History of Economic Ideas, XI/2003/1

KALECKI’S CONTRIBUTION TO THE EMERGENCE OFENDOGENOUS CYCLE THEORIES:

AN INTERPRETATION OF HIS 1939 ESSAYS

Michael Assous

Thema-PhareUniversity of Cergy-Pontoise and CNRS

The aim of this paper is to focus on Kalecki’s contribution to the emergence of en-dogenous business cycle theories, of which Kaldor (in Kaldor 1960, pp. 177-192) is theWrst. More precisely, I want to demonstrate that this new type of theory is the resultof a two-step process of which Kalecki’s 1939 Essays (in Kalecki 1990, pp. 223-318) formthe Wrst one and Kaldor’s model the second one. From this study, it appears thatKalecki’s contribution is altogether puzzling. Indeed, after his 1933 unsuccessful at-tempt to explain the business cycle endogenously, Kalecki changed the course of hisresearch and adopted Frisch’s cycle explanation. As his work was reaching its highestpoint, he put together the essential elements Kaldor would use to construct the Wrstendogenous business cycle theory. In order to develop this idea I shall proceed inthree points. First I shall deal with the origin of Kalecki’s Essays. Then, after showinghow Kalecki introduced a non-linear function to his system I will discuss the degreeof endogeneity of his business cycle theory. Finally, I will study how Kaldor, in refer-ence to Kalecki’s system achieved his aim: building an endogenous cycle theory.

In the Weld of mathematical business cycle the will to analyse Xuctua-tions endogenously is not new. In 1933, when Wrst constructing such atheory, Kalecki’s purpose is obvious. It consists in explaining observedcycles with a system whose solutions are endogenous, deterministiccycles of constant amplitude. In substance, the demonstration of theintrinsic instability of capitalist economy is at stake. From this point ofview, using a linear mixed diVerence and diVerential equation, Kalec-ki tried to convince economists at the Leyden 1933 meeting of the Econo-metric Society that this aim had been reached thanks to the speciWca-tion of the parameters of his system. That is to say that for a particularvalue of the parameters, the solution of his system gave rise to cyclicalsolution of constant amplitude.

“Alas, Frisch was there to point out that since the Greeks it has been accepted thatone can never say an empirical quantity is exactly equal to a precise number. Givenhis aim, this was a deadly blow to Kalecki…”.

(Goodwin 1989, in Sebastiani 1989, pp. 249-250)

As a consequence, since this date Kalecki has changed the course ofhis research. In reference to Frisch’s “Swinging Sytem”, he acceptedthe idea that economy had a natural tendency, in absence of erratic

110 Michael Assous

shocks, to reach its equilibrium state. From this standpoint, Kalecki’sgenius is to have succeeded in demonstrating in 1934, and thus twoyears ahead of Keynes’ General Theory, that economy could reach anunemployment equilibrium. It is however in 1939, in his Essays in theTheory of Economic Fluctuations, that on this issue Kalecki’s analysisreached its highest point. Indeed, by attempting to improve Keynes’sanalysis, he showed that economy could attain a stable equilibriumeven if during the adjustment process long-term expectations deWnedby Keynes are assumed to vary. Then, it is precisely at this momentthat he put together the essential elements and especially a non-linearinvestment function necessary to construct an endogenous businesscycle theory. This didn’t escape Kaldor since it is thanks to Kalecki’sanalysis that he managed to conceive the Wrst theory of this new type.Thus, I will attempt to demonstrate that Kalecki’s contribution to en-dogenous dynamical analysis, though involuntary is altogether crucial.

In order to throw some light on this unusual episode of the historyof economic thought, I will proceed in three points. First, I will dealwith the origin of Kalecki’s 1939 Essays. Then I will analyse it, empha-sizing the reasons that led him to introduce a non-linear investmentfunction. Finally, I will study how, in 1940, thanks to Kalecki’s analy-sis, Kaldor succeeded in explaining cycle endogenously seven yearsafter the unsuccessful attempt of Kalecki.

