The Economic Consequences of a Declining Rate of Population Growth

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Tm momma oo»sa$*H^mW bam

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w Don w« Paden

A dissertation submit ted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, In the Department of Economics» in the Graduate College of the State University of Iowa Jfcly, 1942

ProQuest N um ber: 10831779

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The author la indebted to Professor Howard B« Bowen for his encouragement* direction, and criticism and to Dr* Harold w* Saunders who very kindly read the manuscript and mad# numerous helpful suggestions *

537005

ill

Table of Contents Page Chapter X

Introduction .........

1

XI

The Background of Facts and Theory •

*

XIX

The Principle of Diminishing Returns

18

IF

The Principle of Increasing Returns,

33

V

Technological Change and Employment •

52

VI

Technological Change and Economic Expansion.................. • *

80

FIX VIII XI X

The Concept of the Optimum Population * . , # » ' » » * • •

101

The Relationship of Capital end the Optimum Population .........

Ill

The Optimum Population and Eeonomle Expansion • * « , , * * * « . * »

123

Summary and Conclusion » » • * « « *

132

Bibliography * * * # . * * . * « » •

143

iir

fable of Charts Page Chart

I XX

fhe Relationship of Average, Marginal, sad fetal Output * * * * » » * • *

31

A Firm under Conditions of Increasing 42

dUA*JU

m v vx

Physical Productivity by Census Periods, 18V0-194Q

50

A Production Surface« * • • • * • • « .

118

Varying Proportions of the Factors with a Constant fetal Output • « •

120

Isoquants

124

V

Table of Tables Pag* Table 1

Estimated Population of the Earth* 16501038* (In 1#QOO*0OO) * #

7

Population of Continental United States by Decades, 1880-1040* * * * * * * *

8

Birth and Death Hate* for the United States by Decades, 1880-1940 « * * «

9

X?

Bet Reproduction Rates. * • • • * • • «

IS

V

Estimate of the Future Population of the United States for Five-Year Intervals

14

Estimated Age Distribution of the Popula­ tion 1950-1980 * , » ' * * • • • * »

15

Labor Foroe In Relation to the Popula­ tion, Ten Years of Age and Over, 19001959 * . . * . * *- . * *

IS

VIXX

Diminishing Returns for labor • * •

* *

81

XX

Diminishing Returns for Land* * * *

* •

85

IX XXX

VX VII

X

Diminishing Returns for Land and Labor*

86

XX

The Marginal Produet of Labor * * * * *

30

XXX

Adjustment of Price and .Output under Conditions of Increasing Returns . •

41

Physical Productivity per worker by Census Periods , 1870-1940 * * * . « • * • •

53

XXIX XXV

A numerical Representation of a Production Surface « * . » • » * * *

180

1

Chapter 1 XNTRODTJCTION To the professional economist the subject matter of each of the following chapters Is more or less familiar* Xhere is, for example, nothing very new in the concept of an optimum population, or of technological change, or, even less, in the laws of return*

It is hut natural, there­

fore, for the reader to Inquire of the reason behind the re-examination at this time of these already well-worn tools of analysis*

In large part the answer to this query

is that these concepts are now being applied to problems which were not, indeed could not be, perceived a generation or two ago*

Like the engineer who builds his road to fit

the traffic which moves over it, so the economist must fashion his tools to fit the changing course of human events * Among these contemporary events one of the most signlfleant««*at least for the western world— la the slowing down of the rate of population growth*

In the past the

influence of this factor upon economic productivity has been discussed largely in terms of the principle of diminishing returns*

How that the growth of population

seems to be coming to an end It is to be wondered if the principle of Inereasing returns will become in its turn the nexus between faet and theory*

8 Wlille Buish of our thinking at the present time Is done in terms of these two principles, It Is to be doubted whether future developments will continue to leave obscure the role of technology In population theory*

The

more spectacular events such as the opening up of new territories* the growth of population* end the accumulation of capital have tended to overshadow technological Improve­ ments as a cause of the Increase in output*

In the future

the partial eclipse of these other factors may serve to reveal the true role which technology plays In our economic life* It Is to the task of re-examlnatlon* modification* and elaboration that the following chapters are largely devoted*

The purpose* apart from the clarification of the

concepts examined* la to relate this material to the problem of productivity in a world in which population growth Is coming to a halt*

The lews of return* technology* and the

concept of the optimum population are first treated separately*

Thereupon these several analyses are brought

together In an attempt to develop a systematic theory of the relation between population and productivity*

In

general the problem is to see how economic theory can aid in a better understanding of the Influence upon productivity of the interaction of scarcity* technological change* and population growth*

At best the contribution can scarcely

be large— the ground has been too well worked for that*

3 Yet because the work Is humble need detract neither from its dignity nor from Its usefulness as a guide to further study#

4

Chapter IX t h e cha n g i n g bac kgro und of f a c t aid t h e o r y

The population problem of the present day is set In a peculiar reversal of circumstances*

It Is almost

needless to point out that the transition from a period of rapidly growing population to one in whieh the growth is leveling off finds its counterpart in population theory* It is thus the purpose of this chapter to trace briefly the evolution of fact and theory in order to better under­ stand the background of the problem*

An examination of the

statistics and a review of the theory should serve to make clear why the traditional treatment of the population problems Is subject to progressive change* Much of our thinking on the subject of population dates back to the days of Thomas Robert Malthas when a rapidly increasing population led to the formulation of his three famous propositions t *1«

Population is necessarily limited by the means of subsistence*

2*

Population Invariably increases where the means of subsistence Increase, unless pre­ vented by some very powerful and obvious check •

3*

These cheeks and the cheeks which repress the superior power of population, end keep its effects on a level with the means of subsistence are all resolvable into moral restraint, vice* and misery*”1

* T. R* Malthas, An Essay on the Principles of Population (London, ISTO) p* 14*

5 While Malthas was not the first to point out these tendencies,^ his statement was put forth at such a time and made in such a manner that It attracted widespread attention.3

The ever-growing population was seen

to necessitate a larger proportion of the population engaged in the production of food*

It was thought that

as land became relatively scarce and more people were set to its cultivation the possibility of any surplus being left over after subsistence had been provided for would become Increasingly remote* Thus not only for the workers (whose lot was that of subsistence at boat) but for the propertied class as well* the doctrine, at least In the hands of Ricardo, became a somewhat gloomy omen feu? all alike*

