Chapter 6
THE DEFINITION OF INCOME, SAVING AND INVESTMENT
I. Income
During any period of time an entrepreneur will have sold
finished output to consumers or to other entrepreneurs for a
certain sum which we will designate as A. He will also
have spent a certain sum, designated by A1, on
purchasing finished output from other entrepreneurs. And he will
end up with a capital equipment, which term includes both his
stocks of unfinished goods or working capital and his stocks of
finished goods, having a value G.
Some part, however, of A + G - A1 will be
attributable, not to the activities of the period in question,
but to the capital equipment which he had at the beginning of the
period. We must, therefore, in order to arrive at what we mean by
the income of the current period, deduct from A + G - A1 a certain sum,
to represent that part of its value which has been (in some
sense) contributed by the equipment inherited from the previous
period. The problem of defining income is solved as soon as we
have found a satisfactory method for calculating this deduction.
There are two possible principles for calculating it, each of
which has a certain significance;¾one
of them in connection with production, and the other in
connection with consumption. Let us consider them in turn.
(i) The actual value G of the capital
equipment at the end of the period is the net result of the entrepreneur,
on the one hand, having maintained and improved it during the
period, both by purchases from other entrepreneurs and by work
done upon it by himself, and, on the other hand, having exhausted
or depreciated it through using it to produce output. If he had
decided not to use it to produce output, there is,
nevertheless, a certain optimum sum which it would have paid him
to spend on maintaining and improving it. Let us suppose that, in
this event, he would have spent B' on its maintenance and
improvement, and that, having had this spent on it, it would have
been worth G' at the end of the period. That is to say, G' - B' is the maximum net value
which might have been conserved from the previous period, if it
had not been used to produce A. The excess of this
potential value of the equipment over G - A1 is the measure
of what has been sacrificed (one way or another) to produce A.
Let us call this quantity, namely
(G' - B') - (G - A1),
which measures the sacrifice of value involved in the
production of A, the user cost of A. User
cost will be written U.
The amount paid out by the entrepreneur to the other factors of
production in return for their services, which from their point
of view is their income, we will call the factor cost of A.
The sum of the factor cost F and the user cost U we
shall call the prime cost of the output A.
We can then define the income
of the entrepreneur as being the excess of the value of his
finished output sold during the period over his prime cost. The
entrepreneur's income, that is to say, is taken as being equal to
the quantity, depending on his scale of production, which he
endeavours to maximise, i.e. to his gross profit in the ordinary sense of this term;¾which
agrees with common sense. Hence, since the income of the rest of
the community is equal to the entrepreneur's factor cost,
aggregate income is equal to A - U.
Income, thus defined, is a completely unambiguous quantity.
Moreover, since it is the entrepreneur's expectation of the
excess of this quantity over his outgoings to the other factors
of production which he endeavours to maximise when he decides how
much employment to give to the other factors of production, it is
the quantity which is causally significant for employment.
It is conceivable, of course, that G - A1 may exceed G' - B', so that user cost will be
negative. For example, this may well be the case if we happen to
choose our period in such a way that input has been increasing
during the period but without there having been time for the
increased output to reach the stage of being finished and sold.
It will also be the case, whenever there is positive investment,
if we imagine industry to be so much integrated that
entrepreneurs make most of their equipment for themselves. Since,
however, user cost is only negative when the entrepreneur has
been increasing his capital equipment by his own labour, we can,
in an economy where capital equipment is largely manufactured by
different firms from those which use it, normally think of user
cost as being positive. Moreover, it is difficult to conceive of
a case where marginal user cost associated with an
increase in A, i.e. dU/dA, will be other than positive.
It may be convenient to mention here, in anticipation of the
latter part of this chapter, that, for the community as a whole,
the aggregate consumption (C) of the period is
equal to S(A - A1), and the
aggregate investment (I) is equal to S(A1 - U). Moreover, U is the
individual entrepreneur's disinvestment (and - U
his investment) in respect of his own equipment exclusive of what he buys from other entrepreneurs. Thus in a completely
integrated system (where A1 = 0)
consumption is equal to A and investment to - U, i.e. to G - (G' - B').
The slight complication of the above, through the introduction of
A1, is simply due to the desirability of
providing in a generalised way for the case of a non-integrated
system of production.
Furthermore, the effective demand is simply the
aggregate income (or proceeds) which the entrepreneurs expect to
receive, inclusive of the incomes which they will hand on to the
other factors of production, from the amount of current
employment which they decide to give. The aggregate demand
function relates various hypothetical quantities of employment to
the proceeds which their outputs are expected to yield; and the
effective demand is the point on the aggregate demand function
which becomes effective because, taken in conjunction with the
conditions of supply, it corresponds to the level of employment
which maximises the entrepreneur's expectation of profit.
