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The Classical Stationary State
Author(s): A. C. Pigou
Source: The Economic Journal, Vol. 53, No. 212 (Dec., 1943), pp. 343-351
Published by: Blackwell Publishing for the Royal Economic Society
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"THE CLASSICAL STATIONARY STATE
1. IN his Fiscal Policy and Business Cycles Professor Hansen
writes: " The classicals were quite right when they argued that
without technological progress,' the price system, including the
rate of interest, would progressively drive the economy to the
point at which there would be no net investment. They were
wrong in assuming that the price system could also ensure a
propensity to consume compatible with this investment situation,
so as to provide full employment " (p. 288). The reason is that,
before the stimulus to investment, associated, say, with the
development of some invention, peters out, " customs, habits and
institutional arrangements . . . have become embodied in the
social structure and set up powerful resistances " to the establishment
of a full-employment equilibrium. Nor are these resistances
merely frictional, impeding the establishment of this kind of
equilibrium. On account of them the economic system is
directed towards a different kind of equilibrium. " Thus total
expenditures decline and the econiomly falls towards an equilibrial
self-perpetuating income level far short of full employment'"
(p. 306). This argument, the reader will understand, is conducted
on the level of abstraction where perfect homogeneity and complete
mobility of labour are assumed, so that " full employment "
signifies a state of things in which everybody seeking employment
at the ruling (uniform) rate of wages is able to obtain it. It does
not have that esoteric meaning, which is given to it in much
current writing, where full employment is allowed to prevail
alongside of large masses of " frictional unemployment." In
this article also I shall stand on that level of abstraction.
2. It is, of course, true, as Professor Hansen says, that the
"classicals " were accustolned to think of the stationary state
as one of full employment. Nevertheless, I suggest, the essential
difference between his view and theirs should be stated in terms
somewhat different from those he uses. The classicals, if pressed,
would not have denied that, should wage-earners not act competitively,
but contrive, by means of combination or otherwise,
to set the real rate of wages " too high," the stationary state
would not be one of full employment. Their essential contention
1 On the assumption, of course, that there is no increase of population or
expansion into new territory.
344 THE ECONOMIC JOURNAL [DEC.
is that in all circumstances a full-employment stationary state is
possible and, if an appropriate wage policy is adopted, will be
secured; Professor Hansen's contention is that in some circumstances
a full-employment stationary state is not possible
and cannot be secured through the adoption of any wage policy;
and, which is not the same thing, that a less-than-full-employment
is possible and will be secured. This is the issue that I propose
to discuss.
3. Define savings and investment in accordance with Lord
Keynes' practice in his General Theory and my own in Employment
and Equilibrium, so that they are both equal to real income minus
real consumption, and, therefore, as aggregates in a closed
community, in all circumstances equal to one another. Then, in
respect of the representative man,' let x be real income; r the
expected net rate of return from investment, i.e., the rate after
allowing for incidental expenses connected with making the
investment. In equilibrium this rate is necessarily equal to the
net rate of interest, and is the same no matter in terms of wihat
oommodity it is measured. Let C be the physical stock of
capital equipment. We have in Professor Hansen's manner an
investment-income function,2 which might equally well be called
a supply function for real investment, with the amount of real
investment written f(C, x, r). Of the characteristics of this
function we know that /\xaaf is positive and less than Ax for all
values of x and r-this is Lord Keynes' " psychological law " (of.
General Theory, p. 114); while Ar- is probably, though not
rar i rbby huh o
certainly, positive and small; and AC Y is negative and smallsince,
the more accumulated wealth people have, the less keen
1 The argument of this paper is not affected by the precise way in which the
representative man is defined. It is natural, perhaps, to think of him as a
private person external to State activities. But he may, alternatively, be
defined in such a way that account is taken, not only of what he does in his
private capacity, but also of what he does as, a constituent element in the State,
so that, if, for example, consumption is cut down by State rationing, the representative
man has chosen to reduce his own consumption. With this definition
there can be no difference between what he desires to do and what under the
suasion of the State he 'does do. Thus what he desires to save in given circumstances
and what he does save are the same thing, and there can be no question
of " forced " saving.
2 The reader will understand that the investment-income function is here
represented in a truncated form, variables which are not important for our
immediate problem being neglected. In a full expression there would have in
particular to be a variable indicative of the distribution of income.
1943] THE CLASSICAL STATIONARY STATE 345
they are to get more.' We also have a demand function for real
investment with the amount of real investment written O(C, r)
in which it is obvious that, given the technical situation, a and
2? are both negative. Some authorities would write here
O{C, x, r} with a- positive. The choice between these two forms
does not affect the issues discussed here save only as regards a
secondary problem to be mentioned in the concluding paragraph.
