Kalecki s 1934 model VS. the IS LM model

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Euro. J. History of Economic Thought 14:1 97 – 118 March 2007

Kalecki’s 1934 model VS. the IS-LM model
of Hicks (1937) and Modigliani (1944)*

Michae¨l Assous

1. Introduction
In his influential book Anticipations of the General Theory? Patinkin (1982)
concluded that before the publication of the General Theory Kalecki did not
deal with the notion of unemployment equilibrium in terms of a general
equilibrium system of simultaneous equations. In short, Patinkin claimed
Kalecki did not anticipate the Keynesian model,1 of which the more
relevant interpretation, according to him, is the IS-LM model (Patinkin
1990a,b). In 1995, Simon Chapple claimed in a closely argued article that:
‘an early version of the mainstream Keynesian model was constructed and
published by Kalecki before 1936’ (Chapple 1995: 521).2 Focusing on
Address for correspondence
PHARE-CNRS, Maison des Sciences Economiques, 106 – 112, boulevard de

l’Hoˆpital, 75647 Paris Cedex 13, France; e-mail: michael.assous@wanadoo.fr
* I am grateful to Professors Richard Arena, Rodolphe Dos Santos Ferreira,
Gilbert Faccarello, Harald Hageman, Heinz Kurz and Antoine Rebeyrol for
helpul comments and suggestions on an earlier draft. I am especially indebted to
Professor Alain Be´raud, with whom I had lengthy exchanges. I also gratefully
acknowledge Claude Marguet for detailed comments and useful observations.
Helpful remarks of two anonymous referees are gratefully acknowledged. Any
remaining errors in this paper are mine.
1 In his 1982 study, Patinkin affirmed that Kalecki had not analysed the
mechanisms by which the economy is likely to reach equilibrium with
unemployment without contrasting it with classical mechanisms. Moreover,
Patinkin did not think that Kalecki defined a general equilibrium model like the
one described by Hicks in 1937 (Patinkin 1982: 10 – 11).
2 Chapple aimed to demonstrate that Kalecki anticipated the key features of the
General Theory, which, as Patinkin defined them, are threefold. First, he claimed
Kalecki’s works prior to the General Theory’s publication contained the notion of
effective demand whose essence is, according to Patinkin, the well-known fortyThe European Journal of the History of Economic Thought
ISSN 0967-2567 print/ISSN 1469-5936 online Ó 2007 Taylor & Francis
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DOI: 10.1080/09672560601168488

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Michae¨l Assous

Kalecki’s (1934) article,3 Chapple showed that Kalecki had constructed
three variants of the IS-LM model that allowed him to mimic the principle
conclusions of the neoclassical theory and to explain the persistence of
unemployment.
Centring on a discussion of Patinkin’s argument, Chapple pushed to the
background the differences between Kalecki’s (1934) model and the IS-LM
model. The aim of this paper is to highlight these differences4 by showing
how Kalecki’s model differs significantly from the two main variants of the
IS-LM model, those of Hicks (1937) and Modigliani (1944).5 Based on this
twofold comparison, the paper then shows that Kalecki’s model offers an
original explanation of the difference between classical models (based on
Say’s law) and types of models that were to be called later Keynesian
models. Showing that Kalecki’s theory is concerned, strictly speaking, with a
situation of unemployment ‘quasi-equilibrium’, one then understands that
the validity of his analysis does not depend on the existence of either of

these special assumptions of the liquidity trap (Hicks) or alternatively
absolute rigid money wages (Modigliani). Indeed, as Kalecki stressed in the
conclusion of his 1934 article, his theory aims at analysing the situation of
five-degree diagram (Chapple 1991). Second, contrary to Patinkin, Chapple
suggests that Kalecki provided an integrated treatment of goods market
equilibrium with money market equilibrium (Chapple 1995, Osiatynski 1985,
1992). Last, he rebutted Patinkin’s argument that Kalecki did not link aggregate
demand with the marginalist theory of short-run aggregate demand (Chapple
1995).
3 Kalecki’s 1934 article was originally published in Polish in the main Polish
economic review Ekonomista and was translated into English only in volume 1 of
Kalecki’s Collected Works. The fact that Kalecki did not choose to translate this
article to claim anticipation of the General Theory continues to be ignored by
Patinkin’s criteria. (See Chapple 1991 on the discussion of Patinkin’s criteria.)
4 Chapple noticed briefly how Kalecki’s model differs from the textbook IS-LM
version, emphasizing only in passing the specificity of Kalecki’s treatment of the
labour market in the unemployment variant of his model.
5 In his influential 1944 article, Modigliani recast Hicks’ initial model into what
was to become the standard version of the IS-LM model (see Darity and Young
1995, Barens and Caspari 1999, De Vroey 2000, Young 1987). Indeed, when

Hicks opposed Keynes and the classics, he admitted that money wages are given
both in the Keynesian and the classical models. Hence, Keynes’s main
contribution is that of having built a model based on the theory of liquidity
preference. Modigliani, however, found Hicks’ analysis flawed. In 1944, he
presented a new version of the difference between Keynes and the classics. To
him, the liquidity preference theory is fully acceptable in a classical model.
Keynes’s essential contribution would be that he showed that a macroeconomic
equilibrium with unemployment is possible when money wages are rigid. It is
around this idea that a synthesis between the classical tradition and the
Keynesian revolution was developed.
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disequilibrium unemployment and not the situation of unemployment
equilibrium. As soon as the assumption of a given volume and structure of
capital equipment is abandoned, then, as a result of changes in capital stock,
there will be a continual movement through a series of ‘quasi-equilibria’.

