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7 Kalecki’s 1934 model VS. the IS-LM modelof Hicks (1937) and Modigliani (1944)*
Michael 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 notdeal with the notion of unemployment equilibrium in terms of a generalequilibrium system of simultaneous equations. In short, Patinkin claimedKalecki did not anticipate the Keynesian model,1 of which the morerelevant interpretation, according to him, is the IS-LM model (Patinkin1990a,b). In 1995, Simon Chapple claimed in a closely argued article that:‘an early version of the mainstream Keynesian model was constructed andpublished 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 forhelpul comments and suggestions on an earlier draft. I am especially indebted toProfessor Alain Beraud, with whom I had lengthy exchanges. I also gratefullyacknowledge Claude Marguet for detailed comments and useful observations.Helpful remarks of two anonymous referees are gratefully acknowledged. Anyremaining errors in this paper are mine.
1 In his 1982 study, Patinkin affirmed that Kalecki had not analysed themechanisms by which the economy is likely to reach equilibrium withunemployment without contrasting it with classical mechanisms. Moreover,Patinkin did not think that Kalecki defined a general equilibrium model like theone described by Hicks in 1937 (Patinkin 1982: 10 – 11).
2 Chapple aimed to demonstrate that Kalecki anticipated the key features of theGeneral Theory, which, as Patinkin defined them, are threefold. First, he claimedKalecki’s works prior to the General Theory’s publication contained the notion ofeffective demand whose essence is, according to Patinkin, the well-known forty-
Address for correspondencePHARE-CNRS, Maison des Sciences Economiques, 106 – 112, boulevard del’Hopital, 75647 Paris Cedex 13, France; e-mail: [email protected]
Euro. J. History of Economic Thought 14:1 97 – 118 March 2007
The European Journal of the History of Economic Thought
ISSN 0967-2567 print/ISSN 1469-5936 online � 2007 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/09672560601168488
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7 Kalecki’s (1934) article,3 Chapple showed that Kalecki had constructedthree variants of the IS-LM model that allowed him to mimic the principleconclusions of the neoclassical theory and to explain the persistence ofunemployment.
Centring on a discussion of Patinkin’s argument, Chapple pushed to thebackground the differences between Kalecki’s (1934) model and the IS-LMmodel. The aim of this paper is to highlight these differences4 by showinghow Kalecki’s model differs significantly from the two main variants of theIS-LM model, those of Hicks (1937) and Modigliani (1944).5 Based on thistwofold comparison, the paper then shows that Kalecki’s model offers anoriginal explanation of the difference between classical models (based onSay’s law) and types of models that were to be called later Keynesianmodels. Showing that Kalecki’s theory is concerned, strictly speaking, with asituation of unemployment ‘quasi-equilibrium’, one then understands thatthe validity of his analysis does not depend on the existence of either ofthese special assumptions of the liquidity trap (Hicks) or alternativelyabsolute rigid money wages (Modigliani). Indeed, as Kalecki stressed in theconclusion of his 1934 article, his theory aims at analysing the situation of
five-degree diagram (Chapple 1991). Second, contrary to Patinkin, Chapplesuggests that Kalecki provided an integrated treatment of goods marketequilibrium with money market equilibrium (Chapple 1995, Osiatynski 1985,1992). Last, he rebutted Patinkin’s argument that Kalecki did not link aggregatedemand with the marginalist theory of short-run aggregate demand (Chapple1995).
3 Kalecki’s 1934 article was originally published in Polish in the main Polisheconomic review Ekonomista and was translated into English only in volume 1 ofKalecki’s Collected Works. The fact that Kalecki did not choose to translate thisarticle to claim anticipation of the General Theory continues to be ignored byPatinkin’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-LMversion, emphasizing only in passing the specificity of Kalecki’s treatment of thelabour market in the unemployment variant of his model.
5 In his influential 1944 article, Modigliani recast Hicks’ initial model into whatwas to become the standard version of the IS-LM model (see Darity and Young1995, Barens and Caspari 1999, De Vroey 2000, Young 1987). Indeed, whenHicks opposed Keynes and the classics, he admitted that money wages are givenboth in the Keynesian and the classical models. Hence, Keynes’s maincontribution is that of having built a model based on the theory of liquiditypreference. Modigliani, however, found Hicks’ analysis flawed. In 1944, hepresented a new version of the difference between Keynes and the classics. Tohim, the liquidity preference theory is fully acceptable in a classical model.Keynes’s essential contribution would be that he showed that a macroeconomicequilibrium with unemployment is possible when money wages are rigid. It isaround this idea that a synthesis between the classical tradition and theKeynesian revolution was developed.