Therefore I shall not argue the matter but simply adopt the form
O(C, r).
4. In the long-period equilibrium of the stationary state
investment must, of course, be nil. We have, therefore, two
equations:-
f{C, x,r) } *. (I)
/(C, r) 0 .(II)
If, then, X be the real income appropriate to full employment,
there is also, according to the "' classicals," a third equation,
x = X (III); and the three equations together determine x, C
and r.
a. The classicals tacitly assumed that investment (i.e., saving)
is made solely for the sake of the income that it is expected to
yield in the future. On this assumption it is easy to see that in
the long-period equilibrium of the stationary state the rate of
interest must be equal to the representative man's rate of discounting
future satisfactions. For, if this were not so, investment
could not be nil, but would be either positive or negative.
Write p for this latter rate and p. z,t(C, x) to represent the relation
between it and the amount of the representative man's real income.
Then, since, as we have seen, r - p, we have, as it appears,
I For an individual there are both theoretical and statistical reasons for
thinking that, as real income increases, not only the absolute amount of investment
but also the proportionate amount will increase, i.e., that not only 3f but f af~~~~~~~~~~~~~~a Ofl
also la is positive. On the other hand, when income increases for the
representative man of a group on account of a larger part of the group finding
employment, prima facie we should expect the proportionate amount of income
saved to be unaltered. It must be remarked, however, that, when more people
in a group find employment, a shift in the distribution of disposable income takes
place, less than hitherto having to be transferred for the upkeep of unemployed
persons, who presumably save nothing. This shift of distribution is evidently
favourable to investment. Hence it may well be that, in this case, as well as
with the isolated individual, increasing real income entails, other things being
equal, an increasing proportion of income saved.
346 THE ECONOMIC JOURNAL [DEC.
two new equations in addition to those set out in the last section,
and only one new unknown: so that the system appears prima
facie to be over-determined. But this is not really so. For the
equations
f(C, x, r) 0,
r p
p = 0(C, x)
are not independent. On the contrary, the two last govern the
functional form f in such wise as to compel the first to be valid.
Thus there is no over-determination. It follows-and this is
the essential point to note here-that, since the rate at which the
representative man discounts future satisfactions can obviously
never be < 0, no matter how large his real income, the functional
form f is necessarily such that, for all possible values of x and C,
the equation f{C, x, r} 0 must yield a positive value for r.
6. The assumption that investment (i.e., saving) is made solely
for the sake of the income that it is expected to yield, is, however,
clearly not in accordance with the facts. People save (i.e.,
invest) partly from other motives, the desire for possession as
such, conformity to tradition or custom and so on. This entails
that the rate of interest is less than the rate at which the representative
man discounts future satisfactions. The fact that this
latter rate cannot be nil or negative does not, therefore, imply
that the rate of interest cannot be nil or negative. The functional
formf need not, therefore, be such that the equationf{C, x, r} 0
yields a positive value for r for all value of x and C. On the
contrary, for some values of x it may yield a negative value for r.
Thus, it appears that a situation not contemplated by the
classicals may arise, in which full employment and stationary
state equilibrium can only be attained together on condition that
the rate of interest is negative.
7. But in stationary state equilibrium, as already indicated,
the rate of interest must be the same, no matter in terms of what
commodity it is expressed. For this type of equilibrium implies
that the future relative values of different commodities are
expected to be the same as their present relative values. Some
commodities, of which the most obvious is money, do not suffer
appreciable wear and tear and can be held at trifling cost. In
these commodities, therefore, the rate of interest in a stationary
state cannot be negative in any serious degree-broadly speaking,
cannot be negative. It follows that the rate of interest cannot be
negative in terms of any commodity. Hence the condition, i.e.,
the existence of a negative rate of interest, which in some circum1943]
THE CLASSICAL STATIONARY STATE 347
stances we have seen to be necessary in order that full employment
shall be compatible with stationary state equilibrium, cannot be
satisfied. When these circumstances occur, therefore, the classical
thesis that full employment in a stationary state can always be
brought about by competition among wage-earners in the matter
of wage-rates fails. Unless, therefore, it can be shown that the
circumstances contemplated above cannot occur, Prof. Hansen is
so far right and the classicals stand convicted of error.
8. Before we debate this ultimate issue there is, however,
something else that should be said. To grant, if we do grant,
that in certain circumstances a full-employment stationary state
is impossible is not necessarily to grant that the less-than-fullemployment
stationary state contemplated by Prof. Hansen is
possible and will be secured. We have a set-up containing three
equalities, one inequality, and three unknowns:
f(C, x, r) -o . .(I)
b(C, r)- 0(II)
x X.(III)
r > O. (IV)
This system obviously may be over-determined. The classicals
and Prof. Hansen both in effect provisionally accept equations
(I) and (II). Prof. liansen then points out that, in some circumstances,
(III) is incompatible with (IV), so that the classicals'
solution of a full-employment stationary state cannot be right.