Thus, even if money wages adjust in response to unemployment movements,
the economy will not necessarily reach a position of full employment.6,7
This paper is organized as follows. The first section outlines the
construction of Kalecki’s (1934) article. Starting from Kalecki’s analysis of
classical economics, this section reconsiders the crucial steps in the process
of constructing Kalecki’s unemployment model and proposes a
formalization of Kalecki’s argument. The last two sections then compare,
respectively, Kalecki’s article with the Hicks and Modigliani IS-LM models,
focusing on differences that affect the structure of the economy, the effect
of demand shocks on employment and unemployment analysis.

2. A reconstruction of Kalecki’s ‘Three Systems’
2.1. Systems I and II
Kalecki’s 1934 model describes a perfectly competitive economy whose
employed workers consume their entire wages.8 The first variant of this
6 It is worth stressing Kalecki’s analysis differs also from Patinkin’s own IS-LM
model in terms of unemployment disequilibrium whose differences with
Modigliani’s 1944 model are discussed by G. Rubin in the 2004 supplement to
History of Political Economy. Patinkin’s model is based on the idea that when
money wages decline in the face of excess supply of labour, the economy does

not steer itself to full employment. His message is that even if full employment
equilibrium is globally stable, disequilibrium can be protracted and stubborn. By
assuming money wages do not fall in the face of excess supply of labour, Kalecki
underlined on the contrary that disequilibrium does not depend on money
wages adjustments – although induced variations on money wages play a part on
employment variations – but on investment variations caused by the evolution of
the profitability of equipment.
7 It is important to stress that in his 1934 perfectly competitive framework, the
focus of attention in terms of sectors of the economy was not the product
markets. In Kalecki’s model, prices are viewed as moving in line with marginal
costs so that the major cause of unemployment cannot be seen to be a mismatch
between the degree of monopoly, equal to zero, and the level of investment
expenditures (see Sawyer 1985, Lopez and Assous 2007 on the importance of
imperfect competition in Kalecki’s latter works) but only on the weakness of
capitalist expenditures.
8 Both production sectors operate with a constant and historically given capital
stock in which technology exhibits decreasing marginal productivity of labour.
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model – System I – is a classical model founded on Say’s law.9 Kalecki
emphasized this point by considering two shocks: a rise in the labour supply
and an exogenous reduction in capitalists’ consumption – capitalists’
consumption being itself considered exogenously given. In both cases he
showed that the production of investment goods increases.
As Kalecki stressed, an excess supply of labour reduces money wages,
causing on the one hand a rise in employment and aggregate production –
because of the fall in real cost – and on the other hand a rise in investment.
Indeed, according to Say’s law and capitalists’ consumption assumed given,
capitalists invest the profits due to the fall in money wages. Finally, because
there is at the same time a rise in demand and in profitable output, a level
of macroeconomic equilibrium, characterized by a higher level of employment and of production of investment goods, is reached.
Considering the labour supply as constant, Kalecki envisioned a second
shock: an exogenous fall in capitalists’ consumption. Again, his analysis
rested on Say’s law. Thus, by reducing their consumption, capitalists
correspondingly increase investment. The price of investment goods rises
because demand is greater whereas the price of consumer goods falls

because demand is smaller. Finally, employment and production rise in the
investment goods sector and shrink in the consumption goods sector
(Kalecki 1990: 205).
Then, Kalecki concluded, the production of investment goods is an
increasing function of the supply of labour (assumed inelastic) and a
decreasing function of capitalists’ consumption:10
I ¼ f N ; Cp




ð1Þ

Investment demand is assumed to depend negatively on the interest rate
and positively on the current profitability of equipment for which
entrepreneurs expect the return of their investment projects:
The number of investment projects which pass the profitability test depends on the
mutual relation at a given moment between prices of consumer goods, prices of

Profit maximization under perfect competition is then assumed as prices are
equal to marginal costs. Implicit assumptions include a closed economy and no

government sector.
9 Kalecki characterize Say’s law as follows: ‘In System I, the principle of
preservation of purchasing power is pushed to the extreme: all income must
be spent immediately on consumer or investment goods. This model is in fact
accepted by all classical economists (Kalecki 1990: 201).
10 The notation used by Kalecki has been replaced by the more conventional ones.
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investment goods, and wages (which are determinants of the expected gross
profitability), and on the rate of interest.
(ibid: 206)

Hence, since the supply of labour and capitalist consumption entirely
determines the relation of prices and

wages, investment demand can be
presented as the function C N ; Cp ; r (ibid: 206).
Assessing the production of investment goods is determined by equation

(1) and the

demand for investment goods is represented by the function
C N ; Cp ; r one obtains the condition of equilibrium in the investment
good market from which the equilibrium rate of interest is obtained:


I ¼ C N ; Cp ; r
ð2Þ
The functions f and C thus determine investment goods output and the
rate of interest.
The formal model underlying Kalecki’s System I can be represented as
follows:
C ¼ fC ðNC Þ

ð1:1Þ

I ¼ fI ðNI Þ

ð1:2Þ

0

W ¼ pC fC ðNC Þ
0

ð1:3Þ

W ¼ pI fI ðNI Þ

ð1:4Þ

NI þ NC ¼ N

ð1:5Þ

I ¼I

p


pI
; r; g
W W
C

;

C ¼ Cp þ

WN
pC

ð1:6Þ

ð1:7Þ

M ¼ kðpI I þ pC C Þ

ð1:8Þ

N ¼N

ð1:9Þ

Equations (1.1) and (1.2) represent the sectoral production functions
where C is the output of consumer goods and I is the output of investment
goods. Nc, NI is employment in the consumer-good (investment-good)
sector. The marginal productivities in both sectors are equal to product
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wages (equations (1.3) and (1.4)). NI plus Nc results in aggregate employment demanded (equation (1.5)). Real investment depends on the inverse
of the product wages of the two production sectors11 and on the rate of
interest (equation (1.6)). The parameter g has been added to represent
explicitly a propensity to invest.12 The level of consumption demand is equal
to the demand of capitalists and the demand of workers who consume their
entire wages (equation (1.7)). Nominal money demand function is written,
in accordance with the quantity theory, as a function of nominal income. By
equating this demand function with the quantity of money, M , one gets the
equilibrium condition of the money market (equation (1.8)). Finally,
because the labour market is balanced, employment is equal to labour
supply (equation (1.9)). The endogenous variables are: Nc, NI, N, C, I, pc, pI,
r, W. The exogenous variables are: N ; M ; Cp . Equations (1.1), (1.2), (1.3),
(1.7) and (1.9) result in Kalecki’s equation (1). Equations (1.1), (1.3),
(1.4), (1.5), (1.6), (1.7) and (1.9) result in Kalecki’s equation (2). (The
solution of the model is discussed in Appendix 1.)
Thus, by constructing a model based on Say’s law, Kalecki described an
economy for which real variables and nominal variables are respectively
determined by the real and the monetary parts of the model and in which
market mechanisms spontaneously re-establish full employment. In order
to determine whether this result depends on the absence of hoarding,
Kalecki considered in his System II the implications of variations of cash
reserves owned by firms.
In Kalecki’s System II, money supply is first assumed given.13 Money
demand is instead assumed to increase with income and to decline with the
interest rate. More precisely, Kalecki argued that agents choose between
‘cash reserves’, which they need in order to make transactions – insisting on
the transaction motive for financing production – and financial assets,
which do not allow making transactions but yield interest.
In contrast to System I, individual economic agents in System II hold cash reserves
which can be increased or decreased. A cash reserve is necessary to run an enterprise
at a given turnover smoothly. The volume of this reserve depends not only on the
turnover of the enterprise, but also on the rate of interest. The higher the rate of
interest, the smaller the cash reserve held by an enterprise at a given turnover. Hence
if sales increase while the volume of money in circulation remains constant, that is, if

11 Current real profits by unit produced in each production sector depend
respectively on pc/W and pI/W; they in turn determine expected profitability and
hence investment.
12 In Kalecki’s analysis, investment can be increased in response to a Schumpeterian ‘new production combination’ (Kalecki 1990: 206).
13 After having presented in depth his second system, Kalecki dealt with the
implications of increasing money supply with interest rates (Kalecki 1990: 213 – 4).
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the velocity of money circulation increases, the rate of interest rises, since there will
be a tendency to increase reserves in the same relation, which must be counteracted
by an increase in the rate of interest. The rate of interest in System II is determined in
this way by the velocity of money circulation.
(ibid: 207)

