The welfare effect of an additional child cannot be stated simply

„«/'^/VERsiTY OP

Digitized by the Internet Archive

in 2011 with funding from

University of Illinois Urbana-Champaign

http://www.archive.org/details/welfareeffectofa80simo

Faculty Working Papers

THE I^LFARE EFFECT OF AN ADDITIONAL
CHILD CANNOT BE STATED SIMPLY

Julian L. Simon

#80

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

FACULTY WORKING PAPERS
College of Conmerce and Business Administration
University of Illinois at Urbana-Champaign
January 4, 1973

THE WELFARE EFFECT OF AN ADDITIONAL
CHILD CANNOT BE STATED SIMPLY

Julian L. Simon

j/80

'M',:. '.) U-^n" .■■4- "^^i •

'i'^ ^.4^

.1 1

Tlie Welfare Effect of an Additional

CKjLld Cannot Be Stated Simply

Julian L. Simon

r. INTRDDUCTItDN

Analyses of tfle welfare economics of population growth make one or
more of the following assumptions: Cl) The criterion of social welfare at
a point in time is per capita Cor per consimer) income, C2) The effect of
a given individual upon society is limited to his own impact during his own
lifetime. C3) There are no externalities, or — somewhat more weakly — all
externalities can be handled by payments between the parents and the community.
(4) Welfare is assessed at a single point in time, or at the same rate
along a growth path> or without distinguishing between the various periods
of his life cycle. .

It is the contention of this paper that the magnitude and even the
direction of the welfare effect of an added child depends upon each of these
assumptions. That is, changing one or more assumptions to equally acceptable
assumptions often shifts the welfare effect from positive to negative or ^ne
opposite. Therefore, tfie aim of the paper is to map out the welfare effect
of additional children under many different sets of these assumptions.

The strategy of this essay is to disaggregate the problem in two
directions. The first disaggregation la over time; Instead of asking for
a single time-discounted value that summarizes whether welfare is higher or
lower, considering all of the future together, welfare judgments will be
discussed for a few separate segments of the future: a) the added individual's

'.■"*-,.. ■ I',

•' i . •-

T- 2

childhood; bi his adulthood; c) after the individual's death: Summary
measures will also he considered critically.

The second kind of disaggregation is bj; groups ; Instead of only
a single criterion of welfare for the community as a whole, judgments will
be shown about al the individual's welfare; b) the welfare of his parents;
cl the welfare of all other persons exclxiding the added Individual; and d)
some overfall judgments, as well.

The paper begins idLth the simplest situation, that in which the
Individual has no negative or positive effects external to his own family,
and where he leaves no negative- or positive inheritance of any kind to
future generations. Then the paper moves on to situations where there are
externalities during his life, and then to situations where there are
continuing external effects after his death. These situations are analyzed
with various welfare functions, on various assumptions about the directions
of the externalities.

The results of the analyses are summarized in Table 1, and the text
merely explains how some illustrative results in Table 1 are arrived at.
The main point of that table — and of the paper as a whole— is that the welfare
effects of an additional person are very mixed and are largely indeterminate;
the judgments must depend upon special conditions, assumptions, and choice
of welfare functions. The aim is to refute all analyses which purport to
arrive at firm scientific conclusions about the welfare effect of population
growth without noting the sensitivity of those conclusions to different
welfare functions and to various possible economic ramifications of additional
people.

.''" I 6 ■ " *

' :> • ■' ■-i)-.-

■p

a

*-»

ID

r-i
05

>

-d

r

J

<

-(-

-:

M

3

ii

-i

a

d

n

.S

3

^

t,

0

i

j:: o

(S

^

3 0

.^

H-

r^-d

3

H J

D
0

-0

z a

VI

c >

(

^T3

-)»

+

t;

0-

i

a.

v„.„..,....„...,

5! 33 \|

'.^ \!.

list

1 1

S I

Ii i, Ji

:! .-1 «

Is Ii n

©o

Q

3 S S

si 4 51
P sS »!

3f IjC af

1~

G>- O

I 1 1

is
i:

i 11 ii

ii I

ii
II

■I i

■e>

S3 as

-.1 i

•I '%

11

II J 1

H; I lis

•- •■ ♦

e
0
©

■G . ©

-Q,-

Q . © .00' o

I ! : !

a ; 1 3

t t t fr

i i

i S

31
=•3 I

>_^ i i

? 31 J

•' ii ? 5

1 15=

ran

1 35
3 5!

ii il

il ;!

3 9 G i

! is

I' I

s t
s s

\ !

i! ii

3 J S3

h 1^

I I
I I

! 9

I !

II

!» la i! 'I .: .1 : .