This set of definitions also has the advantage that we can
equate the marginal proceeds (or income) to the marginal factor
cost; and thus arrive at the same sort of propositions relating
marginal proceeds thus defined to marginal factor costs as have
been stated by those economists who, by ignoring user cost or
assuming it to be zero, have equated supply price
to marginal factor cost.
(ii) We turn, next, to the second of the principles referred
to above. We have dealt so far with that part of the change in
the value of the capital equipment at the end of the period as
compared with its value at the beginning which is due to the voluntary
decisions of the entrepreneur in seeking to maximise his
profit. But there may, in addition, be an involuntary loss
(or gain) in the value of his capital equipment, occurring for
reasons beyond his control and irrespective of his current
decisions, on account of (e.g.) a change in market values,
wastage by obsolescence or the mere passage of time, or
destruction by catastrophe such as war or earthquake. Now some
part of these involuntary losses, whilst they are unavoidable,
are¾broadly speaking¾not unexpected; such as losses through the
lapse of time irrespective of use, and also 'normal' obsolescence
which, as Professor Pigou expresses it, 'is sufficiently regular
to be foreseen, if not in detail, at least in the large',
including, we may add, those losses to the community as a whole
which are sufficiently regular to be commonly regarded as
'insurable risks'. Let us ignore for the moment the fact that the
amount of the expected loss depends on when the expectation is
assumed to be framed, and let us call the depreciation of the
equipment, which is involuntary but not unexpected, i.e. the
excess of the expected depreciation over the user cost, the supplementary
cost, which will be written V. It is, perhaps, hardly
necessary to point out that this definition is not the same as
Marshall's definition of supplementary cost, though the
underlying idea, namely, of dealing with that part of the
expected depreciation which does not enter into prime cost, is
similar.
In reckoning, therefore, the net income and the net
profit of the entrepreneur it is usual to deduct the
estimated amount of the supplementary cost from his income and
gross profit as defined above. For the psychological effect on
the entrepreneur, when he is considering what he is free to spend
and to save, of the supplementary cost is virtually the same as
though it came off his gross profit. In his capacity as a producer
deciding whether or not to use the equipment, prime cost and
gross profit, as defined above, are the significant concepts. But
in his capacity as a consumer the amount of the
supplementary cost works on his mind in the same way as if it
were a part of the prime cost. Hence we shall not only come
nearest to common usage but will also arrive at a concept which
is relevant to the amount of consumption, if, in defining
aggregate net income, we deduct the supplementary cost as well as
the user cost, so that aggregate net income is equal to A - U - V.
There remains the change in the value of the equipment, due to
unforeseen changes in market values, exceptional obsolescence or
destruction by catastrophe, which is both involuntary and¾in a broad sense¾unforeseen.
The actual loss under this head, which we disregard even in
reckoning net income and charge to capital account, may be called
the windfall loss.
The causal significance of net income lies in the
psychological influence of the magnitude of V on the
amount of current consumption, since net income is what we
suppose the ordinary man to reckon his available income to be
when he is deciding how much to spend on current consumption.
This is not, of course, the only factor of which he takes account
when he is deciding how much to spend. It makes a considerable
difference, for example, how much windfall gain or loss he is
making on capital account. But there is a difference between the
supplementary cost and a windfall loss in that changes in the
former are apt to affect him in just the same way as changes in his gross profit. It is
the excess of the proceeds of the current output over the sum of
the prime cost and the supplementary cost which is relevant to
the entrepreneur's consumption; whereas, although the windfall
loss (or gain) enters into his decisions, it does not enter into
them on the same scale¾a given
windfall loss does not have the same effect as an equal
supplementary cost.
We must now recur, however, to the point that the line between
supplementary costs and windfall losses, i.e. between those
unavoidable losses which we think it proper to debit to income
account and those which it is reasonable to reckon as a windfall
loss (or gain) on capital account, is partly a conventional or
psychological one, depending on what are the commonly accepted
criteria for estimating the former. For no unique principle can
be established for the estimation of supplementary cost, and its
amount will depend on our choice of an accounting method. The
expected value of the supplementary cost, when the equipment was
originally produced, is a definite quantity. But if it is
re-estimated subsequently, its amount over the remainder of the
life of the equipment may have changed as a result of a change in
the meantime in our expectations; the windfall capital loss being
the discounted value of the difference between the former and the
revised expectation of the prospective series of U + V.