But it is open to the classicals to retort that in these same circumstances
(IV) is incompatible with (III), so that the alternative
solution of a less-than-full-employment stationary state cannot be
right. Unless, therefore, cause can be shown for rejecting equation
(III), the logical outcome is that Prof. Hansen is right in what he
denies but wrong in what he affirms.
9. The assertion x = X derives from the proposition that
workpeople are able to reduce as much as they like the rate of
real wages for which they ask, and, by reducing it far enough, are
able to secure employment for as many people as desire it.' Is
there any way in which this proposition can be contested with
any degree of plausibility'? In an economy in which wages were
contracted for in kind clearly there is not. But those who think
with Prof. Hansen are entitled to claim that in the economy with
which they are interested wages are contracted for in money. In
such an economy suppose that a less-than-full-employment
1 The suggestion that the rate may possibly have to be negative may
reasonably be ignored over the range of our present problem.
348 THE ECONOMIC JOURNAL [DEC.
stationary state is established at a net rate of interest approaching
nil. Then, the argument will run, it is out of the power of wageearners
to make cuts in the rate of real wages for which they ask,
and so to secure additional employment, because every cut in
money wage-rates will automatically bring about an equiproportionate
reduction in prices. This argument is sometimes
found in popular expositions of what the expositors mistakenly
believe to be Lord Keynes' views. It is not necessary, I think,
to examine it at any length. With any known type of banking
system, and equally under an arrangement in which the stock of
money is rigidly fixed, money income must be a function of the rate
of interest, being lower or higher according as that rate is lower or
higher. This follows from the fact that, for equilibrium, the
convenience and so on yielded to the representative man by the
marginal unit of resources held in the form of money must be
equally attractive with the interest yielded by the marginal unit
invested in real capital. For the degree of this convenience is
greater or less according as real income divided into the real value
of the stock of money is less or greater; i.e., according as money
income divided into the stock of money (i.e., the Marshallian k,
which is the inverse of the income velocity of money), is less or
greater, i.e., when the stock of money is given, according as money
income is greater or less. We may express this, writing T for the
real value of the stock of money, by the equation r- g T
T~~~~~~~~~~~~
where Tis always positive, and the functional form g is such that
x
(I {q( ) is negative and gTis positive, for all possible
T T (i.e., all positive) values of -; whence it follows that, asT
x ~~~~~~~x
increases towards infinity, g T falls asymptotically towards, but
never reaches 0. Thus, monetary arrangements being given,
money income cannot fall unless the rate of interest falls. Since,
however, in our supposed less-than'-full-employment stationary
state, the rate of interest is already at the minimum admissible
level, it cannot fall any farther. Therefore the acceptance of
lower money wage-rates by wage-earners cannot cause money
income to fall. Therefore, with given employment, it cannot
cause prices to fall. It follows that by cutting money wage-rates
workpeople can cut real wage-rates, and so can expand employment
above the amount proper to any less-than-full-employment
1943] THE CLASSICAL STATIONARY STATE 349
stationary state. The attempted rebuttal of the classicals'
attack fails. The logical outcome is that in circumstances where
a full-employment stationary state is impossible a less-than-fullemployment
stationary state is also impossible; in other words,
that no position of long-period equilibrium can be attained.
10. Escape from this impasse can be achieved if and only if
it can be shown that the circumstances we have been contemplating,
out of which the impasse is generated, are such as cannot
in fact occur. I have now, resuming the main argument as it was
left in ? 7, to maintain that this can be shown. The stock of
money being given, r is a function of money income, in such
wise that, as the one tends towards nothing so also does the other,
but neither can ever actually reach nothing. Suppose, then,
that we start from a condition of full employment in which some
investment is taking place. As time passes-on the assumption,
of course, that technique remains unchanged-profitable openings
for investment gradually get filled up. In our symbolism- C
increases, and, consequently, for any given value of r, -h(C, r)
contracts; till finally no investment is demanded even at a nil
rate of interest. Suppose that at this rate, with the real income
proper to full employment, people still wish to supply some investment-
to save something. Since, for the reasons given above,
the rate of interest cannot fall below nothing, the only way in
which demand and supply can be brought into equilibrium is
by workpeople being forced out of employment, till a new and
lower level of real income is established, in respect of which the
representative man does not desire to invest (i.e., save) anything
at a nil (or small positive) rate of interest. What, then, happens ?
To resist this movement and maintain themselves in work, wageearners
offer to accept lower rates of money wages, and go on
doing this so long as the pressure to reduce employment is maintained.