1. The origins of Kalecki inspiration for his 1939 Essays

Frisch and Keynes represent two major sources of inspiration for Ka-lecki. Each, in his own way, leads him to deal with the question of theconvergence of economy towards a stable equilibrium. From this pointof view, Frisch’s inXuence, though less apparent than Keynes’s, may bemore crucial in the development of Kalecki’s thought. Indeed, throughhis criticism of Kalecki’s Wrst business cycle theory, he demonstratedthat Kalecki’s analysis was Xawed, insofar as he explained Xuctuationswithout considering that economy could naturally converge towards astate equilibrium. Moreover, it was Frisch and not Keynes who causedKalecki to concentrate on the question of equilibrium. However, thisdoes not mean that Keynes has exerted only a minor inXuence on Ka-lecki’s thought. As we will see, one of the most original aspects of Ka-lecki’s theory results from an attempt to improve Keynes’s General The-ory, in particular his analysis of the determinants of investment and, asa consequence, his analysis of unemployment equilibrium.

1.1. Frisch’s “Swinging System”

To understand Frisch’s impact on Kalecki’s thought, it is worth mak-

111An interpretation of Kalecki’s 1939 Essays

ing a comparison of Kalecki’s Wrst theory of the business cycle withFrisch’s “Swinging Sytem”. This will show that Frisch’s critiques ofKalecki’s original business cycles, which are prima facie merely techni-cal, are in fact of deep theoretical signiWcance.

Frisch’s and Kalecki’s theories of the business cycle both have incommon to be expressed mathematically. Thus they can both be con-sidered as the Wrst result of the econometric approach Frisch deWnedso brillantly in the Wrst issue of Econometrica in 19311. Each combinestwo essential elements. Indeed, a soluble mathematical model is de-veloped in each case from a set of carefully chosen and empiricallyobservable facts. That is the reason why the diVerence between hisown and Kalecki’s system appeared so clearly to Frisch. As Tinbergenemphasized in 1935 “the exact form in which it is presented [Kalecki’stheory] creates the possibility of a clear and fruitful discussion” (Tin-bergen 1935, p. 270). Furthermore Frisch and Kalecki presented theirbusiness cycle theories in the form of a linear mixed diVerence anddiVerential equation so that the contrast between their approachesbecomes obvious when their equations are solved.

Kalecki suggested the following solution based on the speciWcationof parameters. As it is now well known, a linear mixed diVerence anddiVerential equation can give rise to any of the three following typesof oscillatory behaviour, depending on the value of the parameterschosen in the equation of the system (the coeYcient of the Wrst orderterm):

a) For a negative coeYcient, its amplitude of Xuctuation may growceaselessly, thus being unstable.

b) For positive coeYcient, it may be stable, with an ever-decreas-ing amplitude,

c) if equal to zero, its behaviour may lie exactly in between theother two so that it neither grows nor decreases in violence.

As Goodwin emphasized

“Kalecki very sensibly chose the value zero thus avoiding the dilemma, since his aim,in the Marxian tradition, was to explain how and why capitalism was, by its verynature, bound to oscillate. His solution combined theoretical necessity with practi-cal convenience since it determined the one parameter for which he had no evi-dence”.

(Goodwin 1989, in Sebastiani 1989, p. 249)

1. In the editorial of the Wrst issue of Econometrica, Frisch wrote: “Thus, econometrics is by nomeans the same as economic theory, atlthough a considerable portion of this theory has adeWnitely quantitative character. Nor should econometrics be taken as synonymous with theapplication of mathematical to economics. Experience has shown that each of these three-points, hat of statistics, economic theory, and mathematics, is a necessary, but not by itself asuYcient, condition for a real understanding of the quantitative relations in modern economiclife. It is the uniWcation (underlined by the author) of all three that is powerful. And it is uniWca-tion that constitutes econometrics” (Frisch 1931, in Hansen 1964, p. 417).