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7 disequilibrium unemployment and not the situation of unemploymentequilibrium. As soon as the assumption of a given volume and structure ofcapital 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 theconstruction of Kalecki’s (1934) article. Starting from Kalecki’s analysis ofclassical economics, this section reconsiders the crucial steps in the processof constructing Kalecki’s unemployment model and proposes aformalization 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 effectof 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 whoseemployed 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-LMmodel in terms of unemployment disequilibrium whose differences withModigliani’s 1944 model are discussed by G. Rubin in the 2004 supplement toHistory of Political Economy. Patinkin’s model is based on the idea that whenmoney wages decline in the face of excess supply of labour, the economy doesnot steer itself to full employment. His message is that even if full employmentequilibrium is globally stable, disequilibrium can be protracted and stubborn. Byassuming money wages do not fall in the face of excess supply of labour, Kaleckiunderlined on the contrary that disequilibrium does not depend on moneywages adjustments – although induced variations on money wages play a part onemployment variations – but on investment variations caused by the evolution ofthe profitability of equipment.
7 It is important to stress that in his 1934 perfectly competitive framework, thefocus of attention in terms of sectors of the economy was not the productmarkets. In Kalecki’s model, prices are viewed as moving in line with marginalcosts so that the major cause of unemployment cannot be seen to be a mismatchbetween the degree of monopoly, equal to zero, and the level of investmentexpenditures (see Sawyer 1985, Lopez and Assous 2007 on the importance ofimperfect competition in Kalecki’s latter works) but only on the weakness ofcapitalist expenditures.
8 Both production sectors operate with a constant and historically given capitalstock in which technology exhibits decreasing marginal productivity of labour.
Kalecki’s (1934) model
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7 model – System I – is a classical model founded on Say’s law.9 Kaleckiemphasized this point by considering two shocks: a rise in the labour supplyand an exogenous reduction in capitalists’ consumption – capitalists’consumption being itself considered exogenously given. In both cases heshowed 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, becausethere is at the same time a rise in demand and in profitable output, a levelof macroeconomic equilibrium, characterized by a higher level of employ-ment and of production of investment goods, is reached.
Considering the labour supply as constant, Kalecki envisioned a secondshock: an exogenous fall in capitalists’ consumption. Again, his analysisrested on Say’s law. Thus, by reducing their consumption, capitalistscorrespondingly increase investment. The price of investment goods risesbecause demand is greater whereas the price of consumer goods fallsbecause demand is smaller. Finally, employment and production rise in theinvestment goods sector and shrink in the consumption goods sector(Kalecki 1990: 205).
Then, Kalecki concluded, the production of investment goods is anincreasing function of the supply of labour (assumed inelastic) and adecreasing function of capitalists’ consumption:10
I ¼ f N ;Cp� �
ð1Þ
Investment demand is assumed to depend negatively on the interest rateand positively on the current profitability of equipment for whichentrepreneurs expect the return of their investment projects:
The number of investment projects which pass the profitability test depends on themutual relation at a given moment between prices of consumer goods, prices of
Profit maximization under perfect competition is then assumed as prices areequal to marginal costs. Implicit assumptions include a closed economy and nogovernment sector.
9 Kalecki characterize Say’s law as follows: ‘In System I, the principle ofpreservation of purchasing power is pushed to the extreme: all income mustbe spent immediately on consumer or investment goods. This model is in factaccepted 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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7 investment goods, and wages (which are determinants of the expected grossprofitability), and on the rate of interest.
(ibid: 206)
Hence, since the supply of labour and capitalist consumption entirelydetermines the relation of prices and wages, investment demand can bepresented 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 functionC N ;Cp; r� �
one obtains the condition of equilibrium in the investmentgood market from which the equilibrium rate of interest is obtained:
I ¼ C N ;Cp; r� �
ð2ÞThe 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
W ¼ pC f0
C NCð Þ ð1:3Þ
W ¼ pI f0
I ðNI Þ ð1:4Þ
NI þ NC ¼ N ð1:5Þ
I ¼ IpC
W;
pI
W; r ; g
� �ð1:6Þ
C ¼ Cp þWN
pCð1:7Þ
M ¼ kðpI I þ pC CÞ ð1:8Þ
N ¼ N ð1:9Þ
Equations (1.1) and (1.2) represent the sectoral production functionswhere C is the output of consumer goods and I is the output of investmentgoods. 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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7 wages (equations (1.3) and (1.4)). NI plus Nc results in aggregate employ-ment demanded (equation (1.5)). Real investment depends on the inverseof the product wages of the two production sectors11 and on the rate ofinterest (equation (1.6)). The parameter g has been added to representexplicitly a propensity to invest.12 The level of consumption demand is equalto the demand of capitalists and the demand of workers who consume theirentire wages (equation (1.7)). Nominal money demand function is written,in accordance with the quantity theory, as a function of nominal income. Byequating this demand function with the quantity of money, M , one gets theequilibrium condition of the money market (equation (1.8)). Finally,because the labour market is balanced, employment is equal to laboursupply (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). (Thesolution of the model is discussed in Appendix 1.)
Thus, by constructing a model based on Say’s law, Kalecki described aneconomy for which real variables and nominal variables are respectivelydetermined by the real and the monetary parts of the model and in whichmarket mechanisms spontaneously re-establish full employment. In orderto determine whether this result depends on the absence of hoarding,Kalecki considered in his System II the implications of variations of cashreserves owned by firms.