Formally, by assuming that the elasticity of money demand with regard to
nominal income is equal to 1, the money demand function described by
Kalecki can be written as follows: Md ¼ (pII þ pcC)L(r), where the function L
is a decreasing function of the rate of interest. From the condition of
equilibrium on the money market, M ¼ ðpI I þ pC C ÞLðr Þ, one obtains the
velocity of money circulation: V ¼ ðpI I þ pC C Þ=M ¼ 1=Lðr Þ. It thus
appears that when nominal income rises, the velocity of money circulation
increases and equilibrium on the money market is re-established by a rise of
the interest rate. By adding this money market conception to his System I,
Kalecki showed, however, that the final position of equilibrium in this
system is the same as under Say’s law.
Consider his analysis of the impact of a rise in labour supply.14 Due to the
complete flexibility of money wages, an excess supply causes money wages
14 Kalecki also illustrated this point by considering the impact of an exogenous
decrease in capitalists’ consumption and a rise in the incentive to invest. Kalecki
dealt with the impact of an exogenous reduction in the volume of capitalists’
consumption given supply labour. Capitalists, instead of investing, increase their
money reserves. In the sector of consumption goods, supply exceeds demand, so
the price decreases until equilibrium is re-established, which causes a rise in real
wages and the reduction of employment (ibid: 210). With an excess supply of
labour, money wages decrease, allowing firms of the investment sector to hire
the workers dismissed from the consumer sector (ibid: 210). Production
increases in the investment goods sector, which enables a lowering in prices and
a rise in real balances. More real balances are then available for the financing of
production, which lowers the interest rate and enables a rise in investment (ibid:
211). Thus, capitalists finally put their demand for consumption goods entirely
on the investment goods sector so that the economy reaches a full employment
equilibrium.
Then, Kalecki focuses on the implications of a rise in the inducement to
invest, given the supply of labour and of capitalists’ consumption. Because of the
rise in demand, prices of investment goods increase, causing a decrease in real
costs and a rise in labour demand. Some workers move from the consumption to
the investment sector, which decreases consumption goods output. For a given
volume of capitalist consumption, demand exceeds supply and consumption.
Prices rise until a new equilibrium is established, which involves a lower real
wage rate, and therefore a somewhat higher output of consumer goods than
without a real wage reduction. Consequently, as Kalecki argued, ‘wages go up,
and a number of workers now return to this industry from the investment sector.
Production of the latter falls. In this way, we return to the initial position, except
that the general level of prices and wages has risen’ (ibid: 209). As a
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to fall. Real wages decrease, causing a rise in employment and production.
As a result, prices decrease due to the appearance of an excess supply of
goods, which results in a rise in the value of money holdings. More real
balances are then available for financing production activities, causing the
interest rate to fall and permitting investment to increase ‘on account of
the falling money value of sales the velocity of money circulation declines
and with it also the money rate of interest, which encourages entrepreneurs
to make investments’ (Kalecki 1990: 212). A set of real variables identical to
the one defined by Kalecki’s first model is thus determined. (The solutions
of Kalecki’s System II are discussed in Appendix 2.)
This adjusting mechanism, through which lower prices and wages could
eventually generate a move towards full employment, relies entirely on the
‘Keynes effect’. Disequilibrium on the labour market indeed entails a
variation in money wages, which causes a variation in price. This variation
of price modifies the real value of money supply, which lowers the interest
rate and stimulates investment. This process occurs until income and
production reach a level ensuring equilibrium in all markets. As Kalecki
stressed: ‘[T]his is the essence of arriving at equilibrium identical with one
which would be established in System I’ (Kalecki 1990: 214 – 5). So, when
prices and money wages are completely flexible and the Keynes effect
applied, Say’s law is still valid. It is by modifying the conception of the
labour market in this second model that Kalecki suggests Say’s law could be
invalidated, thus showing that the economy could get stuck in a position of
‘quasi-equilibrium’.
2.2. System III
There is a radical difference between Kalecki’s third model and his first two
models with regard to the functioning of the labour market. The central
hypothesis at the core of this difference is that unemployment, as such, is
no longer supposed to push money wages down. Kalecki argues as follows:
[A]s long as it remains unchanged, existing unemployment does not ‘pressure’ the
market. Without going into the reasons for this, we shall continue to study System II,
except that now it permits the existence of some reserve army of the unemployed.
This we call System III.
(Kalecki 1990: 215)

consequence, less real balances are available for financing production. So the
interest rate increases until ‘the volume of investment projects is reduced to the
initial level (and naturally new production combinations are realized by
cancelling other projects which are unprofitable at a higher rate of interest)’
(ibid: 209).
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Was Kalecki insisting on the difficulty and the time necessary to render
money wages flexibly downwards or was he referring to some different
adjustment mechanism? The second characteristic of his conception of the
labour market provides some clarification:
Namely, while the existing [emphasis in the original] unemployment does not exert
any pressure on the market, we postulate that changes [emphasis in the original] in
unemployment cause a definite increase or fall in money wages, depending on the
direction and volume of these changes.
(Kalecki 1990: 215)