112 Michael Assous

Indeed, Kalecki’s purpose was to construct a system whose solutionwould have been endogenous, deterministic cycles of constant ampli-tude. Therefore, according to him, the demonstration of the intrinsicinstability of economy was at stake2.

This feature of Kalecki’s approach becomes all the more evident whencompared to Frisch’s solution. Contrary to Kalecki, Frisch accepts theidea that economy has a natural tendency to reach its equilibrium state,in other words, that the system is intrinsically stable. From this point ofview, if the cycles observed are undamped, it is because of erratic shocks.Using an idea of Wicksell as well as the results of Yule and Slutsky ontime series, Frisch showed that these shocks do not need to have anyregularity in timing and violence to explain the maintenance of theoscillation. As regards Frisch’s analysis of the cycle, it is not surprizingthat Kalecki’s solution did not convince him. Frisch wrote in 1935:

“The imposition of the condition that the solution shall be undamped is in my opin-ion not well founded. It is more corect, I think, to be prepared to accept any dampingwhich the empirically determined constants entail, and then explain the maintenanceof the swings by erratic shocks”.

(Frisch 1935, in Kalecki 1990, p. 447)

Thus, when Frisch criticized Kalecki’s solution, it is in reality Kalecki’sapproach to the dynamics of capitalist economy he criticized. This didnot escape Kalecki and from 1934, Kalecki was wondering what themechanisms were by which economy could converge to a stable equi-librium. His genius, on this precise point, was to succeed, two yearsbefore the publication of the General Theory, in demonstrating the sta-bility of an unemployment equilibrium3. However, on this question,Kalecki encountered diYculties, which he tried to overcome in 1936,by referring to the General Theory

1.2. Keynes’s General Theory

Keynes’ General Theory constitutes a major source of inspiration for

2. In the preface of his Essay on the Business Cycle Theory published in polish, Kalecki wrote that:“the aim of this study is to provide an explanation, indeed one of several possible explanations,of the automatic mechanism of business Xuctuations in a closed economy […]. Moreover, theautomatic mechanism of business Xuctuations is deWned here much more stricly than usual.We do not, for instance, seek to examine an automatic restoration of equilibrium which hasbeen distorted by disproportions of development. Instead, we want to set out a mechanismwhich would explain the relative regularity (stressed by the author) of business Xuctuations”(Kalecki 1933, in Kalecki 1990, p. 66).3. Kalecki dealt with unemployment equilibrium when he discussed the validity of Say’s Lawin an article entitled “Three System”, published in the Polish review Ekhonomista and onlytranslated in english in 1990 (Kalecki 1934, in Kalecki 1990, p. 201). In respect to the link be-tween this article and the anticipation of the General Theory issue, see Osiatinsky (1985); Chap-

ple (1995); Assous (2001).

113An interpretation of Kalecki’s 1939 Essays

Kalecki’s Essays insofar as it deals in a slightly diVerent manner withthe problem of the convergence of economy to a stable underemploy-ment equilibrium. Indeed Keynes, in contrast with Kalecki, laid theemphasis more on expectations. And, as we will see in the secondsection, a fundamental innovation of Kalecki’s Essays results from hiswish to incorporate this aspect into his theory of business cycles. How-ever, if Keynes’s book seems to have persuaded Kalecki to treat thistopic more thoroughly, this does not mean that he adopted the sameanalysis as that of Keynes. On the contrary, from this standpoint, Ka-lecki’s reading of Keynes’s theory is highly critical. In order to under-stand this point, we must examine Kalecki’s review of Keynes’GeneralTheory published in Polish in 1936.

Kalecki’s main criticism of Keynes was that he assumed exogenouslong-term expectations impling in the short-term that the level of in-vestment was determined by the rise in price of investment goodsthrough which the marginal eYciency of capital and the rate of inter-est equalised.

