisdefinedrelativetoaspecificsocialwelfarefunction.Ifirstshow
that under the standard dynastic social welfare function, which is commonly applied to
intergenerationalmodels,childlaborisneverexploitative.Incontrast,underaninclusive
welfarefunction,whichplacesadditionalweightonthewelfareofchildren,childlaboris
alwaysexploitative.Neitherwelfarefunctioncapturesthemoregradualdistinctionsthat
common usage of the term exploitation allows. I resolve this conflict by introducing a
welfare function with minimum altruism, in which child labor in a given family is judged
relativetoa specific social standard. Under thiscriterion,child labor is exploitativeonly
infamilieswheretheparent(orguardian)displaysinsufficientaltruismtowardsthechild.
I argue that this welfarefunction bestcaptures the conventional conceptofexploitation
andhasusefulpropertiesforinformingpoliticalchoicesregardingchildlabor.
Keywords
Child labor, exploitation,social welfarefunction, altruism
Introduction
In both popular and scientific writing, child labor is frequently portrayed as a form of
exploitationofchildren.1Indeed,searchingfor‘‘childlabor’’and‘‘exploitation’’onGoo-
gle Scholar yields about 22,000 hits in June 2013.2 Yet within the context of economic
Correspondingauthor:
Matthias Doepke, Department of Economics, Northwestern University, 2001 Sheridan Road, Evanston,
IL60208,USA.
Email:[email protected]
376 Politics, Philosophy & Economics 12(4)
modelsofchildlabor,thereisusuallynoclearlydefinednotionofexploitation.Tobesure,
theliteraturehasidentifiedanumberofconditionsunderwhichsomerestrictionsofchild
labor may be desirable. However, these arguments are based on standard efficiency
grounds(generatedby,forexample,humancapitalexternalities)andarenotlinkedtothe
conceptofexploitation.3
Inthispaper,Iexplorehowexploitationcanbedefinedinthecontextofaneconomic
modelinawaythatrhymeswiththeconventionalunderstandingoftheterm.Thatis,I
am taking seriously the moral intuitions that lie behind the usage of ‘‘exploitation’’ in
commonlanguage,andaimtotranslatetheseintuitionsintothelanguageofwelfareeco-
nomics.Centraltothisundertakingistodevelopawelfarecriterionthatcanbeusedto
decide which forms ofchild laboramount toexploitation,andwhich do not.
To see why this is not a trivial undertaking, consider the standard welfare concept
usedindynamiceconomicmodels.SincetheseminalworkofBarro(1974),Beckerand
Barro(1988),andBarroandBecker(1989),ithasbeenstandardpracticetotreataltruis-
ticallylinkeddynastiesinawaythatisanalogoustoasingleagentwhohasaninfinite
lifespan.4Inthecaseofasingleagentwholivesforever,thenaturalwelfareconceptis
theinitiallifetimeutilityoftheagent.Iftherearemultiplesuchagents,thewelfarecri-
terionisa(possiblyweighted)sumoflifetimeutilities.Applyingthesameconcepttoa
world of dynasties, a welfare criterion emerges that evaluates the welfare of the entire
dynastythroughtheutilityoftheheadofthedynasty.Futuremembersofadynastyonly
enter consideration insofar as the initial member of the dynasty is altruistic towards
them, i.e. theirutility enters theutility ofthe dynastyhead.
Defining a dynastic utility criterion in this way has practical advantages. Standard
resultsfromdynamiceconomicscarryovertothedynasticsetting,implying,forexam-
ple,that,intheabsenceofexternalitiesandwithcompletemarkets,competitiveequili-
briaare efficient.
However, using the standard dynastic welfare criterion also makes it impossible to
second-guesswhetherparentsmakethe‘‘right’’choicesfortheirchildren.Theimplicit
socialwelfarefunctionacceptstherevealedpreferenceofparentsfortheirchildren,and
doesnotattachanyimportancetothechildrenotherthanthroughthealtruismthattheir
parentsfeelforthem.Thislimitationofstandarddynasticwelfareexplainswhyitisdif-
ficulttospeakofexploitationofchildreninthisclassofeconomicmodels.Whenwefeel
that children are being exploited, implicitly we are saying that their parents (or, more
generally,guardians)arenottakingsufficientcareofthem.Yetsuchajudgementcannot
beexpressedwhenawelfarecriterionisusedthatassumesfromtheoutsetthatthepar-
entscarejusttherightamount.Hence,thestandarddynasticsocialwelfarefunctionren-
ders theconcept ofexploitation vacuous.
