Chapter 4
THE CHOICE OF UNITS
I
In this and the next three chapters we shall be occupied with
an attempt to clear up certain perplexities which have no
peculiar or exclusive relevance to the problems which it is our
special purpose to examine. Thus these chapters are in the nature
of a digression, which will prevent us for a time from pursulng
our main theme. Their subject-matter is only discussed here
because it does not happen to have been already treated elsewhere
in a way which I find adequate to the needs of my own particular
enquiry.
The three perplexities which most impeded my progress in
writing this book, so that I could not express myself
conveniently until I had found some solution for them, are:
firstly, the choice of the units of quantity appropriate to the
problems of the economic system as a whole; secondly, the part
played by expectation in economic analysis; and, thirdly, the
definition of income.
II
That the units, in terms of which economists commonly work,
are unsatisfactory can be illustrated by the concepts of the
national dividend, the stock of real capital and the general
price-level:
(i) The national dividend, as defined by Marshall and Professor Pigou,
measures the volume of current output or real income and not the
value of output or money-income.
Furthermore, it depends, in some sense, on net output;¾on the net addition, that is to say, to
the resources of the community available for consumption or for
retention as capital stock, due to the economic activities and
sacrifices of the current period, after allowing for the wastage
of the stock of real capital existing at the commencement of the
period. On this basis an attempt is made to erect a quantitative
science. But it is a grave objection to this definition for such
a purpose that the community's output of goods and services is a
non-homogeneous complex which cannot be measured, strictly
speaking, except in certain special cases, as for example when
all the items of one output are included in the same proportions
in another output.
(ii) The difficulty is even greater when, in order
to calculate net output, we try to measure the net addition to
capital equipment; for we have to find some basis for a
quantitative comparison between the new items of equipment
produced during the period and the old items which have perished
by wastage. In order to arrive at the net national dividend,
Professor Pigou
deducts such obsolescence, etc., 'as may fairly be called
"normal"; and the practical test of normality is that
the depletion is sufficiently regular to be foreseen, if not in
detail, at least in the large'. But, since this deduction is not
a deduction in terms of money, he is involved in assuming that
there can be a change in physical quantity, although there has
been no physical change; i.e. he is covertly introducing changes
in value.
Moreover, he is unable to devise any satisfactory
formula
to evaluate new equipment against old when, owing to changes in
technique, the two are not identical. I believe that the concept
at which Professor Pigou is aiming is the right and appropriate
concept for economic analysis. But, until a satisfactory system
of units has been adopted, its precise definition is an
impossible task. The problem of comparing one real output with
another and of then calculating net output by setting off new
items of equipment against the wastage of old items presents
conundrums which permit, one can confidently say, of no solution.
(iii) Thirdly, the well-known, but unavoidable,
element of vagueness which admittedly attends the concept of the
general price-level makes this term very unsatisfactory for the
purposes of a causal analysis, which ought to be exact.
Nevertheless these difficulties are rightly regarded as
'conundrums'. They are 'purely theoretical' in the sense that
they never perplex, or indeed enter in any way into, business
decisions and have no relevance to the causal sequence of
economic events, which are clear-cut and determinate in spite of
the quantitative indeterminacy of these concepts. It is natural,
therefore, to conclude that they not only lack precision but are
unnecessary. Obviously our quantitative analysis must be
expressed without using any quantitatively vague expressions.
And, indeed, as soon as one makes the attempt, it becomes clear,
as I hope to show, that one can get on much better without them.
The fact that two incommensurable collections of miscellaneous
objects cannot in themselves provide the material for a
quantitative analysis need not, of course, prevent us from making
approximate statistical comparisons, depending on some broad
element of judgment rather than of strict calculation, which may
possess significance and validity within certain limits.
But the proper place for such things as net real output and
the general level of prices lies within the field of historical
and statistical description, and their purpose should be to
satisfy historical or social curiosity, a purpose for which
perfect precision¾such as our causal
analysis requires, whether or not our knowledge of the actual
values of the relevant quantities is complete or exact¾is neither usual nor necessary. To say
that net output to-day is greater, but the price-level lower,
than ten years ago or one year ago, is a proposition of a similar
character to the statement that Queen Victoria was a better queen
but not a happier woman than Queen Elizabeth¾a
proposition not without meaning and not without interest, but
unsuitable as material for the differential calculus. Our
precision will be a mock precision if we try to use such partly
vague and non-quantitative concepts as the basis of a
quantitative analysis.
III
On every particular occasion, let it be remembered, an
entrepreneur is concerned with decisions as to the scale on which
to work a given capital equipment; and when we say that the
expectation of an increased demand, i.e. a raising of the
aggregate demand function, will lead to an increase in aggregate
output, we really mean that the firms, which own the capital
equipment, will be induced to associate with it a greater
aggregate employment of labour. In the case of an individual firm
or industry producing a homogeneous product we can speak
legitimately, if we wish, of increases or decreases of output.
