GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.80

Revisiting the unemployment controversy: Pigou's viewpoint

Norikazu Takami

August 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Revisiting the unemployment controversy: Pigou’s
viewpoint
Norikazu Takami,1the Graduate School of Economics, Osaka University
and Suntory Foundation Torii Fellow
This paper examines the unemployment controversy between J. M. Keynes and A. C. Pigou,
mainly from the latter’s viewpoint. In this controversy, although he eventually conceded defeat, Pigou attempted to prove that money wage cuts were eﬀective on employment regardlessof the level of interest rate. His defeat in the controversy was not due to the inconsistency
in his perspective, but rather due to his inability to theorize a relevant notion, “forced antilevies” as expounded in Industrial Fluctuations (1927). The “Pigou eﬀect” devised later in1943 could be considered as theorization of forced anti-levies. This allowed Pigou to formallydemonstrate that money wage cuts were eﬀective in increasing employment regardless of thelevel of interest rate. Thus, we conclude that the unemployment controversy was gainful atleast to Pigou, resulting in the formulation of the notion originated in Industrial Fluctuations.

JEL Classification: B22, B31, E24
Keywords: Pigou, unemployment, macroeconomics, Pigou eﬀect, Keynes

1 Introduction
This paper studies the unemployment controversy between J. M. Keynes and A. C. Pigou, particularly the phase after the publication of General Theory. The controversy mainly concerns

1 dg067tn@mail2.econ.osaka-u.ac.jp

1

the eﬀect of money wage cuts on unemployment. Keynes and his sidekick N. Kaldor argued
that such cuts were ineﬀective in times of minimum interest rate, whereas Pigou attempted toprove that they were eﬀective regardless of the level of interest rate. The controversy ended
with Pigou conceding defeat. This paper deals with Pigou’s initial conception of Keynes’s
argument in General Theory and the reason for his eventual concession to the views of Keynes
and Kaldor.
Following the controversy, Pigou made full use of the method acquired through the controversy and systematically exposited the essence of inchoate macroeconomics in Employment
and Equilibrium (1941). Even so, he still occasionally expressed disbelief in Keynes’s views
on money wages, and in 1943, he finally attempted to set up a model in which money wage
cuts increase employment regardless of the level of interest rate in 1943. This achievement
is now known as the Pigou eﬀect, or wealth eﬀect—as price declines, consumption expands.
This paper proposes that the source of inspiration for the Pigou eﬀect is to be found in his
earlier notion presented in Industrial Fluctuations (1927).
There is extensive literature on the unemployment controversy between Keynes and Pigou
in the 1930s. Collard (1999) rather briefly outlined the controversy after General Theory.
He oﬀered a short summary on Pigou’s 1937 article and approvingly quoted the criticismsof Keynes’s and others’ that were privately exchanged in correspondence, such as “It is outrageous rubbish beyond all possibility of redemption” (Keynes 1973, 250). Thus, even forthe sympathetic commentator, this controversy appears to have been a humiliation for Pigou.
This paper attempts to redeem Pigou by revealing the reasons why he found it diﬃcult tounderstand Keynes’s argument, which are to be found in the argument of monetary aspects
in Theory of Unemployment.
More recently, Ambrosi (2003) contributed considerably to the understanding of this controversy. He clarified the diﬀerences in the theories advanced by the three above-mentioned
2

economists, Keynes, Pigou, and Kaldor, and highlighted that the latter two used the assumption of a stationary state to theorize short-period economic interactions, whereas Keynes
privately complained about the oddity of this assumption. Ambrosi eventually concluded thatin terms of this issue and others, the unemployment controversy was inadequately engaged andended without any clear development. This paper contradicts his conclusion and claims thatat least from Pigou’s viewpoint, the development of a useful analytical method was achieved,
which resulted in the formulation of the Pigou eﬀect.

Section 2 deals with how Pigou came to accept Keynes’s views on the eﬀect of money wagechanges on employment. Pigou adopted a rather peculiar way of theorizing monetary aspects ofthe economy in Theory of Unemployment, which hindered him from rightly evaluating Keynes’s
argument in General Theory. However, Pigou eventually came to understand the interactionsof real and monetary variables through the controversy with Keynes and Kaldor between 1937
and 1938. These concepts were illuminated for Pigou by Kaldor’s use of a mathematical toolthat calculates diﬀerential coeﬃcients. Section 3 outlines the results Pigou derived from that
newly acquired analytical tool. While this tool enabled him to fully understand the interactive
movements of variables in an equation system, it likewise demonstrate clearly that a normal
macroeconomic system gave rise to a result unfavorable to Pigou, namely that money wage
cuts do not aﬀect employment if the interest rate is minimum. Section 4 outlines how Pigou
exactly formalized the Pigou eﬀect and succeeded in arguing for the validity of money wage
cuts even in times of the minimum interest rate. I will examine the relations between the
Pigou eﬀect and his earlier notion related to business cycles. Section 5 concludes that, atleast from Pigou’s viewpoint, the unemployment controversy was thoroughly ventilated andallowed him to better understand the interactions of money and real variables and formallyrestate an older notion in defense of his basic position.
3