“However, because, as Keynes holds in another part of his book, ‘the fact of theexisting situation enter, in a sense disproportionately, into the formation of our long-term expectations’, the expectations will become more optimistic and a diVerencebetween the marginal eYciency of investment and the rate of interest will arise again.‘Equilibrium’, then, is not reached, and the growth of investment will still persist…”

(Kalecki 1936, in Kalecki 1990, p. 231)

Therefore, according to Kalecki, if expectations have to be taken intoaccount for the determination of a short-run equilibrium, their inte-gration must be fully made. That is to say, the economist must beprepared to accept that expectations are determined endogenously.In a way, Kalecki’s criticism amounts to denying the split made byKeynes in his book between chapter 11 on marginal eYciency and chap-ter 12 on long term-expectations.

But, in rejecting Keynes’s distinction between short and long-term ex-pectations Kalecki is compelled to discover what the mechanims by whichthe investment level can reach a deWnite level are, his aim being to ex-plain how the economy converges to an unemployment equilibrium.To deal with this problem, he suggested abandoning the assumption ofan inWnitely elastic supply of equity capital by turning to the principle ofincreasing risk. As we will see, it is thanks to this principle that Kaleckisucceeded in integrating endogenous expectations into his analysis andin explaining both the convergence of economy to a stable unemploy-ment equilibrium and the business cycle with a non-linear model.

2. Kalecki’s 1939 contribution: a non-linear business cycle theory

A crucial innovation of Kalecki’s 1939 Essays consists in the introduc-

114 Michael Assous

tion of a non-linear function into a dynamical system. By discussingFrisch’s and Keynes’s inXuences on Kalecki, we observed that the lat-ter aimed at demonstrating how economy could converge to a stableunemployment equilibrium. In this section, our purpose is to showthat Kalecki’s wish to express his theory of the business cycle with anon-linear function originated in research on this question. More pre-cisely, we want to stress that Kalecki’s used this new type of functionin order to demonstrate the stability of unemployment equilibriumand that his analysis of the business cycle are based on the results ob-tained thereby. It is therefore appropriate to consider on the one hand,the degree of stability of Kalecki’s unemployment equilibrium, andon the second hand the degree of endogeneity of his business cycletheory.

2.1. The degree of stability of equilibrium

We have previously explained the reasons why Kalecki disagreed withKeynes’s analysis of investment insofar that it is based on the assump-tion that long-term expectations are exogenous. As he wrote to Key-nes in a letter dated from 1937, in an attempt to convince him:

“… the increase of prices of investment goods which equates the marginal eYciencybased on the initial state of expectations to the rate of interest, does not create an‘equilibrium’; for at the same time expectations improve to some extent and thusinvestment increases further”.

(Kalecki 1939, in Kalecki 1990, p. 524)

And it is why, according to him, instead of assuming that long-termexpectations are exogenous, the principle of increasing risk would bemore appropriate. For, as he underlined it in his fourth essay:

“It is this assumption [that the rate of risk is independent of the amount invested]which has to be dropped, I think, in oder to obtain a realistic solution of the problemof limited investment. It is reasonable to assume that marginal risk increases withthe amount invested. For the greater the investment, the greater is the reduction ofthe entrepreneur’s income from his own capital when the average rate of proWt fallsshort of the rate of interest”.

(ibid., p. 287-88)

Indeed, if marginal risk increases with capital invested, it becomes pos-sible to justify the deWnite level of investment without assuming thateither the prices of investment will rise or the expected future returnsare a decreasing function of the amount invested. On the contrary,with this principle it becomes possible to explain the convergence ofeconomy to a stable equilibrium when expectations vary during theprocess whatever the variations. For, by virtue of this principle, evenif prospective proWts improve rapidly, investment spending cannot

115An interpretation of Kalecki’s 1939 Essays

increase at the same pace. After some time the risk will become sohigh that entrepreneurs will be discouraged from investing.