In Kalecki’s System II, money supply is first assumed given.13 Moneydemand is instead assumed to increase with income and to decline with theinterest rate. More precisely, Kalecki argued that agents choose between‘cash reserves’, which they need in order to make transactions – insisting onthe 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 reserveswhich can be increased or decreased. A cash reserve is necessary to run an enterpriseat a given turnover smoothly. The volume of this reserve depends not only on theturnover of the enterprise, but also on the rate of interest. The higher the rate ofinterest, the smaller the cash reserve held by an enterprise at a given turnover. Henceif 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 dependrespectively on pc/W and pI/W; they in turn determine expected profitability andhence investment.
12 In Kalecki’s analysis, investment can be increased in response to a Schumpeter-ian ‘new production combination’ (Kalecki 1990: 206).
13 After having presented in depth his second system, Kalecki dealt with theimplications of increasing money supply with interest rates (Kalecki 1990: 213 – 4).
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7 the velocity of money circulation increases, the rate of interest rises, since there willbe a tendency to increase reserves in the same relation, which must be counteractedby an increase in the rate of interest. The rate of interest in System II is determined inthis way by the velocity of money circulation.
(ibid: 207)
Formally, by assuming that the elasticity of money demand with regard tonominal income is equal to 1, the money demand function described byKalecki can be written as follows: Md¼ (pIIþ pcC)L(r), where the function Lis a decreasing function of the rate of interest. From the condition ofequilibrium on the money market, M ¼ ðpI I þ pC CÞLðr Þ, one obtains thevelocity of money circulation: V ¼ ðpI I þ pC CÞ=M ¼ 1=Lðr Þ. It thusappears that when nominal income rises, the velocity of money circulationincreases and equilibrium on the money market is re-established by a rise ofthe interest rate. By adding this money market conception to his System I,Kalecki showed, however, that the final position of equilibrium in thissystem is the same as under Say’s law.
Consider his analysis of the impact of a rise in labour supply.14 Due to thecomplete flexibility of money wages, an excess supply causes money wages
14 Kalecki also illustrated this point by considering the impact of an exogenousdecrease in capitalists’ consumption and a rise in the incentive to invest. Kaleckidealt with the impact of an exogenous reduction in the volume of capitalists’consumption given supply labour. Capitalists, instead of investing, increase theirmoney reserves. In the sector of consumption goods, supply exceeds demand, sothe price decreases until equilibrium is re-established, which causes a rise in realwages and the reduction of employment (ibid: 210). With an excess supply oflabour, money wages decrease, allowing firms of the investment sector to hirethe workers dismissed from the consumer sector (ibid: 210). Productionincreases in the investment goods sector, which enables a lowering in prices anda rise in real balances. More real balances are then available for the financing ofproduction, which lowers the interest rate and enables a rise in investment (ibid:211). Thus, capitalists finally put their demand for consumption goods entirelyon the investment goods sector so that the economy reaches a full employmentequilibrium.
Then, Kalecki focuses on the implications of a rise in the inducement toinvest, given the supply of labour and of capitalists’ consumption. Because of therise in demand, prices of investment goods increase, causing a decrease in realcosts and a rise in labour demand. Some workers move from the consumption tothe investment sector, which decreases consumption goods output. For a givenvolume of capitalist consumption, demand exceeds supply and consumption.Prices rise until a new equilibrium is established, which involves a lower realwage rate, and therefore a somewhat higher output of consumer goods thanwithout 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, exceptthat the general level of prices and wages has risen’ (ibid: 209). As a
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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 ofgoods, which results in a rise in the value of money holdings. More realbalances are then available for financing production activities, causing theinterest rate to fall and permitting investment to increase ‘on account ofthe falling money value of sales the velocity of money circulation declinesand with it also the money rate of interest, which encourages entrepreneursto make investments’ (Kalecki 1990: 212). A set of real variables identical tothe one defined by Kalecki’s first model is thus determined. (The solutionsof Kalecki’s System II are discussed in Appendix 2.)
This adjusting mechanism, through which lower prices and wages couldeventually generate a move towards full employment, relies entirely on the‘Keynes effect’. Disequilibrium on the labour market indeed entails avariation in money wages, which causes a variation in price. This variationof price modifies the real value of money supply, which lowers the interestrate and stimulates investment. This process occurs until income andproduction reach a level ensuring equilibrium in all markets. As Kaleckistressed: ‘[T]his is the essence of arriving at equilibrium identical with onewhich would be established in System I’ (Kalecki 1990: 214 – 5). So, whenprices and money wages are completely flexible and the Keynes effectapplied, Say’s law is still valid. It is by modifying the conception of thelabour market in this second model that Kalecki suggests Say’s law could beinvalidated, 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 twomodels with regard to the functioning of the labour market. The centralhypothesis at the core of this difference is that unemployment, as such, isno longer supposed to push money wages down. Kalecki argues as follows:
[A]s long as it remains unchanged, existing unemployment does not ‘pressure’ themarket. 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 theinterest rate increases until ‘the volume of investment projects is reduced to theinitial level (and naturally new production combinations are realized bycancelling other projects which are unprofitable at a higher rate of interest)’(ibid: 209).