It is a widely approved principle of business accounting,
endorsed by the Inland Revenue authorities, to establish a figure
for the sum of the supplementary cost and the user cost when the
equipment is acquired and to maintain this unaltered during the
life of the equipment, irrespective of subsequent changes in
expectation. In this case the supplementary cost over any period
must be taken as the excess of this predetermined figure over the
actual user cost. This has the advantage of ensuring that the
windfall gain or loss shall be zero over the life of the equipment taken as a whole. But it is also reasonable in
certain circumstances to recalculate the allowance for
supplementary cost on the basis of current values and
expectations at an arbitrary accounting interval, e.g. annually.
Business men in fact differ as to which course they adopt. It may
be convenient to call the initial expectation of supplementary
cost when the equipment is first acquired the basic
supplementary cost, and the same quantity recalculated up to
date on the basis of current values and expectations the current
supplementary cost.
Thus we cannot get closer to a quantitative definition of
supplementary cost than that it comprises those deductions from
his income which a typical entrepreneur makes before reckoning
what he considers his net income for the purpose of declaring a
dividend (in the case of a corporation) or of deciding the scale
of his current consumption (in the case of an individual). Since
windfall charges on capital account are not going to be ruled out
of the picture, it is clearly better, in case of doubt, to assign
an item to capital account, and to include in supplementary cost
only what rather obviously belongs there. For any overloading of
the former can be corrected by allowing it more influence on the
rate of current consumption than it would otherwise have had.
It will be seen that our definition of net income comes very
close to Marshall's definition of income, when he decided to take
refuge in the practices of the Income Tax Commissioners and¾broadly speaking to regard as income
whatever they, with their experience, choose to treat as such.
For the fabric of their decisions can be regarded as the result
of the most careful and extensive investigation which is
available, to interpret what, in practice, it is usual to treat
as net income. It also corresponds to the money value of
Professor Pigou's most recent definition of the national
dividend.
It remains true, however, that net income, being based on an
equivocal criterion which different authorities might interpret
differently, is not perfectly clear-cut. Professor Hayek, for
example, has suggested that an individual owner of capital goods
might aim at keeping the income he derives from his possessions
constant, so that he would not feel himself free to spend his
income on consumption until he had set aside sufficient to offset
any tendency of his investment-income to decline for whatever
reason.
I doubt if such an individual exists; but, obviously, no
theoretical objection can be raised against this deduction as
providing a possible psychological criterion of net income. But
when Professor Hayek infers that the concepts of saving and
investment suffer from a corresponding vagueness, he is only
right if he means net saving and net investment.
The saving and the investment, which are relevant to the theory
of employment, are clear of this defect, and are capable of
objective definition, as we have shown above.
Thus it is a mistake to put all the emphasis on net income,
which is only relevant to decisions concerning consumption, and
is, moreover, only separated from various other factors affecting
consumption by a narrow line; and to overlook (as has been usual)
the concept of income proper, which is the concept
relevant to decisions concerning current production and is quite
unambiguous.
The above definitions of income and of net income are intended
to conform as closely as possible to common usage. It is
necessary, therefore, that I should at once remind the reader
that in my Treatise on Money I defined income in a special
sense. The peculiarity in my former definition related to that
part of aggregate income which accrues to the entrepreneurs,
since I took neither the profit (whether gross or net) actually
realised from their current operations nor the profit which they
expected when they decided to undertake their current operations, but in some sense (not, as I
now think, sufficiently defined if we allow for the possibility
of changes in the scale of output) a normal or equilibrium
profit; with the result that on this definition saving exceeded
investment by the amount of the excess of normal profit over the
actual profit. I am afraid that this use of terms has caused
considerable confusion, especially in the case of the correlative
use of saving; since conclusions (relating, in particular, to the
excess of saving over investment), which were only valid if the
terms employed were interpreted in my special sense, have been
frequently adopted in popular discussion as though the terms were
being employed in their more familiar sense. For this reason, and
also because I no longer require my former terms to express my
ideas accurately, I have decided to discard them¾with much regret for the confusion which
they have caused.
II. Saving and Investment
Amidst the welter of divergent usages of terms, it is
agreeable to discover one fixed point. So far as I know, everyone
is agreed that saving means the excess of income over
expenditure on consumption. Thus any doubts about the meaning of
saving must arise from doubts about the meaning either of income
or of consumption. Income we have defined
above. Expenditure on consumption during any period must mean the
value of goods sold to consumers during that period, which throws
us back to the question of what is meant by a consumer-purchaser.
Any reasonable definition of the line between consumer-purchasers
and investor-purchasers will serve us equally well, provided that
it is consistently applied. Such problem as there is, e.g.
whether it is right to regard the purchase of a motor-car as a
consumer-purchase and the purchase of a house as an
investor-purchase, has been frequently discussed and I have
nothing material to add to the discussion.