2 How Pigou came to accept Keynes’s views
2.1 Monetary aspects of Theory of Unemployment
First in this section, I will examine the monetary framework as expounded in Theory of Unemployment (1933). Aslanbeigui (1992) briefly mentioned the assumption of a “standard monetary system” in that volume. She defended Pigou by arguing that since prices are constantunder this system, this would guarantee the validity of his theoretical framework exclusively
based on a real analysis. I will look at the monetary aspects of Theory of Unemployment
including the “standard monetary system,” and show that the excessively strong assumptions
made in this volume deterred Pigou from rightly understanding Keynes’s General Theory.
In Theory of Unemployment, Pigou for the first time dealt explicitly with the question ofwhether a cut in monetary wage rates will result in reducing real wage rates and expanding
employment (Pigou 1933, 101–102). He admits that if one assumes that all incomes are directly
related to industrial activities and that there are no fixed income strata, a decline in money
wages will not reduce real wages. This is because, assuming prime costs consist mainly ofwages and so the commodity prices depend largely on money wage rates, money wage cuts
will soon bring down commodity prices to the same extent and consequently will not bringabout a reduction in real wage rates. In this case, employment will not be augmented.
However, if one assumes that there are fixed income strata, Pigou claims that a money
wage cut will have an eﬀect on employment. He divides the aggregate money income Im into
labor income Il and non-labor fixed-income strata’s income In . A cut in money wages will notaﬀect the latter. When money wages are reduced from w to (w − h), the labor income will
decrease to w−hw Il while the fixed-income strata’s income will remain the same. The aggregate4money income will therefore become w−hw Il + In . Supposing, for the moment, that prices
are proportionate to aggregate money income, prices will decrease less than the extent of the
reduction of money wages, and therefore, real wages will certainly decrease.
If we highly value the consistency of this argument with those espoused in Industrial Fluctuations (1927), the above-mentioned process should be considered as referring to “forced
anti-levies”. Forced anti-levies mean the eﬀect of a price decline expanding the real incomeof fixed income strata. In Industrial Fluctuations, Pigou treats this eﬀect as a cause to checkthe activity of entrepreneurs in times of economic downturns, which usually involve a pricedecline. Here, he views the fixed income strata as a buﬀer against a price decline due to amoney wage cut. M. Blaug seems to interpret the above process as referring to “lags between
wage cuts and price reductions” (Blaug 1997, 664). If employment remains unchanged during
those lags in which prices have not yet declined, aggregate money income does not decreaseat all, contrary to Pigou’s own statement. That is because, under the current postulate, thereduction in labor income due to a money wage cut is oﬀset by the rise in employers’ income.
Although the above argument is suﬃcient to claim the eﬀectiveness of money wage cuts,
Pigou further discusses how the cut in money wage rates will aﬀect aggregate money income
under a realistic monetary policy. A ‘standard monetary system’ is one where aggregate money
income should be changed by the exact amount of the diﬀerence in employment multiplied by
the original money wage rate. If we write pi (i = 0, 1) for general prices and Fi for aggregate
real income, and suppose employment is augmented by h, thenp1 F1 − p0 F0 = p0 F00 h.

Since the general prices in period 1 (p1 ) equals

p0 (F0 +F00 h), the general prices in period 1
F1

become exactly the same as those in period 0 when the diﬀerence of employment is suﬃciently

5small, or constant returns prevail. Thus, under the standard monetary system, prices areheld rigid or changed according to the labor eﬃciency. Under this monetary policy, a cut inmoney wage rates leads to the proportional reduction in real wage rates, and this substantially
increases employment along the labor demand schedule that Pigou supposes is highly elastic—
the elasticity is well beyond unity according to him. He seems to think, therefore, that
aggregate money income will rise, rather than decline, after money wage cuts because they
will surely augment the aggregate labor income.
Pigou briefly mentions that the enlargement of public expenditure is required to carrythrough the standard monetary system in times of severe recession. Open market operations
by the monetary authorities can increase the quantity of money supply even in those times.
Even so, “there may be no positive rate of money interest that will avail to get this moneyused” (Pigou 1933, 213). Unless the government props up the aggregate money demand byincreasing its expenditure, those monetary operations will be futile in realizing the aimed
level of aggregate money income. This argument must be based on the notion of aggregatemoney expenditure that is ad hoc yet suﬃcient to allow the making of eﬀective policy recommendations. Behind Pigou’s conception that aggregate money expenditure depends on theinterest rate, must lie the implicit postulate that aggregate money expenditure depends on
investment and investment in turn on the interest rate. It should be noted that in Theory of
Unemployment, Pigou does not entertain the Say’s Law type of argument that a decrease ininvestment will be compensated for by an enlargement of consumption so that the aggregatemoney income will not be aﬀected.
Pigou thus argues for the validity of money wage cuts on employment from two aspects.
First, regardless of the kind of monetary policy adopted, the cut in money wage rates brings
down real wage rates through the process of a forced anti-levy and expands employment.
Second, under the realistic monetary policy of the standard monetary system, it is more6

certain that money wage cuts decrease real rates. In the second setting, in which prices areheld rigid, aggregate money income rises after the cut in money wage rates. For Pigou, thecut in money wage rate leading to the enlargement of employment is evident.
As will be stated below, the assumption of the standard monetary system was too strong a
condition in the sense that it enshrouds the monetary movements later treated by J. M. Keynes.
Since, under this assumption, changes in money wage rates is examined independently of themonetary framework determining the interest rate and the money income, one cannot deal
with the relations between the movements of money wage rates and other monetary variables.
Thus, Keynes should have directed his criticism at this very point had he not misunderstood
Pigou.

2.2 Keynes’s criticism
In General Theory, Keynes bitterly criticized Pigou’s Theory of Unemployment. The criticism
can be divided mainly into two points: First, Keynes states that Pigou assumed a labor supply
function with finite real wage elasticity (i.e., the upward-sloping curve). According to Keynes,
therefore, Pigou absurdly concludes that the existent unemployment is due to an aversion tolabor. As Ralph Hawtrey at that time and Aslanbeigui (1992) recently pointed out,2 it ismore reasonable to suppose that Pigou postulates the labor supply function with perfect wage
elasticity at the “stipulated rate” (i.e. the horizontal line).
The second criticism of Keynes’s is the one directed at the monetary aspects propoundedin Theory of Unemployment. Keynes points to the lack of the condition determining generalprices in its framework. In a literary sense, this is not correct because Pigou makes the as-

2 Brady (1994) claims otherwise, however. Since Pigou assumed perfect competition in Theory of Unem-

ployment, this must mean he assumed an upward-sloping labor supply curve. Ambrosi (2003, 78) rulesthat textual evidences cannot illuminate what kind of labor supply curve Pigou had in mind in Theoryof Unemployment.

