Chapter 11
THE MARGINAL EFFICIENCY OF CAPITAL
I
When a man buys an investment or capital-asset, he purchases
the right to the series of prospective returns, which he expects
to obtain from selling its output, after deducting the running
expenses of obtaining that output, during the life of the asset.
This series of annuities
Q
1
,
Q
2
, . . .
Q
n
it is convenient to call the
prospective yield
of the
investment.
Over against the prospective yield of the investment we have
the
supply price
of the capital-asset, meaning by this,
not the market-price at which an asset of the type in question
can actually be purchased in the market, but the price which
would just induce a manufacturer newly to produce an additional
unit of such assets, i.e. what is sometimes called its
replacement
cost
. The relation between the prospective yield of a
capital-asset and its supply price or replacement cost, i.e. the
relation between the prospective yield of one more unit of that
type of capital and the cost of producing that unit, furnishes us
with the
marginal efficiency of capital
of that type. More
precisely, I define the marginal efficiency of capital as being
equal to that rate of discount which would make the present value
of the series of annuities given by the returns expected from the
capital-asset during its life just equal to its supply price.
This gives us the marginal efficiencies of particular types of
capital-assets. The greatest of these marginal efficiencies can then be regarded as the
marginal efficiency of capital in general.
The reader should note that the marginal efficiency of capital
is here defined in terms of the
expectation
of yield and
of the
current
supply price of the capital-asset. It
depends on the rate of return expected to be obtainable on money
if it were invested in a
newly
produced asset; not on the
historical result of what an investment has yielded on its
original cost if we look back on its record after its life is
over.
If there is an increased investment in any given type of
capital during any period of time, the marginal efficiency of
that type of capital will diminish as the investment in it is
increased, partly because the prospective yield will fall as the
supply of that type of capital is increased, and partly because,
as a rule, pressure on the facilities for producing that type of
capital will cause its supply price to increase; the second of
these factors being usually the more important in producing
equilibrium in the short run, but the longer the period in view
the more does the first factor take its place. Thus for each type
of capital we can build up a schedule, showing by how much
investment in it will have to increase within the period, in
order that its marginal efficiency should fall to any given
figure. We can then aggregate these schedules for all the
different types of capital, so as to provide a schedule relating
the rate of aggregate investment to the corresponding marginal
efficiency of capital in general which that rate of investment
will establish. We shall call this the investment
demand-schedule; or, alternatively, the schedule of the marginal
efficiency of capital.
Now it is obvious that the actual rate of current investment
will be pushed to the point where there is no longer any class of
capital-asset of which the marginal efficiency exceeds the
current rate of interest. In other words, the rate of investment
will be pushed to the point on the investment demand-schedule where the marginal
efficiency of capital in general is equal to the market rate of
interest.
The same thing can also be expressed as follows. If
Q
r
is the prospective yield from an asset at time
r
, and
d
r
is the present value of £1 deferred
r
years at the
current rate of interest,
S
Q
r
d
r
is the demand price of the investment; and investment will be
carried to the point where
S
Q
r
d
r
becomes equal to the supply price of the investment as defined
above. If, on the other hand,
S
Q
r
d
r
falls short of the supply price, there will be no current
investment in the asset in question.
It follows that the inducement to invest depends partly on the
investment demand-schedule and partly on the rate of interest.
Only at the conclusion of Book IV will it be possible to take a
comprehensive view of the factors determining the rate of
investment in their actual complexity. I would, however, ask the
reader to note at once that neither the knowledge of an asset's
prospective yield nor the knowledge of the marginal efficiency of
the asset enables us to deduce either the rate of interest or the
present value of the asset. We must ascertain the rate of
interest from some other source, and only then can we value the
asset by 'capitalising' its prospective yield.
II
How is the above definition of the marginal efficiency of
capital related to common usage? The
Marginal Productivity
or
Yield
or
Efficiency
or
Utility
of Capital
are familiar terms which we have all frequently used. But it is
not easy by searching the literature of economics to find a clear statement of what economists have usually
intended by these terms.