The futility

of improving the lot of the poor soon developed into a "theory of poverty" f the belief that any social policy designed to relieve the press upon subsistence would at once release the superior power of population and the poor ® See Charles E* Stangeland, Fre-Malthusian Doctrines o£ a Study In the Hletory ot feoneialc~^^y Tssw York, 1004)* 3 It should be noted that in presenting the Malthusian Theory of Population as It Is popularly interpreted, con­ siderable injustice is done to Malthas1 later work* In his Principles of Political Economy the doctrine Is modifled''^-b1"'lake account”' of comfort. Here this concept tended to replace subsistence as a norm about which the population tended to fluctuate* Thus increased output might not result in an increase in the population but rather to an Increase in the scale of living* T* R* Malthas, Principles of Political Economy, second edition (London* I W & T . l^or a more adequate discussion see E* B* Reuter, Population Problems (Hew York, 1937) pp* 167-171*

6 would sink again to their former level*

The economist,

fortifying himself behind the logically impregnable prin­ ciple of diminishing returns, continued to maintain, long after the facts suggested modification of the doctrine, that an increase in population necessarily must lead to a decrease in the output per head* As time has passed, however, the impact of a new situation has made itself felt#

The opening up of new

farming areas, the development of cheap moan® of transpor­ tation, and the application of science to industry and the farm— things which were perhaps unforeseeable in the days of Maithus— have served to alter the basis upon which the population theory was predicated# was being done by fewer hands*

Everywhere more work

Gradually the “arithmetical

jingle of the gloomy parson1*^ no longer suited the facts to which it was applied# Hot only this but in recent years the amassing growth of population shown in the table below has shown signs of leveling off*

This is particularly true in

c o m tries such as France, Sweden, and Great Britain where the increase is not only slowing down but the total popula­ tion is actually threatening to decline* ~ 1 This' 'apt characterisation of Maithus* observation that the population, if given the chance, would Increase to a geometrical ratio while, at best, food production could be expected to increase in an arithmetical ratio, was found a® a quotation in Political Arithmetic* £ josium w—wvwiiiimieiai of ikim wPopulation wewiji^jaoism atii\t studies1edited by 47 Eaiieefot P#R*s# >on tfondoh, 1938) p# 32*

7 Table I Estimated Population of the Earth, !650**1958 (In 1*000,000) Tear

Population

1660 17S0 1800 1850 1900 1938

405 660 856 1,098 1,551 8,145#

Sources B* R* Kucsynski, "Populations History and Statistics" EncycioTmedl&of the Social Sciences (Hew YorM, 19341) p# 81T* $&ague of B f B B P t a w Book, 1939-1840* ~ The once almost exoluslve concern over the danger of Qver~populafcion-*~*the condition which exists whan an Increase in population leads to a lower standard of llvlng*-has gradually subsided*

The possibility of under-

population, noticed by John Stuart Mill, has been given more place In economic thought*

In the English speaking

world the work of Edwin Caiman has been most Influential In securing the acceptance of what Is now known as the c

"optimum theory of population#11

Her© preoccupation over

subsistence has given way to speculation concerning the sis© of population which Is compatible with the highest possible standard of living} that la, the "optimum population"* The slowing down of ih© rat© of population growth has not occurred suddenly or ©ven unexpectedly*

In some

* For a good account of the evolution of the Idea of an optimum population see 1rare Ferenc si, The Synthetic Optimum of Population (Paris, 1938) Chapter I#

3 sections of the United States, for example, a slackening of the rate of increase has been evident since the turn of the nineteenth century.6

A rough picture of what has

happened to the rate of growth of the population can he obtained from an examination of fable II*

The rate of

growth for the total population shows a decided decline* fable II Population of Continental united States by Decades, 1680 • 1040 Year 1880 1000 1900 1910 1920 1960 1840

Population

Hate of Increase (per cent)

80,186,788 68,947,714 76,994,578 91,972,266 105,710,620 182,776,046 131,409,881 (Provisional)

30*1 00*6 20*7 21*0 14*9 16*1 7*0

Source : Statistical Abstract off the united States *

IM P * p* 3% The device which has been most frequently used in the past for measuring population growth is a comparison of the birth and death rates*

The birth rate represents

the number of births per thousand of the population in a given year| the death rate, the number of deaths per thousand population in the given year*

Birth and death

rates for the United states are shown In the following tablet 8 See Enid Charles, The Twilight of Parenthood (New York, 1934) p* 79*

9 Table III Birth and Death Bates for the United States by Decades 1880 - 1940 P»ath R»t»» X880 1890 1900 1910 1920 1930 1940

18.8 19.6 17.fi 18*0 18.1 11.8 10.8****

Birth Rsteww®* 37.7*»* 31.0*** 29.8*»» 07.3»*» 23.7* 18.9* 17.8**

Bate of increase _U22ELSS$SSS6— 17.9 11.4 11*9 12.3 10*6 7.6 7.0

^afcigtiesi m s s m i j i f m m m Uni ted States Department o f c osraeree, Bureau of the Census (Washington, D# C., 1940) p* 91, 77* ^Provisional figure, Peculation Index, School of Public Affairs, Princeton ^SversTty anS FopulatIon Assoelation of America, Vol* 7, Ho* 4, Oet* 1941* 4hh*BouIb *T« Dublin and Alfred J* Dotka, "On the True Bate of natural Increase,u Jhg Journal of the American Statistical Association, September, SbsHJ vS I * W , PP* 317ijO&*rrr'Tfeier''rates are baaed on present age die tribution# Statistics— Special Beport, Deaths and Death Bates, Vol* 15, Ho* 24, June 9, 1942* ^ ’^Sinoe the federal birth registration area was not organised until 1915, the birth rates for prior years are rough estimates only* A glance at these figures shows at once that the number of births per thousand of the population exceeds the number of deaths per thousand*

The rate of increase again

shows a decided decline* While it is possible with the use of these figures to get an entirely accurate picture of what has happened to the population within the periods examined, the trend in the future is not so easily predicted*

The situation is

somewhat skin to that of the business concern whose profit

10 and loss statement perpetually shows an excess of Income over outgo, yet each year approaches nearer a state of bankruptcy because of a failure to provide properly for the depreciation of the original investment,

while it Is

not meant to imply that a decline in the population means national bankruptcy* in substantially the same fashion a nation may show a surplus of births over deaths and yet Inevitably be headed for a day when Its population will start to diminish# 'She reason for this lies in the age distribution of the population*

m

exaggeratedexample given by B* P.