3 3

iii

J !
I }

i 3

13 ll
!5 tj.

3 3S 3

33 3a 39

r-

If I 11 11

11

IS
nil]

I nil

U = 51

il i .'1

'{ u «s

jl =3 [i

h Ii

n
1 1

3 a

3 i

< !

II

3 35

t bl

111

- 3 -

It. NO EXTEBNALITIES DURING OR AFTKK HIS LITE.

During His Childhood

If an additional first child In a family has no effects external to
the family during its childhood, then the welfare of all other persona in
the society is unaffected by his hirth^ — by assumption. The welfare of his
parents is increased By the occurrence of an e^/ent the parents desire.
Beyond this, a variety of welfare judgments is possible even in this very
simplest of cases, the judgments depending upon one's assumptions and
criteria. Cli To start, the judgment about the welfare of the child himself
depends upon one's assimiption about the human utility function, together with
the facts of the case. According to the assumption made by Meade (1955),
Dasgupta CX969) , Ehrlich (1968), and others, the welfare of a very poor child
Is negative (column 1, line 3 in Table 1) . But of course one can j;ist as
reasonably assume that the child's welfare is neutral or positive when he
is very young. Clater, after he is old enough so that one can impute
choice to him, we can argue about his welfare In a different fashion as
Will be discussed later-) (2) By the test of pet capita income, general"
welfare falls during this childhood period, because the same amount of product
(assuming no increase in labor by the parents) is divided among more
people (column 1, line 11). (3) If one uses as a welfare criterion the
sum of individual utilities, general welfare rises if the additional child's
utility is positive. The same conclusion can be reached by a more economical
and powerful approach, that of an expanded Pareto optimum: If a person
whose utility is positive is added to the society, and if none of the existing
people thereby have their positions altered for the worse, this must represent

- 4 -

an increase in the society's utility function. The application of this
criterion is unique to the very simple case under discussionj however; even
the existence of brothers or sisters makes the criterion inapplicable without
further assumptions, as we shall see.

Now for a side-examination of a curious but not-unreasonable im-
plication in this simple situation: Parents have fev/er children than would

2

maximize the total utility of the community. The reasoning is as follows.

The parent continues to have children until he is at his own margin, indifferent
between the birth and non-birth of another child. But an additional child
would himself enjoy positive utility, by assumption, and hence his birth
would add his own utility to the community's utility, with no net utility
change to his parents .

Despite that families do not choose to have enough children to reach
the point of zero net marginal social utility, without complete knowledge of
people's welfare functions one cannot know hew far from the margin is the
lalsser faire outcome. Hence, it seems that the only sensible course consis-
tent with the above conclusion is to let parents set their own limits on
the number of children, subject to consideration of external costs and
conmjunity values (to be disctissed immediately).

With the above analysis in hand, one ;aay judge the welfare effect
of contraceptive knowledge and of public health measures to reduce infant
jBortality. Consider contraception first. In a society where no one dies
until old age, the ability to practice contraception increases the welfare
of parents because it allows them to achieve the number of children that
will maximize their (parental) utility. That is, ability to contrac'ept

" 5 -

Increases parents' options, a Paretian baste wtelfare gain. If lack of
contraceptive knowledge leads to more children than th.e couple wants
ex ante, this ma^ increase the total welfare of the family, and hence of
the community. But to argue that people should he hindered from practicing
contraception one must argue that ai one kjiows the parents' and children's
utility functions; and b) by overcoming the parents' "selfishness" one forces
them to a tiigher level of comiaunity utility, (This is implicitly the position
of the Catholic Church, as I understand it.)

Now consider infant mortality. If the main thrust of this section
is correct - that welfare is maximized by there being at least as many
children as parents desire, subject to community values and external costs -
and if parents iare able to control fertility accuratelyj then infant mortality
is an unmitigated evil. This is because infant mortality must result in
the parents often having more or leas children than they desire, with con-
sequently lower utility for the parents. Only by luck will the nun^er of
children they desire ex ante live to maturity. And even if parents are luclqr
enough to end up ^-rtth the number of children they'desirSj they will have
suffered the grief of children's deaths that would not have occurred with a
zero infant-mortality regime.

