[p.66]
APPENDIX ON USER COST
I
User cost has, I think, an importance for the classical theory
of value which has been overlooked. There is more to be said
about it than would be relevant or appropriate in this place.
But, as a digression, we will examine it somewhat further in this
appendix.
An entrepreneur's user cost is by definition equal to
A1 + (G' - B') - G,
where A1 is the amount of our entrepreneur's
purchases from other entrepreneurs, G the actual value of
his capital equipment at the end of the period, and G' the
value it might have had at the end of the period if he had
refrained from using it and had spent the optimum sum B'
on its maintenance and improvement. Now G - (G' - B'),
namely the increment in the value of the entrepreneur's equipment
beyond the net value which he has inherited from the previous
period, represents the entrepreneur's current investment in his
equipment and can be written I. Thus U, the user
cost of his sales-turnover A, is equal to A1 - I where A1 is
what he has bought from other entrepreneurs and I is what
he has currently invested in his own equipment. A little
reflection will show that all this is no more than common sense.
Some part of his outgoings to other entrepreneurs is balanced by
the value of his current investment in his own equipment, and the
rest represents the sacrifice which the output he has sold must
have cost him over and above the total sum which he has paid out
to the factors of production. If the reader tries to express the
substance of this otherwise, he will find that its advantage lies
in its avoidance of insoluble (and unnecessary) accounting
problems. There is, I think, no other way of analysing the
current proceeds of production unambiguously. If industry is
completely integrated or if the entrepreneur has bought nothing
from outside, so that A1 = 0,
the [p.67] user cost is simply the equivalent of the current
disinvestment involved in using the equipment; but we are still
left with the advantage that we do not require at any stage of
the analysis to allocate the factor cost between the goods which
are sold and the equipment which is retained. Thus we can regard
the employment given by a firm, whether integrated or individual,
as depending on a single consolidated decision¾a
procedure which corresponds to the actual interlocking character
of the production of what is currently sold with total
production.
The concept of user cost enables us, moreover, to give a
clearer definition than that usually adopted of the short-period
supply price of a unit of a firm's saleable output. For the
short-period supply price is the sum of the marginal factor cost
and the marginal user cost.
Now in the modern theory of value it has been a usual practice
to equate the short-period supply price to the marginal factor
cost alone. It is obvious, however, that this is only legitimate
if marginal user cost is zero or if supply price is specially
defined so as to be net of marginal user cost, just as I have
defined (p. 24 above) "proceeds" and "aggregate supply
price" as
being net of aggregate user cost. But, whereas it may be
occasionally convenient in dealing with output as a whole to
deduct user cost, this procedure deprives our analysis of all reality if it is habitually (and tacitly) applied to the
output of a single industry or firm, since it divorces the "supply price" of an article from any ordinary sense of its
"price"; and some confusion may have resulted from the practice
of doing so. It seems to have been assumed that "supply price"
has an obvious meaning as applied to a unit of the saleable
output of an individual firm, and the matter has not been deemed
to require discussion. Yet the treatment both of what is
purchased from other firms and of the wastage of the firm's own
equipment as a consequence of producing the marginal output
involves the whole pack of perplexities which attend the
definition of income. For, even if we assume that the marginal
cost of purchases from other firms involved in selling an
additional unit of output has to be deducted from the
sale-proceeds per unit in order to give us what we mean by our
firm's supply price, we still have to allow for the marginal
disinvestment in the firm's own equipment involved in producing
the marginal output. Even if all production is carried on by a
completely integrated firm, it is still illegitimate to suppose
that the marginal user cost is zero, i.e. that the marginal
disinvestment in equipment due to the production of the marginal
output can generally be neglected. [p.68]
The concepts of user cost and of supplementary cost also
enable us to establish a clearer relationship between long-period
supply price and short-period supply price. Long-period cost must
obviously include an amount to cover the basic supplementary cost
as well as the expected prime cost appropriately averaged over
the life of the equipment. That is to say, the long-period cost
of the output is equal to the expected sum of the prime cost and
the supplementary cost; and, furthermore, in order to yield a
normal profit, the long-period supply price must exceed the
long-period cost thus calculated by an amount determined by the
current rate of interest on loans of comparable term and risk,
reckoned as a percentage of the cost of the equipment. Or if we
prefer to take a standard "pure" rate of interest, we must
include in the long-period cost a third term which we might call
the risk-cost to cover the unknown possibilities of the
actual yield differing from the expected yield. Thus the
long-period supply price is equal to the sum of the prime cost,
the supplementary cost, the risk cost and the interest cost, into
which several components it can be analysed. The short-period
supply price, on the other hand, is equal to the marginal prime
cost. The entrepreneur must, therefore, expect, when he buys or
constructs his equipment, to cover his supplementary cost, his
risk cost and his interest cost out of the excess of the marginal
value of the prime cost over its average value; so that in
long-period equilibrium the excess of the marginal prime cost
over the average prime cost is equal to the sum of the
supplementary, risk and interest costs.[1]
The level of output, at which marginal prime cost is exactly
equal to the sum of the average prime and supplementary costs,
has a special importance, because it is the point at which the
entrepreneur's trading account breaks even. It corresponds, [p.69] that is to say, to the point of zero net profit; whilst with a
smaller output than this he is trading at a net loss.
