Neo-Kaleckian and Sraffian Controversies on the Theory of Accumulation

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Cesaratto, S. (2015). Neo-Kaleckian and Sraffian Controversies on the Theory of Accumulation. REVIEW OF
POLITICAL ECONOMY, 27(2), 154-182 [10.1080/09538259.2015.1010708].

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04 October 2024

Neo-Kaleckian and Sraffian Controversies on the Theory of
Accumulation*
SERGIO CESARATTO
Dipartimento di Economia Politica e Statistica, Università di Siena, Italy
ABSTRACT Non-orthodox economists generally share the Keynesian Hypothesis of the
independence of investment from capacity savings, in the long run no less than in the short run. Thishypothesis marks an essential point of difference from neoclassical theory. Keynes showed that within
the limits of the existing capacity utilisation, investment determines savings rather than the other way
around. How best to extend this conclusion to the long run is the object of the present paper. The
paper assesses the controversy on demand-led growth that has taken place since the mid-1980s
between neo-Kaleckian and Sraffian authors. The Sraffian front may be divided into a first and asecond Sraffian position, the latter being the Sraffian supermultiplier approach. I shall argue that thissecond approach is the most promising framework for analysing economic growth.

1. Introduction
Most non-orthodox economists share what Nicholas Kaldor called the ‘Keynesian
Hypothesis’―the idea that investment is, in both the long run and the short run, independentof the savings that would be forthcoming from the normal utilisation of productive capacity(Garegnani, 1992, p. 47). Some heterodox economists, however, maintain that the Keynesian
Hypothesis applies only to the short run, a position similar to that held by mainstream
Keynesian economists. Keynes showed that within the limits of the existing capacity
utilisation, it is investment that determines savings rather than the other way around. The
outcomes of the capital theory controversy have reinforced this conclusion (Garegnani,
1978‒79). How to extend the Keynesian Hypothesis to the long run is the object of thepresent paper. In particular, I shall assess the theoretical debates on demand-led growth thathave taken place since the mid-1980s between neo-Kaleckian and some Sraffian authors*

Correspondence Address: Sergio Cesaratto, Università degli Studi di Siena, Dipartmento di

Economia Politica e Statistica, Piazza S. Francisco, 00153 Siena, Italia. Email: Cesaratto@unisi.it

close to the surplus approach as expounded in the writings of the late Pierangelo Garegnani.
Without overstressing the discord, I will distinguish between a first and a second Sraffian
position. The former is mainly sustained by some Sraffian economists at the Third Universityof Rome; the second, perhaps more accurately described as the Sraffian supermultiplier (SM)approach, is supported mainly by a group of Sraffians at the Federal University of Rio deJaneiro. We shall refer to the two positions as the FSP and SM approaches, respectively. The
divergence between these two Sraffian outlooks arose in the mid-1990s.
As is well known, the early efforts to deal with the instability problems inherent in the
Harrod growth model were based either on the neoclassical factor substitution mechanisms oron the assumption of an endogenously determined income distribution as in the Cambridge
Equation; these efforts are considered in Section 3. Both approaches were later rejected by
neo-Kaleckian and Sraffian economists, whose writings on the topic (which are discussed in
Sections 4 and 5) engendered an intense controversy. Notably, they all took investment as theindependent variable. This hypothesis is rejected by SM scholars, who take the long-term
pattern of the autonomous components of aggregate demand as the independent variable (seeSection 6). Their approach was later criticised―not altogether persuasively, as we shallsee―by adherents of the FSP. The driving role of the autonomous components of aggregate
demand sustained by credit creation may be associated with financial crises, as will be notedin the final Section 7, where, additionally, we shall identify potential routes to convergencewith other heterodox traditions.
We begin by re-examining two arguments against the treatment of investment as theindependent variable in order to avoid Harrod’s knife-edge problem.

2. Long-Term Expectations and External Markets
2.1. Eatwell on Keynes and Harrod
John Eatwell (1983, pp. 281‒283) has advanced some useful propositions that set the stage
for the discussion of the following pages.
Keynes’s notion of effective demand is the macroeconomic counterpart ofAdam Smith’s notion of effectual demand: the demand that obtains when the
product (a single commodity or aggregate output) is offered at normal prices,
those associated with a normal profit rate and a normal degree of capacity
utilisation, given the real wage rate and the technical conditions of production.

Capacity utilisation varies over the trade cycle; there is, however, a tendency
to adjust capacity to the level of long-period effective demand.

The process of adjustment of capacity to demand gives rise to somecomplications: ‘Demand has been supposed to be the independent variable, yet
the process of adjustment of sectoral capacity to demand must involve changes
in investment.... At the aggregate level, this difficulty is manifest in the
instability of Harrod’s warranted rate of growth. … The origin of the problem
is that on the one hand investment is assumed to be the independent variable,
whilst on the other hand variation … of investment is the mechanism by which
capacity is adjusted to demand’ (ibid., p. 282).

‘The solution may be found in Keynes’s own analysis of long-period
employment; it is not investment which is the independent variable, it is the“state of long term expectations”’ (ibid.).

These observations amount to a proposal for an ordered approach to the analysis of economic
growth. Eatwell suggests that much of what has gone wrong in the discussion of growth may

be explained by the failure to recognise that ‘it is not investment which is the independent
variable, it is the “state of long term expectations.”’ But how long-term expectations areformed and, more importantly, how they are revised when economic circumstances change,
are questions that Eatwell leaves unanswered.

2.2. Kalecki on Tugan-Say-Harrod and on Luxemburg’s External Markets
To my knowledge, it has not hitherto been noticed that Michal Kalecki’s masterful 1967
paper on Tugan-Baranowski and Rosa Luxemburg is a contribution on how to overcome theHarrod instability problem. The argument of the paper is well known. Tugan-Baranowski
shows that, in principle, a capitalist system can maintain an equilibrium growth path as longas capitalists employ all their savings to create new capital goods. This reflects a distinctive
characteristic of capitalism, i.e., that it is a system in which the aim of production is not thesatisfaction of human needs, but the generation of profits, which can well be achieved
through the production of means of production. A tacit pact could, in principle, be stipulated
amongst capitalist to ensure that the entire social surplus, if not consumed, is invested so that
all output is sold. But of course, we cannot expect capitalists to follow Say’s Law, either
blindly or deliberately, since ‘capitalists do many things as a class but they certainly do notinvest as a class. And if that were the case they might do it just in the way prescribed by
Tugan-Baranowski’ (Kalecki, 1967, p. 152).
Rosa Luxemburg saw more clearly than Tugan-Baranowski the difficulty of capitalists
to absorb the social surplus through their own consumption and investment. Hence thenecessity of ‘external markets’―external to the capitalist income circuit―that might serve toabsorb the surplus production. Typically these markets are financed by the capitalist systemitself through the financial system (Kalecki, 1934, pp. 15n, 18‒19; 1967, p. 153). Kalecki

includes in these markets net exports to the peripheral countries and government spending.
We may usefully add consumer credit.
A numerical example used by Kalecki (1967) to illustrate the difficulties with Tuganis implicitly intended to expose the difficulties of Harrod’s model. Kalecki assumes an
economy in which consumption and investment are the only components of aggregate
demand. The rate of net investment in the capital stock is 4% (or 7% in gross terms), at which
capacity is fully utilised. If output and aggregate demand also grow at 4%, ‘full utilisation ofequipment continues and the problem of effective demand does not seem to arise’ (Kalecki,
1967, p. 149). But, he asks himself: ‘why should capitalists continue to invest at a level of 7
per cent of capital? Simply because the process has been going for some time, this investment
has been “justified” and the capitalists … do not hesitate to continue their game’ (ibid.).
Indeed, he argues, if capitalists for whatever reason decide to accumulate at a rate of only
6%, without increasing their consumption correspondingly, ‘[t]he problem of effective
demand makes then immediately its appearance.… There arises thus a problem of
overproduction [that] affects in turn adversely the investment decisions of capitalists’ (ibid.,
pp. 149‒150). One might argue that ‘this is a typical crisis which will be followed by a periodof prosperity. … There is, however, nothing to substantiate this argument. After a breakdownof the moving equilibrium no trace of the 4 or 3 per cent annual long-run increase was left inthe economy. The economy may as well settle to a state of simple reproduction with cyclicalfluctuations around it’ (ibid., p. 150). Kalecki suggests that a Tugan-Harrod model issustainable only as long as capitalists invest ‘as a class’ all profits that they do not consume,an untenable supposition.
To escape the Tugan-Harrod knife-edge problem, and to explain why capitalism does
not settle into a stationary state, Kalecki suggests that external markets be taken into accountas the ultimate explanation of investment. Most of the critical growth literature has so far