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7 Was Kalecki insisting on the difficulty and the time necessary to rendermoney wages flexibly downwards or was he referring to some differentadjustment mechanism? The second characteristic of his conception of thelabour market provides some clarification:
Namely, while the existing [emphasis in the original] unemployment does not exertany pressure on the market, we postulate that changes [emphasis in the original] inunemployment cause a definite increase or fall in money wages, depending on thedirection and volume of these changes.
(Kalecki 1990: 215)
This conception of the labour market obviously has its roots in Marxianeconomics. It is indeed Marx who developed the concept of the reservearmy of the unemployed, the role of which was to regulate the capitalistsystem by exerting a disciplinary effect. Kalecki certainly thought thatfalling (rising) unemployment increases (decreases) the power of workersto press for higher (lower) wages.15
The first hypothesis allows the determination of what Kalecki called aposition of quasi-equilibrium; it can be defined by a set of equationsidentical to that of Kalecki’s second model, except that in each equationthe level of the supply of labour has been replaced by the level of actualemployment. 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 towhich money wages are related to the level of unemployment – referred toas follows with the equation W ¼ g ðN � N Þ, where g5 0 – allows oneto 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 theexogenous ones are N ;M ;Cp. The model still has nine equations (seeAppendix 3). However, contrary to the other model, it is not dichotomic sothat shocks in demand now have an impact on employment. To show this,Kalecki carries out two comparative statics exercises: first, an improvementin the inducement to invest; and second, a cut in capitalists’ consumptionexpenditures.
Consider the effects of an increase in the inducement to invest. Thisleads to an increase in the price of investment goods. As a result,production and employment expand in the investment sector. In turn, thiscauses increased worker’s consumption, which boosts price and production
15 In an imperfect competition framework, Kalecki represented the increase inworker’s power associated with a boom by a decline in mark-up in the pricingequation (Kalecki 1971).
Kalecki’s (1934) model
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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 amountas the increase in real investment. Kalecki’s System III allows then theexpression of his theory of profit whereby capitalists get what they spend(Kalecki 1990: 216 – 7). However, this is not the end result. As Kaleckiemphasized, the rise in prices and in money wages due to increases inemployment and production, leads to a rise in the ‘money value ofturnover’; this also causes a rise in the transaction demand for money thatcan only be met by an increase in the rate of interest, which in turn reducesthe volume of investment (see Kalecki 1990: 217). But despite thisdepressive effect, the new quasi-equilibrium is established at a higher levelof employment because of the upward movement of the schedule ofmarginal profitability of new investment projects: ‘the increased output andrise in prices in relation to wages in turn increase profitability, whichadditionally stimulates investment activity’ (Kalecki 1990: 217).
Now consider how Kalecki envisions the effect of an exogenous decreasein capitalists’ consumption. The price of consumption goods decreases andproduction falls, which results in workers being pushed to the reserve armyof labour. Higher unemployment reduces consumer goods demand. Prices,output and employment in the consumer goods sector decrease untilprofits 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 consumptiongoods sector fall pari passu as the money wages do, without entailing areduction in real cost. But if the lowering of money wages does not affectfirms’ costs, they reduce, however, the interest rate, which causes a rise ininvestment and the hiring of some workers pushed initially into the reservearmy of the unemployed. Yet, in spite of the decrease in interest rate,investment is likely to fall due to profitability deterioration. Thus, Kaleckicame to the conclusion that a decrease in capitalists’ consumption, and so arise in savings, can reduce investment and drive the economy into aposition where unemployment is higher.
Having explained the three variants of Kalecki’s 1934 model,nowcompare it with the IS-LM model, focusing attention on the versionsdescribed 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 beingclassical;16 the second Keynesian;17 and the third a synthesis,18 two variants
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7
16 Hicks’ first system is a classical system in which money demand, in accordancewith 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 nðr Þ; I n ¼ Snðr ;Y nÞ
Yn, is nominal income, In is nominal investment, r is the interest rate, M thequantity of money in circulation supposed given and k a constant correspondingto the inverse of the velocity of money circulation. Hicks showed how a rise inthe inducement to invest in this model affects only the interest rate and leavesnominal income as it is. Consequently, employment will vary only if the supplyelasticity of each sector is not equal so that as he pointed out: ‘labour will beemployed more in the investment trades, less in the consumption trades; this willincrease total employment if elasticity of supply in the investment trades isgreater 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 quantityof money, by raising nominal income, will cause an increase in employment.This first model, although Hicks calls it classical, is neither dichotomic norneutral. This characteristic comes from the fact that it is nominal investment andnominal savings and not real investment and real savings that depend on interestrate. Thus the investment function is not homogeneous of degree one vis-a-visnominal variables, which, as d’Autume remarks ‘translates a generalised moneyillusion’ (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 dependson 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 nðr Þ; I n ¼ SnðY nÞ
The singularity is that it is the interest rate and not nominal income that isdetermined by the quantity of money: the interest rate determines nominalinvestment, which, via the multiplier, determines nominal income. It results in arise in the inducement to invest, which increases national income withoutaffecting interest rate. Obviously a rise in the quantity of money, by reducing theinterest rate, increases nominal investment and employment. Keynes’s essentialcontribution 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 moreclosely to the following model:
M ¼ LðY n ; r Þ; I n ¼ I nðr Þ; I n ¼ SnðY nÞ
in which nominal income has been introduced in the function of the demand ofmoney. For Hicks, this modification restricts considerably the oppositionbetween Keynesian theory and classical theory. Indeed, henceforth, a rise inthe inducement to invest triggers an increase in nominal income as well as ininterest rate, whereas a rise in the quantity of money reduces the interest rateand increases employment. Graphically this result appears clearly. If LL, thecurve representing equilibrium of the money market in the plan (r, Yn) isincreasing, a rise in the inducement to invest shifts IS to the right and generates
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7 of the first two enabling passage easily from one to the other. He stressedthat the opposition between Keynes and the classical authors is neither aconflict between rigidity and flexibility of money wages nor a conflictbetween unemployment and full employment, but originates in liquiditypreference theory.
