Appendix to Chapter 19
PROFESSOR PIGOU'S 'THEORY OF UNEMPLOYMENT'
Professor Pigou in his Theory of Unemployment makes the
volume of employment to depend on two fundamental factors, namely
(i) the real rates of wages for which workpeople stipulate, and
(2) the shape of the Real Demand Function for Labour. The central
sections of his book are concerned with determining the shape of
the latter function. The fact that workpeople in fact stipulate,
not for a real rate of wages, but for a money-rate, is not
ignored; but, in effect, it is assumed that the actual money-rate
of wages divided by the price of wage-goods can be taken to
measure the real rate demanded.
The equations which, as he says, 'form the starting point of
the enquiry' into the Real Demand Function for Labour are given
in his Theory of Unemployment, p. 90. Since the tacit
assumptions, which govern the application of his analysis, slip
in near the outset of his argument, I will summarise his
treatment up to the crucial point.
Professor Pigou divides industries into those 'engaged in
making wage-goods at home and in making exports the sale of which
creates claims to wage-goods abroad' and the 'other' industries:
which it is convenient to call the wage-goods industries and the
non-wage-goods industries respectively. He supposes x men
to be employed in the former and y men in the latter. The
output in value of wage-goods of the x men he calls F(x);
and the general rate of wages F'(x). This, though
he does not stop to mention it, is tantamount to assuming that
marginal wage-cost is equal to marginal prime cost.
Further, he assumes that x + y = f(x), i.e. that the number of men
employed in the wage-goods industries is a function of total
employment. He then shows that the elasticity of the real demand
for labour in the aggregate (which gives us the shape of our
quaesitum, namely the Real Demand Function for Labour) can be
written
f'(x) F'(x)
Er = ¾¾¾ × ¾¾¾¾
f(x) F"(x)
So far as notation goes, there is no significant difference
between this and my own modes of expression. In so far as we can
identify Professor Pigou's wage-goods with my consumption-goods,
and his 'other goods' with my investment-goods, it follows that
his F(x) / F'(x),
being the value of the output of the wage-goods industries in
terms of the wage-unit, is the same as my Cw.
Furthermore, his function is (subject to the identification of
wage-goods with consumption-goods) a function of what I have
called above the employment multiplier k'. For
Dx = k'Dy,
1
so that f'(x) = 1 + ¾¾
k
Thus Professor Pigou's 'elasticity of the real demand for
labour in the aggregate' is a concoction similar to some of my
own, depending partly on the physical and technical conditions in
industry (as given by his function F) and partly on the
propensity to consume wage-goods (as given by his function f); provided always that we are limiting
ourselves to the special case where marginal labour-cost is equal
to marginal prime cost.
To determine the quantity of employment, Professor Pigou then combines with his 'real demand for labour', a supply
function for labour. He assumes that this is a function of the
real wage and of nothing else. But, as he has also assumed that
the real wage is a function of the number of men x who are
employed in the wage-goods industries, this amounts to assuming
that the total supply of labour at the existing real wage is a
function of x and of nothing else. That is to say, n = c(x), where n is the supply of
labour available at a real wage F'(x).
Thus, cleared of all complication, Professor Pigou's analysis
amounts to an attempt to discover the volume of actual employment
from the equations
x + y = f(x)
and n = c(x).
But there are here three unknowns and only two equations. It
seems clear that he gets round this difficulty by taking n = x + y.
This amounts, of course, to assuming that there is no involuntary
unemployment in the strict sense, i.e. that all labour available
at the existing real wage is in fact employed. In this case x
has the value which satisfies the equation
f(x) = c(x)
and when we have thus found that the value of x is
equal to (say) n1, y must be equal to c(n1) - n1, and total
employment n is equal to (n1).
It is worth pausing for a moment to consider what this
involves. It means that, if the supply function of labour
changes, more labour being available at a given real wage (so
that n1 + dn1 is
now the value of x which satisfies the equation f(x) = c(x)), the demand for the output of
the non-wage-goods industries is such that employment in these
industries is bound to increase by just the amount which will
preserve equality between f(n1 + dn1)
and c(n1 + dn1).
The only other way in which it is possible for aggregate
employment to change is through a modification of the propensity
to purchase wage-goods and non-wage-goods respectively such that
there is an increase of y accompanied by a greater
decrease of x.
The assumption that n = x + y
means, of course, that labour is always in a position to
determine its own real wage. Thus, the assumption that labour is
in a position to determine its own real wage, means that the
demand for the output of the non-wage-goods industries obeys the
above laws. In other words, it is assumed that the rate of
interest always adjusts itself to the schedule of the marginal
efficiency of capital in such a way as to preserve full employment. Without this assumption Professor
Pigou's analysis breaks down and provides no means of determining
what the volume of employment will be. It is, indeed, strange
that Professor Pigou should have supposed that he could furnish a
theory of unemployment which involves no reference at all to
changes in the rate of investment (i.e. to changes in employment
in the non-wage-goods industries) due, not to a change in the
supply function of labour, but to changes in (e.g.) either the
rate of interest or the state of confidence.