Graphically, it allows Kalecki to describe the process of adjustmentof economy with a non-linear function of investment decisions. As-suming that the expected receipts of each investment projects are esti-mated on the basis of the present state of aVairs, these receipts beingestimated on the basis of current proWts determined by the currentnational income, Kalecki suggested expressing investment decisionsof entrepreneurs, D, as a S-shaped function Φ of the current nationalincome Y. For according to him

“… when things are improving entrepreneurs become more optimistic about theirfuture, and the rate of investment decisions increases strongly; but after a certainpoint doubts begin to arise as to the stability of this development, optimisim ceasesto keep pace with boom, and the rate of investment decisions tends to increase lessrapidely. In the slump a symetrical development is likely to occur”.

(ibid., p. 310)

Therefore, thanks to the principle of increasing risk, and in spite ofwaves of optimism or pessimism Kalecki can explain the mechanismby which economy reaches a stable unemployment equilibrium. Inorder to demonstrate this, it is still necessary to expose the systemfrom which Kalecki drew a second function f between current nation-al income and the spending of investment. The originality of this lastfunction is to integrate the determinants of income distribution and atime-lag of investment.

The model concerns a closed economic system without trend. Indi-cating with Π

t, total real income of capitalists at time t, capitalists’

consumption is related to gross real proWts (capitalists’income) bymeans of the linear function4

C Cτπ

τ πλ= +Π

where Cπ is a positive constant (Wxed volume of capitalists’ consump-tion) and λ is a positive constant too, but smaller than 1. Then ignor-ing workers’ saving, so that workers’consumption is equal to the totalreal wages received

C Wwtτ =

and assuming that the relative share of wages in real national incomeis Wxed and determined by the degree of monopoly, real national in-

4. For convenience, we have changed Kalecki’s notation. Kalecki wrote the real gross proWtsy, real capitalists consumption c, the undelivered investment goods W and λ the consumptioncapitalist delay. The other symbols have not been changed.

116 Michael Assous

come can be related to investment spending by means of a function f.For, since

WY

at

t

=

we can write

Y C C I Wt tw

t t t= + + = +τπ Π

Then, after transformation

Y

I Catt= +

− −π

λ( )( )1 1

or

Yt = f (I

t)

Furthermore, under the assumption that there is an average gestationlag of investment equal to a positive υ, we can rewrite Y

t in function

of Dt. Indeed, if the production of the investment goods requires theWxed time interval υ, then the value of the undelivered investmentgoods at time t is

UD D dt t=

−∫ ( )τ τυ

τ

and accordingly, the average production value of the investment goods

industry per unit of time is I

UDt

t=υ

:

I D dt t

=−∫

1υ

τ τυ

τ( )

which means that the output of capital goods at time t is equal to anaverage-expressed in continuous terms-of the orders placed in the in-terval (t – υ, t). Therefore it follows approximately that

I Dt

t=

−υ2

117An interpretation of Kalecki’s 1939 Essays

and if we assume that there exists a lag between capitalist income, Πt,

and consumption out of it, ctπ, we get:

Y = f (Dt–τ)

or

Yt+τ = f (D

t)

Where τ γ υ= +

2, with γ being the consumption capitalist delay,

which represents the dependence of the rate of investment decisionsat time t on the national income at the same time.

Thus, on the assumption that only φ is non-linear and that the stockof capital is Wxed, Kalecki describes the process of adjustment of theeconomy as follows in the plane (D, Y):

It appears from this chart that, according to Kalecki, the “dynamicprocess” leads economy to a stable equilibrium. Indeed, we can sup-pose the time is divided into τ periods and that in the Wrst τ period thelevel of national income is Y1 and the rate of investment decision is D1.Since investment decisions determine the national income in the nextτ period, the national income will be Y

2 in the second period. But, for

this new level of income, the rate of investment decision is above D1

and equal to D2. Therefore, the national income goes on growing.