Furtliermore, because people are generally risk-averse when it cOmes
to the number of children and to the number of sons they have, the error will
likely be on the side of achieving more children than were desired ex ante,
as has been shown vividly by Heer and Smith (1968) and May sxtA Heer (1969) .
Infant mortality might increase total utility by offsetting parental selfishness,
but it might also reduce total utility by carrying the process beyond the

'.>. ',r.'j \,■^

^ 6 ~

point of dljminishing total utility. Whicfi is true cannot be known a priori^

One migh.t fault the above conclusion because tile utility function
does not take account of such, important disutilities as death and suffering.
But since we do not have any Intimate or metaphysical knowledge of death
itself, the only disutilities we can sensibly attach to death are a) the
loss of the utility tliat might have occurred if death did not Intervene, which
is not an operative argument here; and b) the suffering of survivors. But
more children might out -weigh the latter. For example, a family might well
choose bearing six children and losing one to accident, in preference to
being limited to bearing one child. Hence the omission of the disutilitiea
of death and suffering is not a defect of the analysis.

The above inference that parents have too few children to maximize
community utility applies only to the childhood period and may well hold only
on the assumptions that (a) there are no other children, (b) utility is
positive, and Cc) there are no externalities. It might, however, hold even
if some of the above assumptions were loosened in some ways.

Kow let us consider the cast in which the additional child's welfare
Is said to be negative. No judgment about the direction of the community
welfare effect can then be made without assigning cardinal values to the
individual utilities of the additional child and his parents, which trade
off if the child's utility is said to be negative (column 1, line 13) . And
If one considers even more complex welfare functions, containing arguments
of per-capita income as well as of total utility or total population size
(e.g., Meade, 1955; Votey, 1969), they will a fortiori also give indeterminate
results in the absence of cardinal specification of the utility function.

■■ .! r:\tlj ». . J

r.-n.

. ;i< ' - :r:»-> v . ' Ij. .11' T'c f'lv

- 7 -

Wh.en a second or subsequent child is considered to be the additional
child, rather than the first child in the family Ccolumn 2), things get
even more complicated, because consumption by existing children will be
reduced by the existence of an additional child. And unlike the parents,
there is no reason to suppose that the existing children desire the
additional child. Rence, the welfare of the previous children is decreased
on balance by an additional child Cline ^» column 2} . The welfare judgment

then must depend upon the assumption one makes about the utility function.

4
If the functions of all the children are assumed positive and concave ,

then the additional child increases total utility of the children in the
family (line 6 column 2) . If the functions can be negative and/or have
inflection points, the welfare effect on the children as a whole depends
on the economic facts and the specific utility functions, and is indeter-
minate without cardinal specifications (line 7, column 2) . The effect
on the family as a whole, and on the community, must also be indeterminate
If the effect on the children is indeterminate Qine 12, column 2) .

Already we may see that even in the very simplest case, and examining
only a single point in time, the evaluation is thoroughly messy and generally
indeterminate.

During His Adulthood

During the additional person's adulthood in this simple world of no
externalities, his welfare effect depends upon which reference group is
being considered, just as it does during his childhood. A peasant in sub-
sistence agriculture affects his brothers and sisters negatively by reducing

- 8 -

their inheritance of land Qine 21, column 2), and therefore the expanded-Pareto
criterion no longer applies. If, however, one assumes that the utility of
all the siblings is positive, and if all their utility functions are concave,
the additional sibling would mean a net welfare gain to the people constituting
the original nuclear family Cline 25 j column 2) and thence— by the expanded
Pareto criterion—to the society as a whole. But if one assimes that utility
can be negative, no such conclusions can be drawn. And of course the per-
capita-income effect is negative Qine 23) .

Now let us leave idealized subsistence agriculture and move to the
more interesting, but still simple, case in which the additional person
enters the labor force but where all markets are competitive and the individual
Is paid his marginal output (column 3) . From the standpoint of average
Income, the rest of the community as a whole benefits from the added person's
presence (lines 35, 37, 39, column 3) as Berry and Soligo (1969) have shown;
the nature of the benefit is exactly the same as the benefit that occurs when
one country opens trade with another country. But assuming that the incre-
mental person is a worker, the population of workers as a whole — and especially
the workers in the trade he enters—will have lower wages because of him
Cline 29) . And the average income of the entire community including the
additional person will fall (line 40) . But if one assumes that all utility
fimctions are positive and concave, then the sum of the individual utilities
in the community will be higher than before, because total output will be
greater (line 42) . So again we see that even for a single period — his
adulthood— and in the simplest case of no externalities and no inheritances,
the welfare effect of an incremental individual can be judged differently

- 9 -

from different points of view. And if one now wlsh.es to coiaBine the judgments
about the welfare effect of the added person during his childhood and during
his adulthood together, the results are even more mixed.

We shall here end the story of the man who does not affect society
beyond his family, either during or after his lifetime, with positive or
negative savings of any kind, except by working in a perfect market.