7

sumption of a standard monetary system that rigidly regulates general prices. Furthermore, weshould notice that Keynes completely misunderstands the argument concerning fixed income
strata and a forced anti-levy discussed in the previous section (Keynes 1936, 276).
We can consider that the diﬀerence between Keynes’s General Theory and Pigou’s Theoryof Unemployment lies in the diﬀerence of assumptions. In contrast to the latter, the former
framework is built on the assumptions (1) that there are no fixed income strata, and therefore,changes in money wages do not aﬀect real wages and (2) that the monetary authorities do
not automatically intervene in the economy. Ironically, Keynes demonstrated that there is achannel where changes in money wage rates aﬀect employment under such an adverse setting.
In Keynes’s world, employment depends exclusively on eﬀective demand, and the reduction
in money wages does not directly aﬀect eﬀective demand since it involves the same extent
of reduction in prices. According to him, however, a money wage decline indirectly aﬀects
eﬀective demand as outlined below. Among those eﬀects advantageous to employment are thefollowing: A cut in money wage rates

1. in an open economy improves the balance of trade and worsens the terms of trade, whichleads to a rise in eﬀective demand and in marginal propensity to consume, respectively.
2. falsely, or temporarily, creates optimism among entrepreneurs by reducing their everyday cash-flow diﬃculties.
3. involves the decline in prices and aggregate money income, and hence, the reduction of
the liquidity preference schedule and the quantity of money supply being the same, thedecrease in the interest rate.

Among the eﬀects unfavorable to employment, are the following: A money wage cut

4. transfers the real income from laborers to rentiers and brings down the marginal propen-

8

sity to consume.
5. creates the expectation of a further wage cut and lowers the marginal eﬃciency of
capital.
6. gives laborers an opportunity to resort to industrial disputes.
7. involves a price decline and so enlarges the real burden of public and private debts.

Of these eﬀects, Keynes pays special attention to the reduction in the interest rates (3) andthe expectation of a further wage cut (5). He admits, at least theoretically, that if the cut inmoney wage rates does not create the expectation of a further cut, it expands employment
through the decline in interest and the resultant expansion of investment.
It should be noted that Keynes’s emphasizing the eﬀect through the interest rate is very
important. Although probably never intending to do so, Keynes actually demonstrates thatwage adjustment is eﬀective on employment even under a less favorable theoretical setting
than Pigou’s. On the other hand, this argument brought about an undesirable conclusion,that is, a cut in money wages does not aﬀect employment unless it involves interest reduction.
Let us look at how Pigou came to accept this new argument concerning money wages to beable to oﬀer an internal criticism.

2.3 Post-General Theory controversy on money wages
Just as Keynes, in General Theory, misrepresents Pigou, Pigou fails to understand Keynes’s
attempt, because he tried to view his argument exclusively through the framework of his
Theory of Unemployment.
Apart from the criticism that he directed toward the overblown rhetoric of General Theory,
Pigou points to two problems. First, he criticizes Keynes’s failure to clarify what sort of monetary policy is assumed to be adopted. As noted above, in Theory of Unemployment, monetary9policy means the standard by which the aggregate money income is regulated, the ways andmeans of which include fiscal policy in a time of need. Of course, this criticism is correct but
it is beside the point. Keynes attempted to investigate how the real and monetary variables
such as employment and the interest rate interact with one another under the assumption of
no external intervention and how they are aﬀected when an external intervention is made.
Second, Pigou argues contrary to Keynes that the cut in money wages is likely to raise,rather than decline, the interest rate if a realistic monetary policy is adopted. In this review,
Pigou notices that Keynes admits a money wage cut expanding employment “in some way, by
a process of repercussion” (Pigou 1936, 128). Clearly, Pigou seems not quite to understandwhat this process of repercussion entails. We can speculate what makes Pigou think that themoney wage cut is likely to raise the interest rate. We mentioned above that Pigou thought
the money wage cut would increase aggregate money income through the highly elastic labordemand curve under the standard monetary system. An increase in the aggregate money
income, other things being equal, involves an increase in the demand for money (or, thedecrease in Cambridge k) and so the rise in the interest rate.3
Since the two economists diﬀer in their assumptions, both conclusions of Keynes and Pigou
might be correct. Under Pigou’s assumptions, a cut in money wage rates directly brings down
the real wage rates through the process of a forced anti-levy. Therefore, it could augment
employment and also the aggregate money income even without a policy intervention to lower
the interest rate. In this case, the money wage cut raises the interest rate. Meanwhile, under
Keynes’s assumptions, a money wage cut does not directly expand employment but necessarily
lowers the interest rate by decreasing the liquidity preference schedule. Thus, we can defend
Pigou’s consistency within his own argument, though we must notice he could not realize what
3 See Pigou (1917).

“[O]ther things being equal, the larger [the total resources, or in so far as a certain
period of time is concerned, the total income] is, the higher will be the demand schedule for money”(Pigou 1917, 43).

10

Keynes meant regarding the eﬀect of a money wage cut.
In an article ‘Real and Money Wage Rates in Relation to Unemployment’ (1937), which
followed this review of General Theory, Pigou formally attempts to challenge Keynes’s views
on money wages. In this article, Pigou sets up a new macroeconomic theory incorporating
both real and monetary aspects. Since the short-period prime costs are equal to the value ofmarginal products, we obtainw(1 + r) = pF 0 (e)where w is money wages, r the interest rate, p general prices, F (·) aggregate production
function, and e employment.4 In contrast to Theory of Unemployment where prices are
assumed to be constant, Pigou succeeds in setting up a macroeconomic model in which pricesVm= FM(e)(Im is aggregate money income, M theare endogenously determined. Since p = FI(e)quantity of money supply, V income velocity), the above equation becomesw(1 + r)F (e)= M V.
F 0 (e)Pigou supposes that money supply depends on the interest rate, and income velocity on boththe interest rate and the proportion of labor income to aggregate income. Thus,

w(1 + r)F (e)= M (r)V (r, e)
F 0 (e)(1)∂V∂V
where dM
dr > 0, ∂r > 0, ∂e < 0. We need another condition to endogenously determine theinterest rate and employment. Pigou brings up a condition of no savings after the mannerof Ramsey (1928). As Ambrosi (2003) noted, the condition of no savings is unfit for a short4 This representation, w(1 + r) = pF 0 (e), exists in Theory of Unemployment (Pigou 1933, 58).

volume, however, Pigou does not treat it as one condition of the overall system.

