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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 theGeneral TheoryKalecki 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
* 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 theGeneral Theory’s publication contained the notion of effective demand whose essence is, according to Patinkin, the well-known forty-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
The European Journal of the History of Economic Thought
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7 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 differences4by showing how Kalecki’s model differs significantly from the two main variants of the IS-LM model, those of Hicks (1937) and Modigliani (1944).5Based 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 reviewEkonomistaand was translated into English only in volume 1 of Kalecki’sCollected Works. The fact that Kalecki did not choose to translate this article to claim anticipation of the General Theorycontinues 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.
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7 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.
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7 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 employ-ment and of production of investemploy-ment 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 ¼f 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).
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7 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 functionC 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 ¼C N;Cp;r ð2Þ
The functionsfandCthus determine investment goods output and the
rate of interest.
The formal model underlying Kalecki’s System I can be represented as follows:
C¼fCðNCÞ ð1:1Þ
I ¼fIðNIÞ ð1:2Þ
W ¼pCf
0
CðNCÞ ð1:3Þ
W ¼pIf
0
IðNIÞ ð1:4Þ
NI þNC ¼N ð1:5Þ
I ¼I pC W ;
pI W ;r;g
ð1:6Þ
C ¼CpþWN pC
ð1:7Þ
M ¼kðpIIþpCCÞ ð1:8Þ
N ¼N ð1:9Þ
Equations (1.1) and (1.2) represent the sectoral production functions whereCis the output of consumer goods andIis the output of investment goods. Nc, NI is employment in the consumer-good (investment-good)
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7 wages (equations (1.3) and (1.4)).NIplusNc results in aggregate
employ-ment demanded (equation (1.5)). Real investemploy-ment depends on the inverse of the product wages of the two production sectors11 and on the rate of interest (equation (1.6)). The parameter ghas been added to represent explicitly a propensity to invest.12The 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 onpc/WandpI/W; they in turn determine expected profitability and
hence investment.
12 In Kalecki’s analysis, investment can be increased in response to a Schumpeter-ian ‘new production combination’ (Kalecki 1990: 206).
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7 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:Md¼(pIIþpcC)L(r), where the functionL
is a decreasing function of the rate of interest. From the condition of equilibrium on the money market, M ¼ ðpII þpCCÞLðrÞ, one obtains the velocity of money circulation: V ¼ ðpII þpCCÞ=M ¼1=LðrÞ. 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.14Due 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.
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7 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)
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7 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 theexisting[emphasis in the original] unemployment does not exert any pressure on the market, we postulate thatchanges[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 quasi-equilibrium 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 ¼gðN NÞ, where g50 – allows one
to define a quasi-equilibrium (Kalecki 1990: 215 – 6). By replacing equation (1.9) with the equationW ¼gðN NÞ, 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
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7 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)
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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:
M¼kYn; In¼InðrÞ; In ¼Snðr;YnÞ
Yn, is nominal income,Inis nominal investment, r is the interest rate, M the quantity of money in circulation supposed given andka 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:
M¼LðrÞ; In¼InðrÞ; In¼SnðYnÞ
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:
M¼LðYn;rÞ; In¼InðrÞ; In¼SnðYnÞ
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7 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 ifLLis 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:
M¼LðYn;rÞ In¼InðYn;rÞ In¼SnðYn;rÞ
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7 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 unemploy-ment 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).
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7 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,20coupled 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:Ns¼F(W/P) or in the inverse
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7 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)
D
goods). But, whereas Kalecki’s and Modigliani’s classical models happen to be so closed, their models with unemployment display some important differences.21
Table 1 The features of the Kalecki, Hicks and Modigliani models
Labour market Demand for money Impact of shocks
Kalecki Flexible money wages
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7 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 unemploy-ment moveunemploy-ments. 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
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7 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 theGeneral Theoryappeared, 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 unemploy-ment 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 due fundamentally to the fluctuations of investment.