III. EXTEBNALITIES DURING HIS LIFETIME AND
BEFORE RIS CHILDREN'S ADULTEOOD

In societies that have advanced economically beyond family subsistence
agriculture, an incremental child usually causes effects external to the
family. These externalities can be distinguished into two sorts: those
whose effects can be appraised and compensated for by way of markets, and
those that cannot. Tlie former are treated in the next section, and the
latter are treated in the section after that.

Where There Are Compensable Externalities

The main "compensalile" externalities are in the labor market, and in
social-welfare expenditures, e.g. s<ihooling. Hie nature of the effect
through the entrance into the labor force of an additional worker would be
difficult to agree upon. But both the labor-force and social-welfare effects
of additional children are calculable in principle even if we cannot now
agree on how to calculate them. Standard welfare-economics argtanents suggest

>-jf' in.

;!

- 10 -

that the total utility of all adults in a society at a given time will be
maximized if families pay for all the services used in raising children,
and to neutralize any labor-market effect. That is, if one considers a
median-income faniily with more than the average number of children, it would
pay taxes to cover Che "extra" child-raising services plus the labor-
market effect of the "extra" children. The proof of the optimality of this
policy is the same as that for other cases of external effects, as shown in
a simple way by Coase (1960) . As long as the parents pay the full market
value of these external effects, a larger number of children produced by a
family cannot be said to reduce community utility. And after the labor-
force and social-welfare externalities are taken care of, and the utility of
existing adults may be assumed to be maximizedj the expanded Pareto criterion
again may be applied; after compensation no one except older siblings would
be made worse off by the added person (line. 14, column 7-10). Hence, if the
additional person's utility is assumed to be positive (and with respect to
the first child only) , parents stop having children before the community's
welfare would be roaxijnized, by the same argument as was given earlier. (If the
added person's utility is not assumed to be positive, or if other children
in the family are considered, no such conclusion can be drawn.)

A technical difficulty which turns into a major political problem
arises with respect to compensable externalities, however. It is all very
well to talk of parents paying nov; for the future effects of their children.
But such payments would have to be discounted for futurity. The community
would have to decide on an appropriate discount rate, because economic logic
alone reveals none (or a multitude of them) . Even if the community were to

OJ

;

•.>J

•■ri'f i '•'! f-

^^■;^■ :;■ J :if:T

:>!.,-.

' ■• "■•■■ .. >i:.,. •■:lfi

~ 11 -

eventually arrive at agreement on such a discount rate, there would be maji>r
conflicts of interest. Old people without children would want a low discount
rate and high sums paid immediately. Parents with ciany children would want
the opposite. It might be suggested that the externalities be paid for as
they occur; this might work for schooling and medical care, but it would
not be feasible for the children's labor-force effect. So, because of this
discount-rate problem, together with the difficulty of estimating the future
effects of the children, it is quite possible that the community would not
arrive at agreement on an externality-neutralizing agreement. If so, it
would not be possible for an additional child to effect a Paretian welfare Increase,
and the total cumulative effect-in his childhood plus his adulthood-is Parentian
Indeterminate (line 14, columns 11-14) . And if externalities are not
neutralized, the welfare effect by a total-utility criterion is also indeter-
minate during his adulthood, and hence indeterminate for his life as a whole
(lines 12 an.d 43 > columns 11-14) .

Now let us consider the per-capit a-i ncome effect of an additional
individual where there are externalities in child-services and labor markets.
The classical diminishing-returns analysis (same total capital and more labor
yields a smaller average product) tells us that the effect is negative during
his adulthood, as it was during his childJriood, and the Berry-Soligo analysis
does not alter this conclusion. But in the more-developed world, it is not
only possible but likely (Kuznets 1960, Simon, 19 71) that after some time
in the labor force an additional person will cause enough new knowledge and
enough economics of scale so that per-capita income is higher than it v;ould
otherwise be. If so, by a per-capita income welfare standard the additional

- 12

person's effect is positive for at least the latter part of his adulthood
(column 15) • And the effect may be sufficiently great to make his lifetime
effect positive (line 4i, column 15). But given that per-capita income is
lower during his childhood because of him» to reckon the lifetime per-capita-
Income effect one would have to specify the effects for each year and choose
a discount rate. A high enough discount rate could of course be chosen so
that the later positive effect would matter little, and hence the lifetime
effect would be negative. But with a lower discount rate the lifetime
effect might well be positive if there are positive externalities from
knowledge and economies of scale during the additional person's adulthood —
as there Is reason to believe there are.

Non-Market Externalities and Community Values

Still confining the discussion to the lifetime of the additional
person, let us now consider externalities that realistically would not be
compensated through taxes and subsidies.