neglected this suggestion.1 Thus, both Eatwell and Kalecki contend that investment should
not be taken as the independent variable in growth theory. Notably, at least in his 1967 paper,
Kalecki does not suggest that the economy might stabilise along a growth path characterisedby a below-normal capacity utilisation rate, as the neo-Kaleckians would later do.
In the 1950s two approaches to resolving the Harrod instability problem emerged:
Solow’s neoclassical growth model and the Post-Keynesian Cambridge tradition associatedwith Nicholas Kaldor and Joan Robinson. We shall not deal with Solow’s model here,
primarily because it has been undermined by the results of the capital theory controversy(Cesaratto, 1999, 2010; Cesaratto & Serrano 2002).

3. The Cambridge Equation and its Critics
3.1. The Cambridge Equation
According to the Cambridge equation,
gw = scrn(1)

where gw is the warranted rate of growth (i.e. the rate at which capacity savings grow at a rateequal to the accumulation rate desired by capitalists), sc is the capitalists’ marginal propensity
to save (we shall assume throughout this paper that workers do not save), and rn is the profit
rate. The main message of the Cambridge equation is that the warranted growth rate is1

The exception seems to be Garegnani’s SVIMEZ Report (1962), of which only the first two sections

have been published in their entirety (Garegnani, 1978‒79). In the portion of the SVIMEZ Reportpublished as part of this symposium, Garegnani (2015) takes ‘final demand’ as the independent
variable. In his view, long-term expectations are the result of a persistent final-demand-led growthrate of the economy. Final demand includes private and government consumption expenditures, net
exports and autonomous investment related to technical innovation (by default, the rest of grossinvestment is induced by the accelerator mechanism). Garegnani also seems to include induced
consumption in final demand while, in our view (see Section 6.1.1) only autonomous private
consumption (financed through consumer credit) should be included.

determined by the rate of capital accumulation gk that results from the investment decisionsof entrepreneurs; this determines the long-period (or normal) income distribution, which
thereby becomes endogenous and subordinated to the rate of accumulation
From an empirical point of view, the association of higher growth rates with a change
of income distribution in favour of profits is not particularly robust. If anything, real wages
tend to rise during periods of faster accumulation because tighter labour markets lead to anincrease in workers’ bargaining power. Wages would instead tend to fall during downswings
when the ‘industrial reserve army’ increases. Not surprisingly, both neo-Kaleckian (notably
Rowthorn, 1981) and Sraffian authors (notably Garegnani, 1992) have criticised theCambridge equation approach, primarily on the ground that capitalism can accommodate an
upsurge in the rate of capital accumulation by utilising productive capacity more fully
through the action of the multiplier, without the necessity of changes in income distribution.2

3.2. The Neo-Kaleckian Critique
Following Steindl (1952) and Kalecki (e.g. 1970), Rowthorn (1981, p. 1) explains theunderutilisation of capacity by referring to the idea of a ‘monopolistic economy which isoperating well below full capacity.’ In such an economy, ‘prices are relatively inflexible andfirms respond to a change in demand by varying the amount they produce. When demand isdepressed firms respond by reducing the amount they produce, whilst keeping their prices
constant. This reduction in output has no effect on real wage rates, but it does reduce both thelevel of capacity utilization and the rate of profit’ (ibid.). Symmetrically, in the case of aninvestment upsurge, ‘there is no need to reduce real wages, and the extra profits required to2

It should also be recognised that the Cambridge equation is a demand-led growth model in a limitedsense. Although capitalists decide the rate of growth of the capital stock independently of capacity
savings, the adjustment of capacity savings does not take place through the variability of output and,in the longer run, of capacity, but through a change in income distribution.

stimulate investment can be generated simply by increasing output and bringing idle capacity
into use’ (ibid, p. 2). What is more, a fuller capacity utilisation may accommodate higher‘total profits … despite the fact that real wages have increased’ (ibid.).

3.3. The Sraffian Critique
3.3.1. The Degree of Capacity Utilisation
Sraffian authors distinguish between full and normal degrees of capacity utilisation. The
normal degree of capacity utilisation is related to the expected normal or average effective
demand when capacity is originally installed. The main reason why entrepreneurs install
additional capacity over average expected output is to be able to meet sudden peaks ofdemand so that customers need not turn to competitors (Ciccone, 1987, p. 97).
A normal degree of capacity utilisation is an essential feature of the Sraffian theory ofnormal prices and distribution. FSP economists are, however, sceptical about a theory ofaccumulation that implies that, on average over significant stretches of time, overall capacity
is normally utilised or fully adjusted to effective demand (Vianello, 1985; Ciccone, 1986).
How to reconcile the two stances? Assume that in one industry effectual demand—thedemand for the commodity at its normal price—increases, so that the market price pm rises
above the normal price pn. Competition would lead firms in the industry to raise the degree ofcapacity utilisation to meet the higher effectual demand thus re-establishing pn. As Ciccone(2011, p. 77) explains, the adjustment of pm to pn would take place at an actual degree ofcapacity utilisation ua, which is different from the normal degree un, so that also the actual
profit rate ra would be different from the normal one rn. In the meantime capacity will havebegun to adjust to the new level of effectual demand, and the rate of profit that firms expect
on the newly installed equipment is the normal rate of profits. Hence, both capital mobility
and variation of capacity utilisation mean that the gravitation of pm to pn is likely to be a rapid

and effective process, while the normal rate of profits and the associated un will be those thatprevail ‘at the margin’, as a guide to the investment decisions of firms. The effective sectorlevel gravitation of prices and distribution towards their long-period levels would therefore bequicker and less problematic than the system-level full adjustment of aggregate capacity,which is more likely to be frustrated by subsequent changes of long-run aggregate demand.
As Ciccone (1986, p. 25) puts it, full adjustment would occur only in a period that is longer
than the long period itself. SM Sraffians do not object to the supposition that price gravitation
is faster than capacity adjustment, although they defend the usefulness of studying ‘normal
accumulation paths’.

3.3.2. Garegnani’s Interpretation of the Cambridge Equation
Garegnani distinguished various meanings of the Cambridge equation. The first, which isequivalent to equation (1), may be written as:
gk = scrn(1.1)

in which gk ‘is treated as an independent variable,’ implying ‘that the incentive to invest …
will determine the real wage and the normal rate of profits’ (Garegnani, 1992, p. 54).
Although Garegnani considers the treatment of gk as given to be compatible with theKeynesian Hypothesis, doing so would be inconsistent with the classical approach to thetheory of distribution. According to the latter, the level of the real wage is not mechanicallylinked to accumulation and, if anything, would vary in relation to the growth rate in a
direction opposite to that predicted by the Cambridge equation. In Garegnani’s view, thevariability in the degree of utilisation of capacity in the short run and the variability in thelevel of installed capacity in the long run render the Keynesian Hypothesis consistent with thedetermination of ‘the real wage and the normal rate of profit ... by the circumstances
envisaged in the classical theories’ (ibid., p. 63). In other words, whereas the Cambridgeequation approach contends that changes in the exogenously determined growth rate areaccommodated by a change in factor prices (i.e. income distribution), Garegnani (ibid., pp.
62–63) argues for an alternative approach in which the routine presence of spare capacity ‘ina capitalist system make it plausible to think that, in the long period, even more than in theKeynesian short period, autonomous changes in the incentive to invest will usually generate
the corresponding amount of savings through changes in output rather than through changes
in the real wage rate and normal rate of profits.’
Alternatively, given the normal profit and wage rates, the Cambridge equation can be
written as:
g* = scrn(1.2)

in which g* should be interpreted as ‘the ratio of saving to capital’ associated with a given
normal profit rate and a normal degree of capacity utilisation, rather than as a ‘rate ofaccumulation’ (Garegnani, 1992, p. 54). Indeed, given rn, if g* is interpreted as a rate of
growth ‘the path of future capital accumulation would be completely determined’ (ibid., p.
58), an outcome that is inconsistent with the Keynesian Hypothesis. Equation (1.2) would
thus be better interpreted as an accounting identity.
Finally, if instead g is interpreted as the actual growth rate the Cambridge equation
would represent a relation between the latter ( g a ) and― there being no reason to believe thatat ga the economy will be operating at normal productive capacity―the actual (or ex post)
profit rate ra, i.e., the profit rate actually obtained on the installed equipment (Garegnani
1992, pp. 54, 60–62):
ga = scra(1.3)