Harrod Illustrates the point wells "....♦Suppose," he says, 11that 95 per cent of the total population consists of people between the ages of 20 and 45 • Then even if married couples had on the average less than one child, a number manifestly insufficient to replace them* it is probable that births would exceed deaths* And this for two reasons s Hi© number of children b o m per thousand of the total population would greatly exceed the number which would be b o m if a normal proportion of the population was under 20 years and over 45* And the number of people dying per thousand would be much less than the number which would die if a normal proportion of the population was over 65 or under 5 years of age* Han® the birth* and death-rates give a^ deceptive clue to what is r e a l l y happening To a less exaggerated degree this is the situation in the United States today*

There is

an abnormallylarge

number of people in the child-bearing age.8

It thus

" R. F. Barred, "Population Trends and Problems," Lloyds Bank Limited Monthly Review, January, 1959* pp. 5*6# r'"'Br f^his is shown diagrammatically by Frank Lorimer and Frederick Osborn, Dynamics of Population (Hew York* 1954)

P* *7*

appears that the abnormally large number of women In the child-bearing age Is for the time being maintaining the birth rate*

When these women move into the older age

groups* there will be an insufficient number of younger women to take their place*

A downward trend In population

growth seems Inevitable unless, of course* a larger per­ centage of the population marry and have children than has been true In the Immediate past, or* unless people start having larger families than at the present time* The statistician has tried to give an accurate accounting of the extent to which the population Is replac­ ing itself (or failing to replace Itself) by the use of the net reproduction rate*®

The net reproduction rate attempts

to show the extent to which women In the child-bearing ages are producing girl children who will survive to take their mother’s places*

The net reproduction rat© is to be Inter­

preted In the light of Its underlying assumption

that the

fertility and death rates for specific age groups for women in the child-bearing ages remain the same during the Interval from birth until the child reaches the age of the mother* This in turn implies ’’that the urban-rural distribution of the population and the corresponding differential fer­ tility* the marital status (or nuptiality) of the 9 The method was brought Into prominence by Kucjsynski, The Balance of Births and Deaths (Hew Vol* I* Chapter Xl* ", for a ’YiKple description of used to calculate this measure see R* F* Harrod, pp* 6-7} or Enid Charles, op* clt*, p* 59,

Robert H* York* 1928) the method op* cit.*

12 population* etc.* should all remain constant”^*0 during this Interval*

Subject to these qualifications a rate

of 1+0 indicates that the population la exactly replacing Itself#

In the long run, if maintained* this would indi­

cate a stationary population*

If the rate la 2*0* it means

that the population la replacing Itself twice over| and* if the rate is 0*5* it indicates that the population Is only producing one-half of the number necessary for replacement The net reproduction rate for the United States at the present time is below 1*0*

Thus the country faces

the certainty of a declining population unless people who ordinarily marry and have children begin to have more children* or, unless a larger percentage of the population marry and have children than is true at the present time* In the face of the long-run decline in the birth rate this does not seem very promising although it is not outside the realm of possibility* It is true that In the last few years the birth rate has taken a sudden spurt upward*

The explanation

probably is to be found not in any significant change In the attitude of people toward having larger families but rather in the circumstances surrounding the war and In Bernard Karplnoa, "Use of Nuptial Reproduction Rates in Population Analysis*® The American Journal of Sociology, March, 1942* p* TOT* **See R* F* Barred* jg* cit** p* 6.

13 the postponed depression marriages which the revival of industrial activity has made it possible to consummate*3*2 In the long run it is probably safer to expect a continued decline in the birth rate than to expect this factor to be over-balanced by a further decline in the death rate or by an Increase in immigration*

The influence

of these factors upon future net reproduction rates can only be imagined*

At the present time the rates for various

countries can be seen from the following tables fable W Het Reproduction Rates England and Wales Sweden France United States Germany Italy Russia Japan Source t P* 140*

*78 *78 *90 *98 *98 1*13 1*70 1.44

1938 1939 1935-39 1940 (.70 in 1933) 1935-37 1988-88 1987 QP* olt*, April, 1942,

Populafcion .as.,

The day when the total population in the United States will start to decline is a questionable matter.

It

might be thought that estimates based upon the net reproduc­ tion rate would furnish an infallible guide to the future* This, however, is not the case* Is itself subject to change*

The net reproduction rate

It cannot take Into account

For the correlation between the marriage rate and economic conditions see the Statistical .Bulletin of the Metropolitan Life Insurance P* 6.

14 such factors as a change in the birth rate* a change in the death rats* or changes in immigration,

These are

things which cannot be known before they happen. To get an estimate of future population growth it is necessary to consider not only things as they are (as reflected in the net reproduction rate) but also t© make some estimate of the future movement of these variables,

The estimate which seems to be most widely

accepted is that prepared for the National Resources Committee by Warren S . Thompson and P. K * Welpton. fable V Estimate of the Future Population of the United States for Five-Year Intervals 2&s£ £940 1945 £950 £956 £660 £985 £670 £975 £980

131,993,000 £36,447,000 £40,661,000 £44,093,000 146,987,000 149,341,000 £51,170,000 £68,433,000 183,028,000

Source I National Resources Committee, ffiae Problems of a Changing Population, (Washington,

P* 14. Tim estimates are based on the assumption of "medium” fertility end mortality15 mid m

net Immigration*

It Is

interesting to note that the estimate for 1940 anticipated the census with an error only 0.2 per cent higher than See National Resources Commit tee, Ibid.. pp. 22*24.

15 the number actually enumerated* From the figures It Is evident that there will be a long period of time In which to contemplate the posslbility of an actual decline in the total population* The problem is peculiar, however* in that a long period of time must elapse before there is a possibility of revers­ ing this trend should such a policy be deemed desirable* The following table serves to indicate the change in the age structure of the population*

A gradual aging of

Table VI Estimated Age Distribution of the Population, 1930-1980 (Assuming medium fertility, medium mortality, no immigration) Age Group - Per cent of Total Population Year

0*4

5**19

1950 194© 195© 1960 197© 1980

9*8 8*3 7*9 7.1 0*7 6*3

89.3 86*4 83.0 88.2 20*6 10*6

m m 38*1 38*8 40*0 37*4 35.0 33*7

JffiStt 17*1 20*2 21*4 83.3 26*9 25*9

m 5*4 6*3 7.0 10.0 11*9 14 *3

80-64 53*2 59.0 61.4 60.7 60*9 39*6

Sources Enterprise and social Progress» The national Industrial "bolferemeT^arS'* ?J&w ybf¥i" 1959) p* 30* the population is seen from the figures*

The proportion of

the population between 90 and 64 (last column} will remain remarkably stable, however, if these estimates are correct* In the past the working fore© which is for the most part derived from this group has remain®! a very stable propor­ tion of the population*

Th© following table shows the

figures for the past few years;

16 Table m Iabor Pore© In Relation to the Population, Tea Years of Age and Over, 19001939 Year

labor Force or Per eeat of Population

1900 1910 1900 1930 1939

50,0 53.3 50,3 49,5 30,0

Source* National Industrial Conference Board, ftblft,* P# 39, While it is dangerous to extrapolate on the basis of the past, the figures serve to give some Justification for the belief that the future working population will r©~ main about the seme proportion of the total population as has been true during this period*