As Professor Arrow has made clear, there may be "a. difference between
the ordering of social states according to the direct consumption of the
Individual and the ordering when the individual adds his general standards of
equity (or perhaps his standards of pecuniary emulation)." (1951-1969,
p. 153). The latter states Arrow calls "values", la contrast to the former
which he labels "tastes". And the "market mechanism. .. takes Into account
only the ordering to tastes". Hence it may be appropriate for the community,
acting together „ to make such laws - which may include taxes on or subsidies
for children - as will achieve the sort of society that its members want.
For example, someone might suggest that the community hold a referendum as

lo

!..'>

- 13 -

to whether there should be a tax of 100 shekels, say, on parents for each
child after the third. People might rationally vote for such a measure if

they believe that a lower birth rate will increase the rate of economic

8
development and if they put a positive value on economJ.c development; or if

they believe that infant mortality will decrease if each family has fewer

children and they get disutility out of neighbor's children dying; or if they

get disutility out of other people's children, e.g. because of the noise; or

other reasons. If people vote unanimously for the tax it would imply that

each person would be willing to have fewer ciiildren if his neighbors also had

f^jer children.

Similarly, a community mj.ght have a positive value for a larger

number of children in the community than people otherwise choose to bear,

given their ovm tastes. Israel may be an example: Je^s there may feel that

the continuation of the historical tradition and the values of Judaism can be

better served by more people rather than fewer, and they may be prepared to

vote subsidies to children, just as a man may try to bribe Ms married son

to have more children to carry on the family name. If people get positive

utility out of their neighbors' children and so vote, a subsidy on children

would be indicated. Or, people may believe that a larger population will

contribute to economic growth within a short enough time span so that their

subjective discount rate (which might be zero, as was Frank Ramsey's) will

make the immediate social costs less than the discounted benefits; this is

now the state of belief in Australia, as it was in the Western United States

in the past.

14

The mechanism for decision — majority vote or monarchy or whatever-==^'
will depend upon the group's constitution. Any population policy may then be
consistent with welfare economics , if voted in accordance with the constitution.
The likeliest cause of distortion with respect to a democratic constitution
is a population policy initiated and executed by bureaucrats who impose their
own values upon the community while asserting that the rationale for the
policy is the "scientific" finding that the policy in question is "provedly"
better than non-interference and governmental neutrality with respect to
parental decisions about family size. I believe that this danger is great

because the officials or legislators may not recognize that their beliefs

9

and values are values and beliefs and are not scientifically proven truths.

In the past decade so many scientists have made it clear that they favor lower
birth rates that one can easily come to think that lower birth rates have
Indeed been shown to be scientifically better for society in every way, though
in fact no such finding has been or could be scientifically arrived at
because of the value considerations involved.

IV. EFFECTS AITER THE ADDED PERSON'S LIFETIME

Jtjst as a person may affect his society for good or bad during his
lifetime, so may he have effects after he dies. Economists are accustomed
to dismissing very-long-run effects because of their small weight in calcula-
tions made with interest rates of 15%, 10%, or even 5%. But the society itself
is more ambivalent about the long-run future and sometimes gives relatively heavy
weight, as the current environmental controversy shows. It may well be that the

.j; : I .

.' J r:

- 15 -

average man's total effects on posterity are more important than his total
effects on his contemporaries — ^who are, after all, smaller in number than his

posterity.

There are many sorts of effects one can have on posterity. The
simplest and most surely positive is the savings that one leaves to his
heirs; usually they exceed his debts, as we know from the fact that society's
total capital generally grows over time. One may also leave knowledge behind
him; ■'"■'■ the knowledge might be satanic, but usually knowledge is positive for
the economy, as we know from the higher rate of productivity now than in
former millenia. Still another effect is the children that the added person
leaves. At first the effect of children seems very complicated. But consider
that the effect of each child is expected to be the same as the effect of the
added parent aside from his children. Therefore, the welfare judgment one
makes about the added person is not changed by his having children — aside
from their different positions in history, of course, which can be ignored
unless there is special information about the course of history.

Another post-life factor is the delayed efconomies-of-scale effect
associated with the creation of additional infra-structure, and with changes
in the nature of society— perhaps especially in less-developed countries.
Aa an example, the population-density-induced changes in land-tenure laws
and cropping systems shown to occur by Boserup (1965) can have long-run
IKJSitlve effects on productivity. "

Let us now get more specific in welfare terms. If the added man
leaves anything at all to posterity and if he has no children — that is, if
his contribution to subsequent economic growth exceeds his contribution to

- 16

population growth, then his welfare effect on posterity is positive (column 16,
lines 48 and 50) . If he does have children, and he and his lineage add
proportionately more to saving than to population growth, then the effect
on per capita income of posterity is positive. If he and his heirs each
leave something positive, but what they leave contributes less (marginally)
to growth than this lineage contributes to population growth, the effect
on posterity then is negative in terms of per capita income unless during his
lifetime he contributed greatly in knowledge and otherwise. In such a case,
the effect in terms of total utility is likely to be positive, however, given
a reasonable distribution of income and no negative utilities. If the
additional individual leaves a negative inheritance, then his effect on
posterity is negative.