Now compare Hicks’ model with Kalecki’s 1934 model. It is worth notingthat the conceptions of the labour market advocated by Hicks and Kaleckiare radically different from one another when one considers classicaltheory. Whereas Hicks assumed that the ‘rate of money wages per head canbe taken as given’ (Hicks 1937: 148), Kalecki supposed on the contrary thatthe money wage rate decreases with an excess supply of labour. Moreover,while Hicks’ article lacked an explicit account of how the labour marketworks and in which state it happens to end up, Kalecki insisted on the ideathat 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 risein the inducement to invest and in the quantity of money differssignificantly in Hicks’ and Kalecki’s classical models.
Focus, to start with, on the way Hicks and Kalecki respectively envisionedthe effects of a rise in the inducement to invest. In his system of twoproduction sectors, Hicks showed that such a shock modifies the structureof production. Thus, because total employment depends on howproduction is divided between sectors, it will not necessarily remainunchanged. Only if sectoral supply elasticities are identical will there be nochange in employment. On this point, Kalecki’s classical models are fully atodds with Hicks’ classical model. Indeed, market clearing and fullemployment exists in both of Kalecki’s classical models. Consequently, anincrease in the inducement to invest (i.e. a rightward movement of theschedule of marginal profitability of new investment projects) alwayselicits 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 inthe case of the liquidity trap that a rise in the inducement to invest only causes arise of national income.
18 Last, aiming to show that it is possible to realise a complete synthesis betweenclassical tradition and the Keynesian theory, Hicks built a variant of the latter,where the nominal income and the interest rate are the arguments for thedemand functions of money, investment, and savings, the model of generalizedGeneral Theory, which he wrote as such:
M ¼ LðY n ; r Þ I n ¼ I nðY n ; r Þ I n ¼ SnðY n ; r Þ
Thanks to this, Hicks can also show that a rise in the inducement to invest causesan increase in nominal income and in the interest rate, whereas a decrease inthe quantity of money reduces the interest rate and raises the nominal income.
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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’slaw, if saving rises, investment spending rises by the same extent. Thus,whatever the differences of supply elasticity between production sectorsare, workers unemployed in the sector of consumption goods are hired inthe investment sector. Because, as long as they are still unemployed, moneywages will fall, inciting capitalists to increase their spending until fullemployment is reached. And this result is not modified when the demandfor money depends on the interest rate as in Kalecki’s System II.
With regard to the effects of monetary expansion, the differencesbetween Kalecki’s and Hicks’ analysis also have their roots in the treatmentof the labour market. In Hicks’ model, an increase in the supply of moneycauses a rise in employment, due to the rigidity of money wages, whereasfor 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 ofmoney demand function, any rise in the supply of money entails only achange in nominal variables. Contrary to Hicks, Kalecki claimed thatintroducing the interest rate in the money demand function alone is notsufficient to get a system that leads to non-classical conclusions. What isneeded 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 withunemployment Kalecki developed a different conception of the labourmarket from Hicks. The central hypothesis of this conception is thatunemployment, as long as it remains unchanged, is not supposed topressure money wages downwards. However, if money wages do not fall andthere is an excess supply of labour, Kalecki did not conclude that wages arecompletely rigid. On the contrary, he believed that money wages respondto variations in unemployment. Unfortunately, this approach is mentionedbut not explained, even if it is highly likely that Kalecki was referring toMarx’s theories. Whatever it may be, however, it is clear that Kaleckibelieved that the labour market, due to the existence of a reserve ofunemployed workers being available, is characterized by a gap betweensupply and demand. This analysis can hereby be distinguished from that ofHicks. For Hicks, on the one hand, money wages are given and on the otherhand the supply of labour is not specified, making it difficult to say whetheror not unemployment exists (see De Vroey 2000).