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7 Kalecki reasoned in a perfect competition framework, whereas he
adopted the hypothesis of imperfect competition when Hicks’ and Modigliani’s articles came out, which drove him to develop a new analysis of the distribution of income. Hence, contrary to what his 1934 article showed, Kalecki insisted on the fact that no negative correlation exists between real wages and employment. Last, as noted previously, Kalecki thought that the adequate frame to his theory was dynamics and not comparative static, a point that he acknowledged to Hicks when criticizing his IS-LM model (Kalecki 1939: 313). Considering certainly that this latter theory filled the gap, Kalecki might have thought it useless to translate this article.
References
Assous, M. (2003). Kalecki’s contribution to the emergence of endogenous business cycle theory: An interpretation of his 1939 essays.History of Economic Ideas, 11: 109 – 23.
Barens, I. and Caspari, V. (1999). Old views and new perspectives: On re-reading Hicks’ ‘Mr. Keynes and the Classics’.The European Journal of the History of Economic Thought, 6: 216 – 41.
Chapple, S. (1991). Did Kalecki get there first? The race for the general theory.History of Political Economy, 23: 243 – 61.
—— (1995). The Kaleckian origins of the Keynesian model. Oxford Economic Papers, 47(3): 525 – 37.
Darity, W. and Young, W. (1995). IS-LM. An inquest.History of Political Economy, 27: 1 – 41. D’Autume, A. (2000). L’essor de la macro-e´conomie. In A. Be´raud and G. Faccarello
(eds),Nouvelle Histoire de la Pense´e Economique,tome 3.Paris: La De´couverte. De Vroey, M. (2000). IS-LM a` la Hicks versus IS-LM a` la Modigliani.History of Political
Economy, 32: 293 – 316.
Dos Santos Ferreira, R. (2000). Keynes et le de´veloppement de la the´orie de l’emploi dans une e´conomie mone´taire. In A. Be´raud and G. Faccarello (eds),Nouvelle Histoire de la Pense´e Economique,tome 3.Paris: La De´couverte.
Hicks, J. (1937). Mr. Keynes and the ‘‘Classics’’: A suggested interpretation.Econometrica, 5: 147 – 59.
Kalecki, M. (1934). Trzy uklady. Ekonomista, 34: 54 – 70. Translated in Kalecki (1990: 201 – 19) as Three Systems.
—— (1939).Essays in the Theory of Economic Fluctuation.London: Allen and Unwin. —— (1944). Prof. Pigou on ‘‘The Classical Stationary State.’’ A comment. Economic
Journal, 1: 131 – 2.
—— (1971). Selected Essays on the Dynamics of the Capitalist Economy 1933 – 1970. Cambridge: Cambridge University Press.
—— (1990).Collected Works of Michal Kalecki. Volume I: Capitalism, Business Cycles, and Full Employment.Oxford: Clarendon Press.
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7 Lopez, J. and Assous, M. (2007)Kalecki’s Theory of Capitalist Economies.Palgrave Macmillan (forthcoming).
Modigliani, F. (1944). Liquidity preference and the theory of interest and money. Econometrica, 12: 44 – 88.
Osiatynski, J. (1985). Don Patinkin on Kalecki and Keynes.Oeconomia Polonia, vol. XII. —— (1992). A note on Kalecki’s and Keynes’s unemployement equilibrium. In
M. Sebastiani (ed.), The Notion of Equilibrium in the Keynesian Theory. London: MacMillan.
Patinkin, D. (1982).Anticipations of the General Theory? and Other Essays on Keynes.Chicago: University of Chicago Press.
—— (1990a). In defense of IS-LM.Banca Nazionale del Lavoro Quarterly Review, l72: 119 – 34.
—— (1990b). On different interpretations of the general theory. Journal of Monetary Economics, 26: 205 – 43.
Rubin, G. (2004). Patinkin on IS-LM: An alternative to Modigliani.History of Political Economy, 36 (annual supplement): 190 – 217.
Sawyer, M. (1985).The Economics of Michal Kalecki.London and Basingstoke: Macmillan. Young, W. (1987).Interpreting Mr. Keynes: The IS-LM Enigma.London: Polity Press.