Each of the sorts of impacts classified above could be combined with
Impacts of the same or opposite sign in earlier periods; if the latter, the
overall evaluation of the added man's welfare impact is indeterminate without
numerical specifications of all impacts and an explicit choice of discount
rates .

One might ask whether the possibility of a positive inheritance, and

expecially an inheritance proportionately as large as the population growth

12

he causes, is just a theoretical nicety wiiich may be disregarded. I think

the answer is clearly "No," the inheritance effect may not be disregarded.
In less-developed countries, of which pre~20th century China is the best
documented example at present, per~capita income remained at much the same
level secularly over 700 years, though it sank seriously during some periods
of rapid population growth. This suggests that the added person set in

u

U.TCi '■ I _ iO

■1": o

- 17 -

motion trains of events that increased saving temporarily. And at some time
later, posterity was no worse (by a per-capita~income test) for the added
person's having lived. On the other hand, it is also possible that in some
places increased population keeps an economy in stagnation, preventing change
and improvement.

In more-developed countries there is secular growth in per capita income.
If population had not grown to something like present population size, con-
temporary per-person income would be far lower in more-developed countries than
it now is. That is, people leave an amount of productive power to the next

generation that is proportionally greater Cperhaps two or three times

13
greater) than the population increase they leave behind. This means that

the added man could leave aii inheritance considerably smaller than average

and still leave proportionally more than the population growth his lineage

contributes ,

This raises the question of whether the added man would contribute

an inheritance anywhere near as great as the average person would contribute

without him, i.e. whether the marginal contribution to posterity is far below

the average contribution. First of all, there is no reason to suppose that

he himself is less endowed with intelligence or chance in life than is the

average person, unless one assumes that he is — and I can think of no special

reason for assuming so. If his endowment is average, then the only factor

causing him to lower the average inheritance would be the lesser physical

and educational capital endowment per person at labor force entry that

population growth probably implies. Given that the average rate of inheritance

in more-developed countries is much greater than the rate of population growth

(in proportional terms) , this classical capital-diluting effect could be

■ C I ./ 1

'> ..'... I .

18 -

of sizable magnitude without making the marginal inheritance smaller than
the population growth contributed by the added person. Furthermore, there are
very solid reasons to agree with Kuznets, as noted earlier » that the knowledge
and economies -of-scale effects lead to a higher per-capita income before the
end of his work life than if he had not been born. If so, the average
Inheritance left at the time of his death will be greater than if he had
not been born, which is a positive effect on posterity by any welfare test.
Of course this happy result is much less likely in a less-developed country
than in a more-developed country, but this only proves once again the
impossibility of making sound _a priori welfare judgments about population
effects without detailed specification of the conditions, asstjmptions , and
criteria.

V. SUMMARY AND CONSLUSIONS

• There is no single calculable welfare effect of an additional person.
The welfare effect depends upon which point in Iiis life-cycle one refers to,
whether he is expected to have a positive effect upon his particular sort of
economy and society during and after his lifetime, and most of all,
on the kind of welfare function used. Furthermore, no matter which
welfare function is used, the welfare effect of an added individual
summarized oyer time is even more sensitive to the particular assumtpions
made.

Footnotes

1. Here and elsewhere in this paper it is assumed that children are brought
into life because their parents desire them, and no more children are
born than parents want. To persuade the doubter of the reasonableness
of this assumption takes more evidence and argument than I have room
for here. The interested reader may, however, consider Firth (1939,

pp. 36-37), Carr-Saunders, (1922, p. 230), Krzywicki (193A), or my
suirvey (Simon, 1971a). The monetary and psychic costs of controlling
fertility are ignored here. I also ignore non-economic welfare benefits
such as the value of liberty.