11

In thisperiod analysis, yet Pigou seems to use it simply out of theoretical necessity. When savings
are nil, the interest rate equals to the rate of discounting future consumption, or the rate oftime preference ρ. Then,r = ρ(e)(2)

where the rate of time preference depends on employment or real income.5
Using the above two equations, Pigou demonstrates with reductio ad absurdum that amoney wage cut increases employment. Suppose first that money wage rates decline andthat employment remains unchanged. Employment being constant, the interest rate will be
constant from equation 2 and so will be the aggregate money income M (r)V (r, e). The money
income being the same, prices are the same, and the money wage cut involves the reduction
in real wages. Since employment must be augmented by the reduction in real wages, then, theoriginal supposition of constant employment contradicts the other assumption of the money
wage decline.
This reasoning is, however, the only result Pigou extrapolates from the above two equations,and we should note that he does not adequately handle them in the 1937 article. While Pigou
admits money wage cuts may decrease the interest rate, he thinks that this decrease is atemporary one that happens before equilibrium is reached.6 In Theory of Unemployment,
Pigou stated that a money wage cut temporarily involves a fall in the labor income andhence, in the aggregate money income to the same extent; however, this temporary fall inincome is soon followed by a rise in employment and the aggregate money income up to its

5 Ambrosi (2003) understands Pigou’s 1937 article as assuming the rate of time preference is always

constant. However, this is not accurate. This view is rather Keynes’s (1937) than Pigou’s. Keynes
replies to Pigou’s 1937 article in the same year. In that reply, Keynes misrepresents Pigou’s theory
perhaps intentionally to make something rational out of Pigou’s statement.
6 Kaldor interpreted that Pigou had already noticed that money wage cuts would directly reduce theinterest rate at the time of the 1937 article (Keynes 1973, 244). Even if Kaldor’s interpretation is right,
it is certain that Pigou failed to oﬀer a theory compatible with that view.

12original amount or even more than this amount. Thus, Pigou relies, once again, on the ad hoc
reasoning presented in Theory of Unemployment and still fails to grasp Keynes’s argument.
Keynes makes a very brief reply to Pigou’s 1937 article. All that Keynes attempts to say inthis note is that the model in the 1937 article is either inadequate to grasp the relationships ofthe variables in reality or internally inconsistent. Keynes mentions the lack of consideration
over the liquidity preference and the dependence of savings on real income. If these relationships are incorporated, Pigou’s model does not behave as Pigou explains. Pigou implicitly
assumes in the 1937 article that money wage cuts do not aﬀect money income. Keynes, however, thinks that a money wage cut directly lowers aggregate money income and if aggregatemoney income were to stay the same, the quantity of money supply must be augmented conversely with the decline in money wage cuts.7 As I mentioned above, this is all that in General
Theory, Keynes should have criticized in Pigou’s argument of Theory of Unemployment. In
this note, however, Keynes phrases it very briefly and almost unintelligibly, so that Pigou wasleft none the wiser with regard to the relationship between money wage rates and the interest
rate.
What enabled Pigou to understand this relationship is an article by Nicholas Kaldor attachednext to Keynes’s note. In this article, Kaldor makes a mathematical argument on how theabove two equations work out, which is quite intelligible to someone not familiar with the
newfangled technical terms. Instead of equation 2, Kaldor uses as an identical condition∂S
S(r, e) = 0 where ∂S∂e > 0, ∂r > 0. He also makes it clear that the income velocity should

be made dependent on the interest rate to incorporate the liquidity preference. Thus, Kaldor

7 “[T]he only banking policy consistent with the conditions of the simplified model [Pigou’s model in the1937 article] is one in which the amount of money created at a given rate of interest is not constant, but
is dependent on the level of money-wages. . .” (Keynes 1937, 744).

13

establishes the following system:w(1 + r) =F0
M (r)V (r, e)F

S(r, e) = 0

(3)
(4)

Though he does not write it in the article, he must have derived analytically the proportionof the change in employment to the change in money wages:(1 + r) ∂Sde∂r= − F 0 ∂S(< 0).8
0 V + M ∂V ) − ∂S M { d ( F 0 )V + F 0 ∂V } − w ∂S
dw
(M
F ∂e
∂r
∂r
de F
F ∂e
∂e
dM
∂V
Kaldor argues that a money wage cut increases employment “if, and only if, ∂S∂r , dr and ∂r∂Vare all positive and finite” (Kaldor 1937, 749).9 He highlights the fact that if dM
dr or ∂r isdebecomes nil, which means a money wage cut does not aﬀect employment (See 3.1
infinite, dw

below). Kaldor therefore concludes that a money wage cut expands employment only throughthe reduction in the interest rate.
Kaldor interprets this theoretical conclusion in the same way as Keynes does in General
Theory. The money wage cut decreases the quantity of money required for a given level ofreal income. This means a decline in the demand for money and hence in the interest rate,
given that the money supply remains the same. This process creates a result identical to thatof the monetary policy, increasing the money supply and decreasing the interest rate. Kaldor,
therefore, states that the adjustment of money wages is in fact “a piece of ritual” that brings
about the same result as could be easily realized by monetary policy.
8 Since there is a term −w ∂S in the denominator, the sign of this fraction as a whole seems undetermined.
∂e
de
dr
d
(1 + r)w is always positive, so dw> 0 and dw< 0 contradicts equation 3.
Yet, dw
9 Though it may be a typo, Kaldor makes one mistake. If ∂S is infinite, a money wage cut expands∂remployment. In this situation, the interest rate does not need to decline, and the money wage cut iseﬀective even when the interest rate is at the minimum level. Provided that ∂S
is a typo for ∂S, Kaldor∂r∂eis set free.

14

Replying to Kaldor in 1938, Pigou states, “I now accept Mr. Kaldor’s main contention”(Pigou 1938, 134). What urges Pigou to convert was “a logical rod wielded privately by
Mr. Champernowne” (Pigou 1938, 134).10 The account in this 1938 note clearly suggeststhat this logical rod refers to the analytical method. Pigou more simply demonstrates that amoney wage cut must involve the interest reduction to augment employment by diﬀerentiating
equation 3 with r. That is,d
de d F 0
F0 0
F 0 ∂VF 0 de ∂V(1 + r)w =( )M V +
MV +
M
+
M
.
dr
dr de F
F
F
∂r
F
dr ∂e

If the money wage cut were to involve the interest decline and the employment expansion,dw
dewere to be negative and dw
namely dr
dr positive, then it requires “(1) dr has the same signdas dr
(1 + r)w and (2) that ∂V∂e is negligible” (Pigou 1938, 137n, the symbols are changed).