At first sight it seems as though this process must land
us in an endless state of disequilibrium with money wage-rates
falling for ever. But this is not so. As money wage-rates fall
money income must fall also and go on falling. Employment, and
so real income, being maintained, this entails that prices fall and
go on falling; which is another way of saying that the stock of
money, as valued in terms of real income, correspondingly rises.
But the extent to which the representative man desires to make
savings otherwise than for the sake of their future income yield
depends in part on the size, in terms of real income, of his existing
possessions. As this increases, the amount that he so desires to
save out of any assigned real income diminishes and ultimately
350 THE ECONOMIC JOURNAL [DEC.
vanishes; so that we are back in the situation described in ? 5,
where a negative rate of interest is impossible. Thus, through
the decline of money income, the investment-income function is
modified in such wise that a set-up emerges in which no condition
incompatibJe with full employment is embodied.
11. This may be expressed symbolically by writing the
investment-income function in the form f(C, x, r, T); where T is
the real value of the stock of money, af is negative and, with r at
its minimum, f(C, x, r, T) can assume a nil value, if T is sufficiently
large, for no matter what values of C and x and r. Our set-up
then is
O(C, r)-O . . . . * (I)
f(C,x, r, T) =0.(II)
.x..-.( ITI)
r-gT. (IV)
Here there are four equations and four unknowns, so that the
system is not over-determined, while our knowledge of the form
of the function g, as set out in ? 9, assures us that r, while it falls
towards zero as T - rises towards infinity, can never fall to zero. x
Thus the " some circumstances," in which it seemed, according
to ? 7, that the classicals' full-employment stationary state was
impossible, have been found to be such as cannot, in fact, occur.
That type of stationary state, provided that wage-earners adopt a
competitive wage policy, is always possible; indeed it is the goal to
which, granted this proviso, the economic system necessarily tends.
12. As was indicated in ? 2, it is quite consistent with the
classicals' general position, as it is with this conclusion, that, if
wage-earners do not follow a competitive wage policy, but hold
money wage-rates " unduly " high, nil investment will be associated
not with full, but with less than full employment. In
place of equations (III) and (IV) in the foregoing set-up, we have
equations relating the rate of interest to money income and to
the rate of money-wages, such as wpre developed in my book on
Employment and Equilibrium. In this case the possibility of a
negative rate of interest cannot be excluded in the manner
described in the last section, because, the money rate of wages
being maintained, and, therefore, prices (approximately) maintained,
the value of the stock of money in terms of real income
cannot be expanded. It is excluded through employment being
cut down in the manner contemplated by Prof. Hansen until real
1943] THE CLASSICAL STATIONARY STATE 351
income is so low that people do not desire to save or invest
anything, and a less-than-full-employment stationary state is
attained.
13. In conclusion a point should be noticed which was raised
by Mr. Kaldor in his review of Prof. Hansen's book in the
EcoNoMIc JOURNALfo r September 1943. He maintains that the
state of nil investment with less than full employment contemplated
by Prof. Hansen, and, as is maintained here, realised if,
and only if, money wage-rates are held above the competitive
level, may not-indeed, is unlikely to-satisfy the conditions of
stable equilibrium; in which case it can hardly claim to be a
stationary state in a strict sense (loc. cit., p. 110). This conclusion
depends on his view that the demand function for investment
ought to be written b(C, x, r), not, as I have written it, O(C, r).
If it is f(C, x, r), one of the conditions of stable equilibrium is
that aB_>f LOa,n d this condition need not be satisfied; whereas
with the function b(C, r), it must be satisfied, since aDf is positive
and aa is then nil.' As already indicated, I do not propose to
debate this matter here, for it is off the track of this discussion.2
I have been concerned to show that, in given conditions of
technique and so on, if wage-earners follow a competitive wage
policy, the economic system must move ultimately to a fullemployment
stationary state; which is the essential thesis of the
classicals. There can be no question at all that in this event the
equilibrium attained is stable. This is so equally whether it is
correct to represent the demand function as O(C, r) or as b(C, x, r).
For, the equation x X having determined x, from the standpoint
of the other equations in the set-up x is not a variable.
A. C. PIGOU
King's Colleye,
Cambridge.
1 Since both ,Dg and 'f are negative, there is no a priori necessity for the other
stability condition, "f > Lo is positive, to, be satisfied. Common sense tells us,
however, that is likely to be a very small negative quantity, while LAI Gmay
well be a considerable one; so that there is a strong probability that the
condition will be satisfied.
2 Cf. EcoNoMIc JouRNAL, June-Sept. 1942, p. 250. It should be noticed that
the form j(C, x, r) cannot be defended by reference to the so-called " acceleration
principle "; for this connects investment, not with consumption, but with rate
of change in consumption, which in equilibrium situations is necessarily nil.