Theaimofthispaperistoaddressthemismatchbetweentherhetoricofexploitation
andthewelfarecriteriathatareusuallyappliedtoeconomicmodels.Todothis,Ipropose
alternativewelfarecriteriathatcanbeusedtogivethetermexploitationamoreprecise
meaning within an economic model of child labor, and then connect this discussion to
arguments for and against regulation of child labor. Based on the common language
understanding of exploitation, for the purposes of this paper we will say that people
arebeingexploitediftheyareunfairlyusedforthebenefitofothers.5Inthecaseofchild
labor, the ‘‘being used for the benefit of others’’ condition will usually be satisfied
Doepke 377
because it is generally parents (or other guardians) who make decisions on child labor
andstandtobenefitfromtheincome.Thequestion,then,iswhetherthisuseofthechild
is unfair.
Anumberofdifferentnotionsoffairnesshavebeenproposedbywritersinethicsand
politicalphilosophy.Myobjectivehereistostayascloseaspossibletoconventionalcon-
ceptsofsocialwelfareineconomicmodels,whilealsoarrivingataformulationthatgives
meaningtothetermexploitation.Thenotionoffairnesswillthereforebebasedonsocial
welfarefunctionsthatareultimatelybasedonindividualpreferences.6Inaddition,acriter-
ionisdesiredunderwhichthequestionofwhetherchildlaboramountstoexploitationdoes
nothaveanabsoluteanswer,butratherdependsonspecificcircumstances.Thiswillrecon-
cile, through the lens of the formal criterion, the common intuition that, for example,
extremeformsofchildlaborsuchasprostitutionconstituteexploitation,whereasactivities
suchashelpingoutonthefamilyfarmaremorebenign.Inevaluatingdifferentsocialwel-
farefunctions,Iwillbelookingforcriteriawheresuchgradualjudgementsarepossible.
Tofindanotionoffairnessthatmeetstheseobjectives,itisessentialtoallowadis-
tinctionbetweenparentalaltruismandthe‘‘social’’altruismthatisusedtodefineexploi-
tation. In particular, the basic idea of the welfare criteria proposed here is to allow for
socialwelfarefunctionsthatmaygivemore(orless)weighttochildrenthantheweight
implicit in their parents’ altruism. Whether child labor amounts to exploitation then
dependsonthedegreeofparentalaltruism.Indeed,ifaparenthadnoregardwhatsoever
forthewelfareofthechild,childlaborwouldbeakintoslavery,andpresumablyslavery
shouldamounttoexploitationunderanydefinition.Conversely,ifaparenthadcomplete
disregardforhisorherownutilityandwassolelymotivatedbymaximizingthechild’s
happiness,childlaborwouldonlyoccurtobenefitthechild,andthusshouldnotconsti-
tute exploitation. Unlike the standard dynastic social welfare function, the preferred
social welfarefunction developedhere leads tothe same conclusions.
Inthenextsection,Ioutlineabasicmodelofchildlaborthatwillprovidetheframe-
workfortheanalysis.Thefollowingsectioncontainsthecoreoftheanalysisandoutlines
how exploitation does or does not arise from the perspective of alternative criteria for
judgingsocialwelfare. Thelast section concludes.
A simple model of child labor and altruism
Whiletheargumentsbelowshouldbeapplicabletoawideclassofeconomicmodels,it
isusefultodevelopthemainideasinaspecificsetting.Thekeyfeaturesoftheenviron-
ment considered here are that there are parents and children; parents decide on child
labor;andparentsarealtruistictowardstheirchildren.Tosimplifytheanalysis,themain
ideasaredevelopedinastaticsettingwithasinglegenerationofparentsandchildren.7A
dynamicextension isconsidered below.
Economic environment
Weenvisionaneconomypopulatedbyafinitenumberofadults,indexedbyi,whoare
characterized by their human capital h >0 and a preference parameter z, where
i i
0(cid:2)z (cid:2)1. Each adult has exactly one child. The preference parameter z represents
i i
378 Politics, Philosophy & Economics 12(4)
altruism,i.e.therelativeweightofthechild’sutilityintheutilityfunctionoftheparent.