The extent to which the supplementary cost has to be provided
for apart from the prime cost varies very much from one type of
equipment to another. Two extreme cases are the following:
(i) Some part of the maintenance of the equipment
must necessarily take place pari passu with the act of
using it (e.g. oiling the machine). The expense of this (apart
from outside purchases) is included in the factor cost. If, for
physical reasons, the exact amount of the whole of the current
depreciation has necessarily to be made good in this way, the
amount of the user cost (apart from outside purchases) would be
equal and opposite to that of the supplementary cost; and in
long-period equilibrium the marginal factor cost would exceed the
average factor cost by an amount equal to the risk and interest
cost.
(ii) Some part of the deterioration in the value of
the equipment only occurs if it is used. The cost of this is
charged in user cost, in so far as it is not made good pari
passu with the act of using it. If loss in the value of the
equipment could only occur in this way, supplementary cost would
be zero.
It may be worth pointing out that an entrepreneur does not use
his oldest and worst equipment first, merely because its user
cost is low; since its low user cost may be outweighed by its
relative inefficiency, i.e. by its high factor cost. Thus an
entrepreneur uses by preference that part of his equipment for
which the user cost plus factor cost is least per unit of
output.[1]
It follows that for any given volume of output of the product in
question there is a corresponding user cost,[2]
but that this total user cost does not bear a uniform relation to
the marginal user cost, i.e. to the increment of user cost due to
an increment in the rate of output.
II
User cost constitutes one of the links between the present and
the future. For in deciding his scale of production an [p.70] entrepreneur has to exercise a choice between using up his
equipment now and preserving it to be used later on. It is the
expected sacrifice of future benefit involved in present use
which determines the amount of the user cost, and it is the
marginal amount of this sacrifice which, together with the
marginal factor cost and the expectation of the marginal
proceeds, determines his scale of production. How, then, is the
user cost of an act of production calculated by the entrepreneur?
We have defined the user cost as the reduction in the value of
the equipment due to using it as compared with not using it,
after allowing for the cost of the maintenance and improvements
which it would be worth while to undertake and for purchases from
other entrepreneurs. It must be arrived at, therefore, by
calculating the discounted value of the additional prospective
yield which would be obtained at some later date if it were not
used now. Now this must be at least equal to the present value of
the opportunity to postpone replacement which will result from
laying up the equipment; and it may be more.[1]
If there is no surplus or redundant stock, so that more units
of similar equipment are being newly produced every year either
as an addition or in replacement, it is evident that marginal
user cost will be calculable by reference to the amount by which
the life or efficiency of the equipment will be shortened if it
is used, and the current replacement cost. If, however, there is
redundant equipment, then the user cost will also depend on the
rate of interest and the current (i.e. re-estimated)
supplementary cost over the period of time before the redundancy
is expected to be absorbed through wastage, etc. In this way
interest cost and current supplementary cost enter indirectly
into the calculation of user cost.
The calculation is exhibited in its simplest and most
intelligible form when the factor cost is zero, e.g. in the case
of a redundant stock of a raw material such as copper, on the
lines which I have worked out in my Treatise on Money,
vol. ii. chap. 29. Let us take the prospective values of copper
at various future dates, a series which will be governed by the
rate at which redundancy is being absorbed and gradually
approaches the [p.71] estimated normal cost. The present value or user
cost of a ton of surplus copper will then be equal to the
greatest of the values obtainable by subtracting from the
estimated future value at any given date of a ton of copper the interest cost and the
current supplementary cost on a ton of copper between that date
and the present.
In the same way the user cost of a ship or factory or machine,
when these equipments are in redundant supply, is its estimated
replacement cost discounted at the percentage rate of its
interest and current supplementary costs to the prospective date
of absorption of the redundancy.
We have assumed above that the equipment will be replaced in
due course by an identical article. If the equipment in question
will not be renewed identically when it is worn out, then its
user cost has to be calculated by taking a proportion of the user
cost of the new equipment, which will be erected to do its work
when it is discarded, given by its comparative efficiency.
III
The reader should notice that, where the equipment is not
obsolescent but merely redundant for the time being, the
difference between the actual user cost and its normal value (i.e. the value when there is no redundant equipment) varies with
the interval of time which is expected to elapse before the
redundancy is absorbed. Thus if the type of equipment in question
is of all ages and not "bunched", so that a fair proportion is
reaching the end of its life annually, the marginal user cost
will not decline greatly unless the redundancy is exceptionally
excessive. In the case of a general slump, marginal user cost
will depend on how long entrepreneurs expect the slump to last.
Thus the rise in the supply price when affairs begin to mend may
be partly due to a sharp increase in marginal user cost due to a
revision of their expectations.
It has sometimes been argued, contrary to the opinion of
business men, that organised schemes for scrapping redundant
plant cannot have the desired effect of raising prices unless
they apply to the whole of the redundant plant. But the
concept of user cost shows how the scrapping of (say) half the
redundant plant may have the effect of raising prices
immediately. For by bringing the date of the absorption of the
redundancy nearer, this policy raises marginal user cost and
consequently increases the current supply price. Thus business
men would seem to [p.72] have the notion of user cost implicitly in
mind, though they do not formulate it distinctly.