The use of this analytical argument leads Pigou to realize the accurate working of his original
theory presented in the 1937 article and finally to accept Keynes’s views on money wages.
Later in 1941, Pigou develops the analytical discussion in Employment and Equilibrium. He
analytically examines the eﬀect of the changes in all the relevant variables on employment.
Let us look at the results below.

3 Analytical argument
This section first deals with the analytical discussion set forth in Employment and Equilibrium(1941). For consistency and simplicity, however, I choose to investigate it with the use of themodel presented in another of Pigou’s volumes, Keynes’ General Theory (1950).

10 Pigou often acknowledged Champernowne’s contributions in his writings (Pigou 1935, v; 1941, 110). It

seems that Pigou actually needed mathematical ability from without, as Collard (2002, xxxn1) states.

15

The model is as follows.11

I(r) = S{r, F (e)}w=

M V (r)
F (e)

(5)
(6)

where I is investment, S savings. Unlike the previous model he used until 1938, Pigou assumes
the equilibrium between savings and investment, rather than no savings, and therewith frames
the model suited to a short-period analysis.
Since the above model consists of two equations and four variables, it requires another two
conditions to be determinate. Pigou stops to mention that the model can be viewed as along-period model by adding specific conditions. In the long-period analysis typified by A.
Marshall’s Principles of Economics, one can ignore the diﬀerences in the rate of employment
and general prices caused by business cycles. The quantity of employment is then determined
exogenously by a certain constant proportion of population. Supposing the level of prices
relates to that of money wages, the above equations work out in the following way: The
population and labor eﬃciency determine the aggregate real income, and then the relations
between savings and investment, I(r) = S(r), determine the interest rate.
Taking short-period cyclical movements into account, the rate of employment must be an
endogenous variable. To realize this, the money wage rate and the quantity of money supply
must be exogenously controlled.
In Employment and Equilibrium, Pigou derives a diﬀerential coeﬃcient with each mn (n =11 In Employment and Equilibrium, the simplest model is as follows.

I(r) = S{r, F (e)}y = S{r, F (e)}C(x + y) = g(r)where x is employment in the consumption-goods sector, y employment in the investment-goods sector,
C a fixed number representing the proportion of labor income, and g the aggregate money income.

16

Variablemoney wages w = m1 w
money supply M = m2 M
income velocity g = m3 g
investment schedule I = m4 I
labor eﬃciency in investment sector I = I( mr5 )savings schedule S = m6 S
overall labor eﬃciency F = m7 F

de
wF ∂S
0
dm1 = − A ( ∂r − I )de
M V ∂S0dm2 = A ( ∂r − I )dededm3 = dm2deIM V 0dm4 =A
derI 0 M V 0
=
−
dm5
A
de
SM V 0
=
−
dm6
A
de
F
dm7 = − F 0

Sign
−
+
+
+
+
−
−

∂S
Table. 1 A = F 0 {w( ∂S− I 0 ) + M V 0 ∂F}. Each m is written as 1.
∂r

1, ..., 7) that is multiplied on each variable.

r) = m6 S{r, m7 F (e)}m5m2 M m3 V (r)m1 w =
m7 F (e)

m4 I(

(7)
(8)

These ms assume the value of slightly more than unity, but only one m is present at a time.
Then, one can derive a diﬀerential coeﬃcient of e in terms of each m. The results of calculation
are summed up in table 1.
We can rely on G.M. Ambrosi’s (2003) graphical tool to explain the above results. In
figure 1, the northeast quadrant shows a downward-sloping curve representing the equilibriumof savings and investment, namely the IS curve.12 The northwest quadrant represents theincome velocity as an increasing function of the interest rate. The southeast quadrant displays
the relationship between the aggregate money income and the real income, which almost
corresponds to the demand for money due to the transaction motive.
A rise in money wages is represented by an increase in the slope of the curve in the southeast
quadrant of figure 1. It is clear that this change leads to the rise in money income and the

12 Diﬀerentiating S = I with F∂S

drproduces dF= − ∂S∂F 0 (< 0). Since ∂S> 0, the Pigouvian IS curve is
∂r
∂r

−I

less steep than the IS curve derived with the saving function that does not include the interest rate.

17

Fig. 1decline of real income and employment.13
An increase in money supply corresponds to the movement of the curve in the northwest
quadrant to the left. This involves the increase in money income, the decrease in the interest
rate, and also the expansion in employment. The expansion of the income velocity function
brings about an identical result.
The enlargement of the investment function means the upward movement of the IS curvein the northeast quadrant. In new equilibrium, therefore, real income, money income, andthe interest rate all go up. Similarly, improvement in labor eﬃciency in the investment-goods
sector is represented by the upward shift of the IS curve, which augments employment.
The increase of the saving function, as table 1 shows, involves a decrease in employment.
Since the increase of the saving function means a reduction in the interest rate to a given
investment function, it is represented by a downward shift of the IS curve. After this change,

13 See 2.3.

We discussed whether a rise (decline) in money wages leads to the rise (decline) in money

income.

18

real income, money income, and the interest rate all decline.
In Keynes’ ‘General Theory’ (1950), Pigou highly values the role played by Keynes inconvincing the public that the increase of savings is harmful to employment. The public
including politicians and bureaucrats had thought that economy campaigns by the publicauthorities did not damage employment at the time of economic slumps. They had had
an implicit theory that even at the time of less than full employment, a restraint on public
expenditure only increased savings and transferred resources from consumption to investment.
However, this is not true, as both Keynes and Pigou claim. Pigou did note the unfavorable
eﬀect of economy campaigns on employment in times of slumps long before the publication ofGeneral Theory. He mentioned that the anticyclical adjustment of public expenditure would
be eﬀective in stabilizing economic fluctuations even before World War I.
Further, in the early 1930s, Pigou cast a reasoned doubt on the economy campaign conducted by the government (Pigou 1930).14 Of course, he well understood the purpose of thegovernment. Under the system of a gold standard, “if foreigners with balances here hold asimilar belief, such a campaign may check a drain of gold abroad, and so help money income”(Pigou 1950, 41). As he then criticized, Pigou suspects that the pursuit of this policy was
based on the underestimation of the adverse eﬀect of increase of savings.
While Pigou thus agrees with Keynes about the eﬀect of changes in savings on employment,
he contradicts Keynes on a related point. Keynes mentions in General Theory that increases
in consumption have a stimulating eﬀect on investment so that investment will eventually
expand, rather than contract. He, therefore, strongly supports a raise in taxes for the rich to
remedy “such large disparities [of incomes and wealth] as exist to-day” (Keynes 1936, 374).