There are at least three ambiguities to clear up. There is, to
begin with, the ambiguity whether we are concerned with the
increment of physical product per unit of time due to the
employment of one more physical unit of capital, or with the
increment of value due to the employment of one more value unit
of capital. The former involves difficulties as to the definition
of the physical unit of capital, which I believe to be both
insoluble and unnecessary. It is, of course, possible to say that
ten labourers will raise more wheat from a given area when they
are in a position to make use of certain additional machines; but
I know no means of reducing this to an intelligible arithmetical
ratio which does not bring in values. Nevertheless many
discussions of this subject seem to be mainly concerned with the
physical productivity of capital in some sense, though the
writers fail to make themselves clear.
Secondly, there is the question whether the marginal
efficiency of capital is some absolute quantity or a ratio. The
contexts in which it is used and the practice of treating it as
being of the same dimension as the rate of interest seem to
require that it should be a ratio. Yet it is not usually made
clear what the two terms of the ratio are supposed to be.
Finally, there is the distinction, the neglect of which has
been the main cause of confusion and misunderstanding, between
the increment of value obtainable by using an additional quantity
of capital in the existing situation, and the series of
increments which it is expected to obtain over
the whole life
of
the additional capital asset;
¾
i.e.
the distinction between
Q
1
and the complete
series
Q
1
,
Q
2
, . . .
Q
r
, . . . .This
involves the whole question of the place of expectation in
economic theory. Most discussions of the marginal efficiency of
capital seem to pay no attention to any member of the series
except
Q
1
. Yet this cannot be legitimate except in a Static theory, for which all the
Q
's
are equal. The ordinary theory of distribution, where it is
assumed that capital is getting
now
its marginal
productivity (in some sense or other), is only valid in a
stationary state. The aggregate current return to capital has no
direct relationship to its marginal efficiency; whilst its
current return at the margin of production (i.e. the return to
capital which enters into the supply price of output) is its
marginal user cost, which also has no close connection with its
marginal efficiency.
There is, as I have said above, a remarkable lack of any clear
account of the matter. At the same time I believe that the
definition which I have given above is fairly close to what
Marshall intended to mean by the term. The phrase which Marshall
himself uses is 'marginal net efficiency' of a factor of
production; or, alternatively, the 'marginal utility of capital'.
The following is a summary of the most relevant passage which I
can find in his
Principles
(6th ed. pp. 519
-
520). I have run together some
non-consecutive sentences to convey the gist of what he says:
In a certain factory an extra £100 worth of machinery can be
applied so as not to involve any other extra expense, and so as
to add annually £3 worth to the net output of the factory after
allowing for its own wear and tear. If the investors of capital
push it into every occupation in which it seems likely to gain a
high reward; and if, after this has been done and equilibrium has
been found, it still pays and only just pays to employ this
machinery, we can infer from this fact that the yearly rate of
interest is 3 per cent. But illustrations of this kind merely
indicate part of the action of the great causes which govern
value. They cannot be made into a theory of interest, any more
than into a theory of wages, without reasoning in a
circle. . . Suppose that the rate of interest is 3 per
cent. per annum on perfectly good security; and that the
hat-making trade absorbs a capital of one million pounds. This
implies that the hat-making trade can turn the whole million
pounds' worth of capital to so good account that they would pay 3
per cent. per annum net for the use of it rather than go without any of it. There may be
machinery which the trade would have refused to dispense with if
the rate of interest had been 20 per cent. per annum. If the rate
had been 10 per cent., more would have been used; if it had been
6 per cent., still more; if 4 per cent. still more; and finally,
the rate being 3 per cent., they use more still. When they have
this amount, the marginal utility of the machinery, i.e. the
utility of that machinery which it is only just worth their while
to employ, is measured by 3 per cent.
It is evident from the above that Marshall was well aware that
we are involved in a circular argument if we try to determine
along these lines what the rate of interest actually
is. In this passage he appears to accept the view set forth above,
that the rate of interest determines the point to which new
investment will be pushed, given the schedule of the marginal
efficiency of capital. If the rate of interest is 3 per cent,
this means that no one will pay £100 for a machine unless he
hopes thereby to add £3 to his annual net output after allowing
for costs and depreciation. But we shall see in chapter 14 that
in other passages Marshall was less cautious
¾
though
still drawing back when his argument was leading him on to
dubious ground.