For Garegnani, of course, an actual profit rate different from normal is perfectly consistent
with the prevalence of a normal profit rate ‘at the margin’, the rate expected on the newly
installed equipment and which is uniquely determined once the normal level of the real wage

and the technical conditions of production are given (see also Ciccone, 1986, pp. 33–35).
Oscillations in the incentive to invest would affect the realised growth rate of the economy gathat would thus ‘be taken as a measure of the incentive to invest’ (Garegnani, 1992, p. 57).
Once productive capacity has adjusted to the new ‘incentive to invest’, Garegnani argues that‘the rate of accumulation will necessarily be back to the ratio of capacity savings’ (ibid.; myitalics). This entails that the long-run ‘trend of investment’, although it may oscillate, isbound to return to the one suggested by equation (1.2)―even though the latter is dismissed asa (warranted) growth rate since it merely represents the ‘ratio of capacity saving’corresponding to a normal degree of capacity utilisation. Moreover, no rigorous
demonstration has been provided that this convergence will occur. Given the instability of theHarrodian context adopted by Garegnani it is unlikely that this proof can be provided.
This approach leaves some puzzles unresolved for Sraffian economists. Garegnani(1992) accepts the Harrodian framework. He seems therefore trapped between the Scylla of
the Cambridge equation, which is consistent with the Keynesian Hypothesis but inconsistent
with classical distribution theory, the empirical evidence and a truly demand-led approach,and the Charybdis of Harrod’s model, which is consistent with ‘exogenous distribution’, but
unstable and inconsistent with the Keynesian Hypothesis. Starting from a reasonable
scepticism about steady-state analysis, Garegnani (1992, pp. 58–59) indicates a third way,suggesting that normal accumulation paths characterised by a normal degree of capacity
utilisation are not representative of capitalist economies, and therefore not a useful object ofanalysis.3

3Garegnani’s argument is that if we consider two regimes with different rates of growth of aggregate

demand, then even if entrepreneurs had perfect foresight, the degree of capacity utilisation over theperiod that encompasses both regimes and the transition period would not be normal (see also
Palumbo & Trezzini, 2003). But this is a deceptive argument, for if we apply it to Solow’s model itStretching a bit beyond Garegnani’s own views, FSP exponents (e.g. Palumbo &Trezzini, 2003; Trezzini, 1995, 2011; Smith, 2012) seem to suppose that any steady statenecessarily contradicts the Keynesian Hypothesis. They forget that on a steady state-path allcats are grey, so to speak: we cannot clearly identify the causal saving-investment nexus, andnational accounting identities are not causal relations.4 As we have seen, Garegnani does notdeny that the steady state advocated by the Cambridge equation is consistent with theKeynesian Hypothesis. So the issue is not that all steady states are necessarily inconsistent
with the Keynesian Hypothesis, but that the specific Cambridge equation steady state isinconsistent with classical distribution theory.

4. The First-Generation Neo-Kaleckian Models and the Sraffian Criticism
4.1. The Canonical First-Generation Neo-Kaleckian Model

In order to provide context for our critique, let us recall a standard first-generation neoKaleckian model that is still widely used in the debate.5 The model consists of threeequations:g s  s c rag i     (u a  u n )
ra 


vn

ua

(2)
(3)
(4)

would lead us to conclude that neoclassical growth theory does not study normal growth paths sincevariations of parameters lead to different normal paths.
4

Aside from the Sraffian supermultiplier model, all growth models, including the neoclassical,

Cambridge equation and neo-Kaleckian approaches, in equilibrium respect the Harrodian warranted
growth equation, though they postulate different causal links between saving and investment.
5

See Lavoie (2006, p. 114). The model draws upon the seminal contributions of Rowthorn (1981) andAmadeo (1986).

Equation (2), the saving equation, expresses the rate of growth permitted by capacity saving
as a function of the saving rate―for simplicity profits are the only source of savings―and of
the actual profit rate. Equation (3) expresses the rate of growth of the capital stock as afunction of the long-term growth of sales expected by firms (α) and of the gap between actualand normal capacity utilisation under the hypothesis that ‘each firm strives to return tonormal capacity utilisation’ (Lavoie, 2006, p. 115). Equation (4) states that the actual profit
rate is a function of the actual rate of capacity utilisation, given the profit share  and thedesired or normal capital coefficient vn.6 Equation (4) is the profit curve in the bottom part of
Figure 1. The unknowns are g, ra and ua.
By substituting equation (4) into (2), we get:

gs 

sc
ua
vn

(5)

Equations (3) and (5) can be drawn in g-u space, as shown in the top part of Figure 1. The
long-run goods market equilibrium is where g s  g i , that is, equating equations (5) and (3),where:ua   u n.
sc vn  (6)Equation (6) shows that ua is the variable that brings the growth of capacity saving into linewith the rate of growth of the capital stock.7 Figure 1 supposes that the initial equilibrium A
6Equation

ra 

(4)

is

easilyobtained

from

the

definition

of

the

actualprofitrate:

P/ X fP/ Xa XaP u a , where P is the sum of profits, Xa is actual aggregate
K
K Xa
K
X f vnXf
X f Xaincome and Xf is the full capacity aggregate income.
7

As in all macroeconomic models, the long-run goods markets equilibrium is where the rate of

growth of the capital stock is equal to the rate of growth of capacity saving. The Keynesian
Hypothesis implies, of course, that outside equilibrium it is the latter that adjusts to the former.

is a Harrod equilibrium in which the economy’s plant and equipment are operated at normal
capacity; hence gw = g i0 = α.8[Figure 1 here]
On this basis, neo-Kaleckian authors extend the Keynesian paradox of thrift to a
dynamic setting. Suppose that a rise in real wages causes a fall of the profit share  (Lavoie
2006, pp. 114–119). This causes a rightward rotation of both the gs and profit curves of
Figure 1. At the initial growth rate g i0   , the higher demand for consumption goods leads toa higher degree of capacity utilisation ua0 (point B). At the constant growth rate α, the new
utilisation rate ua0 would need to be such that the realised rate would still be rn, because withno change in the saving rate, the equation gw = scrn needs to hold, and hence there would be
no change in the realised rate of profit. In practice, the higher rate of extraction of profits outof a given capital stock precisely counterbalances the fall in the profit share, so that theresulting actual profit rate is equal to the initial one. The higher ua then leads to a higher
growth rate of investment―the investment function becomes g 1i     (u a0  u n ) ―and toan even higher utilisation rate until a new equilibrium is reached in correspondence with u 1a(point C). At u1a the realised profit rate is higher than the initial one. The paradox of thrift
would hold in a growth context, since a lower saving rate leads to a higher growth rate.9

8

At point A, u a  u n . If we normalise the capacity utilisation rate so that un = 1, equation (6) boils

down to α = s/vn. Bringing us back to Harrod, point A violates the Keynesian hypothesis since α
cannot be exogenously determined.
9

Incidentally, the empirical evidence strongly suggests a positive relation between the rate of growth

and the saving (investment) rate (S/X = I/X) (see Cesaratto, 2010). This is embarrassing for the
standard Solow model and, more importantly as regards the present paper, it appears also toundermine the neo-Kaleckian attempt to demonstrate the thrift paradox in a growth context. The
puzzle is solved once the autonomous components of aggregate demand are introduced with theGiven this framework, neo-Kaleckians speak also of a ‘paradox of costs’: ‘A higher
real wage, and therefore higher costs of production, leads to a higher long-period [actual]profit rate. In other words, a reduction in the gross costing margin of each individual firm
ultimately leads to a higher [realised] profit rate for the economy as a whole’ (Lavoie, 2006,
p. 117; my insertions in square brackets). The possibility of wage-led growth appears to be in
sharp contrast not only with the Cambridge tradition’s inverse relation between real wages
and growth rates, but also with the classical economists’ inverse relation between real wages
and the normal profit rate.