If this Is true, the

fears which have frequently been expressed that the working population will be forced to carry an ever-increasIng burden in the near future appear to be largely groundless*^

This

is not to say that in a rapidly decreasing population this concern would be unfounded*

For the United States, how­

ever, the problem is scarcely likely to be very pressing In the near future,

The date of the actual decline in

total numbers is still far off,

Bee Harold Saunders, "Population Trends in U. S*,° The o^Buslmea, State University of Iowa, February,

17 The forgoing discussion has indicated that population theory has progressed from concern over sub­ sistence as embodied In the writings of Mai thus and his followers to considerations of over- and under-population* Out of this Has evolved the concept of the optimum popula­ tion of the present day*

This transition in the theory of

population has come as a concomitant to the increased pro­ ductive power of the modern worlds

the discovery and

exploitation of new land and resources * and the application of science to industry, transportation, and the farm* At the present time a third factor is beginning to assume an increasingly important part in the factual background*

The rapid growth of population in the western

world seems to be coming to an end*

Such a change In the

facts is bound to be reflected in the theory*

It is the

purpose of the following chapters to examine how this third factor, the decline in the rate of population growth, will tend to bring about modification in the m y in which the laws of return, technology, and the concept of the optimum population are to be applied to the population problem*

18

Chapter III the m i m i v m of dimxnishxho hbtorhs The Ideas embodied in the principle of diminishing returns have long bean associated with the growth of population,^

In a country such as eighteenth

century England* where a natural scarcity of land was made more evident by the closeness of its holding, this inference of a necessary decline In output occasioned by an increase in the population was readily unders tandabls« To the "economic royalist*1 of the time the doctrine that the press upon subsistence was caused by the fecundity of the lower classes provided an avenue of escape from a contrary train of thought which all sense of moral discrimination found repugnant*

That the misery of the poor in England might

be laid at the door of the rich was not a pleasant subject for contemplation for a class which judged itself to be among the benefactors of mankind# The principle of diminishing returns as it was applied in the Malthusian Theory of Population played the peculiar role of shifting the responsibility for the Ignoble social conditions current in England from the conscience of the rich to the shoulders of the poor#

They

in turn were left to blame either the niggardliness of ■■■—

* For a good but brief history of the development of the principle of diminishing returns see C# J. Bullock, 11The Variations of Productive Forces," The Quarterly Journal of Economics * August, 1933, p* W I .

19 nature or their emu fecundity for the poverty which engulfed them*

they were estopped from a criticism of

the 30cial order.

So it was that logic* Itself impeccable,

succeeded in appeasing the credulity of the Interested and the discernment of those who should hsure known b otter * As the years fell away and social conditions became somewhat improved this inference of a necessary decline In the standard of living accoaipanying an increase in the population continued to hold a certain amount of fascination for the gloomy.

Proof, perhaps, of the

assertion that habit is more convincing than the fact* The optimistic# on the other hand, gathering strength from the evidence everywhere about them# set out to demonstrate that a quite opposite relationship existed in the real worldj that an increase in the population might have a beneficial effect on the standard of living*

The quad*

rupling of the population within the past two and a half centuries and the accompanying rise In the standard of living has lent strength to their argument* Thus the logic of the pessimists and the evidence of the optimists has presented a perplexing enigma*

The

controversy# real or imagined* still goes on today in a slightly more elegant form*

On the one hand are those

who* having fallen heir to all the analytical parapherna­ lia of the neo-classical economist, continue to defend what has come to be known popularly as ’’scarcity economics

20 On the other hand ore those who believe that this Is hut a secondary problem! that the real problems are those which have to do with the modification of social institu­ tions to make them consistent with a bounteous nature# The difference of opinion Is a challenge to all contendere* While little is to be said of the latter problem in the pages immediately following* it is hoped that some light m y be shed on the physical basis underlying the con­ flicting claims— at least with reference to population growth#

This chapter and the following chapter on increas­

ing returns is written in an endeavor to define clearly the laws of return*

The concepts are to be used with reference

to the later material on the optimum population and its relationship to the growth of eapital and economic expansion#

A closer examination of the principle of diminishing returns Is to be cur first task#

A familiar

text-book Illustration will serve as a point of departure* The usual exposition begins with the successive applica­ tions of labor upon a fixed amount of land* below will serve as m

example *

Table VIII

005

m.

Tmi* n xx Diminishing Ho turns for X*abor lores 1 The Point of pjmlnjnfclng Returns

The Point of Diminishing Total Output!

Total Output

Hen X

Average Output per Man

7

7

(1

8

20

10)

1 1 1

S 4 8

27 52 33

9 8 7

&

a

m

6)

7 * IS

m

8 f 1

1 I 1

i 20

Tiro points are of particular Interest*

The point

of diminishing returns for men is defined as the combine** tlon of men and acres where the output per man (shown in the last column) reaches a maximum#

IJ£ to this point an

increase in the variable factor, men, leads to a more than proportionate increase in the output*

The effort of but

one man scattering his efforts over a whole acre produces but an indifferent result*

He might better have concentra­

ted on a smaller amount of land*- At:the: point of-diminish** ing returns the increase In the variable.factor yields a proportionate increase in output*

•

Once the point of diminishing”retui'ns is passed an increase in the number of men being applied to the land will yield a less than proportionate return*

Finally the

point of diminishing total output for men is reached*

This

22 Is defined as the combination of men and sores where the total, output reaches a maximum and thereafter starts to decline*

Since the us© of more men after the point of

diminishing total output for men la reached has a continu­ ing unfavorable influence upon output, it is readily seen that in any rationally organised economy their use is ruled out*

it would be foolish, for example, to use seven men at

a task six can perform with more satisfactory results* It should be noted in passing that the production function used in the preceding Illustration was chosen arbitrarily*

In reality increases in the variable factor

might for a large segment of the curve give rise to a proportionate increase in output or to a constant total output or to other peculiar variants depending on the process studied*

In any case suitable modifications of

the discussion could easily be made* The marked over-abundance of men at the bottom of the table is to be contrasted with the relative sear* city of men at the beginning of the table— particularly before the point of diminishing returns is reached*

The

significance of the range between the point of diminishing returns and the point of diminishing total output will become apparent very shortly*

hot it suffice for the

time to note that these two limiting points define the o range (or stage) of diminishing return®* 3 Fo p a more complete statement of the principle of diminishing returns see the the Law of Variable Proportions" in in Economics ¥7 w r m siTg