His title the 'Theory of Unemployment' is, therefore,
something of a misnomer. His book is not really concerned with
this subject. It is a discussion of how much employment there
will be, given the supply function of labour, when the conditions
for full employment are satisfied. The purpose of the concept of
the elasticity of the real demand for labour in the aggregate is
to show by how much full employment will rise or fall
corresponding to a given shift in the supply function of labour.
Or¾alternatively and perhaps better¾we may regard his book as a non-causative
investigation into the functional relationship which determines
what level of real wages will correspond to any given level of
employment. But it is not capable of telling us what determines
the actual level of employment; and on the problem of
involuntary unemployment it has no direct bearing.
If Professor Pigou were to deny the possibility of involuntary
unemployment in the sense in which I have defined it above, as,
perhaps, he would, it is still difficult to see how his analysis
could be applied. For his omission to discuss what determines the
connection between x and y, i.e. between employment
in the wage-goods and non-wage-goods industries respectively,
still remains fatal.
Moreover, he agrees that within certain limits labour in fact
often stipulates, not for a given real wage, but for a given
money-wage. But in this case the supply function of labour is not
a function of F'(x) alone but also of the
money-price of wage-goods;¾with the
result that the previous analysis breaks down and an additional
factor has to be introduced, without there being an additional
equation to provide for this additional unknown. The pitfalls of
a pseudo-mathematical method, which can make no progress except
by making everything a function of a single variable and assuming
that all the partial differentials vanish, could not be better
illustrated. For it is no good to admit later on that there are
in fact other variables, and yet to proceed without re-writing
everything that has been written up to that point. Thus if (within limits) it is a money-wage for which
labour stipulates, we still have insufficient data, even if we
assume that n = x + y,
unless we know what determines the money-price of wage-goods.
For, the money-price of wage-goods will depend on the aggregate
amount of employment. Therefore we cannot say what aggregate
employment will be, until we know the money-price of wage-goods;
and we cannot know the money-price of wage-goods until we know
the aggregate amount of employment. We are, as I have said, one
equation short. Yet it might be a provisional assumption of a
rigidity of money-wages, rather than of real wages, which would
bring our theory nearest to the facts. For example, money-wages
in Great Britain during the turmoil and uncertainty and wide
price fluctuations of the decade 1924-1934
were stable within a range of 6 per cent, whereas real wages
fluctuated by more than 20 per cent. A theory cannot claim to be
a general theory, unless it is applicable to the case
where (or the range within which) money-wages are fixed, just as
much as to any other case. Politicians are entitled to complain
that money-wages ought to be highly flexible; but a
theorist must be prepared to deal indifferently with either state
of affairs. A scientific theory cannot require the facts to
conform to its own assumptions.
When Professor Pigou comes to deal expressly with the effect
of a reduction of money-wages, he again, palpably (to my mind),
introduces too few data to permit of any definite answer being
obtainable. He begins by rejecting the argument (op. cit.
p. 101) that, if marginal prime cost is equal to marginal
wage-cost, non-wage-earners' incomes will be altered, when
money-wages are reduced, in the same proportion as wage-earners',
on the ground that this is only valid, if the quantity of
employment remains unaltered¾which is
the very point under discussion. But he proceeds on the next page
(op. cit. p. 102) to make the same mistake himself by
taking as his assumption that 'at the outset nothing has happened
to non-wage-earners money-income', which, as he has just shown,
is only valid if the quantity of employment does not remain
unaltered-which is the very point under discussion In fact, no
answer is possible, unless other factors are included in our
data.
The manner in which the admission, that labour in fact
stipulates for a given money-wage and not for a given real wage
(provided that the real wage does not fall below a certain
minimum), affects the analysis, can also be shown by pointing out
that in this case the assumption that more labour is not
available except at a greater real wage, which is fundamental to
most of the argument, breaks down. For example, Professor Pigou
rejects (op. cit. p. 75) the theory of the multiplier
by assuming that the rate of real wages is given, i.e. that,
there being already full employment, no additional labour is
forthcoming at a lower real wage. Subject to this assumption, the
argument is, of course, correct. But in this passage Professor
Pigou is criticising a proposal relating to practical policy; and
it is fantastically far removed from the facts to assume, at a
time when statistical unemployment in Great Britain exceeded
2,000,000 (i.e. when there were 2,000,000 men willing to work at
the existing money-wage), that any rise in the cost of living,
however moderate, relatively to the money-wage would cause the
withdrawal from the labour market of more than the equivalent of
all these 2,000,000 men.