Theremaybevariationinthedegreeofaltruismamongtheparents.Theparent’slifetime
utility V asafunctionof humancapital h is givenby
P;i i
V ðhÞ¼ð1(cid:3)zÞuðc ðh;lÞÞþzV ðh Þ: ð1Þ
P;i i i P i i i C C
Herec ðh;lÞistheparent’sconsumption(whichdependsonhumancapitalandthe
P i i
supply of child labor) and V is the child’s utility (as an adult). The parent works full
C
time, and chooses the child’s labor supply l. The remaining time 1(cid:3)l serves to raise
i i
the child’shumancapital. The child’shumancapital is givenby
h ¼eð1(cid:3)lÞ: ð2Þ
C i
We can think of e as a production function for human capital. One interpretation is
that1(cid:3)l istimethatchildrenspendinschoolandthatthereforeraisestheirhumancap-
i
ital. However, wider interpretations are also possible; for example, one component of
human capital is health, and e might represent the detrimental effects of child labor
onfuture health. Thechild’spreferences are givenby
V ðhÞ¼uðc ðhÞÞ: ð3Þ
C C
Ofcourse,inadynamicdynasticsettingthechild’sutilitywouldhavethesamefunc-
tionalformasthatoftheparent,withanadditionaltermfortheutilityofthegrandchildren.
Forillustration,Iwilladoptparticularfunctionalforms.Parentalconsumptionisgivenby
c ¼hþl: ð4Þ
P
That is, the wage is equal to one per unit of human capital, and children’s human
capital is normalized to one. Alternatively, we can abstract from labor markets alto-
gether and interpret (4) as a linear production function that is available to each
household.
Theproductionfunction foreducation is assumed tobelinear
eð1(cid:3)lÞ¼1(cid:3)l: ð5Þ
Given thatthere are nograndchildren, the children’sconsumption is givenby
c ¼h ¼1(cid:3)l: ð6Þ
C C
We alsoassume thatthe utilityfunction is logarithmic
uðcÞ¼lnðcÞ: ð7Þ
i
Unconstrained equilibrium
Wecannowcharacterizetheoutcomeinthiseconomyifparentsareunconstrainedinthe
choice oftheir child’slaborsupply.
Proposition 1 (Unconstrained Equilibrium) In the unconstrained equilibrium,
parentschoose the followingchild laborsupplyl
i
l ¼maxf1(cid:3)zð1þhÞ;0g:
i i i
Doepke 379
Proof: Theparent’s optimization problemis
maxfð1(cid:3)zÞlnðh þlÞþz lnð1(cid:3)lÞg:
i i i i i
0(cid:2)li(cid:2)1
Thefirst-order conditionfor aninterior optimumis
1(cid:3)z z
i ¼ i ;
h þl 1(cid:3)l
i i i
which yields
l ¼1(cid:3)zð1þhÞ
i i i
Thiscondition,togetherwiththenon-negativityconstraintonligivestheresult.c
As intuition suggests, a parent that is entirely selfish (z ¼0) will always set child
i
labor to the maximum level, l ¼1. Altruistic parents will leave at least some time
i
for their child’s education, l <1, and the more so the higher their own human capital
i
h is.
i
Exploitation and social welfare
Defining exploitation relative to a social welfare function
Havingdescribedtheunconstrainedoutcomeintheeconomy,Inowwouldliketocon-
siderethicalcriteriaforevaluatingtheequilibriumallocation.Isitappropriatetosaythat
childrenarebeingexploitedinthisworld?Forthepurposesofthediscussion,wewillsay
thatpeoplearebeingexploitediftheyareunfairlyusedforthebenefitofothers.Inthe
specificcaseofalaborrelationship,exploitationhappensifonepersonforcesanotherto
workwithout adequate compensation.
Atfirstsight,itmaythenappearthatinourmodelchildlaboramountstoexploita-
tionbydefinition,giventhatoneeconomicagent(theparent)imposesaworkrequire-
ment on the other (the child), and no formal compensation is provided. But this does
not rhyme with common sense: the parent does care about the child after all, and if
zisclosetoone,theparentwouldbewillingtoenduregreatsufferingforthewelfare
ofthechild.Itwouldbedifficulttoarguethatasmallamountofchildlaborthathelps
toprovidesubsistenceincometotheparentrepresentsexploitation.Itistruethatinthe
modelthechilddoesnotreceiveformalcompensationforthelabor.However,itisalso
truethattheparentpresumablyincurredexpensesandeffortinraisingthechild(which
isimplicitintheadultbudgetconstraint),andchildlaborcouldbeviewedascompen-
sation for such efforts.