This conception of the labour market obviously has its roots in Marxian
economics. It is indeed Marx who developed the concept of the reserve
army of the unemployed, the role of which was to regulate the capitalist
system by exerting a disciplinary effect. Kalecki certainly thought that
falling (rising) unemployment increases (decreases) the power of workers
to press for higher (lower) wages.15
The first hypothesis allows the determination of what Kalecki called a
position of quasi-equilibrium; it can be defined by a set of equations
identical to that of Kalecki’s second model, except that in each equation
the level of the supply of labour has been replaced by the level of actual
employment. Thus, as soon as actual employment is known, the quasiequilibrium is determined. Yet if this level of employment is undetermined,
then so are quasi-equilibria. Kalecki’s second hypothesis, according to
which money wages are related to the level of unemployment – referred to
as follows with the equation W ¼ g ðN  N Þ, where g 5 0 – allows one
to define a quasi-equilibrium (Kalecki 1990: 215 – 6). By replacing equation
(1.9) with the equation W ¼ g ðN  N Þ, Kalecki’s third model is obtained.
The endogenous variables remain Nc, NI, N, C, I, pc, pI, r, W. and the
exogenous ones are N ; M ; Cp . The model still has nine equations (see
Appendix 3). However, contrary to the other model, it is not dichotomic so
that shocks in demand now have an impact on employment. To show this,
Kalecki carries out two comparative statics exercises: first, an improvement
in the inducement to invest; and second, a cut in capitalists’ consumption
expenditures.
Consider the effects of an increase in the inducement to invest. This
leads to an increase in the price of investment goods. As a result,
production and employment expand in the investment sector. In turn, this
causes increased worker’s consumption, which boosts price and production
15 In an imperfect competition framework, Kalecki represented the increase in
worker’s power associated with a boom by a decline in mark-up in the pricing
equation (Kalecki 1971).
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in the consumption good sector. As capitalists’ consumption is given,
aggregate production will expand until profits increase by the same amount
as the increase in real investment. Kalecki’s System III allows then the
expression of his theory of profit whereby capitalists get what they spend
(Kalecki 1990: 216 – 7). However, this is not the end result. As Kalecki
emphasized, the rise in prices and in money wages due to increases in
employment and production, leads to a rise in the ‘money value of
turnover’; this also causes a rise in the transaction demand for money that
can only be met by an increase in the rate of interest, which in turn reduces
the volume of investment (see Kalecki 1990: 217). But despite this
depressive effect, the new quasi-equilibrium is established at a higher level
of employment because of the upward movement of the schedule of
marginal profitability of new investment projects: ‘the increased output and
rise in prices in relation to wages in turn increase profitability, which
additionally stimulates investment activity’ (Kalecki 1990: 217).
Now consider how Kalecki envisions the effect of an exogenous decrease
in capitalists’ consumption. The price of consumption goods decreases and
production falls, which results in workers being pushed to the reserve army
of labour. Higher unemployment reduces consumer goods demand. Prices,
output and employment in the consumer goods sector decrease until
profits have fallen by the amount of the capitalist consumption decrease.
Then, because of the rise in unemployment, wages eventually go down.
However, as long as investment does not vary, prices in the consumption
goods sector fall pari passu as the money wages do, without entailing a
reduction in real cost. But if the lowering of money wages does not affect
firms’ costs, they reduce, however, the interest rate, which causes a rise in
investment and the hiring of some workers pushed initially into the reserve
army of the unemployed. Yet, in spite of the decrease in interest rate,
investment is likely to fall due to profitability deterioration. Thus, Kalecki
came to the conclusion that a decrease in capitalists’ consumption, and so a
rise in savings, can reduce investment and drive the economy into a
position where unemployment is higher.
Having explained the three variants of Kalecki’s 1934 model,now
compare it with the IS-LM model, focusing attention on the versions
described by Hicks (1937) and Modigliani (1944).

3. ‘Three Systems’ vs. the IS-LM model of Hicks (1937)
To draw a contrast between the classical and the Keynesian perspectives,
Hicks also constructed three models: the first he qualified as being
classical;16 the second Keynesian;17 and the third a synthesis,18 two variants
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16 Hicks’ first system is a classical system in which money demand, in accordance
with the quantitative theory of money, does not depend on the interest rate.
Hicks presented it as follow:
M ¼ kY n ;

I n ¼ I n ðr Þ;

I n ¼ S n ðr ; Y n Þ

Yn, is nominal income, In is nominal investment, r is the interest rate, M the
quantity of money in circulation supposed given and k a constant corresponding
to the inverse of the velocity of money circulation. Hicks showed how a rise in
the inducement to invest in this model affects only the interest rate and leaves
nominal income as it is. Consequently, employment will vary only if the supply
elasticity of each sector is not equal so that as he pointed out: ‘labour will be
employed more in the investment trades, less in the consumption trades; this will
increase total employment if elasticity of supply in the investment trades is
greater than that in the consumption-goods trades – diminish it if vice versa’
(Hicks 1937: 149).
In this model, curiously, it is necessary to note that an increase in the quantity
of money, by raising nominal income, will cause an increase in employment.
This first model, although Hicks calls it classical, is neither dichotomic nor
neutral. This characteristic comes from the fact that it is nominal investment and
nominal savings and not real investment and real savings that depend on interest
rate. Thus the investment function is not homogeneous of degree one vis-a`-vis
nominal variables, which, as d’Autume remarks ‘translates a generalised money
illusion’ (2000: 421), a characteristic that can be found in each of these models.
17 A Keynesian model opposes the above in that the demand for money depends
on interest rate and in that nominal savings, in accordance with the multiplier,
depends only on nominal income. Hicks wrote it as follow:
M ¼ Lðr Þ;

I n ¼ I n ðr Þ;

I n ¼ S n ðY n Þ

The singularity is that it is the interest rate and not nominal income that is
determined by the quantity of money: the interest rate determines nominal
investment, which, via the multiplier, determines nominal income. It results in a
rise in the inducement to invest, which increases national income without
affecting interest rate. Obviously a rise in the quantity of money, by reducing the
interest rate, increases nominal investment and employment. Keynes’s essential
contribution is therefore, according to Hicks, his liquidity preference analysis,
because without it the multiplier would have no role.
However, Hicks thought the economy described by Keynes corresponds more
closely to the following model:
M ¼ LðY n ; r Þ;

I n ¼ I n ðr Þ;