2. Notice that the grounds used here to reach this conclusion are quite
different than the grounds on which Phelps (1969) reached a somewhat
similar conclusion from a welfare function that would maximize utility

of the parental generation. His grounds were essentially a Berry-Soligo-
type International- trade argument plus consideration of savings ratios.
3.' Now in a matter that may be passed over by all except the most demanding
reader: In a full formal treatment it is necessary to distinguish between
(i) the utility that the parents get from the utility the children get
from consigning resources, and (ii) the utility of the children to the
parents for the parents' own sake. The distinction might be phrased as
the difference between the parent's utility from the parent's "consumption"
cf the child, and the parent's utility from the child's own consumption.
For example, a father takes pleasure in his newborn son, it would seem,
not because he believes that the child now enjoys life, but for the
father's own sake. On the other hand, it is clear that parents can feel

■J .; ■

.' :,., <..i

,f."-. -f '. . '■-

*!':■ : t; .■ » ■■:.:> T-r.T . :ii/

' :' it , hnj-

happy because they believe that the children are happy, e.g., the
sensation the parent feels as the child eats a piece of cake. "I feel
happy for you" is the expression we use to describe this situation. I
shall assume that the utility a parent gets from the utility the child
derives from consumption of the Income the child uses is less than the
child's own utility from that consumption. This need not be true a priori,
of course. A parent might believe very strongly in the value and im-
portance and joy of life, and hence bring a child into the world despite
the fact that the parent himself does not expect to get any personal
pleasure from beholding the child, but on the contrary, expects the
child to be only a burden to the parent. If in fact that child also gets
little joy from his life, one could imagine that the child's positive
utility is less than the parent's negative utility from the child, giving
a net negative balance. But it seems reasonable to me that a parent
•generally gets less utility from a child's constanption of resources than
does the child himself, which justifies this assumption. I am painfully
aware that this distinction is vague, perhaps impossible to measure
sensibly, and at least bordering on the metaphysical. But one cannot
get around such a distinction unless one wishes to assume that the parent's
utility from the child is ail his own. pleasure of the senses in "consuming"
the child, rather than "indirect" utility derived from the child's
pleasure in life. And if one does wish to so assume, all conclusions
of this paper are the same as otherwise, and are arrived at even more
directly.

4. Such an assumption is not at ail inconsistent with the Friedman-Savage
hypothesis, as those authors themselves agree (1952).

5. I think that the notion of negative utility is quite indefensible
after a person is old enough to maVce serious choices, for technical and
empirical (as well as moral) reasons. Meade's concept (1955, Chapter VI)
of a "welfare-subsistence level" of income, below which a person is as-
sumed to have negative utility, is inconsistent with consumer-preference
theory. By the standard logic of consumer-preference theory, the avail-
able evidence tells us plainly that life does have positive value, be-
cause people almost invariably choose life in preference to death, no
matter what their economic circumstances. Life seems to have more value
than does death for a destitute toothless widowed crone who lives — until
the police evict her — in a rag-and-newspaper tent by the side of the
road in India, just as your life seems to have value for you. The rate

of suicide is everywhere sufficiently low that it is clearly an exception
when life ceases to have positive value. Therefore, to assume that some
people are sufficiently poor that their lives have negative value is
quite incompatible with the basic concept of modern economics: That
which is chosen is defined to be better. Without this concept all modern
welfare economics falls apart. This should be reason enough to eschew
Meade's point of view in a discussion of welfare economics. But for me
as for many others, the positive value of all human life, adults and
children, too, is also a point of faith.
5a. If he is paid his marginal output, there is some increase in total
productivity minus his consumption. Hence, total saving will rise
somewhat, but this can be disregarded for now.

,.,;•>■; vf':A.

J ( ' I :; »• ,,

';.; (■: y)

WSiiOoi^ (1 5

'JIU- -J. - i- .1 ■*<

'.,..,' t ;.' .';>n , ;.

:-;j''; ,, ' ;v 1

•■■...f|i TV), -.m:" -^i

6. I assume here that the society charges the full cost for all consumption
products, including the cost of physical pollution prevention and removal.
This assumption may be well on the way to becoming fact.

7. This includes the use of natural resources as raw materials in production,
and is supported by the finding by Barnett and Morse (1963) of no increase
in natural-resource scarcities. The over-all basis for the positive
effect of more people in more-developed countries is the "residual,"
which at once sums up the effects of natural resources, knowledge, and
economics of scale. For a quantitative estimate of the interaction of
this force with the classical capital-dilution effect, see Simon (1971).

One might argue that the concept of GNP, which underlies all previous
reckoning, does not measure over-all economic utility sufficiently well,
because it leaves out some "quality of life" features. Perhaps so.
But in the absence of calculations, or at least cogent reasoning, about
the results of using the wider measure, there is no reason to assume the
results would be different in any particular way from work based on GNP.

8. Please notice that though the effects people are interested in may occur
after the added person's lifetime is over, the values of other people
are held and acted upon during (or before) his lifetime. Hence the
placement of this discussion in this section.

9. "There is a personal bias that colors one's view of the (relatively)
poor which comes from appraising others* Incomes against the standard
of one's own aspirations. This bias is Implicit in many conventional
economic-welfare judgments, and it seems to me to be both indefensible
and in fact without defenders. This is merely shoddy practice, not
doctrine." (Weeks tein, 1962, p. 137.)