03 The same general effect upon output might have been observed if, instead of applying varying amounts of labor to a fixed amount of land, the amount of labor had been held constant and the amount of land had been varied* The following table might be typical of the results fable XX Diminishing Returns for land teas

X The Point of Diminishing Returns

(0

3 4 5 The Point of Diminishing fotel Output

(6

7 I

10

(Proportions) .Lte-teteaJi

te

Total tesst

Average 2steS_

(Ill2)

12

SO

SO

(lid)

10

78

36)

(1|4 ) (1 «3 ) ,

(Its s/s)

10 10 12

93 108 115

31 07 23

(1|2)

12

180

80)

&/?) (111)

10

103

(111 «

i

18

l

84

18 l

7

Here a constant number of men (column three) la used with a varying number of acres (column one) * The total output produced by the twelve men first increases and then decreases as in the previous example*

The output per acre,

shown In the last column, follows much the seme pattern* The maximum output per acre or the point of diminishing returns for land is reached with the use of two acres*

The

point of diminishing total output occurs with the use of six seres*

24 At the top of the table there la represented a situation In which there la an overabundance of men and a scarcity of land*

The paucity of the output under these

circumstances may be attributed to the fact that the efforts of the twelve men all working ©a a single acre tend to be mutually detrimental.

As one reads down the table this

situation is at first corrected and then over«*eorrected« At the bottom of the table the opposite situation is represented#

The over-abundance of men has given way to

a relative scarcity of men* abundance of land*

Coupled with this Is an over*

The scarcity of men and overabundance

of land finally causes total output to decline*

JUst as

in the ease of an over~abundance of men, so* now* in the situation where there Is m overabundance of land* total output is adversely affected.3 The above account describes the principle of diminishing returns in terms of average and total output* A more familiar* and sometimes more useful* statement of the same principle runs as followst In any productive process* given the state of-the arts* if one or more of the factors of production Is held constant* and one or more other of the factors of production is allowed to vary, the output will first vary more than proportionally* next* r~*~"^"FiKaps the illustrations give an over-simplified picture of the actual situations* A* B* Wolfe says * ”There seems to be no a priori reason* however* for supposing that increasing returns might not set In after diminishing returns «••••* though with continuing additions of input diminishing retails must set in permanently sooner or later.” from “Rent Under Increasing Returns*” The American Economic Review* December* 1929* p* 599.

25 less than proportionately and, last, output will decline in total*

Thus, within the range of diminishing returns,

a small change in the variable factor will lead to a smaller percentage change in output# We will have occasion to refer to the principle of diminishing returns in these terms In the following pages a s two tables used above to illustrate the principle of diminishing returns may now be brought together, demonstrating that they are mutually eons is tent* This can be seen in Table X* The output shown for the last line of Table IX (twelve acres, twelve men) is exactly twelve times as large as the output shown in the first line of Table VIII (one man and one acre)*

The compatibility of the two tables is

even more clearly shown by a glance at the last line of Table VIII and the first line of Table XX*

In this ease

the two lines are identical with the exception of the average output* The rest of the table is likewise mutually consistent*

It will be noted in Table VIII that the point

of diminishing returns for men occurs where two men per acre are used, while In Table IX this same combination of two men per acre occurs at the point of diminishing total ' 1' in 'the above discussion only one variable factor has been considered at a time* It is entirely possible to take account of additional variables although the material becomes excessively complicated if too many factors are allowed to vary* See Jbhn B« Black and Albert 0* Black, Production Organization (Pew York, 1929) p* 124*

26

IP

&*

H

$« sg ft p 4?

CD

n

N

H

H H

5 g

o

«rl -p

& ©

a

«*

f4

#*

< 10 H**

H••

r4

rt

I1 ftj ►

H

i

fe rj i to M*

©3

IP

is

t l

iH

4 O ft

«j £

H*■ HI

©3 H

I** *1 H

HI

•* H

**

H

m output for land*

likewise In Table VIII the point of

diminishing total returns for sain occurs where six men are used per sere*

The same proportions in Table IX give

rise to the point of diminishing returns for land*

The

arrows on the chart emphasis© this fact of singular impor­ tances namely, that the point of diminishing returns on one chart corresponds to the point of diminishing total returns on the other chart* As one reads down Table VIII the total output finally starts to decline because of a superabundance of men which becomes progressively greater down the table* This same super-abundance of men may also be seen In Table IX as It I® read from the bottom up past the point of diminishing returns for land*

since labor Is need In

exactly the same super-abundant proportions in the last line of Table VIII as in the first lino of Table IX, It should be apparent that such a combination as this would be equally foolish in either ease*

Output could be increased merely

by using loss of the over-abundant factor (or more of the scarce factor)*

Thus It Is that the point of diminishing

returns and the point of diminishing total output set limits within which all rationally controlled production w i n take place* All the factors of production are ordinarily used past the point of diminishing returns*

Hone are used past

the point of diminishing total output*

It Is the function

38 of price to indicate to the business man which combination will be used within these limits In order to yield the product at the least cost*

if one of the factors Is scarce

(high priced)* less of it and more of the relatively abundant (low priced) factor will be used*

Production will

be carried on ajj the point of diminishing total output only In the limiting case where one of the factors Is so abundant as to be free*

In this case the other factor would be used

at the point of diminishing returns*

'Thus, to say that a

factor Is used past the point of diminishing returns Is merely to say that some other factor is relatively scarce* We are now In a position to make several observe-* tlons concerning the nature of the principle of diminishing returns * First* it is to be noted* that any demonstration of the principle of diminishing returns Is predicated upon the assumption that the factors of production are neatly divisible into very small units#

If this were not the

case* It would be impossible to observe the symmetry exist­ ing between the points of diminishing returns and the points of diminishing total output for the various factors# A corollary of the assumption that the factors of production are Infinitely divisible Is that the law of diminishing returns deals exclusively with the proportions In which the factors are combined^ and has nothing at all to do with the absolute s.iso of the process In question# ® fhie will be brought out in almost any good discussion of the subject* For example, see the discussion of «T* M# Cassel, ibid#, p* 283#

This is likewise a condition underlying the internal consistency of the above tables*

For examples, the output

in the last line of Table IX (twelve men, twelve acres) Is exactly twelve times as great as the output shown In the first line of Table TOtl (one man, one acre)*

In order

that this should be the case it must have been assumed that the absolute size of the process is a matter of indifference — an existing situation has merely been duplicated twelve times over* One last observation concerning the nature of diminishing returns*

Any discussion of the subject deals

exclusively with a given atfete of

arts * it would have

been useless to speak about applying successive units of one factor to another factor, if the very substance of the factors In the meantime had changed* would have been futile*