It is important to emphasise that the whole of Professor
Pigou's book is written on the assumption that any rise in the
cost of living, however moderate, relatively to the money-wage
will cause the withdrawal from the labour market ofa number of
workers greater than that of all the existing unemployed.
Moreover, Professor Pigou does not notice in this passage (op.
cit. p. 75) that the argument, which he advances against
'secondary' employment as a result of public works, is, on the
same assumptions, equally fatal to increased 'primary' employment
from the same policy. For if the real rate of wages ruling in the
wage-goods industries is given, no increased employment whatever
is possible¾except, indeed, as a
result of non-wage-earners reducing their consumption of
wage-goods. For those newly engaged in the primary employment
will presumably increase their consumption of wage-goods which
will reduce the real wage and hence (on his assumptions) lead to
a withdrawal of labour previously employed elsewhere. Yet
Professor Pigou accepts, apparently, the possibility of increased
primary employment. The line between primary and secondary
employment seems to be the critical psychological point at which
his good common sense ceases to overbear his bad theory.
The difference in the conclusions to which the above
differences in assumptions and in analysis lead can be shown by
the following important passage in which Professor Pigou sums up
his point of view: 'With perfectly free competition among
workpeople and labour perfectly mobile, the nature of the
relation (i.e. between the real wage-rates for which people
stipulate and the demand function for labour) will be very
simple. There will always be at work a strong tendency for
wage-rates to be so related to demand that everybody is employed.
Hence, in stable conditions everyone will actually be employed. The implication
is that such unemployment as exists at any time is due wholly to
the fact that changes in demand conditions are continually taking
place and that frictional resistances prevent the appropriate
wage adjustments from being made instantaneously.'
He concludes (op. cit. p. 253) that unemployment
is primarily due to a wage policy which fails to adjust itself
sufficiently to changes in the real demand function for labour.
Thus Professor Pigou believes that in the long run unemployment
can be cured by wage adjustments;
whereas I maintain that the real wage (subject only to a minimum
set by the marginal disutility of employment) is not primarily
determined by 'wage adjustments' (though these may have
repercussions) but by the other forces of the system, some of
which (in particular the relation between the schedule of the
marginal efficiency of capital and the rate of interest)
Professor Pigou has failed, if I am right, to include in his
formal scheme.
Finally, when Professor Pigou comes to the 'Causation of
Unemployment' he speaks, it is true, of fluctuations in the state
of demand, much as I do. But he identifies the state of demand
with the Real Demand Function for Labour, forgetful of how narrow
a thing the latter is on his definition. For the Real Demand
Function for Labour depends by definition (as we have seen above)
on nothing but two factors, namely (1) the relationship in
any given environment between the total number of men employed
and the number who have to be employed in the wage-goods
industries to provide them with what they consume, and (2) the
state of marginal productivity in the wage-goods industries. Yet
in Part V of his Theory of Unemployment fluctuations in
the state of 'the real demand for labour' are given a position of
importance. The 'real demand for labour' is regarded as a factor
which is susceptible of wide short-period fluctuations (op.
cit. Part V, chaps. vi.-xii.),
and the suggestion seems to be that swings in 'the real demand
for labour' are, in combination with the failure of wage policy
to respond sensitively to such changes, largely responsible for
the trade cycle. To the reader all this seems, at first,
reasonable and familiar. For, unless he goes back to the
definition, 'fluctuations in the real demand for labour' will
convey to his mind the same sort of suggestion as I mean to
convey by 'fluctuations in the state of aggregate demand'. But if
we go back to the definition of the 'real demand for labour', all
this loses its plausibility. For we shall find that there is
nothing in the world less likely to be subject to sharp
short-period swings than this factor.
Professor Pigou's 'real demand for labour' depends, by
definition, on nothing but F(x), which represents
the physical conditions of production in the wage-goods
industries, and (x), which represents the functional
relationship between employment in the wage-goods industries and
total employment corresponding to any given level of the latter.
It is difficult to see a reason why either of these functions
should change, except gradually over a long period. Certainly
there seems no reason to suppose that they are likely to
fluctuate during a trade cycle. For F(x) can only change
slowly, and, in a technically progressive community, only in the
forward direction; whilst (x) will remain stable, unless
we suppose a sudden outbreak of thrift in the working classes,
or, more generally, a sudden shift in the propensity to consume.
I should expect, therefore, that the real demand for labour would
remain virtually constant throughout a trade cycle. I repeat that
Professor Pigou has altogether omitted from his analysis the
unstable factor, namely fluctuations in the scale of investment,
which is most often at the bottom of the phenomenon of
fluctuations in employment.
I have criticised at length Professor Pigou's theory of
unemployment not because he seems to me to be more open to
criticism than other economists of the classical school; but
because his is the only attempt with which I am acquainted to
write down the classical theory of unemployment precisely. Thus
it has been incumbent on me to raise my objections to this theory
in the most formidable presentment in which it has been advanced.