The criterion must obviously correspond to where we draw the
line between the consumer and the entrepreneur. Thus when we have
defined A1 as the value of what one
entrepreneur has purchased from another, we have implicitly
settled the question. It follows that expenditure on consumption
can be unambiguously defined as S(A - A1), where A
is the total sales made during the period and A1
is the total sales made by one entrepreneur to another. In what
follows it will be convenient, as a rule, to omit and write A
for the aggregate sales of all kinds, A1 for
the aggregate sales from one entrepreneur to another and U
for the aggregate user costs of the entrepreneurs.
Having now defined both income and consumption,
the definition of saving, which is the excess of income
over consumption, naturally follows. Since income is equal to A - U and consumption is equal to A - A1, it follows that
saving is equal to A1 - U.
Similarly, we have net saving for the excess of net
income over consumption, equal to A1 - U - V.
Our definition of income also leads at once to the definition
of current investment. For we must mean by this the
current addition to the value of the capital equipment which has
resulted from the productive activity of the period. This is,
clearly, equal to what we have just defined as saving. For it is
that part of the income of the period which has not passed into
consumption. We have seen above that as the result of the
production of any period entrepreneurs end up with having sold
finished output having a value A and with a capital equipment
which has suffered a deterioration measured by U (or an
improvement measured by - U
where U is negative) as a result of having produced and
parted with A, after allowing for purchases A1
from other entrepreneurs. During the same period finished output
having a value A - A1
will have passed into consumption. The excess of A - U over A - A1, namely A1 - U, is the addition to capital equipment as a result of the productive activities of the
period and is, therefore, the investment of the period.
Similarly A1 - U - V; which is the net addition
to capital equipment, after allowing for normal impairment in the
value of capital apart from its being used and apart from
windfall changes in the value of the equipment chargeable to
capital account, is the net investment of the period.
Whilst, therefore, the amount of saving is an outcome of the
collective behaviour of individual consumers and the amount of
investment of the collective behaviour of individual
entrepreneurs, these two amounts are necessarily equal, since
each of them is equal to the excess of income over consumption.
Moreover, this conclusion in no way depends on any subtleties or
peculiarities in the definition of income given above. Provided
it is agreed that income is equal to the value of current output,
that current investment is equal to the value of that part of
current output which is not consumed, and that saving is equal to
the excess of income over consumption¾all
of which is conformable both to common sense and to the
traditional usage of the great majority of economists¾the equality of saving and investment
necessarily follows. In short-
Income = value of
output = consumption + investment.
Saving = income - consumption.
Therefore saving = investment.
Thus any set of definitions which satisfy the above conditions
leads to the same conclusion. It is only by denying the validity
of one or other of them that the conclusion can be avoided.
The equivalence between the quantity of saving and the
quantity of investment emerges from the bilateral character of
the transactions between the producer on the one hand and, on the
other hand, the consumer or the purchaser of capital equipment.
Income is created by the value in excess of user cost which
the producer obtains for the output he has sold; but the whole of
this output must obviously have been sold either to a consumer or
to another entrepreneur; and each entrepreneur's current
investment is equal to the excess of the equipment which he has
purchased from other entrepreneurs over his own user cost. Hence,
in the aggregate the excess of income over consumption, which we
call saving, cannot differ from the addition to capital equipment
which we call investment. And similarly with net saving and net
investment. Saving, in fact, is a mere residual. The decisions to
consume and the decisions to invest between them determine
incomes. Assuming that the decisions to invest become effective,
they must in doing so either curtail consumption or expand
income. Thus the act of investment in itself cannot help causing
the residual or margin, which we call saving, to increase by a
corresponding amount.
It might be, of course, that individuals were so tête
montée in their decisions as to how much they themselves
would save and invest respectively, that there would be no point
of price equilibrium at which transactions could take place. In
this case our terms would cease to be applicable, since output
would no longer have a definite market value, prices would find
no resting-place between zero and infinity. Experience shows,
however, that this, in fact, is not so; and that there are habits
of psychological response which allow of an equilibrium being
reached at which the readiness to buy is equal to the readiness
to sell. That there should be such a thing as a market value for
output is, at the same time, a necessary condition for
money-income to possess a definite value and a sufficient
condition for the aggregate amount which saving individuals
decide to save to be equal to the aggregate amount which
investing individuals decide to invest.
Clearness of mind on this matter is best reached, perhaps, by thinking in terms of decisions to consume (or to
refrain from consuming) rather than of decisions to save. A
decision to consume or not to consume truly lies within the power
of the individual; so does a decision to invest or not to invest.
The amounts of aggregate income and of aggregate saving are the results
of the free choices of individuals whether or not to consume
and whether or not to invest; but they are neither of them
capable of assuming an independent value resulting from a
separate set of decisions taken irrespective of the decisions
concerning consumption and investment. In accordance with this
principle, the conception of the propensity to consume will,
in what follows, take the place of the propensity or disposition
to save.