Attempts to generalise

in postulating a given state of the

arts a great many barn doors have prudently been fastened with a permanence which, it is hoped, falls short of finality For the moment, however, the assumption rules out new die* eoveries, and aptitudes, indeed, all changes in wthe totality of devices mid expedients which the men of the society in question have developed” for the satisfaction of human wants

H*. P. Fairchild. "Ontimum Pomilafcion." Proceedings tlon conference, edited oy Margaret sanger

so Shifting the emphasis for a moment from production to distribution it is interesting to note what happens to the return® to the factors of production at various combinations of those factors assuming that the reward® of the factors correspond to their marginal productivities. A portion of TableVHI is reproduced below together with a column show­ ing the marginal productivity of the variable factor Table XX The Marginal Product of Labor

7 BO

1

§■

m m m m

3 4 5 6 V

35 i BO

« IB

Marginal Product of the Variable Factor

Average 1

Total Output

I

Amount of the Variable Factor Used with On© th&t of the Fixed Factor

13 7 5 3 X -1 : I

7 10 0 0 7 6

a s . 1 B/3

*

At the point of diminishing returns the average product is equal to the marginal product#

This ©an better

be seen on Chart X# At this point If the factors are paid in accordance with their marginal productivity the stun of the amounts paid to the factors in question will be equal to the total product#

A little arithmetic will verify the fact#

(The

average product was obtained by dividing the total output by the quantity of the variable factor used; thus, if

31

Chart I The Relationship of Average, Marginal, and Total Output

Point of Diminishing Returns

10

Quantity of Variable Factor

Point of \ Diminishing ITotal Output

32 marginal productivity is ©qua! to the average product, to multiply roarginal productivity by the quantity of the variable factor would result in a figure equal to the total product#)

This means that at this point th© marginal

productivity of the other factor must be aero#

This may

be verified by glancing at Table XX and calculating th© marginal products* or* if analogy is trusted, by looking at the graph above and noting that the marginal productivity for the factor here shown becomes aero at th© point of diminishing total output— the point of diminishing returns for the other factor# If the symmetrical nature of the charts b© granted* the total product Is thus exhausted at the point of diminishing returns and th© point of diminishing total output#

Between these two extremes th© marginal productivity

of both factors la positive*

Because of th© crudeness of

th© data it is difficult to demonstrate that the total product Is likewise exhausted between th© point of diminish** ing returns and the point of diminishing total output*

The

proposition* however* is well known and under static condi­ tions seems well founded*^

Oh© observations mad© above

agree with th© cojmnon-sense conclusion that one factor receives th© greatest return per unit when the other factor receives nothing*

^ The development of the idea is traced by George .T. Stlgler* Production and Distribution Theories (New York, (1941) Chapter13Hfl£~# '

33

Chapter IV THE £RIH0IPX$ OF INCREASING RETURNS Aiay discussion which Involves the term "increasing returns" planes a burden upon the user of giving it a meaning appropriate to th© analytical task at hand*

To do more than this and attempt to give It a mean­

ing consistent with its use by others is to bring upon oneself the task of bringing order out of chaos.

That this

is unfortunate needs no demonstration? that It is true needs only the substantiation to be obtained from a passing familiarity with economic literature*

The following remarks

are mad© In th© Interest of internal consistency within the following chapters on the optimum population and economic expansion.

It Is hardly to be hoped that what is said will

change appreciably the general usage of the term* The term "increasing returns" at once suggests to the reader that It is the counterpart of decreasing returns*

This view is substantiated by th© fact that in

the examples in the last chapter there Is a range of com­ binations of the factors of production within which succes­ sive applications of the variable factor to the fixed factor yields a mere than proportionate increase in output) that ls# th© return per unit of th© variable factor increases rather than decreases as is the case after the point of diminishing returns is reached*

These combinations of

34 v

the factors of production occurring before the point of diminishing returns is reached ere said to be within the stage Cor range) of increasing returns*

in this nemo the

principle of Increasing returns has already been demon** strated*

A duplication of the first two lines of fable

V in in the last chapter will adequately Illustrate the point* Here there Is shown a 100 per cent increase In the variable factor while the output has increased @86 per sent* Percentage Percentage increase Increase *»**■ *** ftrtwrt. OtttOTt to Labor Aa Output Total Average

State of

1

Returns

1

Increasing

1 £

7

7

00

10

^ 100#

Increasing returns are clearly in evidence*

006# Apparently one

man working on a single acre must so divide his attention that his effectiveness Is not very great * The second man has more than doubled the output because each man is now able to work a smaller amount of land with greater efficiency* The increase has come about net because of any division of labor between the two men but rather because of a division of land*

This Is- at once apparent when it is remembered

that the absolute else of the process has nothing to do with the outcome*

The same desirable result could have

been obtained by halving the land instead of doubling the

35 labor force.

The first man could bars increased tea

output by working only part of tbs aero*

The increase

has been due to a betterment of the proportions In which the two factors are employed* It was brought out In the last chapter that In any rationally organised society all of the factors of production are ordinarily m a d in quantities sufficiently large to carry the productive process In question past the point of diminishing returns*

If this were not the ease,

as In the above example, output could be increased by the simple expedient of using leas of the overabundant factor {land, above}* To be combining one of the factors with another in combinations which yield increasing returns is simply another way of saying that the other factor Is being used past the point of diminishing total output.

Obviously such

a procedure would not be followed unless there were power* ful compelling factors at work dictating the choice*

what

reason then can be advanced for a productive process ever being carried on under conditions of increasing returns? One of the assumptions underlying the above discussion is that the factors of production ace infinitely divisible*

An examination of this assumption may lead to

a reason for actual production being carried on within the stage of increasing returns*

In the real world perfect

divisibility of the factors of production Is only

36 Imperfectly realized*

Machines , geographical areas,

human talent, cannot always be chopped up Into Infinitely email bits and than be effectively applied to the produc­ tive process In this die Integrated form#

Some elements

most he added in very large doses or not at all, A large indivisible element of this kind ean he used in its optimum relation with the other factors of production only if a large quantity of the divisible faetor

Is used at the same time*

If this is not the ease,

then it may Indeed he possible that the variable factor will net be employed past the point of diminishing returns. There is then the possibility that a process will be carried on under conditions of increasing returns*

Xn this sense,

the term increasing returns has frequently been used to Indicate a condition where the increase in output caused by a more advantageous proportioning of the factors of production, augments the effectiveness of the factors already employed and produces a more than proportionate return*

The next step is to try to evaluate the impor­

tance of the possibility noted above* Xt was pointed out in the last chapter that it might be economically sound to use any combination of the factors of production within the range marked off by the point of diminishing returns and the point of diminishing total output*