Giventhesearguments,itappearsthatthequestionofwhetherchildlaborisexploi-
tation is not an either–or question; rather, the answer should depend on the degree of
altruismz.Arelationshipwhereoneagentcontrolsthelaborsupplyoftheothermaystill
not represent exploitation as long as the controlling agent cares sufficiently about the
controlled agent. Of course, what ‘‘sufficiently’’ means here depends on the meaning
of‘‘fairness’’inthe definitionofexploitation.
380 Politics, Philosophy & Economics 12(4)
Asoutlinedintheintroduction,thepositionadoptedhereisthat‘‘exploitation’’needs
tobejudgedrelativetosomesocialwelfarefunction.Foragivensocialwelfarefunction,
Idefine exploitation asfollows.
Definition1(Exploitation)Foragivensocialwelfarefunction,childlaboriscon-
sideredexploitation if thefollowing conditions aresatisfied:
1. Achildisrequiredtoworkmorethanwhatthesocialwelfarefunctionprescribes.
2. Theadditionalwork benefits the parentrelative tothe socialoptimum.
Ofcourse,thecontentofthedefinitiondependsonthesocialwelfarefunction.Rather
thantryingtogiveonespecificmeaningtothetermexploitation,thepurposeofthedef-
initionisthereverse:Iwouldliketocomparedifferentpossiblesocialwelfarefunctions
intermsoftheirimplicationsforthemeaningofexploitation,andthenuseourintuitive
understanding of exploitation to determine which social welfare function most closely
matches this understanding. Thus, the analysis will help determine what kind of social
welfare function may usefully represent the moral intuitions behind the common-
language useofexploitation.
The dynastic social welfare function
We limit attention to social welfare functions that are utilitarian in the sense of being
functions ofthe utilitiesof themembers ofthe society
(cid:4)(cid:2) (cid:3)(cid:5)
SWF¼f V ;V :
P;i C;i
Thesocialoptimumistheallocationthatmaximizesthesocialwelfarefunctionsub-
ject toresourceconstraints.
Definition2(SocialOptimum)Thesocialoptimumgivenasocialwelfarefunc-
tionf is the allocation thatsolves the followingproblem
(cid:2) (cid:2) (cid:3)(cid:3)
max f V ;V
P;i C;i
subject to(1)to(7) above.
We will start with the social welfare function that is most commonly employed in
dynasticeconomicmodelsofthekindusedhere,namelywhatItermthedynasticsocial
welfarefunction.Thisfunctionisgivenbythesumoftheutilitiesoftheparents,without
directlyaccountingforthechildren(giventhattheyarealreadyincludedintheirparents’
utility).This socialwelfare functionis asfollows.8
Definition 3 (Dynastic Social Welfare Function) The dynastic social welfare
functionis given by
X
SWF ¼ V :
Dynastic P;i
i
Doepke 381
Whilethissocialwelfarefunctioniscommonlyapplied,itimpliesthataslongasmar-
ketsarecompleteandtherearenoexternalities,thedecentralizedequilibriumcoincides
withthesocialoptimum.Thus,parentstreattheirchildrenexactlyasthesocialwelfare
functionprescribes, andinthissense there is noexploitation.
Proposition2(NoExploitationunderDynasticSocialWelfareFunction)Under
thedynasticsocialwelfarefunction,thesocialoptimumcoincideswiththeuncon-
strainedequilibrium.
Proof:Thesocialwelfarefunctionisasumoftheindividualobjectivefunctionsthat
underlytheunconstrainedequilibrium,theconstraintsetisthesame,andthereisno
interaction between different dynasties, implying that the optimum is the same as
well.c
ThisfindingreflectsthefamiliarFirstWelfareTheorem,namelythat,intheabsence
ofexternalitiesandmarketincompleteness,equilibriumoutcomesareParetooptimal.Of
course,Paretooptimalisdefinedhererelativetoonlytheparents’utility,butthesame
judgement is includedinthe dynasticsocial welfarefunction.