14 “When,

however, as at the present time, there is an enormous mass of unemployment, [the virtue
and relevance of criticisms of the State’s action to reduce unemployment] are lost. If employment is“artificially created” in these conditions, men are available to come into it, not merely from more usefuloccupations elsewhere, but from soul-destroying idleness” (Pigou 1930, 12).

19

Pigou, on the other hand, thinks that the reduction of the saving function, while augmenting
employment, involves a reduced amount of realized investment. This opinion is borne out byan analytical calculation by which we obtain the proportion of the increment of the savingdIfunction to the variation of the amount of investment, dm= − IwS
0 A (> 0), from equations 5
6

and 6. Pigou accordingly states that the policy to reduce income disparity impedes capital
accumulation.
Lastly, an improvement in overall labor eﬃciency analytically produces the simple result
7F
of no change in real income because dm
dm7 = 0. This means that an improvement in the

productivity of each worker exactly balances out the decrease in employment due to thischange. Since a production function itself is used as an abscissa axis, we cannot describe thisprocess in figure 1. This change also causes no variations in the interest rate or money income.
All the results shown above depend on the diﬀerential coeﬃcients of functions having specificsigns and finite values. As Kaldor mentions in his 1937 article, however, it is plausible in areal economy for the diﬀerential coeﬃcient of the income velocity function to have an infinite
value. This is the situation when the interest rate is at the minimum level. In figure 1, it isrepresented by the horizontal part of the curve Im = M V (r) in the northwest quadrant. Next,
let us look at what change the perfect elasticity of income velocity function brings about toeach result of analytical calculation.

3.1 Perfect elasticity of the income velocity function
Insofar as the income velocity function has perfect elasticity, we can recast table 1 into table
2. Between these two tables, all results except the last one vary. The changes in the first
three variables do not aﬀect employment in the present setting. The changes in the next threevariables, however, have stronger eﬀects on employment.

20

Variablemoney wages w = m1 w
money supply M = m2 M
income velocity g = m3 g
investment I = m4 I
labor eﬃciency in investment sector I = I( mr5 )savings S = m6 S
overall labor eﬃciency F = m7 F

dedm1 = 0dedm2 = 0dedm3 = 0deI∂S
dm4 = F 0 ∂F
de
rI 0
∂S
dm5 = − F 0 ∂F
deS∂S
dm6 = − F 0 ∂FdeF
dm7 = − F 0

Sign
0
0
0
+
+
−
−

Table. 2 Each m is written as 1.

Let us look at figure 2. First, the changes in variables m4 , m5 and m6 are all represented by
the shift of the IS curve in the northeast quadrant. Since the interest rate is now fixed at theminimum level, the shift of the IS curve aﬀects employment without any set-oﬀ through the
movement of the interest rate. These changes involve changes in money income in the same
direction and of the same extent as the change in real income.

Fig. 2

Next, changes in variables m2 and m3 mean the leftward movement of the curve in thenorthwest quadrant. When the interest rate is already at the minimum level, however, these21changes do not bring down the interest rate any further. Equilibrium is attained at the same
point on the same IS curve in the northeast quadrant, and employment, real income, andmoney income all stay the same.
Lastly, a change in money wages (m1 ) consists of the change in the slope of the line in thesoutheast quadrant. As long as the interest rate is at the minimum level, the fixed rate ofinterest and the IS curve determine the level of real income and employment. A change inmoney wages only varies the money income because the latter is obtained by multiplying themoney wage rate and the real income already decided. Thus, a rise in money wages results in
no change in real income and a proportional rise in money income.
The result that a money wage cut does not influence employment in times of the minimum
interest rate stands in conflict with Pigou’s general views. It is, however, certain that Pigou
admits this theoretical result. He states the following in the 1938 note:

We may conclude, therefore, that, within the framework of our model, a cut in money
wage-rates is fairly certain to entail a reduction in the rate of interest, and so an increasein employment. In the sense that it would not entail an increase in employment unlessit entailed a reduction in the rate of interest, we may properly say that it acts on thevolume of employment through the rate of interest. (Pigou 1938, 137)

In this citation, however, Pigou seems to provisionally accept only the mathematical result,
not the economic argument that Kaldor, or Keynes before him, uses to explain it. In Theory of
Unemployment, Pigou had highlighted that the existence of a fixed-income class should cause
a “forced anti-levy” and claimed that a money wage cut would directly increase employment.
Therefore, even though a money wage cut is ineﬀective in times of the minimum interest
rate under the Keynesian setting, Pigou still had a reason to argue that it is eﬀective undera diﬀerent setting. In fact, he continues to argue so in Employment and Equilibrium, and22

later.15 In 1943, Pigou succeeds in devising an original model to formally support his claimthat a money wage cut is eﬀective in times of minimum interest rate. As mentioned below, I
propose that the model presented in 1943 should be built on the idea of forced anti-levy.

4 The Pigou eﬀect
4.1 How Pigou actually presents it
In his review of General Theory, Pigou criticized Keynes’s notion of unemployment
equilibrium—in Pigou’s terms, the “Day of Judgment”—apart from the two points mentioned
in the preceding section. According to Keynes, as capital accumulation substantially advances
and the marginal eﬃciency of capital declines, desired investment and desired savings would
be equilibrated if the interest rate were proportionally lowered; yet, since there is a limit below
which the interest rate could not decline, they would not be necessarily equilibrated. Whenthe marginal eﬃciency of capital as a long-period trend has come to fall short of the minimum
interest rate, desired investment becomes zero, and desired savings must accordingly be zero;and if not, the disequilibrium between them leads to the gradual fall of aggregate income.
Desired savings, however, do not easily become zero because if they were to be zero, themarginal propensity to consume must become unity, and this will require the real income to
substantially decline. Thus, Keynes anticipates that the goal to which the economy leadsin the long run will be “one in which employment is low enough and the standard of life
suﬃciently miserable” (Keynes 1936, 217–218).
In his 1936 review, Pigou claims that the ultimate situation after eﬀective investment outlets

15 In Employment and Equilibrium, Pigou states that under a hypothetical situation where the interest rate

is zero and people still desire to save, it is possible that “full employment is still maintained, in accordancewith the ‘classical view’, through an appropriate succession of adjustments in money wage-rates” (Pigou
1941, 132).