19 As real savings do not depend on interest, the distribution of employmentbetween sectors will not be affected.
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7 Despite this difference, Kalecki’s model with unemployment behavesfundamentally in the same way as Hicks’. Concerning the effects of a rise inthe inducement to invest and the supply of money, both models react inexactly the same way. The only difference between Kalecki’s analysis andHicks’ is the existence of a liquidity trap in the latter. Kalecki did not referto a situation in which the liquidity preference schedule is interest inelastic.Consequently, whereas in Hicks’ model, a rise in the inducement to investcan trigger a rise in employment without affecting the interest rate, such ashock in Kalecki’s model obviously creates a rise in employment and in theinterest rate.
In his attempt to highlight the differences between classical theory andKeynesian theory, Modigliani also came up with three models but reachedradically different conclusions from Hicks. Whereas to Hicks thedistinguishing feature is liquidity preference analysis, to Modigliani it isthe rigidity in money wages. Although Kalecki adopted a representation ofthe classical theory that is not very different from Modigliani’s, his modelincluding unemployment is different from Modigliani’s Keynesian system.Kalecki’s 1934 article offers both anticipation of the IS-LM model on theone hand and of the difference between the classical and the Keynesianmodels on the other.
4. ‘Three Systems’ vs. the IS-LM model of Modigliani (1944)
In his 1944 article, Modigliani reconsidered the difference betweenKeynesian theory and classical theory. Keynesian theory is now defined bythe hypothesis of rigidity of money wages that Hicks considered common toclassical and Keynesian models. Henceforth, the opposition betweenKeynes and classical authors becomes an opposition between rigidity andflexibility of wages and between unemployment and full employment.Modigliani’s analysis of the labour market,20 coupled with two conceptionsof the money market, then allows the definition of three models: a crudeclassical model; a generalized classical model; and a Keynesian model.
The specificity of the crude classical model is that ‘the real part of thesystem, 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, Modiglianiwrote the supply of labour in a conventional way: Ns¼ F(W/P) or in the inverseform: W¼ F71(N)P. Therefore, by introducing a hypothesis of rigidity of moneywages, corresponding for him to the benchmark between classical andKeynesian models, he rewrote this equation as W¼W0.
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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 thisproperty in an obvious way. In fact, the quantity of money determinesnational nominal income and the interest rate. Thus, it is only if onesupposes nominal investment and savings to be homogenous of degree onewith regard to the price level that this occurs. In 1944, Modigliani curiouslydid not totally resolve Hicks’ (1937) problem.
In his second model, Modigliani replaced the quantity equation by afunction of money demand for which the arguments are nominal incomeand interest rate. This meant to show that the introduction of the interestrate in the demand function for money is perfectly acceptable in a classicalmodel when money wages are perfectly flexible. Indeed, as long as thesupply of labour depends on the level of real wages, the equilibriumreached by the economy is not modified. Once again, this is true only if thefunctions of nominal investment and nominal savings are homogeneous ofdegree one in prices. It is worth noting that Modigliani’s classical modelsare characterized by the flexibility of money wages and prices and itsensuing clearance of the labour market; it is also characterized by theineffectiveness of a monetary expansion in increasing employment and bythe failure of an increase in the inducement to invest to reach the samegoal.
Last, Modigliani elaborated on a model representing the Keynesiantheory. He claimed a Keynesian outcome arises when two factors are jointlypresent: rigidity of money wages and money demand depends on theinterest rate and nominal income. Thus, Modigliani argues that theKeynesian model is characterized by a basic maladjustment between thequantity of money and the wage rate, which explains the low level ofinvestment. He expands as follows:
What is required to improve the situation is an increase in the quantity of money (andnot necessarily in the propensity to invest); then employment will increase in everyfield of production including investment.
(Modigliani 1944: 76 – 7)
The contrast between Kalecki’s and Modigliani’s approaches can beeasily drawn and synthesized in Table 1. As seen, Modigliani’s classicalmodels are characterized by the flexibility of money wages and its ensuingclearance of the labour market, on one hand, and by the ineffectiveness ofan increase in the inducement to invest in increasing employment on theother. It thus seems these are exactly Kalecki’s classical models. Kalecki’smodels differ from Modigliani’s only by distinguishing between two classes(capitalists and workers) and two sectors (consumption and investment
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7
goods). But, whereas Kalecki’s and Modigliani’s classical models happen tobe so closed, their models with unemployment display some importantdifferences.21
Table 1 The features of the Kalecki, Hicks and Modigliani models
Labour market Demand for money Impact of shocks
Kalecki Flexible money wagesin classical models(Systems I and II),resulting in fullemployment; andflexible moneywage in System III,which results inunemployment.
Demand for moneyindependent frominterest rate inSystem I. Demandfor moneydependent oninterest rate andnational income inSystem II and III.
Rises in theinducement toinvest and in thequantity of moneydo not affectemployment inSystems I and IIand entail both arise in employmentand interest rate inSystem III.
Hicks Fixed money wages inthe classical andKeynesian models,resulting in anon-specifiedsituation in thelabour market.
Demand for moneyindependent frominterest rate in theclassical model anddependent oninterest rate inKeynesian models.
Rises in theinducement toinvest (whensectoral supplyelasticities are notidentical) and inthe quantity ofmoney affect thelevel of employmentin the classicalmodel but may haveno effect on it in theKeynesian modeldue to the existenceof the liquidity trap.