Although he does not call it the 'marginal efficiency of
capital', Professor Irving Fisher has given in his
Theory of
Interest
(1930) a definition of what he calls 'the rate of
return over cost' which is identical with my definition. 'The
rate of return over cost', he writes, 'is that rate which, employed in computing the present worth of
all the costs and the present worth of all the returns, will make
these two equal.' Professor Fisher explains that the extent of
investment in any direction will depend on a comparison between
the rate of return over cost and the rate of interest. To induce
new investment 'the rate of return over cost must exceed the rate of interest'.
'This new magnitude (or factor) in our study plays the central
rôle on the investment opportunity side of interest
theory.' Thus Professor Fisher uses his 'rate of return over cost in the
same sense and for precisely the same purpose as I employ 'the
marginal efficiency of capital'.
III
The most important confusion concerning the meaning and
significance of the marginal efficiency of capital has ensued on
the failure to see that it depends on the
prospective
yield
of capital, and not merely on its current yield. This can be best
illustrated by pointing out the effect on the marginal efficiency
of capital of an expectation of changes in the prospective cost
of production, whether these changes are expected to come from
changes in labour cost, i.e. in the wage-unit, or from inventions
and new technique. The output from equipment produced to-day will
have to compete, in the course of its life, with the output from
equipment produced subsequently, perhaps at a lower labour cost,
perhaps by an improved technique, which is content with a lower
price for its output and will be increased in quantity until the
price of its output has fallen to the lower figure with which it
is content. Moreover, the entrepreneur's profit (in terms of
money) from equipment, old or new, will be reduced, if all output
comes to be produced more cheaply. In so far as such developments
are foreseen as probable, or even as possible, the marginal
efficiency of capital produced to-day is appropriately
diminished.
This is the factor through which the expectation of changes in
the value of money influences the volume of current output. The
expectation of a fall in the value of money stimulates
investment, and hence employment generally, because it raises the
schedule of the marginal efficiency of capital, i.e. the investment
demand-schedule; and the expectation of a rise in the value of
money is depressing, because it lowers the schedule of the
marginal efficiency of capital.
This is the truth which lies behind Professor Irving Fisher's
theory of what he originally called 'Appreciation and Interest'
¾
the distinction between the money rate of
interest and the real rate of interest where the latter is equal
to the former after correction for changes in the value of money.
It is difficult to make sense of this theory as stated, because
it is not clear whether the change in the value of money is or is
not assumed to be foreseen. There is no escape from the dilemma
that, if it is not foreseen, there will be no effect on current
affairs; whilst, if it is foreseen, the prices of existing goods
will be forthwith so adjusted that the advantages of holding
money and of holding goods are again equalised, and it will be
too late for holders of money to gain or to suffer a change in
the rate of interest which will offset the prospective change
during the period of the loan in the value of the money lent. For
the dilemma is not successfully escaped by Professor Pigou's
expedient of supposing that the prospective change in the value
of money is foreseen by one set of people but not foreseen by
another.
The mistake lies in supposing that it is the rate of interest
on which prospective changes in the value of money will directly
react, instead of the marginal efficiency of a given stock of
capital. The prices of
existing
assets will always adjust
themselves to changes in expectation concerning the prospective
value of money. The significance of such changes in expectation
lies in their effect on the readiness to produce
new
assets
through their reaction on the marginal efficiency of capital. The
stimulating effect of the expectation of higher prices is due,
not to its raising the rate of interest (that would be a
paradoxical way of stimulating output
¾
in
so far as the rate of interest rises, the stimulating effect is to that extent offset), but to its
raising the marginal efficiency of a given stock of capital.
If
the rate of interest were to rise
pari passu
with the
marginal efficiency of capital, there would be no stimulating
effect from the expectation of rising prices. For the stimulus to
output depends on the marginal efficiency of a given stock of
capital rising
relatively
to the rate of interest. Indeed
Professor Fisher's theory could be best re-written in terms of a
'real rate of interest' defined as being the rate of interest
which would have to rule, consequently on a change in the state
of expectation as to the future value of money, in order that
this change should have no effect on current output.