23

disappear should not be the Day of Judgment as Keynes predicts. Pigou claims this on the
grounds that a money wage cut will prevent unemployment from expanding. Even so, in thisvolume, Pigou does not fully address the related theoretical considerations.
Later in Employment and Equilibrium (1941) and in journal articles, Pigou formally deals
with the doctrine of the Day of Judgment. Among the treatments of this theoretical matter, I
focus on that presented in an article “The Classical Stationary State” (1943). In that article,
Pigou sets up the following model:

I(r) = 0(9)S(e, r, T ) = 0(10)

V (r) =

F (e)
T

(11)

where T is the real value of the stock of money.16 Let us suppose that capital accumulation
advances beyond a certain limit, and that the amount of desired investment as a long-period
trend is nil. These suppositions naturally entail that the interest rate be minimum.
To attain the equilibrium between desired savings and desired investment, the former mustbe zero; yet, like Keynes, Pigou does not think that the proportion of consumption to income
easily becomes unity. This is, first, because, since the interest rate cannot fall below zero, thedecline in desired savings due to the fall in the interest rate will cease at a certain point. Second,he thinks that the motives for savings include the desire for the possession of wealth itself and
16 I have omitted the capital stock C

from saving and investment functions because Pigou treats thatvariable as exogenously given. In addition, in the article, Pigou sets up the equation r = g( FT(e) ) insteadof equation 11. Even so, it is clear that by this equation, he means the liquidity preference schedule or theF (e)Cambridge cash balance equation. Therefore, I have chosen to more directly write V (r) = T . Thereis a diﬀerent interpretation by Melitz (1967) that this function concerns the portfolio eﬀect balancing
yield from physical stock and opportunity yield from cash. However, this is wrong simply because r in
the above equation is not the rate of yield from physical investment, but the interest rate or the rates
of securities whose increases should decrease the present value of the yields from physical stock. He also
overlooks the real value of cash included in the saving function, which is crucial to his conclusion thatthe wealth eﬀect is immaterial in Pigou’s 1943 article.

24not just for the income from interest and dividends. In regard to these two considerations,Pigou admits that even when the interest rate is minimum, savings will not usually become
zero.
Pigou, at the same time, proposes that the desire for the possession of wealth is variableand dependent on the real value of wealth, or the real value of the stock of money in this∂S
framework: thus, ∂T< 0.17 The real value of money stock depends on money supply andgeneral prices, but money supply is not necessarily a relevant factor. Open market operations
and other common ways of adjusting money supply change only the proportion of money in the
total stock of all kinds of wealth, and do not increase that stock. Therefore, these ordinary
monetary policy tools cannot have the eﬀect of aﬀecting savings. Thus, what is essential
is general prices, which are supposed to move parallel with money wage rates. With these
considerations in mind, we can more correctly write the above equation system as follows:

I(r) = 0S(e, r, p) = 0
V (r) =

pF (e)
M

w=p

where ∂S
∂p > 0，and w and M are exogenous variables.
Let us then examine this equation system. We can obtain the proportion of the incrementof money wages to the change in employment:∂S 0
0
F ( ∂Sde∂r − I ) + ∂p V M= − ∂S.
0dw
w( ∂r − I 0 ) + ∂S
∂e V M
17 Pigou notices that not all the money held by the public is aﬀected by price declines (Pigou 1947b, 250).

Price declines do not aﬀect the real value of the money based on bank loans since they also increase thereal value of the debts.

25

If the interest rate is minimum and the income velocity function has a perfect elasticity,
∂S

de
∂p
= − ∂S .
dw∂e
Pigou estimates that savings will be negative when the real value of money stock is suﬃciently
large, or general prices suﬃciently decrease, and he means by this that desired savings anddesired investment will certainly come to equilibrate with one another at some point. Thus,
the sign of ∂S∂p continues to be positive after savings become negative, and consequently thedesign of dw
should always be negative despite the current situation where investment is zero andthe interest rate is minimum.18 Flexible wage adjustment cannot only solve the disequilibrium
between desired savings and desired investment but also expand employment by decreasing
desired savings. Under this Pigouvian setting, the Day of Judgment will not materialize.
Pigou thus demonstrates that the goal toward which the economy moves is a classicalstationary state with full employment. On the other hand, he considers it implausible forthe described process to fully appear because of the following external causes. First, thegovernment will give in to demands from workers and set up a minimum wage to check thedecline in money wages. This, of course, starts the pressure of income reduction again. Second,
the government will also undertake investment by itself to prevent the decline in employment.
Pigou thinks that this government action will halt the process toward the Day of Judgment.
Third, Pigou doubts the validity of the very assumption that new investment outlets will
entirely disappear for a long time. “Since . . . there is every reason to expect that scientificdiscoveries will continue to be made, and so that new openings for profitable investment willappear in the future, as they have in the past, it may well be that no stationary state of any

18 Incidentally, we can obtain exactly the same result with regard to the eﬀect of the changes in othervariables listed in tables 1 and 2. The addition of p in the savings function only aﬀects the result ofchanges in money wage rates.

26

kind, neither heaven nor hell, will ever be attained; but economic man for the remainder of
his career will continue rather to live and move in purgatory” (Pigou 1950, 38).