4.2. What is Actual is Normal: the ‘New Normal’
Assume we are at point C in Figure1. From equation (6) we get:or, given that s = sc and v1a  v n / u1a ,sc    (u a0  u n )1(v n / u a )s    (u a0  u n ) .10 Suppose that capitalists
1va

consider the degree of capacity utilisation corresponding to C to be the ‘new normal’, that is
u 1a  u nn . We might then redefine the actual capital coefficient v1a as the ‘new normal’ capitalcoefficientgw 

v1a  v nn 

vn
u 1a



vn
u nn

, and obtain a warranted growth rate equal tos    (u a0  u n ) . The growth rate is determined by the ‘animal spirits’ ofv nn

entrepreneurs (α) in combination with their ceaseless effort to restore the ‘old normal’ensuing distinction between the marginal (s) and the average (S/X) propensities to save. It will beshown in Section 6 below that while a lower s has a positive level effect on output, a higher growthrate is necessarily associated with a higher S/X.
10

K/Xf
v
Recall that, in general, v a  n ua

Xa / X f



K
.
Xa

utilisation rate un; as suggested by Hein, Lavoie& van Treeck (2012, p. 144), however, thelatter effort becomes a stable component of the growth rate that might usefully be redefinedas  1     (u a0  u n ) so that gw = α1.
There are serious consistency problems here, however. As noted before, the initial
equilibrium A of Figure 1 is a Harrod equilibrium, i.e. α is the only growth rate consistent
with normal capacity utilisation (‘normal growth’). So abandoning the concept of normal
growth is essential in order for the neo-Kaleckians to sustain the Keynesian Hypothesis. But
we see now that they cannot abandon it completely if they want to demonstrate the thrift
paradox, which entails going to point C. The equilibrium at C, however, will be lasting only
if some reason exists to take u 1a as the ‘new normal’ rate of capacity utilisation u nn .11 But
then, why should capitalist want to recover the old u n ? The problem is that if they don’t, theterm  (u a0  u n ) would disappear from the investment function and the economy would
return to point B, with the consequence that the thrift paradox is not demonstrated. So the
neo-Kaleckians must at the same time maintain that while at C capitalists redefine a ‘newnormal’ utilisation rate u 1a  u nn , at the same time they still want to fill the gap (u a0  u n ) . On
the other hand, if capitalists do not consider u 1a to be the new normal the economy will be led
to points D, E etc, as we shall shortly see.

11

Some rationalisations for the endogenity of un are suggested by Hein, Lavoie & van Treeck (2011,2012). Not very persuasively, they refer to ‘provisional’, ‘conventional’ or even ‘aspirational’

notions of the degree of capacity utilisation.

4.3. The Stability Issue
Hein, Lavoie & van Treeck (2012; see also Lavoie 2003) are aware of the problems and notethat once the term  (u a  u n ) is introduced into the investment function (3) the Harrod
instability problems resurface.
Figure 1 elaborates Hein and his co-authors’ own presentation of the instability
dynamics (ibid., Figure 5). The economy starts from point A where g s0  g i0 and g i0   . As
before, we assume that at A un and rn prevail (which is to say that a Harrodian warranted raterules there). After a decrease in the propensity to save, the gs function shifts downwards andthe economy provisionally goes to B. At B the higher demand for wage goods is satisfied bya higher ua, while the growth rate is still g i0   . Supposing that capitalists try to restore un,
the economy moves towards a new investment function g 1i     (u a0  u n ) to reach point
C. Following the suggestion of Hein, Lavoie & van Treeck (2012, p. 144) that ‘entrepreneurs… make a new, higher, assessment of the trend growth rate of sales, thus making use of alarger  parameter in the investment function’, at point C the new investment function
becomesg i2   1   (u 1a  u a0 ) , where  1     (u a0  u n ) , and a new provisional

equilibrium is reached at D. There, though, a new investment function g 3i   2   (u a2  u 1a )prevails, where  2   1   (u 1a  u a0 ) , and so on and so forth.
As we have noted, the neo-Kaleckians would like to locate their ‘new normal’ growth
path at C. But if we suppose that entrepreneurs interpret whatever the rate of capacity
utilisation happens to be as the ‘new normal’, we would be begging the question of why they
have not taken u a0 (corresponding to point B) as the ‘new normal’, that is u a0  u nn ; on theother hand, if we take u 1a  u nn then the adjustment term  (u a0  u n ) would disappear fromthe investment function and the economy returns to point B. If the economy stops at B, then afall in the saving propensity would have no effect on the growth rate, that is, the thrift

paradox would not have been proved in the dynamic context. However, if capitalists do notassume u 1a  u nn and we allow them to adjust capacity to restore the ‘old normal’ un, there is
no reason why they should stop at C, or D etc.12
In summation, the neo-Kaleckians acknowledge that once adjustment of capacity isallowed, Harrod instability does reappear (the economy would move to C, D, etc). To avoid
instability, they introduce the ad hoc assumption that entrepreneurs take the actual degree ofcapacity utilisation as the ‘new normal’. A second ad hoc device, to demonstrate the paradoxof thrift, is to assume, without justification, that entrepreneurs select u 1a (point C) and not u a0
(point B) as the new normal.
Finally, let us provide an economic explanation of the neo-Kaleckians’ contortions.
These are due to the fact that wages are an induced component of aggregate demand, and assuch they cannot be the primum movens of growth. By creating a never-resolved discrepancy
between ua and un, however, a rise of real wages may affect growth; but the weakness of thetrick is patent. (Compare this result with the effect of a rise of real wages in the Sraffian
supermultiplier context in Section 6.1.4 below).
12

Ciampalini & Vianello (2000) have put forth a parallel critique looking at capitalists’ behaviour

from the point of view of the profit rate. Suppose for instance that the economy settles at C in Figure
1. In the neo-Kaleckians’ view the realised profit rate, e.g. ra1 , is the rate expected on new investment,
as if entrepreneurs never realise that this higher realised profit rate depends on the current
overutilisation of capacity. This amounts to supposing that investors exhibit a sort of Faustian
behaviour: ‘The thesis according to which the expected profit rate is governed by the realised profit
rate presupposes … that every time existing capacity is over- or underutilised―and a profit rate
higher or, respectively, lower, than the normal one is therefore obtained―investors would expect thatthe productive capacity they plan to install will also end up being over- or underutilised. But toattribute to investors such an expectation is to … consider them to be victims of an irremediableinterior discord, which induces them to plan to put in place a certain productive capacity and, at thesame time, not consider it adequate to their wishes. “Two souls, alas! reside within my breast; andeach withdraws from and repels its brother”’ (Ciampalini & Vianello, 2000, p. 383; my translation).