Appendix 1 Kalecki’s System I
First of all, real variables are determined. With (1.1), (1.3) and (1.7) real wages in the consumption goods sector are determined as an implicit function of aggregate employment and capitalists’ consumption:
C¼fC f
01
C W pC
¼N W pC
þCp
KnowingW/Pc, one may determine the employment in the consumption
goods sector. Because employment in the two sectors of production is equal to the supply of labour, one can then deduce the employment in the investment goods sector. The quantities of consumption goods and investment goods are then given by (1.1) and (1.2). From (1.4) one can determine W/PI, from which the value of interest rate can be deduced.
Indeed, the equilibrium condition is fI(NI)¼I(pC/W, pI/W, r, g), which
implies that the rate of interest is an implicit function ofNI,W/pcandW/pI.
With these variables now determined, the value of the equilibrium interest rate can be deduced. The money variables are determined by (1.8). KnowingW/pIandW/pc,W is given by:
M ¼Wk C
f0
cðNcÞ þ I
fI0ðNIÞ
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Appendix 2 Kalecki’s System II
Its resolution reveals that its real solutions are identical to those of System I. Indeed, the real wages in the consumption goods sector are still defined as an implicit function of aggregate employment and capitalists’ consump-tion. Thus:
C ¼fC f
01
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¼N W pC
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Knowing W/pc, employment in the consumption goods sector can be
determined. Because employment in the two sectors of production, according to (1.5), is equal to the supply of labour, employment in the investment goods sector can also be determined. Equations (1.1) and (1.2) give the quantities of consumption and investment goods. Equation (1.4) helps to determine real wages in the investment goods sector,W/pI, from
which the value of interest rate can be determined. Thus, in equilibrium, fI(NI)¼I(pc/W,pI/W,r,g), which means that the interest rate is an implicit
function of NI, W/pI and W/pc. These variables being determined, the
equilibrium interest rate and nominal variables can also be deduced. When W ¼pIf
0
IðNIÞ and W ¼pCf
0
CðNCÞ, by considering the new equilibrium relation in the money market, one reaches the value of the nominal wage. Thus:
M ¼W C
f0
cðNcÞ þ I
fI0ðNcÞ
LðrÞ
Through (1.3) and (1.4) one determinepcandpI. System II, like System I,
is therefore also dichotomic.
Appendix 3 Kalecki’s System III
Recalling that the function of money balance is homogenous of degree one in prices, it can be brought down in the following way:
fCðNCÞ ¼Cpþ ðNI þNCÞf
0
CðNCÞ
M ¼W fIðNIÞ fI0ðNIÞ
þfCðNcÞ fC0ðNcÞ
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fIðNIÞ ¼I pC W ;
pI W ;r;g
W ¼gðN NÞ
or
fCðNCÞ ¼Cpþ ðNI þNCÞf
0
CðNCÞ;
M ¼gðN NI NCÞ fI ðNIÞ fI0ðNIÞ
þfCðNcÞ fC0ðNcÞ
L fðfIðNIÞ;f
0
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0
IðNIÞÞ
h i
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variables areNc andNI. The exogenous variables areN;M andCp. Thus, employment in the two sectors is an implicit function of capitalists’ consumption, of the quantity of money, and of the supply of labour. Kalecki’s second system is therefore no longer dichotomic.
Abstract
This article is based on Kalecki’s 1934 study entitled ‘Three Systems’. It aims to show that before the General Theory Kalecki developed a mathematical model capable of expressing both the main conclusions of the neoclassical theory – Kalecki’s Systems I and II – and the persistence of unemployment – Kalecki’s System III. The present analysis stresses the relevance and the originality of Kalecki’s 1934 model by comparing it to the two main variants of the IS-LM model – Hicks (1937) and Modigliani (1944) – around which the neoclassical synthesis was built. It shows that although there does indeed exist a formal proximity between Kalecki’s model and those of Hicks and Modigliani, Kalecki can be considered the first to offer an original explanation of the difference between classical and Keynesian models that depends neither on liquidity preference as proposed by Hicks nor on the rigidity of money wages as proposed by Modigliani.
Keywords