But when we are aggregating the activities of all firms, we
cannot speak accurately except in terms of quantities of
employment applied to a given equipment. The concepts of output
as a whole and its price-level are not required in this context,
since we have no need of an absolute measure of current aggregate output, such as would enable us
to compare its amount with the amount which would result from the
association of a different capital equipment with a different
quantity of employment. When, for purposes of description or
rough comparison, we wish to speak of an increase of output, we
must rely on the general presumption that the amount of
employment associated with a given capital equipment will be a
satisfactory index of the amount of resultant output;¾the two being presumed to increase and
decrease together, though not in a definite numerical proportion.
In dealing with the theory of employment I propose, therefore,
to make use of only two fundamental units of quantity, namely,
quantities of money-value and quantities of employment. The first
of these is strictly homogeneous, and the second can be made so.
For, in so far as different grades and kinds of labour and
salaried assistance enjoy a more or less fixed relative
remuneration, the quantity of employment can be sufficiently
defined for our purpose by taking an hour's employment of
ordinary labour as our unit and weighting an hour's employment of
special labour in proportion to its remuneration; i.e. an hour of
special labour remunerated at double ordinary rates will count as
two units. We shall call the unit in which the quantity of
employment is measured the labour-unit; and the money-wage of a
labour-unit we shall call the wage-unit.
Thus, if E is the wages (and salaries) bill, W the
wage-unit, and N the quantity of employment, E = N × W.
This assumption of homogeneity in the supply of labour is not
upset by the obvious fact of great differences in the specialised
skill of individual workers and in their suitability for
different occupations. For, if the remuneration of the workers is proportional to their
efficiency, the differences are dealt with by our having regarded
individuals as contributing to the supply of labour in proportion
to their remuneration; whilst if, as output increases, a given
firm has to bring in labour which is less and less efficient for
its special purposes per wage-unit paid to it, this is merely one
factor among others leading to a diminishing return from the
capital equipment in terms of output as more labour is employed
on it. We subsume, so to speak, the non-homogeneity of equally
remunerated labour units in the equipment, which we regard as
less and less adapted to employ the available labour units as
output increases, instead of regarding the available labour units
as less and less adapted to use a homogeneous capital equipment.
Thus if there is no surplus of specialised or practised labour
and the use of less suitable labour involves a higher labour cost
per unit of output, this means that the rate at which the return
from the equipment diminishes as employment increases is more
rapid than it would be if there were such a surplus.
Even in the limiting case where different labour units were so
highly specialised as to be altogether incapable of being
substituted for one another, there is no awkwardness; for this
merely means that the elasticity of supply of output from a
particular type of capital equipment falls suddenly to zero when
all the available labour specialised to its use is already
employed.
Thus our assumption of a homogeneous unit of labour involves no difficulties unless there
is great instability in the relative remuneration of different
labour-units; and even this difficulty can be dealt with, if it
arises, by supposing a rapid liability to change in the supply of
labour and the shape of the aggregate supply function.
It is my belief that much unnecessary perplexity can be
avoided if we limit ourselves strictly to the two units, money
and labour, when we are dealing with the behaviour of the
economic system as a whole; reserving the use of units of
particular outputs and equipments to the occasions when we are
analysing the output of individual firms or industries in
isolation; and the use of vague concepts, such as the quantity of
output as a whole, the quantity of capital equipment as a whole
and the general level of prices, to the occasions when we are
attempting some historical comparison which is within certain
(perhaps fairly wide) limits avowedly unprecise and approximate.
It follows that we shall measure changes in current output by
reference to the number of hours of labour paid for (whether to
satisfy consumers or to produce fresh capital equipment) on the
existing capital equipment, hours of skilled labour being
weighted in proportion to their remuneration. We have no need of
a quantitative comparison between this output and the output
which would result from associating a different set of workers
with a different capital equipment. To predict how entrepreneurs
possessing a given equipment will respond to a shift in the
aggregate demand function it is not necessary to know how the
quantity of the resulting output, the standard of life and the
general level of prices would compare with what they were at a
different date or in another country.
IV
It is easily shown that the conditions of supply, such as are
usually expressed in terms of the supply curve, and the
elasticity of supply relating output to price, can be handled in
terms of our two chosen units by means of the aggregate supply
function, without reference to quantities of output, whether we
are concerned with a particular firm or industry or with economic
activity as a whole. For the aggregate supply function for a
given firm (and similarly for a given industry or for industry as
a whole) is given by
Zr = fr(Nr),
where Zr is the proceeds (net of user
cost) the expectation of which will induce a level of employment Nr.
If, therefore, the relation between employment and output is such
that an employment Nr results in an
output Or, where Or = yr(Nr),
it follows that
Zr
+ Ur(Nr) fr(Nr)
+ Ur(Nr)
p = ¾¾¾¾¾¾¾ = ¾¾¾¾¾¾¾¾¾
Or yr(Nr)
is the ordinary supply curve, where Ur(Nr)
is the (expected) user cost corresponding to a level of
employment Nr.
Thus in the case of each homogeneous commodity, for which Or = yr(Nr)
has a definite meaning, we can evaluate Zr = fr(Nr)
in the ordinary way; but we can then aggregate the Nr's
in a way in which we cannot aggregate the Or's,
since SOr
is not a numerical quantity. Moreover, if we can assume that, in
a given environment, a given aggregate employment will be
distributed in a unique way between different industries, so that
Nr is a function of N, further
simplifications are possible.