4.4. The Inconsistent Trinity
As seen above, there is a prima facie convergence between the neo-Kaleckian and FSP
critiques of the Cambridge equation. This junction is, however, reached through two different
routes: via steady-state models without normal capacity utilisation by the neo-Kaleckian
authors; or, with the FSP supporters, by rejecting steady-state analysis. Echoing earlier
criticism (e.g. by Auerbach & Skott, 1988, and Committeri, 1986), Trezzini (2011) deems thefirst position to be unsustainable since the adoption of the steady-state method would lead toan inconsistent association of a given actual growth rate with a systematic, persistent degreeof under- or overutilisation of capacity. According to the FSP authors once the straitjackets ofsteady-state analysis are abandoned, a long-run average utilisation different from normal, farfrom being inconsistent with long-run analysis, would be a manifestation of the independence
of investment from capacity saving.
In summation, we may draw the inconsistency growth triangle (Figure 2) defined by
the three corners: (i) the Keynesian Hypothesis of investment independent of exogenously
given capacity saving; (ii) the classical supposition of an exogenously given income
distribution; and (iii) a long-run normal degree of capacity utilisation.
To resolve the inconsistency, the various approaches examined so far discard,
respectively: angle (ii) according to the Cambridge equation supporters; and angle (iii)
according to both neo-Kaleckians―who heroically retain steady-state analysis―and to the
FSP (and Garegnani, 1992) who, however, more consistently have abandoned theinvestigation of normal accumulation paths. We shall see below that a ‘fourth way’ is takenby the Sraffian SM scholars by discarding the Harrodian context that underlies the trilemma.

[Insert Figure 2 here]5. Accumulation and the Profit Rate
Sraffians closer to the surplus approach tend to share the idea that gross investment isdetermined by expected effective demand. Variations of the normal rate of profit, as such,
have no direct and mechanical influence on gross investment, as is often argued by PostKeynesian authors of various persuasions.13 Hence, variations of rn only concern the sphereof income distribution. The latter can in turn influence investment decisions in two broad
ways. First, a change in distribution might affect expected effective demand: a higher orlower rn might, for instance, negatively or positively affect consumption demand to the extent
that the latter is sensitive to changes in the real wages. Second, changes in distribution canhave an impact on investment in so far as they trigger within the capitalist class a greater
inclination to constrain the bargaining power of workers by regulating the reserve army oflabour; but this is generally accomplished through fiscal, monetary and exchange rate policies
and not through a coordinated set of decisions among capitalists to alter the rate ofaccumulation.14
There is, accordingly, no reason to suppose that an increase in rn would have apositive effect on investment. Likewise, a lower rn will, in general, leave gross investment
unaffected as long as capitalists fear the loss of market share to competitors: each capitalist ishomo homini lupus with respect to her classmates. As Serrano (2006, p. 14) observes:

although politically entrepreneurs prefer higher profit margins and normal profit
rates, capitalists do not ‘invest as a class’ but according to the existing investment
opportunities and the pressure of competition. Their investment decisions are not an
13

I have in mind here Sraffian authors such as Serrano (2006) and Petri (1994). Other Sraffian

economists, e.g. Vianello, hold somewhat different views, as we shall see.
14

For instance, the ‘independence’ of central banks is nothing other than an assignment to a ‘super-partes’ institution the role of watchdog of wage discipline. The most striking example is the
Bundesbank (Cesaratto & Stirati, 2011).

inverse function of the level of the normal rate of profits but a positive function of thesize of the market. In the long run the size of lucrative investment opportunities
depends on the level and rate of growth of effective demand―the demand of those
who can pay normal prices (that price that allows firms to obtain the normal rate ofprofits, which defines the minimum accepted standard of profitability). If effective
demand is expanding, whether normal profit margins and rates happen to be ‘high’ or‘low’, competition and the search for maximum profits impel the firms collectively to
expand productive investment.

Sraffian authors also reject the idea that a higher normal (or realised) profit rate might
positively affect investment through the higher internal availability of funds. Garegnani(1962, p. 91, fn. 1) observes that it is investment that, in the short run, through a fuller
utilisation of capacity and, in the long run, through the creation of new capacity, determinessaving (including retained profits) and not the other way round. In addition, as Ciampalini &Vianello (2000, p. 391; my translation) point out: while ‘the availability of internal financial
resources can well enable [a firm] to undertake an investment that presents a sufficientinducement, [it] certainly does not compel the undertaking of investment in the absence of an
inducement.’
In the light of what has been said in Section 3, much confusion has been shown by
neo-Kaleckian authors with regard to the relation between actual and normal profit rates. In
this connection, Garegnani rejects the neo-Kaleckian interpretation of the post-war capitalist‘golden age’ of capitalism as a wage-led regime in which the interests of capitalists andworkers were aligned (Cavalieri, Garegnani & Lucii, 2004). In Garegnani’s view, the profit
rate relevant for capitalists is not the ex post, realised one, but the ex ante, normal one, i.e. therate they expect to earn on newly installed equipment. A rise in the real wage rate, given thetechniques in use, must lead to a fall in the normal profit rate. It is possible that in certain
historical circumstances capitalists acquiesce to such a fall without resorting to economic
policies aimed at enlarging the industrial reserve army; but in these circumstances we should

talk of a compromise between clashing interests rather than of coincidence of interests. For
comparison, in two influential contributions Stephen Marglin and Amit Bhaduri (Bhaduri &Marglin, 1990; Marglin & Bhaduri, 1990) express similar scepticism towards the cooperative
vision of capitalism put forth in the neo-Kaleckian literature, but their criticism is predicatedon the supposition that a fall in the normal rate of profit might have a negative impact on
investment. But, as Serrano (2006, p. 13) points out, Marglin & Bhaduri perpetrate a
confusion when they ‘mechanically try to associate the squeeze in profit margins to a
reduction in pace of investment by arbitrarily assuming that investment is a direct function of
the level of the profit share. The fact that lower profit margins lead to lower normal rates of
profit does not imply that the most lucrative option in this situation will be a reduction of
investment and the size of productive capacity. The adequate size of productive capacity does
not depend on the level of the normal rate of profit but on the size of the demand of those
who can pay the prices that guarantee that the minimum normal profitability requirement ismet, irrespectively [of whether] this normal rate is high or low.’15
If real wages rise and the normal profit rate falls, capitalists would of course bedisappointed and would desire the restoration of the former profit rate. This task is likely tobe left to the economic policies of pro-capitalist states since, from the point of view of each
capitalist, the decision to reduce investment and leave forthcoming demand unsatisfied would
entail the risk of opening a market opportunity to competitors. For this reason, although a fallin the normal profit rate may affect the general policy stance and, therefore, investment, thisdoes not involve a general inverse association between rn and the pace of accumulation in thesphere of investment decisions. When we deal with accumulation theory it is better to regard
investment as determined by expected effective demand at the given normal profit rate,

15

Vianello (1989), Ciampalini & Vianello (2000) and Pivetti (2015), referring to Marx, maintain thata lower normal profit rate discourages investment.

whatever it is, leaving the effects on accumulation due to changes in income distribution andpolicy stance to a different analytical stage.