If the
supplementary cost is heavy, it follows that the marginal user
cost will be low when there is surplus equipment. Moreover, when there is surplus equipment, the marginal factor and user
costs are unlikely to be much in excess of their average value.
If both these conditions are fulfilled, the existence of surplus
equipment is likely to lead to the entrepreneur's working at a
net loss, and perhaps at a heavy net loss. There will not be a
sudden transition from this state of affairs to a normal profit,
taking place at the moment when the redundancy is absorbed. As
the redundancy becomes less, the user cost will gradually
increase; and the excess of marginal over average factor and user
cost may also gradually increase.
IV
In Marshall's Principles of Economics (6th ed. p.360) a
part of user cost is included in prime cost under the heading of "extra wear-and-tear of
plant". But no guidance is given as to
how this item is to be calculated or as to its importance. In his
Theory of Unemployment (p.42) Professor Pigou expressly
assumes that the marginal disinvestment in equipment due to the
marginal output can, in general, be neglected: "The differences
in the quantity of wear-and-tear suffered by equipment and in the
costs of non-manual labour employed, that are associated with
differences in output, are ignored, as being, in general, of
secondary importance".[1]
Indeed, the notion that the disinvestment in equipment is zero at
the margin of production runs through a good deal of recent
economic theory. But the whole problem is brought to an obvious
head as soon as it is thought necessary to explain exactly what
is meant by the supply price of an individual firm.
It is true that the cost of maintenance of idle plant may
often, for the reasons given above, reduce the magnitude of
marginal user cost, especially in a slump which is expected to
last a long time. Nevertheless a very low user cost at the margin
is not a characteristic of the short period as such, but of
particular situations and types of equipment where the cost of
maintaining [p.73] idle plant happens to be heavy, and of those
disequilibria which are characterised by very rapid obsolescence
or great redundancy, especially if it is coupled with a large
proportion of comparatively new plant.
In the case of raw materials the necessity of allowing for
user cost is obvious;¾if a ton of
copper is used up to-day it cannot be used to-morrow, and the value which the copper would have for
the purposes of to-morrow must clearly he reckoned as a part of
the marginal cost. But the fact has been overlooked that copper
is only an extreme case of what occurs whenever capital equipment
is used to produce. The assumption that there is a sharp division
between raw materials where we must allow for the disinvestment
due to using them and fixed capital where we can safely neglect
it does not correspond to the facts;¾especially
in normal conditions where equipment is falling due for
replacement every year and the use of equipment brings nearer the
date at which replacement is necessary.
It is an advantage of the concepts of user cost and
supplementary cost that they are as applicable to working and
liquid capital as to fixed capital. The essential difference
between raw materials and fixed capital lies not in their
liability to user and supplementary costs, but in the fact that
the return to liquid capital consists of a single term; whereas
in the case of fixed capital, which is durable and used up
gradually, the return consists of a series of user costs and
profits earned in successive periods.
Footnotes: [p.68] 1 -
This way of putting it depends on the convenient assumption that the marginal
prime cost curve is continuous throughout its length for changes in output
. In fact, this assumption is often unrealistic, and there may be one or
more points of discontinuity, especially when we reach an output corresponding
to the technical full capacity of the equipment. In this case the marginal
analysis partially breaks down; and the price may exceed the marginal
prime cost, where the latter is reckoned in respect of a small decrease
of output. (Similarly there may often be a discontinuity in the downward
direction, i.e. for a reduction in output below a certain
point.) This is important when we are considering the short-period supply
price in long-period equilibrium, since in that case any discontinuities, which
may exist corresponding to a point of technical full capacity, must be supposed
to be in operation. Thus the short-period supply price in long-period
equilibrium may have to exceed the marginal prime cost (reckoned in terms of a
small decrease of output). [back to text]
[p.69] 1 - Since user cost
partly depends on expectations as to the future level of wages, a reduction in
the wage -unit which is expected to be short-lived will cause factor cost and
user cost to move in different proportions and so affect what equipment is used,
and, conceivably, the level of effective demand, since factor cost may enter
into the determination of effective demand in a different way from user cost.
[back to text]
[p.69] 2 - The user cost of
the equipment which is first brought into use is not necessarily independent of
the total volume of output (see below); i.e. the [p.70] user cost
may be affected all along the line when the total volume of output is
changed. [back to text]
[p.70] 1 - It will be more
when it is expected that a more than normal yield can be obtained at some later
date, which, however, is not expected to last long enough to justify (or give
time for) the production of new equipment. To-day's user cost is equal to
the maximum of the discounted values of the potential expected yields of all the
to-morrows. [back to text]
[p.72] 1 - Mr. Hawtrey
(Economica, May 1934, p.145) has called attention to Prof. Pigou's
identification of supply price with marginal labour cost, and has contended that
Prof. Pigou's argument is thereby seriously vitiated. [back to text]
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