I n ¼ S n ðY n Þ

in which nominal income has been introduced in the function of the demand of
money. For Hicks, this modification restricts considerably the opposition
between Keynesian theory and classical theory. Indeed, henceforth, a rise in
the inducement to invest triggers an increase in nominal income as well as in
interest rate, whereas a rise in the quantity of money reduces the interest rate
and increases employment. Graphically this result appears clearly. If LL, the
curve representing equilibrium of the money market in the plan (r, Yn) is
increasing, a rise in the inducement to invest shifts IS to the right and generates
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of the first two enabling passage easily from one to the other. He stressed
that the opposition between Keynes and the classical authors is neither a
conflict between rigidity and flexibility of money wages nor a conflict
between unemployment and full employment, but originates in liquidity
preference theory.
Now compare Hicks’ model with Kalecki’s 1934 model. It is worth noting
that the conceptions of the labour market advocated by Hicks and Kalecki
are radically different from one another when one considers classical
theory. Whereas Hicks assumed that the ‘rate of money wages per head can
be taken as given’ (Hicks 1937: 148), Kalecki supposed on the contrary that
the money wage rate decreases with an excess supply of labour. Moreover,
while Hicks’ article lacked an explicit account of how the labour market
works and in which state it happens to end up, Kalecki insisted on the idea
that for a system to be accepted by classical economists (Kalecki 1990: 201)
it must display full-employment equilibrium. As a result, the impact of a rise
in the inducement to invest and in the quantity of money differs
significantly in Hicks’ and Kalecki’s classical models.
Focus, to start with, on the way Hicks and Kalecki respectively envisioned
the effects of a rise in the inducement to invest. In his system of two
production sectors, Hicks showed that such a shock modifies the structure
of production. Thus, because total employment depends on how
production is divided between sectors, it will not necessarily remain
unchanged. Only if sectoral supply elasticities are identical will there be no
change in employment. On this point, Kalecki’s classical models are fully at
odds with Hicks’ classical model. Indeed, market clearing and full
employment exists in both of Kalecki’s classical models. Consequently, an
increase in the inducement to invest (i.e. a rightward movement of the
schedule of marginal profitability of new investment projects) always
elicits a rise in the rate of interest, which results in unchanged total
a rise of national income and of the interest rate. It is only if LL is horizontal in
the case of the liquidity trap that a rise in the inducement to invest only causes a
rise of national income.
18 Last, aiming to show that it is possible to realise a complete synthesis between
classical tradition and the Keynesian theory, Hicks built a variant of the latter,
where the nominal income and the interest rate are the arguments for the
demand functions of money, investment, and savings, the model of generalized
General Theory, which he wrote as such:
M ¼ LðY n ; r Þ I n ¼ I n ðY n ; r Þ I n ¼ S n ðY n ; r Þ
Thanks to this, Hicks can also show that a rise in the inducement to invest causes
an increase in nominal income and in the interest rate, whereas a decrease in
the quantity of money reduces the interest rate and raises the nominal income.
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employment.19 In the same way, an exogenous decrease in capitalists’
consumption will not affect total employment. Indeed, according to Say’s
law, if saving rises, investment spending rises by the same extent. Thus,
whatever the differences of supply elasticity between production sectors
are, workers unemployed in the sector of consumption goods are hired in
the investment sector. Because, as long as they are still unemployed, money
wages will fall, inciting capitalists to increase their spending until full
employment is reached. And this result is not modified when the demand
for money depends on the interest rate as in Kalecki’s System II.
With regard to the effects of monetary expansion, the differences
between Kalecki’s and Hicks’ analysis also have their roots in the treatment
of the labour market. In Hicks’ model, an increase in the supply of money
causes a rise in employment, due to the rigidity of money wages, whereas
for Kalecki, money is neutral due to the flexibility of money wages. Indeed,
whether it is in his System I, founded on quantity theory, or in his System II,
in which nominal income and the interest rate are the two arguments of
money demand function, any rise in the supply of money entails only a
change in nominal variables. Contrary to Hicks, Kalecki claimed that
introducing the interest rate in the money demand function alone is not
sufficient to get a system that leads to non-classical conclusions. What is
needed is to add a particular conception of the labour market.
This paper now turns to the differences between Kalecki’s unemployment model and Hicks’ Keynesian model. In order to build a model with
unemployment Kalecki developed a different conception of the labour
market from Hicks. The central hypothesis of this conception is that
unemployment, as long as it remains unchanged, is not supposed to
pressure money wages downwards. However, if money wages do not fall and
there is an excess supply of labour, Kalecki did not conclude that wages are
completely rigid. On the contrary, he believed that money wages respond
to variations in unemployment. Unfortunately, this approach is mentioned
but not explained, even if it is highly likely that Kalecki was referring to
Marx’s theories. Whatever it may be, however, it is clear that Kalecki
believed that the labour market, due to the existence of a reserve of
unemployed workers being available, is characterized by a gap between
supply and demand. This analysis can hereby be distinguished from that of
Hicks. For Hicks, on the one hand, money wages are given and on the other
hand the supply of labour is not specified, making it difficult to say whether
or not unemployment exists (see De Vroey 2000).