A factor will be used at th© point of

diminishing returns only if th© other factor is free; it

57 will be used at the point of diminishing total output only if jit is free and there is no necessity of economizing on its use#

Ordinarily neither capital nor labor is free and

hence production is carried on some place between these two limits* The ^capacity* of an industry varies within this range and it is the function of price to indicate to the business man which one of the combinations within this range is to be used*

The rules of competitive business

dictate that the combination which yields the product for the least cost shall be chosen*^ When monopoly is present and these rules are departed from* the use of the least cost combination may no longer be a condition forced upon the Individual business man#

Even so* the combination

decided upon may be well within the range between the point Of diminishing returns and diminishing total output* To stop before the point of diminishing returns is reached would be equivalent to society making the variable factors available to the monopolist at a price of less than nothings that is* the producer would have to be paid for their use#

In a sense this is what is involved

in monopoly profit*

The producer gets paid something above

th© cost of the hire of the factors*

Again it Is noted

that it is conceivable for a firm to be operating under conditions of Increasing returns* 1 The role of price is discussed in John D* Black and Albert 6* Black* og* olt*. Chapter VI*

38 It has undoubtedly been noticed that in the above paragraph there has been a subtle shifting of ground* Th© emphasis has been shifted from increasing returns in a physical sense to decreasing cost in a monetary sense# two are not, however, necessarily coextensive*

The

Decreasing

cost starts in the above example with the application of the first unit of the variable factor and extend well into the range of decreasing returns*

Unless the variable factor

is free,decreasing costs stop short of the point of diminish­ ing total output and increasing costs take its place*

The

place where costs cease to diminish and start to increase is the least cost point# The theory of monopolistic competition has demonstrated that it may not pay a producer to operate at an output which minimises cost*

Will it ever pay the

producer to restriot output so greatly that increasing returns become evident?2

The answer to this question may

be found by examining still another question* Students are eternally observingt ,?Why should producers restrict output when the demand for their product Is not perfectly elastic but still not Inelastic?

An

elastic demand means that a decreased quantity of goods will be exchanged for the smaller output (a reduction in g course, the other question of whether or not it will pay a producer to so over-utilise the fixed factor that it— the fixed factor— will be used in the stage of increasing returns* The answer here is clear since if this were the case the variable factor would be used past the point of diminishing total returns*

39 the total amount spent)*

Surely this is not good business.*

The answer to their query is that total costs decrease faster than total Incomef or, that although unit costs are rising (with restriction of output), price per'unit of output is rising still more rapidly*

This is surely sometimes true*

To return then to the original question, would a producer continue to restrict output to the extent that he would depart from th© range of combinations of the factors of production encompassed by the stage of diminishing returnsf

If output were decreased to a point within the

stage of increasing returns, each successive decrease in output would necessitate a more than proportionate Increase in the use of the variable factor*

Unless this decrease in

output were accompanied by a fall in the prices of the fac­ tors of production, unit costs would rise more than the proportionate decrease In output*

If the demand for the

product were elastic, the rise in price would be leas than the proportionate decrease in output*

Thus th© only con­

dition under which a producer would operate within th© range of increasing returns would be that of an Inelastic demand where a decrease in output would lead to a more than proportionate rise in price*

Bven where the demand Is in­

elastic, unit costs might be rising fester than price, in which ease further restriction of output would be unprofitable*

40 It has been assumed thus far that coats and the physical Input of the variable factor vary at the same rate— the case of pur® competition in the market for the fee tors of production#

Where such Is not the case and the

producer is In a position to decrease the price for the factors of production as he decreases his employment of them (and hence his output), the increase In the physical Input of the variable factor may be increasing more than proportionately, while the increase In monetary costs decrease less than in proportion to the decrease in output# In this case even where the demand for the product is elastic there remains the possibility that the price will rise faster than the Increase in costs# The possibility of a producer operating within the range of increasing returns is then greater than would at first be thought#

Table XII and Chart XI serve to

illustrate many of th© points emphasised above# The illustration in Chapter III (Table VIII) has again been used#

A price has been placed upon both labor

and land and the coat per unit of output calculated.

It

w i H be noted that the least ©oat combination occurs between the point of diminishing returns and the point of diminish­ ing total output (marked by th© two broken vertical lines)# Imperfect competition with respect to the sale of the product and th© hire of labor is shown in column (5) and (11) respectively#

The producer would stop production at the

intersection of the marginal cost and the marginal revenue

41

s♦ 02 *5«P h m0 «

© ©4 fr*

O Q4 fr It

10 0? • rf rt

© r o O * l * 10 # elt», p. 204* 10 There seems to be general agreement that the optimum population Is a shifting thing conditioned largely by cir­ cumstances* Xionel Robbins comments "The optimum of modern theory Is one which Is continually shifting! It is essen­ tially a function of the 'progress of improvement’M o£. c£t* p# 111* Also y* A* Robson, op. cl£., p* 345* T. E. Wegory, "Mwln Cannon* A Personal Impression,w Eoonomioa, R°«8* 1935* p* m ?| and H* P# Fairchild, People* flgrQuantity and Quality of Population* op* oit*» p* 155*

106 institutional structures*

The affect of variations in

the items included under these headings will be discussed briefly In the following paragraphs• Changes in human institution® may have a profound effect upon the else of the optimum population*

A change

in the distribution of income* for example, might alter it in favor

of a smaller number*

f&gh

Dalton ventures the

suggestion that, "There is some grounds for supposing that a less unequal distribution of income would lower the optimum, partly through increasing the relative demand for food and other commodities produced under conditions where diminishing returns come relatively early***•*t* ^ A m m in favor

equal distribution of incomes might react

of a smaller population in

still another way*By

Improving the lot of the lower classes their effectiveness might be vastly Increased so that a smaller number of men might perform the same tasks without diminution of output* Willingness to work has often been mentioned as on© of the determinants of the optimum population and it also closely associated with the distribution of income* if the population should suddenly put a greater premium on leisure than is true at the present, the result might very well be of a nature to raise the optimum— assuming Of course that a condition of full employment Dalton, op* oit*, p* 4®* See also Alfred Plumer, *The Theory of Population* Some Questions of Quantity and Quality," The Journal of FplltioaJ. Jfeonom^, October, 1938*

107 exls ts initially and that the decision does n©t reflect one way or another on the effectiveness of the laborer during his working hours*

There is always the possibility,

of course, that the increase in leisure might significantly alter tastes and demands*

Indeed this might occur inde­

pendently of any other change in the economic structure— although this is highly improbable* There seems to be a tendency for basic wants to be satisfied by more and more complicated mechanisms* Travel, for example, is a highly complicated method of satisfying the desire for variety*

These wants place a

Strain upon resources and require highly specialised industrial structures for their satisfaction. Another social institution which may Influence the optimum population within a given area involves facili­ ties which are set up for economic cooperation between these areas*

#The 1optimum density1 of population for any

country may be diminished not by anything happening in that country, but by *.*« tariff changes #wl^ whether or not the optimum would be lowered or not is open to question*18

The

poiht to be noticed is that the optimum would probably be changed* w. H* Beveridge, ^Population and unemployment, The Economic ftmvml* December, 1923, pp* 470-1. lo & population might be required if the country were previously highly specialised* A wheat-growing community for exestple might find itself robbed of practically all the benefits of specialisation unless a larger popula­ tion came to its rescue.