6. Growth with Autonomous Components of Aggregate Demand
6. 1. The Supermultiplier6.1.1. The Neglect of Autonomous DemandThe ‘strict uniqueness’ and instability of Harrod’s warranted growth rate are problems thatneed to be resolved. By ‘strict uniqueness’ I mean that the variables that enter into thewarranted growth rate are necessarily inconsistent with an independent determination of
long-run aggregate demand. Once we rule out the endogenous change in income distribution
envisaged by the Cambridge economists, in the equally unsatisfactory neo-Kaleckian and
FSP approaches, the degree of capacity utilisation becomes the adjusting variable. If we
could show the existence of a multiplicity of normal or warranted demand-led growth rates,
we will have taken a significant step towards overcoming the Harrodian ‘strict uniqueness’
problem, the odd neo-Kaleckian steady states and the FSP abandonment of normal
accumulation paths. This I call the existence problem.
Serrano approaches this question by noting the surprising neglect of theautonomous/non-capacity-creating components of aggregate demand in the Post-Keynesian
literature. These autonomous components, which we shall denote by Z, are defined as thosethat (a) do not depend on actual or expected income (as induced consumption and induced
investment do) and (b) do not create capacity. The neglect is all the more surprising in viewof the role that government spending plays in Keynes’s General Theory (1936) and ‘externalmarkets’ in the writings of Kalecki (1934, 1967). Reviving Eatwell’s criticisms noted in
Section 2.1 above, Serrano (1995, p. 97) points out that, indeed, in all ‘Post-Keynesian
theories of growth, the long-period version of the principle of effective demand is seen as

being essentially a proposition about investment. … [I]nvestment is the key independent
variable.’ Investment is often explained by invoking ‘animal spirits’ or Schumpeteriancompetition.16 Leaving aside the vagueness of such explanations, the conceptualisation of
investment as autonomous appears inconsistent with its induced nature, as the adjusting forceof capacity to demand. The way out proposed by Serrano consists of three steps:(i) Model investment as fully induced:
I  vn g e X n(7)

where Xn is the normal level of output and ge is the expected rate of growth ofeffective demand.
(ii) Take account of the autonomous/non-capacity-creating components of aggregate
demand (Z).
(iii) Anchor the formation of expectations regarding long-term demand (ge) to thegrowth rate (gz) of those autonomous components; the idea is that this anchor permits
a progressive adjustment of expectations to gz.

6.1.2. Assumptions and Preliminaries
Serrano (1995, p. 18‒24) simplifies the economy along Kaleckian lines, adopting the dictumthat ‘capitalists earn what they spend while workers spend what they earn.’ The
simplifications are not essential to the model, but are intended to emphasise the distinctive
traits of a capitalistic economy.
Look at capitalists first. Serrano assumes that workers do not save while capitalists
save all their earnings, so the marginal propensity to save of capitalists is sc = 1. The overall

16

Dennis Robertson (1915, p. 9) and Garegnani (1978–79, p. 347) advance similar criticisms of thetreatment of expectations in purely psychological terms; they favour an approach based on real
economic circumstances. The Schumpeterian view is criticised in Cesaratto (1996).

marginal propensity to save is then s = sc = , where  = P/Xn is the profit share in normal
output Xn. The supposition that sc = 1 does not imply that capitalists do not consume: at the
beginning of the period considered, they consume all they wish (perhaps financing theirconsumption by using overdraft facilities). The capitalists’ spending is thus comprised of
their autonomous consumption (Z) and their investment decisions, induced during the period
by expected demand according to the accelerator principle as reflected in equation (7).
Although at the end of the period capitalists do not spend all their accrued profits, not all theirearnings consist of saving since part are offset by their autonomous consumption Z, which isdissaving.
Look now at workers. To simplify, we assume they have no access to credit andsimply spend what they get, so that the economy’s marginal propensity to consume is equal
to the wage share of income wl (given that capitalists have a marginal propensity to consume
equal to 0), where w is the given real wage and l = N/Xn is the labour input coefficient.
Given the wage bill W, profits are equal to P = Xn – W = Z + I, and saving to S = scP– Z = P – Z = I. Recalling that s = sc P/Xn, saving is equal to S = –Z + sXn, we get:
S
Z
 s
Xn
Xn

(8)

Equation (8) expresses the average propensity to save of the economy as the difference
between the marginal propensity to save (profit share) and the share of autonomous
consumption in output (share of dissaving). As Serrano (1995, p. 126) explains: ‘whenever
we take into consideration the presence of autonomous expenditures, as we do in our Sraffian
supermultiplier, there simply cannot be any univocal and direct relation between the
distribution of income and the share of savings in the economy, even if all saving comes fromprofits.’

6.1.3. Income Determination and the Limits of Demand-Led GrowthAggregate demand is defined as AD = Z + I + C, or AD = Z + vn g e X + wlXn, and,following the principle of effective demand, Xn = AD. From this, the Sraffian supermultiplierdetermination of output can be derived:
Xn 

1
Z
(1  wl )  vn g z(9)In equation (9) we are provisionally assuming that firms form their growth expectations andinvestment decisions on the basis of a known rate of growth of Z: g e  g z . Equation (9)suggests that the growth of ‘external markets’, as reflected in Z, governs the rate of growth ofaggregate demand and output. With a little manipulation, we can rewrite equation (9) as Xn= Z + vngeXn to show that in the model capitalists ‘earn what they spend’.
Equation (9) provides economically meaningful solutions if:
wl  v n g z  1

(10)

Z>0

(11)

and

Serrano offers a double interpretation of these conditions (see also Dejuan, 2005, p. 240n). To
begin with, he observes that if the equality sign prevailed, then the only equilibrium ratewould be g e s, and we are back to Harrod’s model and Say’s Law, since there would bevnno room left for the autonomous components of aggregate demand; Z should then be set
equal to 0. In other words, if wl  v n g z  1 , this means that the overall marginal propensity
to spend is equal to one, which ‘is exactly what we mean by Say’s Law’ (Serrano, 1995, p.
37). Of course, if the overall marginal propensity to spend is lower than one, the level of theautonomous components must be positive, as set by equation (11).

6.1.4. Investment and Saving SharesRewriting condition (10) as g e s, Serrano envisages a further limit to demand-led
vn

growth: gz (and ge) cannot be ‘too high’, otherwise the share of induced investment will alsobe ‘too high’ and we breach ‘the upper limit of feasible rates of demand-led capacity growth’(Serrano, 1995, p. 40). To see this, note that from the investment function (7) we
get I / X n  v n g e . That is, comparing two normal paths, the one with a higher gz (and ge)
requires not just a higher rate of growth of investment (gk), but also a higher share ofinvestment in current normal output: ‘given the capital-output ratio, a higher rate of growth ofcapacity will necessarily require that a higher share of current level capacity output be
dedicated to capacity-generating investment’ (Serrano, 1995, p. 32). A positive relation
between the rate of growth and the investment share I/X is a widely recognised stylised factof economic growth. This does not mean that higher growth requires a fall in
consumption―the Samuelsonian trade-off between butter and guns: on the new normal path,capacity X n has risen enough to accommodate both the larger share of induced investment
required by the higher g z and a larger absolute level of both induced and autonomous
consumption.17
In the SM context, it can be shown that, given the exogenous levels of Z, g z , s and vn,
a level of X exists such that

17

S
I
and the economy grows along a normal path gw = gz.
Xn XnSerrano allows both a short-period adjustment of capacity savings to higher investment through ahigher degree of capacity utilisation, and once the maximum capacity has been reached, a Cambridge
equation style adjustment: ‘what the maximum rate of growth says is that capacity output cannot growfaster than that rate if the degree of utilization is to be kept at its “planned” or normal level. Thatmeans that both actual output and also capacity can grow a bit faster at least for a while, to the extent
that there are always planned margins of spare capacity. For very high rates of growth of demand suchthat neither capacity nor output can respond fast enough the result will be demand inflation and“forced saving” in a way similar to the Cambridge theory of distribution’ (1995, p. 44n).

This would represent a step forward with respect to the inflexible Harrodian context in which
the given s and vn determine a strictly unique warranted path. By taking the autonomouscomponents of aggregate demand into account, a range of normal growth paths is in principle
feasible, each one defined, given s and vn, for certain levels of Z and gz. Observe that theautonomous components (which in general include government spending and exports) arealso instrumental to demand-side policies whose role is concealed in investment-driven
models.
The presence of the autonomous components of aggregate demand entails a
distinction between the marginal and the average propensity to save; see equation (8).
Serrano’s idea is precisely that through the operation of the supermultiplier, the level andgrowth of Z will generate a level of productive capacity such that the average propensity tosaveS
is able to accommodate any level of induced investment at a normal degree ofXncapacity utilisation. Note first that, given that in equilibrium S = I, and recalling that Xn =sXn = Z + I, equation (8) can also be re-expressed as:

S
I
S
I

, that iss , orsX n I  Z
Xn I  ZS
 sP sXn(12)Equation (12) expresses the average propensity to save as a function of s and of sp, what
Serrano (1995, p. 126) calls the ‘fraction’, the share of profits which is invested. Let us now
derive the SM’s warranted growth rate.

