Optimum Saving, Individual Decisions, and the Diminishing Marginal Productivity of Capital
Author(s): Y. K. Ng
Source: The Economic Journal, Vol. 80, No. 319 (Sep., 1970), pp. 749-752
Published by: Wiley on behalf of the Royal Economic Society
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970]
DIMINISHING MARGINAL PRODUCTIVITY OF CAPITAL
749
2. R. Dorfman, P. A. Samuelson, and R. M. Solow, Linear Programmingand
EconomicAnalysis,New York: McGraw-Hill, 1958.
3. Norman C. Miller, " A General Equilibrium Theory of International Capital
Flows," EcoNoMIC JOURNAL, June 1968, 312-20.
Ethic) Consumer,Many Good
4. Trout Rader, Growthin a Many (non-Protestant
EconomyLeads to Immiserizationof all but one Consumer,mimeographed (no
date), Washington University, St. Louis.
5. Roy L. Webb, The Role of InternationalCapitalMovementsin Tradeand Growth:
The Fisherian Approach,mimeographed, November 21, 1969, La Trobe
University, Bundoora, Victoria, 3083, Australia.
OPTIMUM SAVING, INDIVIDUAL DECISIONS,
AND THE DIMINISHING MARGINAL
PRODUCTIVITY OF CAPITAL
THE purpose of this note is to refute a fallacious argument in the problem
of optimum rate of saving. The essence of the argument is that, as capital
accumulation enhances the productivity of labour (and other non-capital
factors of production), the social benefit of investment is not adequately
reflected in the rate of return to the private investors. Savings undertaken
by the individual savers, therefore, fall short of the social optimum. To
show that this argument is widely held and to see the precise way it is argued,
the following quotations are not out of place:
". . . even if a perfect (italics added) market interest rate could guide
private investors to maximise their welfare over time, it would not produce socially optimal investment decisions ... Investment enhances
the productivity of labour and other factors of production, and, as a
result, increases their income. This is a cost to the private investor,
who calculates his rate of return net of payments to other factors. But
to society as a whole, those increased factor incomes should be treated
as a gain. The social rate of return on investment, i.e., the marginal
output-capital ratio, may therefore be much greater than the private
marginal efficiency of capital."'" As time goes by, the rate of return on further investment falls.
The faster accumulation takes place, the faster the wage rate rises and
the faster the rate of profit falls. It seems that the benefit to ' society '
from saving is not properly reflected in the ' reward ' to the savers.
How then does 'society' secure that the optimum amount of saving
takes place?. "2
1 M. S. Feldstein, "The Social Time Preference Discount Rate in Cost-Benefit Analysis,"
June 1964, p. 364.
J. Robinson, " Consumer's Sovereignty in a Planned Economy," in On Political Economyand
Econometrics,Essays in Honour of Oskar Lange (Oxford: Pergamon, 1965), p. 518.
ECONOMIC JOURNAL,
2
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750
THE ECONOMIC JOURNAL
[SEPT.
when we are looking at the matter from the social standpoint,
why should profitability be the criterion, evenif we ignoreexternalefects?
(Italics added.) Why should not the socialreturn on investment be regarded as being the totalresulting addition to national output, without
any such deduction of the values of other factors? In other words, why
should it not be identified with the inverse of the capital: output ratio
(Domar's ' investment productivity)? "1
". .. it is impossible to achieve a consistent solution of the saving
problem on the basis of the individual saver's decisions. The following
two properties of the economic machine make for this impossibility.
First, the volume of saving is assumed to be determined by the rate of
interest. The rate of interest is equal to the marginal net productivity
of investment. But because of the diminishing marginal productivity
of investment, interest does not exhaust the net benefit of saving (investment). Thus savers get only a part of the new product resulting
from investment, which must affect their marginalvaluations(italics
added) in making saving decisions. Secondly, even allowing for the
deduction of the 'investment surplus', savers still do not get the full
award for their abstinence from consumption, because as production
increases real wages rise as well and a part of the new product is distributed as additional wages."2
By arguments of non sequitur,Horvat pulls two rabbits (which are two
sides of a non-existent coin) out of an empty hat, though the other authors
quoted above find themselves able to pull out only one. We turn now to
examine the reason why the hat is actually empty.
Employing the same arguments as those of the above quotations, one
could argue that the supply of every factor of production falls short of the
optimum. For example, one may say, " As the increased supply of labour
enhances the productivity of capital (and other non-labour factors of production), the social benefit of labour is not adequately reflected in the payment of wages to the private workers. Labour supplied by the individual
workers, therefore, falls short of the social optimum." Thus, Dobb should
ask as well, " Why should wages be the criterion, even if we ignore external
effects? Why should not the social return on labour be regarded as being
the total resulting addition to national output, without any such deduction of
the values of other factors? In other words, why should it not be identified
with the inverse of the labour: output ratio ?"