However, “after a relatively small number of periods the diVerencebetween Y, D and YB, DB

is negligible, i.e. the position of equilibrium ispratically reached” (ibid., p. 315). Of course, if the point Y, D is belowthe f curve so that investment decisions are lower than those which

118 Michael Assous

have determined the present national income “this process is reversed,and the system travels downwards towards B” (ibid., p. 315). In a nut-shell, if capital stock is constant, a deviation of income from equilibri-um, whatever the reasons, initiates an adjustment process towardsthe stable equilibrium B. Now, it is worth putting the emphasis on thefact that Kalecki focuses only on this type of situation. In retrospect, itcan appear puzzling. Indeed, with a non linear function, we could ex-pect Kalecki to have discussed the case in which φ cuts f by below,that is to say a situation in which the economy can attain both stableand unstable equilibrium. However, as we have seen, Kalecki intro-duced a non-linear function for taking into account long-term expec-tations. Then, according to him, it is necessary to demonstrate thestability of equilibrium in spite of the variations of the expectations.As we shall see in the third section, it is precisely because Kaldor aban-donned this idea that he succeeded in oVering a new theory of thebusiness cycle built on Kalecki’s system. However, before dealing withthis problem, it is still necessary to consider how Kalecki explains thedynamic process described in this paragraph when capital stock is vari-able. As we will see, his explanation is directly linked to his concep-tion of equilibrium in the short-term.

2.2. The degree of endogeneity of the business cycle

Up to now, we have implicitly assumed that investment spendingdoesn’t aVect the capital stock during the dynamic process so that theeconomy reached equilibrium in moving up φ. However, by relaxingthis assumption, the dynamic of the economy changes. Economical-ly, it results from the existence of the investment time-lag previouslymentionned. The latter, indeed, introduced two diVerences of timeinto the system. A Wrst one between investment decision and invest-ment spending which increases global demand and a second one be-tween investment decisions and deliveries of equipment which, inaVecting positively the capital stock, decreases global demand. Then,since the pace of variation of investment decisions is diVerent fromthe one of capital stock, the dynamic becomes cyclical.

In order to represent it, Kalecki kept reasoning in the (Y, D) plane.However, he then drew a family of φ curves related to a diVerent stockof capital, and hence to a given value of investment necessary to themaintenance of the existing capacity (the amount of depreciation be-ing Wxed). The superior curves are connected with the lowest level ofcapital stock. For, with a same level of income, investment decisionsare greater when the volume of equipment is low. From this conclu-sion, it follows that if equipment deliveries are weaker than the main-tenance level of equipment, so that the equipment is decreasing, the

119An interpretation of Kalecki’s 1939 Essays

increase in the investment decision described previously will be streng-htened. That is to say that the φ curve on which the economy movesup will also move upwards. On the contrary, if the volume of equip-ment deliveries is greater than the volume of depreciated equipment,the dynamic process will be hampered. So that the φ curve on whicheconomy moves up will move downwards. Therefore, if at the inter-section of curves f and φ, investment decisions are greater than themaintenance volume of equipment, the volume of capital will growand the economy will move up on a downward-shifting φ curve in-stead of being in equilibrium. However, if investment decisions arelower than the maintenance volume of equipment, the reverse willoccur. Eventually, Kalecki suggested the following representation ofthe trajectory of the economy.

As we can see, the case considered is a self-stimulated cycle. In orderto understand the conditions necessary to obtain this result, we needto focus on Kalecki’s explanation of the cycle mechanism. Let us Wrstconsider the inXexion point E for which the deliveries of investmentgoods are just equal to the maintenance level of equipment. Thus, asthe volume of equipment is constant, the φ curve is stationnary in theconsidered period, and since E is above f, national income increasesand the point Y, D tends to move up this curve. However, in follow-ing periods investment activity increases causing the growth of equip-ment and the φ curve shifts downwards. As a consequence the “self-stimulating process” of the rise in investment decisions and nationalincome is hampered and the economy attains point F located on alower φ curve. At this point, where φ intersects f, national income isneither expanding nor shrinking. However, because of deliveries ofinvestment ordered previously, capital equipment is expanding. Con-sequently, investment decisions fall causing a decrease in income,which in turn depresses investment decisions. Graphically the φ curve

120 Michael Assous

shifts downward causing point Y, D to move vertically and up this oneuntil investment activity is equal to the level of maintenance. As aconsequence, from this moment, capital equipment shrinks, thus ham-pering the downward movement. Finally, point Y, D reaches H. Here,income ceases to fall, but the φ curve shifts upwards because of thedecrease of equipment, “thus the moving point comes back to point Eand a new cycle begins” (ibid., p. 317).