4.2 Link between forced anti-levy and Pigou eﬀect
Thus far, we have seen that Pigou emphasizes the eﬀect of decreases in prices to expand
consumption to criticize Keynes’s notion of long-period unemployment equilibrium. In thissection, I propose that Pigou intends this eﬀect of price declines to stimulate employment also
as a short-period eﬀect. The most important evidence is the similarity between that eﬀect
and the process of a “forced anti-levy” mentioned in Theory of Unemployment.
As noted in section 2.1, Pigou argues in Theory of Unemployment that a money wage reduction acts on employment through the buﬀer of a fixed-income class. Although in that volume,
he simply states that this eﬀect leads to the divergence between money wages and productprices, more precisely it is through the expansion of aggregate expenditure in real terms thata forced anti-levy aﬀects employment. An anti-forced levy, namely the increased income ratioof a fixed-income class, does not directly increase aggregate expenditure in real terms and sodoes not increase employment. The fixed-income class must enlarge its consumption and investment when faced with decreased prices. If the fixed-income class does not remain content
with the same standard of living and raises its consumption in real terms, it would be due tothe enlargement of its expending capacity in real terms by the price decline.
Using the present symbols, the eﬀect of a forced anti-levy to expand aggregate real consumption is represented in the same way as the expansion of consumption due to the wealtheﬀect shown above, that is to say, ∂S∂p > 0. The equation system incorporating the former
short-period eﬀect is identical with the system stated in the previous section. Thus, thisequation system can be seen as either a long-period analysis incorporating the wealth eﬀect27

or a short-period analysis equipped with a forced anti-levy. We can, at least, reasonably inferthat the source of inspiration for the Pigou eﬀect was Pigou’s own earlier notion of a forced
anti-levy.
Further evidence suggesting that the above system is meant as a short-period analysis isthat there is another instance where Pigou clearly examines short-period movements under
the assumption of a stationary state. As discussed above in section 2.3, Pigou postulates astationary state to investigate the eﬀect of money wage cuts on employment. In spite of hisevident intention to analyze a short-period eﬀect, he chooses a less intricate situation withno investment or savings. Kaldor appears to support Pigou’s methodology by stating, “theargument [advanced with the assumption of no investment] is equally applicable to the moregeneral case where investment is assumed to be constant and positive” (Kaldor 1937, 751).
The above considerations lead us to propose to formulate the Pigouvian macroeconomic
model reflecting his true intentions as follows.

I(r) = S(e, r, p)
V (r) =

pF (e)
M

w=p

Pigou never abandoned his belief that money wage cuts are eﬀective in raising employment
regardless of whether the interest rate is at the minimum level or above it. This model
unambiguously states why he could hold firmly to that belief.

28

4.3 Implications for the reality
We have so far discussed Pigou’s views on money wages and seen that he invariably stresses
the validity of money wage adjustment. What makes him think it important to demonstrate
its validity? Two real-life points determine his interest.
First, Pigou thinks that apart from the 1930s, the large amount of unemployment in thelatter half of the 1920s is mainly attributable to the failure of money wage adjustment. This
failure, he argues, was caused by the bargaining power on workers’ side being strengthened by
newly introduced social legislation.19 The prevailing circumstances were also important. In
the latter half of the 1920s, monetary policy was restricted by the gold standard, and fiscal
policy was also shackled because of the enormous amount of war debts. Pigou seems to bewell aware of these policy constrictions because he noted in Industrial Fluctuations (1927) thata gold standard could restrict monetary policy and he also joined the controversy over war
debts during the 1920s. Considering these circumstances, it is probable that Pigou thoughtthat money wage cuts were the only eﬀective way to remedy prevailing unemployment.
In the economic circumstances of the 1920s, it was crucial whether money wage cuts wereeﬀective or not when the interest rate was minimum. This is because in the 1920s, themonetary authorities had to keep the domestic interest rate high to maintain the international
exchange rate of sterling, and so the prevailing interest rate at those times was, though quite
high, practically at the minimum level. Consequently, if it was admitted that money wage
cuts aﬀect employment only through the decline in the interest rate, money wage cuts would
be ineﬀective under these conditions. This seems to be the reason why Pigou so persistently
argued for the validity of money wage cuts regardless of the level of interest rate.

19 See Pigou (1927b, 355; 1933, 252–6; 1941, 93; 1945, 73; 1947, Pt. 2; 1952, 103).

29

Second, Pigou notes that money wage rates are determined by negotiations between workers
and employers, and that workers tend to view the improvement in business conditions as agood opportunity to claim for wage increase.20 If employers yield to these claims and money
wages rise each time the economy improves, the recovery of employment will be partly cancelled. Pigou fears the possibility that the degree of this setoﬀ might be very large dependingon labor’s attitudes. When workers behave based only on the interests within unions, unemployment would be kept high even if the economy improves. To achieve full employment inthis situation, progressive increases of public expenditure will be necessary, but this surely
involves uncontrollable inflation. Thus, Pigou regards the cost-push inflation as a real danger
and calls for responsible actions on the part of workers. For him, the suggestion that changes
in money wages do not aﬀect employment was a hazardous one.

5 Conclusion
This paper has focused on A.C. Pigou’s unemployment theory after his Theory of Unemployment (1933) was published. In hindsight, Pigou argued from an inadequate framework in
Theory of Unemployment. Even so, with the aid of the notion highlighted in his earlier work,
namely, a forced anti-levy, he claims that money wage cuts will certainly expand employment.
After the publication of Keynes’s General Theory, a controversy arose between Keynes andPigou concerning the eﬀect of money wage cuts on employment. Although Pigou eventuallyacknowledged his defeat and accepted Keynes’s conclusion on money wages, he gained a theoretical tool in the bargain. In his 1943 article, he returns to the battleground and succeeds informalizing and incorporating his earlier notion of a forced anti-levy to conclude that money
wage adjustment is eﬀective on employment irrespective of the interest rate.

20 See Pigou (1927b, 368; 1933, 250–251; 1945, 39; 1946, 267).

30

What did Pigou actually gain from Keynes or their controversy? We have seen that Pigou
set up a macroeconomic model by himself in his 1937 article, although he could not turn it tofull account or realize the interaction between money and real movements. Therefore, we cannote that what he lacked was an analytical method to calculate diﬀerential coeﬃcients. Thus,
acquiring this method served as a catalyst for Pigou to understand the Keynesian macroeconomic framework. In Employment and Equilibrium (1941), Pigou boldly takes advantageof this analytical method, and finally in 1943, he could oﬀer a valid counterargument using
both the newly acquired method and the idea originated in the 1920s. We can conclude thatat least from Pigou’s point of view, the unemployment controversy in the 1930s was sincerely
fought and produced meaningful results.

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