It is worth noting that an expectation of a future fall in the
rate of interest will have the effect of
lowering
the
schedule of the marginal efficiency of capital; since it means
that the output from equipment produced to-day will have to
compete during part of its life with the output from equipment
which is content with a lower return. This expectation will have
no great depressing effect, since the expectations, which are
held concerning the complex of rates of interest for various
terms which will rule in the future, will be partially reflected
in the complex of rates of interest which rule to-day.
Nevertheless there may be some depressing effect, since the
output from equipment produced to-day, which will emerge towards
the end of the life of this equipment, may have to compete with
the output of much younger equipment which is content with a
lower return because of the lower rate of interest which rules
for periods subsequent to the end of the life of equipment
produced to-day.
It is important to understand the dependence of the marginal
efficiency of a given stock of capital on changes in expectation,
because it is chiefly this dependence which renders the marginal efficiency of capital subject
to the somewhat violent fluctuations which are the explanation of
the trade cycle. In chapter 22 below we shall show that the
succession of boom and slump can be described and analysed in
terms of the fluctuations of the marginal efficiency of capital
relatively to the rate of interest.
IV
Two types of risk affect the volume of investment which have
not commonly been distinguished, but which it is important to
distinguish. The first is the entrepreneur's or borrower's risk
and arises out of doubts in his own mind as to the probability of
his actually earning the prospective yield for which he hopes. If
a man is venturing his own money, this is the only risk which is
relevant.
But where a system of borrowing and lending exists, by which I
mean the ranting of loans with a margin of real or personal
security, a second type of risk is relevant which we may call the
lender's risk. This may be due either to moral hazard, i.e.
voluntary default or other means of escape, possibly lawful, from
the fulfilment of the obligation, or to the possible
insufficiency of the margin of security, i.e. involuntary default
due to the disappointment of expectation. A third source of risk
might be added, namely, a possible adverse change in the value of
the monetary standard which renders a money-loan to this extent
less secure than a real asset; though all or most of this should
be already reflected, and therefore absorbed, in the price of
durable real assets.
Now the first type of risk is, in a sense, a real social cost,
though susceptible to diminution by averaging as well as by an
increased accuracy of foresight. The second, however, is a pure
addition to the cost of investment which would not exist if the
borrower and lender were the same person. Moreover, it involves
in part a duplication of a proportion of the entrepreneur's risk,
which is added
twice
to the pure rate of interest to give
the minimum prospective yield which will induce the investment.
For if a venture is a risky one, the borrower will require a
wider margin between his expectation of yield and the rate of
interest at which he will think it worth his while to borrow;
whilst the very same reason will lead the lender to require a
wider margin between what he charges and the pure rate of
interest in order to induce him to lend (except where the
borrower is so strong and wealthy that he is in a position to
offer an exceptional margin of security). The hope of a very
favourable outcome, which may balance the risk in the mind of the
borrower, is not available to solace the lender.
This duplication of allowance for a portion of the risk has
not hitherto been emphasised, so far as I am aware; but it may be
important in certain circumstances. During a boom the popular
estimation of the magnitude of both these risks, both borrower's
risk and lender's risk, is apt to become unusually and
imprudently low.
V
The schedule of the marginal efficiency of capital is of
fundamental importance because it is mainly through this factor
(much more than through the rate of interest) that the
expectation of the future influences the present. The mistake of
regarding the marginal efficiency of capital primarily in terms
of the
current
yield of capital equipment, which would be
correct only in the static state where there is no changing
future to influence the present, has had the result of breaking
the theoretical link between to-day and to-morrow. Even the rate
of interest is, virtually, a
current
phenomenon; and if we reduce the marginal
efficiency of capital to the same status, we cut ourselves off
from taking any direct account of the influence of the future in
our analysis of the existing equilibrium.
The fact that the assumptions of the static state often
underlie present-day economic theory, imports into it a large
element of unreality. But the introduction of the concepts of
user cost and of the marginal efficiency of capital, as defined
above, will have the effect, I think, of bringing it back to
reality, whilst reducing to a minimum the necessary degree of
adaptation.
It is by reason of the existence of durable equipment that the
economic future is linked to the present. It is, therefore,
consonant with, and agreeable to, our broad principles of
thought, that the expectation of the future should affect the
present through the demand price for durable equipment.