We could generate a different result with the same welfare function by introducing
market failures. To illustrate, consider an extension of the model with a humancapital
externality. All dynasties are identical with the same altruism factor z and same initial
humancapitalh.Theutilityfunctionsandtheproductionfunctionforhumancapitalare
asabove.However,Inowassumethatproductioninthesecondperiod(whenthechil-
dren areadult) involvesa humancapital externality
c ¼pffihffiffiffiffiffipffih(cid:2)ffiffiffiffiffi: ð8Þ
C C C
Thatis,thechildren’sconsumptiondependsnotjustontheirownhumancapitalh ,
C
butalsoontheaveragehumancapitalh(cid:2) inthepopulation.Householdsarenotcompen-
C
sated for their contribution to average human capital in the economy; thus, a classic
externality is now present in the model. The externality leads to a wedge between the
equilibriumallocation oflaborandthe socially optimalallocation.
Proposition3(EquilibriumandSocialOptimumwithHumanCapitalExtern-
ality)Inthemodelwithahumancapitalexternalityasin(8),theequilibriumlabor
allocation is
(cid:9) (cid:7) (cid:7) (cid:8)(cid:8) (cid:10)
2 h
l¼max 1(cid:3)z 1þ ;0 ;
2(cid:3)z 2
whereas thesocially optimal allocation is
l¼maxf1(cid:3)zð1þhÞ;0g:
Thus,allchildrenworkmoreintheequilibriumallocationcomparedtothesocial
optimum (aslong asequilibrium child laboris positive).
382 Politics, Philosophy & Economics 12(4)
Proof:Theparent’soptimizationproblemis(afterpluggingallconstraintsintothe
objective andomittingconstants)
(cid:9) (cid:10)
1
max ð1(cid:3)zÞ lnðhþlÞþ z lnð1(cid:3)lÞ :
0(cid:2)l(cid:2)1 2
The first-orderconditionfor aninterior optimum is
1(cid:3)z z
¼ ;
hþl 2ð1(cid:3)lÞ
which yields
(cid:7) (cid:7) (cid:8)(cid:8)
2 z 2 h
l¼ (cid:3) ð2þhÞ¼ 1(cid:3)z 1þ :
2(cid:3)z 2(cid:3)z 2(cid:3)z 2
This conditiontogether with the non-negativityconstraintonl givesthe result.
Forthesocialoptimum,theplannerrecognizesthath ¼h(cid:2) inequilibrium,imply-
C C
ingthatchildren’sconsumption is stillgivenby
c ¼h
C C
asin(8),sothatthesocialoptimumcoincideswiththeequilibriumallocationchar-
acterized inProposition 1. c
Thus,inthemodelwiththehumancapitalexternality,childlaborisinefficientlyhigh
intheequilibriumallocation.However,eventhoughchildrenworktoomuch,themodel
stilldoesnotfulfillourdefinitionofexploitation.Thereasonisthattheincreasedlabor
supply of the children in the equilibrium allocation does not actually make the parents
betteroffrelativetothesocialoptimum,whichwasthesecondrequirementinthedef-
initionofexploitation.Infact,theparentsareworseoffintheequilibrium:alleconomic
agents, parentsandchildren,are negativelyaffectedbythe presenceoftheexternality.
Thefollowing corollarysummarizes the result.
Corollary1(NoExploitationdespiteHumanCapitalExternality)Inthemodel
withahumancapitalexternality,childrenworkmorethaninthesocialoptimum,
but nevertheless child labor does not constitute exploitation in the sense of
Definition1.
Thisexample should make clear that it is difficult to satisfy the definition of exploi-
tation when the usual dynastic social welfare function is used. If all parents are identi-
cal, the social optimum under this welfare function delivers the highest possible utility
to the parents given the constraints of the economy, so that they cannot be made better
off by exploiting their children through child labor in some way. A parallel argument
would apply to other forms of market failures.9 We therefore move on to alternative
welfare functions where the tight link between social optima and parental welfare no
longer applies.
Doepke 383
A social welfare function with direct weight on children
Onecanarguethatthebasicdefectofthedynasticsocialwelfarefunctionisthatitplaces
direct weightonly on the parents,while ignoring the children. Thus,let usconsider an
alternative welfare function where the utility of children enters directly, in addition to
theindirectweightingthroughparentalaltruism.Amongothers,thissocialwelfarefunc-
tion is advocated by Farhi and Werning (2007).10 We term this welfare function the
inclusive socialwelfare function.
Definition 4 (Inclusive Social Welfare Function) The inclusive social welfare
functionis given by
X X
SWF ¼ V þg V :
Inclusive P;i C;i
i i
Hereg>0istheadditional,directweightattachedtotheutilityofthechildren.
