THE MARGINAL EFFICIENCY OF CAPITAL
When a man buys an investment or capital-asset or looks for some expert to do this for him via a job search web site, 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 Q1 ,
Q2 , . . . 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
Qr is the prospective yield from an
asset at time r , and dr is
the present value of ?1 deferred r years at the current
rate of interest,?Qrdr
is the demand price of the investment; and investment will be
carried to the point where
?Qrdr
becomes equal to the supply price of the investment as defined
above. If, on the other hand,
?Qrdr
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.
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; - i.e. the distinction between
Q1 and the complete series
Q1 , Q2
, . . . Qr
, . . . .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 Q1 . 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 - 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 r?le 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'.