The whole mess is, of course, caused by inadequate understandingof the
" marginal analysis." In the figure the horizontal axis measuresthe amount
of capital, and the curve P measures the marginal productivity of capital.
1 M. Dobb, An Essay on Economic,.Growth
and Planning (London: Routledge and Kegan Paul,
1960), p. 16.
2 B. Horvat, TowardA Theoryof Planned Economy(Beograd: Yugoslav Institute of Economic
Research, 1964), p. 176. Similar examples could be multiplied; e.g., R. Harrod, " Optimum
Investment for Growth," in Problemsof EconomicDynamics and Planning, Essays in Honour of M.
Kalecki (Oxford: Pergamon Press, 1966), pp. 176-8.
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1970]
DIMINISHING
MARGINAL
PRODUCTIVITY
OF CAPITAL
751
OA is the amount of capital stock at the beginning of the period under consideration. For this relevant period, therefore, the horizontal axis after A
measuresthe amount of capital accumulation. The curve S is the marginal
cost of saving or the supply schedule of saving, taking A as the origin. The
intersection of the two curves at E determinesthe optimum amount of capital
S
G
c
E
D
F
A
B
accumulation AB; EB being the rate of return for capital. Thus the total
"' social return " of AB amount of investment, i.e., the area ABEG is greater
than the total payment to the investors (or savers) ABEF by the amount
FEG. The extent to which " the productivity of labour and other factors of
production " is enhanced by capital accumulation AB is measuredby CDEG,
as the pre-existing capital OA also suffers decrease in return measured by
CDFG. However, the relevant question for efficient allocation' is the relation at the margin. It can clearly be seen from the figure that at the margin
the " social return " equals the " private return," both being EB; the
marginal output-capital ratio 2 is equal to the private marginal efficiency of
capital. Thus, the marginal valuation curve of the saversis still the curve P,
though they are not paid the whole area under the curve.
Only if a saver is in a monopolistic position so that he can influence
appreciablythe market rate of interest,3will savings fall short of the optimum
due to the diminishing marginal returnsof capital. In this case, the more he
himself saves, the smaller rate of return he gets. Thus, he will be guided by
a curve marginal to the demand curve facing him (i.e., rates of interest at
1 Even for the problem of income distribution, capital is not entitled to claim the whole area
under P curve, as every factor of production could then claim all of the social product, if it is indispensable in production See the literatures on the " adding-up problem."
2 If the net figure is taken, and market imperfection and externality assumed non-existent.
3 This type of monopolistic power virtually does not exist, except in the case of Government's
savings, especially in a centrally planned economy. But the Government should, presumably,
ignore its monopolistic power and still be guided by the P curve.
No. 31 9.-VOL. LXXX.
3 0
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THE ECONOMIC JOURNAL
752
[SEPT.
different levels of his savings). Deviation from the optimum caused by this
reason is, of course, similar to the common case of the monopolisticrestriction
in the commodity market. The argument criticised in this note, however,
does not refer to this type of deviation, as is clearly indicated in the first
quotation above.
We conclude that savings undertaken by the individual savers do not fall
short of the social optimum owingto the fact of diminishing marginal productivity of investment, unless there is monopolistic power involved. The
widely held argument criticised in this note is therefore clearly erroneous.
Our argument does not mean, however, that individual savings may not fall
short of the optimum owing to some otherreasons.
Y. K. NG
New
Australia.
Universityof
England,
CURRENT TOPICS
THEAnnual Meeting of the Royal EconomicSocietywas held at the
BritishAcademy, BurlingtonHouse, on July 2, 1970. ProfessorE. H.
PhelpsBrown,M.B.E.,F.B.A.,was electedPresident. Sir Alec Cairncross,
K.C.M.G.,F.B.A.,(theretiringPresident),SirDonaldMacDougall,C.B.E.,
F.B.A.,Sir ArnoldPlant and ProfessorE. A. G. Robinson,C.M.G.,F.B.A.,
were electedVice-Presidents. The followingwere electedto hold officeas
membersof the Council until 1975: ProfessorA. Beacham; Mr. C. F.
Carter; ProfessorMiles Fleming; Mr. C. W. McMahon; ProfessorW. B.
Reddaway,F.B.A.; ProfessorI. G. Stewart.
THEmeetingwas informedthat Mr. A. D. Marris,C.M.G., had asked
to be relievedof the officeof Treasurerthat he had held since 1954. The
Councilhad nominatedMr. W. M. Allen, who had servedon the Council
for many years to succeedhim in that office. The meeting was also informedof the new arrangementsfor the conductof the Society by which
Mr. C. F. Carterwould succeedProfessorE. A. G. Robinsonin the office
of SecretaryGeneral,and ProfessorW. B. Reddawayand ProfessorD. G.
Champernownewould be responsiblewith Miss Phyllis Deane for the
editing of the
EcONOMIC
JOURNAL.
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