Theinclusivewelfarefunctionleads totheoppositeconclusionofthedynasticwel-
farefunction:aslongaschildrenareworkingatall,thisalwaysrepresentsexploitation,
regardless of the degree of altruism z. To establish this result, I revert to the original
modelwithoutahumancapitalexternality(allowingforexternalitieswouldnotalterthe
results).
Proposition4(SocialOptimumunderInclusiveWelfareFunction)Underthe
inclusivesocialwelfarefunction,thesociallyoptimalchild laborsupplyisgiven
by:
(cid:9) (cid:10)
1
l ¼max ð1(cid:3)zð1þhÞ(cid:3)ghÞ;0 :
i 1þg i
Thus, if child labor is positive in equilibrium, the socially optimal child labor
supplyislowerthanequilibriumlaborsupply(whichischaracterizedinProposi-
tion1).
Proof: Given that there is no interaction across dynasties, we can solve for the
socially optimal child labor supply for each dynasty individually. For dynasty i,
the problemofmaximizing socialwelfare is givenby
maxfð1(cid:3)zÞ lnðh þlÞþðz þgÞlnð1(cid:3)lÞg:
i i i i i
0(cid:2)li(cid:2)1
Thefirst-order conditionfor aninterior optimumis
1(cid:3)z z þg
i ¼ i ;
h þl 1(cid:3)l
i i i
which yields
1
l ¼ ð1(cid:3)zð1þhÞ(cid:3)ghÞ:
i 1þg i
384 Politics, Philosophy & Economics 12(4)
Thisconditiontogetherwiththenon-negativityconstraintonligivestheresult.c
Corollary2(ExploitationunderInclusiveWelfareFunction)Undertheinclu-
sivesocialwelfarefunction,ifchildlaborispositiveintheunconstrainedequili-
brium, itconstitutes exploitation inthesense ofDefinition 1.
Proof: Proposition 4 shows that if child labor is positive in equilibrium, it has
to be lower in the social optimum under the inclusive welfare criterion, satis-
fying the first requirement of the definition. In addition, the equilibrium allo-
cation yields the highest feasible utility for the parents, implying that parents
are better off in equilibrium compared to the social optimum, which satisfies
the second requirement of the definition. c
Theresultundertheinclusivesocialwelfarefunctionisequallyunsatisfactoryasour
findingsunderthedynasticsocialwelfarefunction.Anychildlaborisnowconsideredto
amounttoexploitation.Nomatterhowmuchtheparentcaresaboutthechild,fromthe
perspectiveofthesocialwelfarefunctiontheparentdoesnotcareenough.Thetechnical
reason is thatthe socialaltruism is inadditiontoparental altruism.
More generally, the welfare criterion implies that parents give too little to their chil-
dren in any dimension, be it protection from child labor, consumption, human capital
investment, orbequests.Whereas under the dynastic socialwelfare function parents can
do no wrong, under the inclusive social welfare function they can do no right. Such a
blanket condemnation appears equally unattractive as the blanket approval of parental
actions that is implied by the dynastic social welfare function. The next proposed wel-
fare criterion tries to find a middle ground between these two extremes.
A social welfare function with universal altruism
Atheart,asocialwelfarefunctiondescribeshowwefeelaboutotherpeople’schoices.In
ourspecificsetting,whatisatissueishowpeoplefeelabouttheappropriatedistributionof
resourcesbetweenparentsandchildreninotherfamilies.Itwouldseemplausiblethatin
making this judgement,people apply the same altruism factorz that they apply intheir
i
ownfamily.Thus,eachindividualwouldpossessasocialwelfarefunctionwherethesame
weightz isattachedtothewelfareofallchildren,regardlessofthepreferencesofthepar-
i
entsofthesechildren.Socialjudgementswouldthendependonwhichfamily’ssocialwel-
farefunctionisused.Asimplepossibilityistosumallfamilies’welfarefunctions,inthe
samewaythatthedynasticwelfarefunctionsumstheutilityofalldynastyheads.Weterm
thiswelfarefunctiontheuniversallyaltruisticwelfarefunction.Thesocialdiscountfactor
z(cid:2)thatisbeingappliedtoallchildrenistheaverageofallindividualaltruismfactors
1X
z(cid:2)¼ z:
i
N
i
Here N is the totalnumber ofdynasties.
Definition 5 (Social Welfare Function with Universal Altruism) The univer-
sally altruisticsocial welfarefunction is givenby