6.1.5. Serrano’s Warranted Rate
In line with previous models, we have a three-equation system:S  sX n  Z(13)I  vn g e X n

(14)

SI

(15)

Substituting equations (13) and (14) into (15) and assuming that ge = gz, we get:gz X n 

gz 

sX n  Z, orvns  (Z / X n )
vn

(16)

Taking advantage of equation (12), equation (16) can be expressed as:
gz  sp

s
vn

(17)

The normal path that assures the dynamic saving-investment equilibrium can finally be
written as:

gw (S / X n )
vn

(18)

Equation (18) shows that the variations in S/Xn accommodate gw to the variations of gz: thenormal rate adjusts to the actual (Serrano, 1995, pp. 124‒129).18 Let us consider the
economics behind this adjustment.
Looking at this through the lens of equation (16), if gz increases, given s, then Z/Xn
must fall. This is so because along a normal growth path investment must precede the growthof demand: equipment must be in place when demand rises so as to assure normal capacity
utilisation. So if gz increases, on the new normal path the ratio I/Xn must be larger and the ratio
Z/Xn lower, given s. Since the share of consumption in normal output is constant—it is in fact
equal to the wage share, which is also constant—then in the new steady state by necessity thehigher share I/Xn is accommodated by a lower Z/Xn. This is possible since in any period along
a normal growth path, for the same given level of Z, a (say) higher expected gz is associated18

By comparison, according to the neo-Kaleckians the actual rate becomes the ‘new normal’.

with a higher level of normal output Xn—not surprisingly since a higher gz implies higher
current investment—such that it generates a share of capacity savings S/Xn adequate to thehigher level of investment required by the higher gz.
Similarly, equation (17) suggests that a higher gz, given s, implies a higher sp = I/(I +Z), that is, that on the new normal path a larger share of profits is invested. The idea is againthat a higher gz for a given Z, implies higher current I, Xn and level of profits. Therefore thefraction of profits invested (and post factum saved) can therefore rise.19 We see here that wecannot know the actual share of saving in income only by looking at the marginal propensity
to save (equal here to the profit share), since the former depends on the share of profits whichis invested, and this depends on the expected rate of growth (Serrano, 1995, p. 126).
Summing up in Serrano’s own words, equations (16) and (17) establishthat the operation of the supermultiplier will always generate the required share of[capacity saving], not by changing [in the long run] the degree of utilisation but bychanging the level of investment [and normal output] by more than consumption(inclusive of autonomous expenditure) and therefore through changes in the ratio
between the (endogenous) average and (the given) marginal propensity to save. …
The idea that such an adjustment was impossible is not a general result and depends
entirely on the fact that if there are no autonomous expenditures then, as we haveseen, it is simply impossible, irrespectively of how much the level of investmentchanges, to change the ratio between investment and output which is given uniquelyby the marginal propensity to save. (1995, pp. 58‒59) 20
19

In a nice example Serrano (1995, pp. 131–132) compare two economies that at a certain point intime have the same level of autonomous/non-capacity-generating expenditure. Assume, however, that
one economy is stagnating with no net investment while the other is on a normal path led by a positive
growth rate of autonomous demand g z . It is plain that the second economy will have a larger‘fraction’ sp. Suppose Z = 100, s = 0.5, vn = 2, and gz = 0.05. Then X = 250 and sp = 0.2. If gz = 0.02,
then X = 217 and sp = 0.08.
20

Serrano (1995, p. 75) seems to acknowledge that he is discussing an existence problem when heargues that through the supermultiplier ‘we have shown how the existence of a definite level ofNote that, in contrast to what we find in the Cambridge equation, here the profit share (equal
to the marginal propensity to save) and the normal profit rate need not change when gz
changes; nor, on the new normal path, must the degree of capacity utilisation be different
from normal as argued by the neo-Kaleckians. In conformity with Garegnani’s insight, thevariable that accommodates capacity saving to the level of investment required by the growthof Z determined by the spending decisions of capitalists is productive capacity: this is assured
by the working of the supermultiplier.
A comparison with the neo-Kaleckian wage-led growth model is also in order here. In
the Sraffian supermultiplier framework, an increase in real wages, and the consequent lower
profit share and marginal propensity to save, have positive level effects, but not the growtheffects alleged in the unconvincing neo-Kaleckian arguments (Serrano, 1995, pp. 134‒137).
The lower marginal propensity to save (1 – wl) will increase the value of the supermultiplierin equation (9) and hence also the level of induced consumption-sector investment, leading toa higher long-period level of productive capacity. The rate of growth may therefore rise
temporarily, but once capacity has adjusted to the new higher level of effective demandentailed by the larger supermultiplier, the economy will return to the former normal growthrate determined by the growth rate of autonomous expenditure.
What has been said so far has to do with an existence question, but it still leaves open
the question of stability, that is, the question of what happen during the transition from one
normal path to another: can we be sure that the faster growth of investment and the abovenormal degree of capacity utilisation stimulated by a higher growth rate of autonomous
capacity output determined by effective demand requires two conditions, namely: a) that theeconomy’s marginal propensity to spend be lower than one; and b) that there is a positive level ofautonomous expenditures that is both independent from income (output) and does not generatecapacity.’demand does not go out of control in a Harrodian fashion? Another limitation is that we have
proved the existence of a warranted rate by assuming that entrepreneurs have perfectforesight about g z (we assumed ge = gz). Nonetheless, the fact that we have now a range of
normal growth paths, each defined for a given gz, makes it possible to talk of a variety ofpaths corresponding, say, to different economic regimes and to the related economic policies
for overcoming Harrod’s ‘strict uniqueness’ problem. Each warranted rate is consistent with aclassical approach to distribution (i.e., distribution is exogenous) and with a long-run normal
degree of capacity utilisation. The task is to prove analytically that gravitation will occur,
moving the economy from one path to another, each path being characterised by a different
growth rate of Z―which, of course, is unknown to the entrepreneurs (this is discussed in
Section 6.4).

6.2. Synthesis: Comparing Normal Paths
Before we come to the matter of stability, it may be helpful to summarise the differences
between the four approaches to growth theory we have been discussing.

Harrod: gw = (s/vn)
The equilibrium growth path is characterised by ‘strict uniqueness’ and instability.
Economic policy may stimulate growth by increasing s and keep instability at bay
through economic planning (not a good positive theory).



The Cambridge equation: gw = α = rnsc
Changes in rn provide flexibility and stability whenever ‘animal spirits’, theunexplained origin of growth, change.

The neo-Kaleckian model: g w     (u a  u n )  s / v nn or  1  s / v nn where v nn isthe ‘new normal’ capital coefficient.
A flexible u a provides the necessary cushion against the instability due to changes in‘animal spirits’, the unexplained origin of growth; no clear role for economic policies(but support to cooperative capitalism).

The Sraffian supermultiplier: g w  g z (S / X n )vn

The endogeneity of S/X provides flexibility with respect to changes of g z ; theautonomous, non-capacity-creating components of aggregate demand explain
economic growth; economic policy, by acting on them, may stimulate growth.