10. Many of the long-run worries of the contemporary environmentalists may
not be real threats, of course, as was the coal shortage foreseen by
Jervons (1865). The point here is, rather, the social discount rate.

..'ii'.l

fyiti'^r' l^'A/'X- v^^;

7l>0.^r-57 if:f:..i :,.,;■•••" ■'!

vvii

11. The argument that some classes of people are likely to contribute to
knowledge, while others are not, will not be considered here. One reason
is that, as a first approximation, this paper assumes the same proportional
change in fertility for all classes of: the society; this is certainly

not unrealistic for the U.S., where the poor clearly do not account for
most of population growth. A second reason is that I have been persueded
by Kuznets' argument (private communication) that all segments of a
society are crucially implicated in the growth of knowledge, and not
just the intellectual elite.

12. In fact, the opposite possibility — • that more people nO'W mean a negative
inheritance for the future — is simply assumed by such writers as
Meade (1955) and Votey (1969).

13. Growth theory assumes that savings equal population growth. But the
life cycle is usually not distinguished into parts in such growth

. analysis, so that work can mostly be disregarded here.

References
Harold J. Barnett and Chandler Morse, Scarcity and Growth: The Economics

of Natural Resource Availability (Baltimore: Johns Hopkins, 1963).
R. Albert Berry and Ronald Soligo, "Some Welfare Aspects of International

Migration,, Journal of Political Economy, Vol. 77, September/Octoberj

1969, pp. 778-794.
Ester Boserup, The Conditions of Agricultural Growth (Chicago: Aldine, 1955).
A. M. Carr-Saunders, The Population Problem: A Study in Human Evolution

(Oxford: OUP, 1922).
Colin Clark, Population Growth and Land Use (New York: St. Martins, 1967).
Ronald H. Coase, "The Problem of Social Cost," Journal of Law and Economics,

Vol. 3, October, 1960, pp. 1-44.
P. S. Dasgupta, "On the Concept of Optimum Population," The Review of

Economic Studies, XXXVI, July 1969, pp, 295-318.
Paul R. Ehrlich, The Population Bomb (New YorkJ Ballantlne, 1968).
Raymond Firth, Primitive Polynesian Economy (London: Routledge Kegan,

1939, 1965).
Milton Friedman and Leonard J. Savage, "The Expected-Utility Hypothesis

and the Measurabllity of Utility," Journal of Political Economy,

60, December 1952, pp. 463--?4.
David M. Heer and Dean 0. Smith, "Mortality Level, Family Size, and Popula-
tion Increase," Demography, Vol. 5, No. 1, 1968, pp. 104-121.
W. Stanley Jevons, The Coal Question (London: MacMillan, 1865).
Ludwik Krzywicki, Primitive Society and Its Vital Statistics (London:

MacMillan, 1934).

( , ' ■■'■

,.vir;"MV ,•• i ■■■.\:/^

ivM

Simon Kuznets, "Population Change and Aggregate Output," in Universities —

National Bureau of Economic Research, DEMOGRAPHIC AND ECONOMIC CHANGE

IN DEVELOPED C0W5TRIES (Princet:on: PUP, 1960), pp. 324-340,
David A. May and David M. Heer, "?on Survivorship, Motivation and Family

Size in India: A Computer Simulation," Population Studies,

Vol. XXII, July, 1969, pp. 199-210.
James E. Meade, The Theory of International Economic Policy, Vol. II,

Trade and Welfare (New York: Oxford University Press, 1935).
Edmund S. Phelps, "Population Increase," Canadian Journal of Economics,

Vol. 1, August, 1968, pp. 497-518.
Frank P. Ramsey, "A Mathematical Theory of Saving," The Economic Journal,

38, (1928), pp. 543-59. Reprinted in K. J. Arrow and T. Scitovsky,

Reading in Welfare Economics (Homewood: Irwin, 1969), pp. 619-633.
Julian L. Simon, "The Effect of Population Growth on Per-Worker Income

in More Developed Countries," mimeo, 1971.
Julian L. Simon, "The Effect of Economic Conditions Upon Fertility: Review,

Analysis, and Prediction," m.meo, 1971a.
Harold L. Votey, Jr., "The Optimum Population and Growth: A New Look,"

Journal of Economic Theory, 1, October, 1969, pp. 273-290.
Richard S. Weckstein, "Welfare Criteria and Changing Tastes," American

Economic Review, Vol. LII, March, 1962, pp. 133-153.

<'<.■*.'.

■^:\' :r^;^

sVl