108 The question of the rate of utilisation of resources Is another variable in the determination of the optimum population which is particularly the subject of human propensities*^

a

rapid exploitation of resources

might increase the optimum population, at least in the short run*

The larger population might be able to benefit

temporarily through the increased specialisation the larger numbers make possible*

The only excuse for such

disregard for the future mould be a divine faith in the ability of mankind to invent himself out of every scarcity* Such an attitude is apt to blind one to the fact that for long centuries technological development was painfully slow*^

Would it not be the better part of valor to trust

the economic welfare of future generations to forces which can reasonably be forseen?

An individual is apt to find

that a frustrated dream of a "fountain of youth” is a poor substitute for the mental and emotional stability which comes of a realistic facing of the passing years,

society

no less than individual® look and plan for the future. tt goes almost without saying that the more abundant the resources the larger the optimum population, unless of course, there appear compensating disadvantages in size from other sources— difficulties of coordination, Suggested by A* B# Wolfe,"The Optimum Theory of Population^" The Annals of tha toerlcan Aeadejg of Political P and Social ScIenceY November, 1936, p* 248. “"’W l l l y n Yeung, op* ©it*, P* 581.

109 to mention only on© possibility#

In the past the

scarcity of resources has usually been considered the chief determinate in th© problem of the optimum popula­ tion*

Wolfe, for eoMBstple, says,

’‘While the Institutional set up with its trend toward vastly greater productivity Is now the most significant factor in the problem, In the longer run of centuries rather than decades the supply of raw materials and power will become more important* for these, even with the most efficient organisation and technique that unhampered engineering ability may achieve, wUJL condition fundamentally the standard of living*”16 The optimists will continue to maintain that man is master of his fate and that by devoting increasing energy to scientific research even the ultimate scarcities of nature become subject to the will of the inventor* Again it l« suggested that the optimum population may be changed by encouraging or discouraging different hinds of Inventions*

Furthermore it suggests that dis­

crepancies between the optimum population and the actual population may be closed by working with the former of these two quantities * MSino© there is no natural harmony between the movements of our two variables***, our practical aim must be a harmony deliberately contrived*”2^ The discussion In the last chapter should have made it clear that technological change exercises no one­ way Influence on the sice of the optimum population. S T X T b . Wolfe, ’’The Optimum Population,” The Encyclopedia of the Social Sciences, Vol* XIX, pW862. ** Hugh Dalton, oju * oit*, P* 384-6*

138

Chapter X SUMMARY A W COUCWSXOK The slowing down of the rate of population growth has raised interesting questions in many different fields *

The special problem examined in the foregoing

pages has been the effect of this trend upon economic productivity# far afield*

At times the discussion seemed to wander

inch digression may be exoused only on the

grounds that the implications inherent in the problem were manifold*

The purpose of this chapter la to summarise the

main contentions while leaving behind many of the details which seemed necessary in the development of the original Ideas# Throughout the preceding pages it has been less our concern to answer specific questions of policy than to examine certain economic concepts on the basis of which policy is usually formulated#

Conclusions to be drown from

such material must in large part relate to the concepts themselves*

The question of guiding social policy* assum­

ing that an identity of the actual and optimum population 1$

desirable* is a task which depends on an examination of

the facts and on estimates of the "cost11 of alternative courses of action,

unfortunately many of the facts are

not available| Indeed* many of the facts do not exist. Today*® social polloy must be based on some hypothesis

155 as to tomorrow*g “state of mind* and tomorrow^ "state of the art** with respect to wants and the means for their satisfaction*

Only by arranging and rearranging

possible situations la the mind1a eye is it possible for the economist to arrive at the Implications inherent in any given social action* The optimum population as it has been developed is not something which is fixed and immutable*

Xt is

determined largely by the unfolding of events— events over which human beings may exercise considerable control*

social

policy designed to establish a harmony between the actual and the optimum population should recognise both quantities as variables*

If it Is true that the population is going

to decline* it may hi easier to reduce the optimum by guiding technological change* industrial organisation* and con­ sumer* s preferences than to try to arrest or reverse the rate of population growth*

This* it seems to me* Is the

chief practical Inference which can be drawn from the material In the preceding pages* a study of productivity as it la defined by output per worker, to the extent that it Is not prompted by a desire for facte in themselves* probably presupposes some Interest in economic welfare*

Particularly is this

true of discussions concerning the optimum population when that tern is defined as the else of population which maximises output per person*

Unless there were some

134 Interest In seeing this output distributed, the concept would here very little funetional value • If society were organised for the benefit of the few rather than the many, the pertinent data would relate not to the output per person hut to total outpufc— proper deductions having been made for the ^shbslstence* of the great bulk of the population*

It la for this reason that the subjects of

unemployment, tariff barriers, economic organisation, etc., have been allowed to enter into the discussion? these factors m y influence productivity as much or more than the change in the slse of the population Itself* The problem of scarcity In economies has been organised around the principle of diminishing returns*

As

the term has been used in economic literature It refers to a situation in Which the ''state of the arts” is taken as given*

Moreover, the principle deals exclusively with

the proportions in which the factors of production are combined*

The absolute slse of the process has nothing to

do with the principle itself* Under ordinary circumstances, the productive process is carried on some place between the point of diminishing returns and the point of diminishing total output*

Within this range occur all of the combinations

of the factors of production which a rationally ordered society would utilise**,*agsln recalling the assumption of the infinite divisibility of the factors of production*

135 If In addition to using marginal productivity as a method of indicating some "beat" combination

of the factors of

production, the factors are also paid according to their marginal productivity, the total output la completely ©xhaustod* c *V Vital Statistics, Special Report, "Deaths and Death Hates a11 VdlV 15, Bo, 24, toie §, 1942, Weintraub, David and Posner, Harold L«. "Unomployiaent and Increasing Productivity," National Research Project, No* 8*1, Philadelphia^ iflW* (Wiloojt, Clair) U* S# Temporary National Economic Committee, Monograph No# 21, Competition and Monopoly in American Industry* Washington. D* c*. 1940,