[p.52]
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 [p.53]
he 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. [1]
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[2]
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 [p.54]
in the ordinary sense of this term; ¾ which 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 [p.55] 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 [1]
to marginal factor cost.[2] [p.56]
(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. [p.57]
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 [p.58] 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 [p.59]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.[1] [p.60]
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 [RES] 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.[1] 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 under-[p.61]take
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.[p.62] 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 SA is the total sales made during the
period and SA1 is the total sales
made by one entrepreneur to another. In what follows it will be convenient, as a
rule, to omit S 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 [p.63]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. [p.64] 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,[p.65] 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.
Footnotes: [p. 53] 1 -
Some further observations on user cost are given in an appendix
to this chapter. [back to text]
[p. 53] 2 - As distinguished from
his net income which we shall define below. [back to text]
[p. 55] 1 - Supply price is, I
think, an incompletely defined term, if the problem of defining user cost has
been ignored. The matter is further discussed in the appendix
to this chapter, where I argue that the exclusion of user cost from supply
price, whilst sometimes appropriate in the case of aggregate supply price, is
inappropriate to the problems of the supply price of a unit of output for an
individual firm. [back to text]
[p. 55] 2 - For example, let us
take Zw= f(N), or
alternatively Z = W·f(N) as the
aggregate supply function (where W is the wage-unit and W·Zw
=
Z). Then, since the proceeds of the marginal product is equal to
the marginal factor-cost at every point on the aggregate supply curve, we have
DN = DAw
= DUw = DZw
= Df(N)
that is to say f´(N) = 1; provided that
factor cost bears a constant ratio to wage cost, and that the aggregate supply
function for each firm (the number [p.55] of which is assumed to be
constant) is independent of the number of men employed in other industries, so
that the terms of the above equation, which hold good for each individual
entrepreneur, can be summed for the entrepreneurs as a awhole. This means
that, if wages are constant and other factor costs are a constant proportion of
the wages-bill, the aggregate supply function is linear with a slope given by
the reciprocal of the money-wage. [back to text]
[p. 59] 1 - Economic Journal,
June 1935, p.235. [back to text]
[p. 60] 1 - "The Maintenance of
Capital", Economica, August 1935, p.241 et seq. [back to text]
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