As regards this explanation, we could believe that Kalecki’s cycleare perfectly endogenous. But this is not the case, and Kalecki himselfemphasized it when he wrote:

“Clearly it is an arbitrary and even unlikely assumption that the moving point comesback to its initial position E – the trajectory may well be a spiral and not a closedcurve. If the Xuctuations produced by our mechanism have a tendency to subside,this means that the spiral converges towards point B, and in this way the systemtends to attain long-run equilibrium. But as shown by the investigations of Prof.Frisch (‘Propagation Problem and Impulse Problems in Dynamics’, in Economic Es-says in Honour of Gustav Cassel, and unpublished works), this is prevented by the exist-ence of ‘erratic shocks’. Since the relationships represented by f and φ are in realitynot quite stable functions, the actual dynamic process may be imagined as the resultof the operation of the mechanism described above and random shocks. Now Pro-fessor Frisch has shown that, if the basic mechanism produces slightly damped Xuc-tuations, the existence of shocks establishes a state of relatively regular undampedXuctuations with an average period similar to that of the Xuctuations created by the‘basic mechanism’”.

(ibid., p. 318)

Consequently, as Kalecki himself recognised, his theory, though non-linear, is only semi-endogenous: its degree of endogeneity dependson the magnitudes of the parameters involved. More precisely, thisdepends on the importance of the shifts of the investment decisioncurve φ and hence on the sensibility of investment decisions to capitalvariations. Indeed, it is only in the case when these shifts are suY-ciently strong that a monotonic return to the stationnary equilibriumdoes not occur.

However, in spite of his low degree of endogeneity, Kalecki’s theo-ry opens up new vistas in the Weld of endogenous cycle research. Kal-dor didn’t miss this fact, since his ground-breaking Wrst endogenouscycle theory published in 1940 (in Kaldor 1960, pp. 177-192), one yearafter the publication of Kalecki’s Essays, was greatly indebted to Ka-lecki’s work.

3. From exogenous to endogenous business cycle theory: the Es-says reconsidered by Kaldor

As regards Kaldor’s analysis of the necessary and suYcient assump-tions from which an endogenous business cycle can be deduced, it

121An interpretation of Kalecki’s 1939 Essays

appears that Kalecki is undoubtedly the economist who most deeplyinXuenced Kaldor. To demonstrate this, we shall deal Wrst with Kal-dor’s innovation and secondly with his reconsideration of Kalecki’stheory.

3.1. Kaldor’s innovation

Although his analysis is in retrospect a turning point in the history ofbusiness cycle theory, Kaldor tells us in the introduction to his articlethat he will “not attempt to put forward any ‘new’ theory of the tradecycle”. As he writes

“The theory here presented is essentially similar to all those theories which explainthe trade cycle as a result of the combined operation of the so-called ‘multiplier’ andthe investment demand function as, e.g.,the theories put forward in recent years byMr. Harrod and Mr. Kalecki. The purpose of the present paper is to show, by meansof a simple diagrammatic apparatus, what are the necessary and suYcient assump-tions under which the combined operation of these two forces inevitably gives riseto a cycle”.