19 As real savings do not depend on interest, the distribution of employment
between sectors will not be affected.
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Despite this difference, Kalecki’s model with unemployment behaves
fundamentally in the same way as Hicks’. Concerning the effects of a rise in
the inducement to invest and the supply of money, both models react in
exactly the same way. The only difference between Kalecki’s analysis and
Hicks’ is the existence of a liquidity trap in the latter. Kalecki did not refer
to a situation in which the liquidity preference schedule is interest inelastic.
Consequently, whereas in Hicks’ model, a rise in the inducement to invest
can trigger a rise in employment without affecting the interest rate, such a
shock in Kalecki’s model obviously creates a rise in employment and in the
interest rate.
In his attempt to highlight the differences between classical theory and
Keynesian theory, Modigliani also came up with three models but reached
radically different conclusions from Hicks. Whereas to Hicks the
distinguishing feature is liquidity preference analysis, to Modigliani it is
the rigidity in money wages. Although Kalecki adopted a representation of
the classical theory that is not very different from Modigliani’s, his model
including unemployment is different from Modigliani’s Keynesian system.
Kalecki’s 1934 article offers both anticipation of the IS-LM model on the
one hand and of the difference between the classical and the Keynesian
models on the other.

4. ‘Three Systems’ vs. the IS-LM model of Modigliani (1944)
In his 1944 article, Modigliani reconsidered the difference between
Keynesian theory and classical theory. Keynesian theory is now defined by
the hypothesis of rigidity of money wages that Hicks considered common to
classical and Keynesian models. Henceforth, the opposition between
Keynes and classical authors becomes an opposition between rigidity and
flexibility of wages and between unemployment and full employment.
Modigliani’s analysis of the labour market,20 coupled with two conceptions
of the money market, then allows the definition of three models: a crude
classical model; a generalized classical model; and a Keynesian model.
The specificity of the crude classical model is that ‘the real part of the
system, namely, employment, interest rate [emphasis in the original] output,
or real income, do not depend on the quantity of money. The quantity of
20 From the idea that in a classical model the workers are rational, Modigliani
wrote the supply of labour in a conventional way: Ns ¼ F(W/P) or in the inverse
form: W ¼ F71(N)P. Therefore, by introducing a hypothesis of rigidity of money
wages, corresponding for him to the benchmark between classical and
Keynesian models, he rewrote this equation as W ¼ W0.
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money has no other function than to determine the price level’
(Modigliani 1944: 68). In this model, one does not however find this
property in an obvious way. In fact, the quantity of money determines
national nominal income and the interest rate. Thus, it is only if one
supposes nominal investment and savings to be homogenous of degree one
with regard to the price level that this occurs. In 1944, Modigliani curiously
did not totally resolve Hicks’ (1937) problem.
In his second model, Modigliani replaced the quantity equation by a
function of money demand for which the arguments are nominal income
and interest rate. This meant to show that the introduction of the interest
rate in the demand function for money is perfectly acceptable in a classical
model when money wages are perfectly flexible. Indeed, as long as the
supply of labour depends on the level of real wages, the equilibrium
reached by the economy is not modified. Once again, this is true only if the
functions of nominal investment and nominal savings are homogeneous of
degree one in prices. It is worth noting that Modigliani’s classical models
are characterized by the flexibility of money wages and prices and its
ensuing clearance of the labour market; it is also characterized by the
ineffectiveness of a monetary expansion in increasing employment and by
the failure of an increase in the inducement to invest to reach the same
goal.
Last, Modigliani elaborated on a model representing the Keynesian
theory. He claimed a Keynesian outcome arises when two factors are jointly
present: rigidity of money wages and money demand depends on the
interest rate and nominal income. Thus, Modigliani argues that the
Keynesian model is characterized by a basic maladjustment between the
quantity of money and the wage rate, which explains the low level of
investment. He expands as follows:
What is required to improve the situation is an increase in the quantity of money (and
not necessarily in the propensity to invest); then employment will increase in every
field of production including investment.
(Modigliani 1944: 76 – 7)

The contrast between Kalecki’s and Modigliani’s approaches can be
easily drawn and synthesized in Table 1. As seen, Modigliani’s classical
models are characterized by the flexibility of money wages and its ensuing
clearance of the labour market, on one hand, and by the ineffectiveness of
an increase in the inducement to invest in increasing employment on the
other. It thus seems these are exactly Kalecki’s classical models. Kalecki’s
models differ from Modigliani’s only by distinguishing between two classes
(capitalists and workers) and two sectors (consumption and investment
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Michae¨l Assous
Table 1 The features of the Kalecki, Hicks and Modigliani models
Labour market

Demand for money

Impact of shocks

Kalecki

Flexible money wages
in classical models
(Systems I and II),
resulting in full
employment; and
flexible money
wage in System III,
which results in
unemployment.

Demand for money
independent from
interest rate in
System I. Demand
for money
dependent on
interest rate and
national income in
System II and III.

Hicks

Fixed money wages in
the classical and
Keynesian models,
resulting in a
non-specified
situation in the
labour market.

Demand for money
independent from
interest rate in the
classical model and
dependent on
interest rate in
Keynesian models.