Modigliani Flexible money wagesin classical modelsand rigid moneywages in theKeynesian model,resultingrespectively in fullemployment andunemployment.
Demand of moneyindependent frominterest rate in thecrude classicalmodel. Demand formoney dependenton national incomeand interest rate inthe amendedclassical andKeynesian models.
Rises in theinducement toinvest and in thequantity of moneyaffect employmentonly in Keynesianmodel.
21 Thus we have : NdI ¼ f0
I
�WpI
�; NdC ¼ f
0
C
�WpC
�; Nd ¼ NdI þNdC ; Nd ¼Nd
�WpI;W
pC
�:
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7 As previously stated, the specificity of Kalecki’s unemployment modelhinges on his conception of the labour market. No difference between hisunemployment model and the classical models would remain were thisargument proved to be flawed. Kalecki’s unemployment model is, however,at odds with Modigliani’s Keynesian model, which rests on an exogenouswage. Indeed, although money wages do not adjust in response to anexcess supply of labour, Kalecki argues that they depend on unemploy-ment movements. Money wages are thus endogenous. It is, however,clear that if Kalecki had proceeded to make use of his unemploymentmodel to discuss the effect of an exogenous decrease in money wages, hewould have reached Modigliani’s conclusion. He would in particular haveargued that the only way a decline in wages could increase employment isthrough its effect in increasing the real quantity of money, hencedecreasing the rate of interest and thereby increasing investment andaggregate demand.
However, contrary to Modigliani, Kalecki’s main interest was notcomparative static equilibria. Instead, Kalecki referred to a temporaryequilibrium position in the Marshallian sense, a position that wouldsubsequently change as variables that had been held constant would bepermitted to change. In the conclusion of his 1934 paper, he indeed notedthat if the assumption of a given volume and structure of capital equipmentwere abandoned, then as a result of changes in capital stock there would bea continual movement through a series of equilibrium or quasi-equilibriauntil the final equilibrium is attained, i.e. a position in which investmentactivity no longer changes the volume and structure of capital equipment’.Moreover, when the time of construction of investment goods is taken intoaccount, this movement will be cyclical and the position of ‘finalequilibrium’ will never be reached, giving rise to endogenous businessfluctuations instead.22 Thus, Kalecki’s unemployment theory should notbe interpreted as a static theory of unemployment disequilibrium. Morespecifically, what concerned Kalecki, according to this interpretation, isnot 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 inwhich aggregate demand is not thereby adequately stimulated, so thatunemployment fluctuations continue to prevail, although the intensitychanges over time. Correspondingly, once it is recognised that Kalecki’sunemployment 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 1939Essays, see Assous (2003).
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7 unemployment quasi-equilibrium, it is also understood that the validity ofits analysis does not depend on the special assumption of absolutely rigidmoney wages.
5. Conclusion
As the 1934 article proved, before the General Theory appeared, Kalecki hadalready built a model able to express the main conclusions of the classicaltheory and to express the persistence of unemployment. In the case of acomplete flexibility of prices and wages, he first elaborated a model of fullemployment founded on Say’s law and then, considering the case in whichthe demand for money depends on the interest rate, showed that theeconomy reaches an identical equilibrium. In a third model, dedicatedto allow for unemployment, he referred to a conception of the labourmarket for which, as long as unemployment remains unchanged, it doesnot push down money wages. In this case, movements of employmentcan be explained in terms of movements in aggregate demand, resultingin Kalecki’s famous doctrine, which states that capitalists get what theyspend.
A formal representation of this argument has made it possible to showthat Kalecki did elaborate on an original IS-LM model that differs from themodels of Hicks and Modigliani. On the one hand, it seems that Kaleckiand Hicks developed a radically different analysis of the classical theory.Contrary to Hicks, Kalecki did not think that the introduction of theinterest rate as an argument in the money demand function necessarily casta shadow on the classical theory, a conclusion Modigliani stressed again tenyears later. On the other hand, this comparison has highlighted the factthat Kalecki developed a different model with unemployment fromModigliani’s. Whereas in Modigliani’s Keynesian model, money wages areexogenous, 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 hisconcept of quasi-equilibrium, a dynamic theory of unemploymentdisequilibrium in which unemployment variations are due fundamentallyto the fluctuations of investment.
However, despite the originality of this model, Kalecki did not find ittimely to have his 1934 article translated. To explain this decision, threehypotheses can be suggested. In 1944 Kalecki wrote that the flexibility ofprices and money wage could cause distribution effects making full-employment equilibrium unstable and he thus put implicitly into doubthis 1934 analysis of the classical theory. Moreover, in his 1934 article
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7 Kalecki reasoned in a perfect competition framework, whereas headopted the hypothesis of imperfect competition when Hicks’ andModigliani’s articles came out, which drove him to develop a new analysisof the distribution of income. Hence, contrary to what his 1934 articleshowed, Kalecki insisted on the fact that no negative correlation existsbetween real wages and employment. Last, as noted previously, Kaleckithought that the adequate frame to his theory was dynamics and notcomparative static, a point that he acknowledged to Hicks when criticizinghis IS-LM model (Kalecki 1939: 313). Considering certainly that this lattertheory filled the gap, Kalecki might have thought it useless to translatethis article.