(Kaldor 1940, in Kaldor 1960, p. 177)

In fact, as regards these “necessary and suYcient assumptions” whichlead to an endogenous business cycle model, Kaldor’s words becomemore understandable. Indeed, such a theory must possess at least onelinear function (investment function or saving function) to make thestationary equilibrium unstable. And from this point of view, the the-ory “nearest to it, […] is Mr. Kalecki’s theory given in chapter 6 of hisEssays in the Theory of Economic Fluctuation” (ibid., p. 188). For if Kalec-ki’s non-linear function is used to obtain this result, business cyclesbecome endogenous. And this is precisely what Kaldor showed in theappendix to his article. Viewed thus, his contribution may seem thin.However, with respect to Kalecki’s use of non-linearity, Kaldor’s con-tribution is revolutionary. As we have seen, Kalecki introduced a non-linear investment function because he knew that when capital stock isWxed, the economy converges to a stable equilibrium. Hence, Kaleckicouldn’t arrive at Kaldor’s result. We can see this clearly by studyinghow Kaldor transforms Kalecki’s theory into an endogenous one.

3.2. Kalecki’s business cycle theory reconsidered

In order to achieve this project, Kaldor referred to the framework de-Wned by Kalecki and especially to his diagram in the plane (Y, D) usedpreviously. Firstly, following Kalecki, Kaldor draws a family of S-shapedcurves φ

e1 … representing the rate of investment decisions at time t,

given the quantity of equipment available, where “e1 represents a small-

122 Michael Assous

er quantity of equipment than e2, and so on” (ibid., pp. 188-189). How-

ever, in contrast to Kalecki, he assumes that for a given quantity ofequipment (e

3 in the chart) a φ curve cuts f from underneath which

corresponds to an unstable equilibrium. That is to say a point fromwhich, if disturbed, the system will diverge. As regards the cycle mech-anism, this change is vital for it allows us to consider the case wherethe stationary equilibrium “‘where saving = Investment’ and net in-vestment is zero is an unstable one” (ibid., p. 189). Hence there can bea conWguration in which if the economy is not initially in this point, itcan never attain it, whatever the parameter values may be. That is tosay, situations for which cyclical Xuctuations are endogenous. Kaldorrepresents this by the trajectory AGCF. Indeed, as he rightly under-lines

“If we assume that the time-lag τ is small relatively to the time needed to reachsuccessive φ curves (i.e. relatively to the rate at which the total quantity of equip-ment is increasing), so that a position of short period equilibrium can be reachedbefore signiWcant changes occur in the amount of equipment in existence, the cycli-cal movement of the system will be indicated by the trajectory AGCF”5.

(ibid., p. 190)

Supposing that, in the initial position, the system is at k. So, under thelatter assumption, the system will move up the same φ curves and

5. In order to render clearer the comparison between Kalecki’s Essays and Kaledor’s model, Bhas been replaced by C.

123An interpretation of Kalecki’s 1939 Essays

reach the point l. Here, owing to the gradual accumulation of equip-ment (the economy is above RR which represent “the locus of pointson the φ

e curve where the level of investment decisions corresponds

to replacement so that net investment is zero” (ibid., p. 189)) the econ-omy will move up the f curve until it reaches F. At this point, sinceequilibrium is unstable, a “downward moving cumulative process isset up which lands the system at A” (ibid., p. 190). Then, as A is belowRR, capital equipment shrinks so that economy moves up the f curveuntil it reaches G. But, as with point F, the latter is unstable. Conse-quently, “an upward cumulative movement follows which lands thesystem at C and a new cycle appears” (ibid., p. 190). In conclusion,whatever the initial position-unless economy is initially in B (the sta-tionnary equilibrium) – the development of economy will inevitablybe cyclical. Indeed, if at the begining the system is placed in proximityof B, a moving cumulative process is set up which on the right of B isdownward and on the left is upward, which will give rise to an endog-enous cycle.

This last development shows that the Wrst endogenous business cycletheory was the result of a two-step process in the Wrst step of whichKalecki played a crucial role. Indeed, we can see that it is by modifyingthe direction of his research under the inXuence of Frisch that Kaleckihas succeeded in introducing a non-linear function thanks to whichKaldor has determined the necessary and suYcient assumptions lead-ing to an endogenous business cycle theory. From this standpoint, hiscontribution is speciWc, for it was by abandoning the goal to producean endogenous theory that he has put together the essential elementsthat such a theory requires.

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