Modigliani

Flexible money wages
in classical models
and rigid money
wages in the
Keynesian model,
resulting
respectively in full
employment and
unemployment.

Demand of money
independent from
interest rate in the
crude classical
model. Demand for
money dependent
on national income
and interest rate in
the amended
classical and
Keynesian models.

Rises in the
inducement to
invest and in the
quantity of money
do not affect
employment in
Systems I and II
and entail both a
rise in employment
and interest rate in
System III.
Rises in the
inducement to
invest (when
sectoral supply
elasticities are not
identical) and in
the quantity of
money affect the
level of employment
in the classical
model but may have
no effect on it in the
Keynesian model
due to the existence
of the liquidity trap.
Rises in the
inducement to
invest and in the
quantity of money
affect employment
only in Keynesian
model.

goods). But, whereas Kalecki’s and Modigliani’s classical models happen to
be so closed, their models with unemployment display some important
differences.21
21 Thus we have : NdI ¼ fI
112

0

 
W
pI

0

; NdC ¼ fC



W
pC



; Nd ¼ NdI þ NdC ; Nd ¼ Nd



W W
pI ; pC



:

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Kalecki’s (1934) model

As previously stated, the specificity of Kalecki’s unemployment model
hinges on his conception of the labour market. No difference between his
unemployment model and the classical models would remain were this
argument proved to be flawed. Kalecki’s unemployment model is, however,
at odds with Modigliani’s Keynesian model, which rests on an exogenous
wage. Indeed, although money wages do not adjust in response to an
excess supply of labour, Kalecki argues that they depend on unemployment movements. Money wages are thus endogenous. It is, however,
clear that if Kalecki had proceeded to make use of his unemployment
model to discuss the effect of an exogenous decrease in money wages, he
would have reached Modigliani’s conclusion. He would in particular have
argued that the only way a decline in wages could increase employment is
through its effect in increasing the real quantity of money, hence
decreasing the rate of interest and thereby increasing investment and
aggregate demand.
However, contrary to Modigliani, Kalecki’s main interest was not
comparative static equilibria. Instead, Kalecki referred to a temporary
equilibrium position in the Marshallian sense, a position that would
subsequently change as variables that had been held constant would be
permitted to change. In the conclusion of his 1934 paper, he indeed noted
that if the assumption of a given volume and structure of capital equipment
were abandoned, then as a result of changes in capital stock there would be
a continual movement through a series of equilibrium or quasi-equilibria
until the final equilibrium is attained, i.e. a position in which investment
activity no longer changes the volume and structure of capital equipment’.
Moreover, when the time of construction of investment goods is taken into
account, this movement will be cyclical and the position of ‘final
equilibrium’ will never be reached, giving rise to endogenous business
fluctuations instead.22 Thus, Kalecki’s unemployment theory should not
be interpreted as a static theory of unemployment disequilibrium. More
specifically, what concerned Kalecki, according to this interpretation, is
not an economy whose level of unemployment remains constant over time,
it is instead an economy whose capital stock is continuously varying,
entailing unemployment movement that causes wages to vary but in
which aggregate demand is not thereby adequately stimulated, so that
unemployment fluctuations continue to prevail, although the intensity
changes over time. Correspondingly, once it is recognised that Kalecki’s
unemployment theory is concerned, strictly speaking, with a situation of
22 On this point, Kalecki’s 1939 Essays are directly related to Kalecki’s 1934 model.
For an account of the relationship of Kalecki’s 1934 model and Kalecki’s 1939
Essays, see Assous (2003).
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unemployment quasi-equilibrium, it is also understood that the validity of
its analysis does not depend on the special assumption of absolutely rigid
money wages.

5. Conclusion
As the 1934 article proved, before the General Theory appeared, Kalecki had
already built a model able to express the main conclusions of the classical
theory and to express the persistence of unemployment. In the case of a
complete flexibility of prices and wages, he first elaborated a model of full
employment founded on Say’s law and then, considering the case in which
the demand for money depends on the interest rate, showed that the
economy reaches an identical equilibrium. In a third model, dedicated
to allow for unemployment, he referred to a conception of the labour
market for which, as long as unemployment remains unchanged, it does
not push down money wages. In this case, movements of employment
can be explained in terms of movements in aggregate demand, resulting
in Kalecki’s famous doctrine, which states that capitalists get what they
spend.
A formal representation of this argument has made it possible to show
that Kalecki did elaborate on an original IS-LM model that differs from the
models of Hicks and Modigliani. On the one hand, it seems that Kalecki
and Hicks developed a radically different analysis of the classical theory.
Contrary to Hicks, Kalecki did not think that the introduction of the
interest rate as an argument in the money demand function necessarily cast
a shadow on the classical theory, a conclusion Modigliani stressed again ten
years later. On the other hand, this comparison has highlighted the fact
that Kalecki developed a different model with unemployment from
Modigliani’s. Whereas in Modigliani’s Keynesian model, money wages are
exogenous, they are endogenous in Kalecki’s model. As a consequence,
while Modigliani, in a static comparative framework, attributed unemployment to the rigidity of money wages, Kalecki originally developed, with his
concept of quasi-equilibrium, a dynamic theory of unemployment
disequilibrium in which unemployment variations are