References
Assous, M. (2003). Kalecki’s contribution to the emergence of endogenous businesscycle 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 ofPolitical 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-economie. In A. Beraud and G. Faccarello
(eds), Nouvelle Histoire de la Pensee Economique, tome 3. Paris: La Decouverte.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 developpement de la theorie de l’emploi
dans une economie monetaire. In A. Beraud and G. Faccarello (eds), Nouvelle Histoirede la Pensee Economique, tome 3. Paris: La Decouverte.
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.Keynes, J.M. (1936) [1973a]. Collected writings of John Maynard Keynes, vol. VII. In
D. Moggridge (ed.), The General Theory of Employment, Interest, and Money. London:Macmillan.
Kalecki’s (1934) model
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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 MonetaryEconomics, 26: 205 – 43.
Rubin, G. (2004). Patinkin on IS-LM: An alternative to Modigliani. History of PoliticalEconomy, 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) realwages in the consumption goods sector are determined as an implicitfunction of aggregate employment and capitalists’ consumption:
C ¼ fC f0�1
C
W
pC
� �� �¼ N W
pCþ Cp
Knowing W/Pc, one may determine the employment in the consumptiongoods sector. Because employment in the two sectors of production is equalto the supply of labour, one can then deduce the employment in theinvestment goods sector. The quantities of consumption goods andinvestment goods are then given by (1.1) and (1.2). From (1.4) one candetermine W/PI, from which the value of interest rate can be deduced.Indeed, the equilibrium condition is fI(NI)¼ I(pC/W, pI/W, r, g), whichimplies that the rate of interest is an implicit function of NI, W/pc and W/pI.With these variables now determined, the value of the equilibrium interestrate can be deduced. The money variables are determined by (1.8).Knowing W/pI and W/pc, W is given by:
M ¼ WkC
f 0c ðNcÞþ I
f0
I ðNI Þ
� �
Then, pI and pC are determined by (1.3) and (1.4).
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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 asan implicit function of aggregate employment and capitalists’ consump-tion. Thus:
C ¼ fC f0�1
C
W
pC
� �� �¼ N W
pCþ Cp
Knowing W/pc, employment in the consumption goods sector can bedetermined. Because employment in the two sectors of production,according to (1.5), is equal to the supply of labour, employment in theinvestment 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, fromwhich the value of interest rate can be determined. Thus, in equilibrium,fI(NI)¼ I(pc/W, pI/W, r, g), which means that the interest rate is an implicitfunction of NI, W/pI and W/pc. These variables being determined, theequilibrium interest rate and nominal variables can also be deduced. WhenW ¼ pI f
0
I ðNI Þ and W ¼ pC f0
C ðNC Þ, by considering the new equilibriumrelation in the money market, one reaches the value of the nominal wage.Thus:
M ¼ WC
f 0c ðNcÞþ I
f0
I ðNcÞ
� �Lðr Þ
Through (1.3) and (1.4) one determine pc and pI. 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 onein prices, it can be brought down in the following way:
fC ðNC Þ ¼ Cp þ ðNI þ NC Þf0
C ðNC Þ
M ¼ WfI ðNI Þf0
I ðNI Þþ fC ðNcÞ
f0
C ðNcÞ
� �LðrÞ
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fI ðNI Þ ¼ IpC
W;
pI
W; r ; g
� �
W ¼ g ðN � N Þ
or
fC ðNC Þ ¼ Cp þ ðNI þ NC Þf0
C ðNC Þ;
M ¼g ðN � NI � NC ÞfI ðNI Þf0
I ðNI Þþ fC ðNcÞ
f0
C ðNcÞ
� �L fðfI ðNI Þ; f
0
C ðNC Þf0
I ðNI ÞÞh i
where the interest rate is an implicit function of NI and Nc. The endogenousvariables are Nc and NI. The exogenous variables are N ;M and Cp. 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 aimsto show that before the General Theory Kalecki developed a mathematicalmodel capable of expressing both the main conclusions of the neoclassicaltheory – Kalecki’s Systems I and II – and the persistence of unemployment –Kalecki’s System III. The present analysis stresses the relevance and theoriginality of Kalecki’s 1934 model by comparing it to the two main variantsof the IS-LM model – Hicks (1937) and Modigliani (1944) – aroundwhich the neoclassical synthesis was built. It shows that although there doesindeed exist a formal proximity between Kalecki’s model and those ofHicks and Modigliani, Kalecki can be considered the first to offer anoriginal explanation of the difference between classical and Keynesianmodels that depends neither on liquidity preference as proposed by Hicksnor on the rigidity of money wages as proposed by Modigliani.
Keywords
Kalecki, Say’s law, quasi-equilibrium, Modigliani, Hicks, IS-LM, theory ofliquidity preference, money wage flexibility
Michael Assous
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