6.3. The FSP Critique of the Supermultiplier
We present here three FSP critiques of the supermultiplier approach.
(i) As mentioned, FSP supporters appear to maintain that any growth model withnormal capacity utilisation, including the supermultiplier framework, would violate theKeynesian Hypothesis. Of course, given an initial capital stock (and s and vn), if we pretendthat the economy proceeds along a steady-state growth path, then investment must equal
capacity saving, and there is only one growth rate of autonomous demand consistent with thislong-period position. But no supermultiplier theorist would argue in these caricatured terms.
Trezzini (1995, p. 49ff) does seem to acknowledge that the correct question is this: given s,vn, the capital stock and a long-run growth rate of autonomous demand gz that is unknown toentrepreneurs, will the economy tend to a normal growth path gw = gz characterised by anormal degree of capacity utilisation? Once the economy converges to a normal path, it is amatter of national accounts that investment is equal to capacity saving. What is relevant froman analytical point of view is that in the process of gravitation to the long-run position it iscapacity savings that adjusts to investment, consistently with the Keynesian Hypothesis. A
full understanding of this point would drastically reduce the distance between the two
Sraffian positions.
(ii) A clear requirement for the stability of the supermultiplier is that any growth rateof autonomous/non-capacity-creating demand must have a sufficient degree of persistence.
Despite the scepticism of Palumbo & Trezzini (2003), the supermultiplier appears to be auseful tool for analysing not only historical periods in which gz and long-term expectations
are relatively stable, but also more erratic phases in which, nevertheless, the pattern ofautonomous demand acts as a temporary attractor. As Dejuan (2005, p. 244) sensibly puts it,even if ‘the pace of autonomous demand is not so stable, the adjustment might never becompleted and capacity would rarely be fully used. However, even in these conditions we arein the realm of a long-period theory of output since the economy gravitates towards fully
adjusted positions.’ The study of normal accumulation paths through the supermultiplier isobviously useful for policy analysis; the supermultiplier is also relevant to the study of crises,
since even long-lived economic regimes may contain the seeds of their own dissolution, as
we shall argue below.21(iii) FSP supporters as well as some supermultiplier economists (e.g., Dejuan, 2005)
would, like Garegnani (1962), include in ‘final demand’ the ‘autonomous investment’associated with technical change. Taking the opposite view, Cesaratto, Stirati & Serrano(2003) maintain that all gross investment is induced in the sense that, ceteris paribus, in thelong run autonomous investment displaces a corresponding amount of induced investment(Serrano, 1995, p. 81n); hence they do not assign to autonomous investment the21

Unfortunately Trezzini (2015) and Palumbo (2013) still do not appreciate the flexibility of the SM

for analysing, also, the instability of capitalism in an ordered way.

Schumpeterian role of the principal driver of growth.22 However, Cesaratto, Stirati & Serrano(2003, pp. 44‒48) suggest a modification of the capital coefficient used in the supermultiplier
which allows the model to take account of the fact that in each period autonomous investment
might be supplemental to induced investment and support effective demand. A higher
depreciation rate would also enable the supermultiplier to address the consequences of fastertechnological obsolescence. Cesaratto (1996) has argued that even technical change is largely
demand driven: innovation is driven not by slumps, as Schumpeterians tend to think, but by
expansions (see also Camara-Neto & Vernengo, 2012). And of course, product innovations
play an essential role in sustaining the marginal propensity to consume and credit-driven
autonomous consumption.

6.4. The Stability of the Supermultiplier Model
In a contribution which is to appear in the second part of this symposium Freitas & Serrano(2015; see also Serrano & Freitas, 2007) integrate into the supermultiplier model an explicit
stability argument that I will heuristically sum up here.
Starting from a fully-adjusted position, suppose that gz rises. The actual growth rate ofoutput and aggregate demand ga also increases, and as a consequence induced consumption
and investment will also grow. The degree of capacity utilisation becomes higher thannormal. The rise in the induced components of aggregate demand generates, in turn, a further
rise in ga, a further climb in the induced components, and so on and so forth. Recalling that ga

22

Kalecki, too, appears to have been somewhat sceptical about the ability of technical change to drive

accumulation. Writing of ‘the influence of technological innovations’, Kalecki (1967, pp. 150‒151)
argues that ‘this factor is by no means necessarily adequate to secure the full utilisation of equipment
or even to keep the degree of this utilization at a constant level. Innovations break the impasse of asimple reproduction only to some extent and they do not warrant the utilization of resources in thesense of Tugan-Baranovski.’is a weighted average of gz and of the growth rate of the induced components of aggregate
demand, among which investment is the fastest growing, it will be the case that gk > ga > gz.
The exogenously given gz anchors, so to speak, g a (unless the reaction of investment is toostrong and gk drags ga away in a Harrodian fashion). Therefore, in spite of the fact that theattempt by firms to adjust the capital stock is an additional stimulus to aggregate demand, thecapital stock and capacity are rising more rapidly than aggregate demand and output, so thatcapacity utilisation ua is falling and tending to normality. The fact that ua tends to normality
means that the escalation of gk is slowing down. This implies that the rise of ga is slowing
down as well, and that gk tends towards ga, which in turn tends towards gz.23
Summarising, while in Harrod investment is the engine of both demand and theadjustment of capacity, and the two roles may compound spiralling instability, in the
supermultiplier approach aggregate demand is anchored to gz, a variable that is not prima
facie affected by the adjustment process. Therefore, as long as the effects of the higher
investment on the supply side (i.e., on capacity) are larger and faster than those on the
demand side, this adjustment will not create instability.
Freitas & Serrano (2007, pp. 33‒34) point out that what we have described satisfies anecessary condition for stability, in the sense that that it shows that the direction of theadjustment is correct. It becomes a sufficient condition if the reaction of investment is not‘too strong’ (see Freitas, 2007).

7. Conclusions: Formal Stability and ‘Destabilising Stability’
I consider the supermultiplier approach to be an important step forward in non-orthodox
growth theory, not just because it overcomes the formal deficiencies of previous models, but
23

Dejuan (2005) argues in a similar vein, but his stability proof assumes, unrealistically, that

entrepreneurs know gz.

because by assigning a central role to Kalecki’s external markets (or Garegnani’s final
demand) it opens the way to a richer description of real capitalism. I also fully acknowledge
the limitations of the investigation of (formally stable) normal accumulation paths in view of
the instability of capitalism, limitations to which the FSP is particularly sensitive. Stylisedmodels are, however, essential to fix our ideas and for policy purposes, as the exponents of
the FSP also generally acknowledge. In view of this, the distance between the two Sraffian
positions should not be exaggerated.
The importance I have attributed to a formal stability proof, moreover, does not in any
sense imply that capitalism is stable.24 Stability is a basic requirement for a good model sincereal phenomena, economic or not, although they are continuously changing, are rarely
explosive. Capitalism is subject to minor and, as we have recently experienced, major crises.
Harrod instability is not a satisfactory explanation of these crises, although it has the merit ofshowing their potential cumulative course in economies without ‘external markets’, as
pointed put by Kalecki. Following his lesson, I have here criticised the investment-centred
theories of capitalist development and crisis that neglect the autonomous components ofaggregate demand. I started from a fundamental contradiction of capitalism, which Kalecki
described in better terms than Keynes: the effects of inequality in income distribution on
aggregate demand or, in other words, the problems of the realisation of the capitalists’ social
surplus. In a market economy ‘external markets’ may temporarily solve the realisation
problem. By definition these markets are financed by the creation of purchasing power, andwe see here an important field of convergence with the literature on endogenous money. The
creation of purchasing power finances the external markets that absorb the capitalists’ surplus
and return it to the capitalists in the form of profits. Capitalists thus become creditors of those

24

These final observations have been prompted by a remark I received from Randall Wray at apresentation in Copenhagen in May 2011.

markets. We find here a main source of instability in the building up of unsustainableimbalances between core-capitalism and the external markets in what is, in the end, a debtdriven model of capitalism that both the US and the Eurozone have played with (Cesaratto &Stirati, 2011; Cesaratto, 2012). There is here a point of convergence with the work of Hyman
Minsky (1986) and his followers on the financial fragility of capitalism. I therefore close by
acknowledging once again the limitations of the investigation of formally stable growth paths
and the necessity, emphasised by Garegnani & Trezzini (2010) among others, of integrating
the analysis of long-run growth with that of the cycle and crises.

Acknowledgments
I am grateful to Franklin Serrano for many helpful discussions on these topics over the years,
and for his detailed comments on this paper. I have incorporated many (although not all) of
his suggestions, particularly in Section 4. I also thank Oscar Dejuan, Ariel Dvoskin, Mark
Lavoie, Riccardo Pariboni, Fabio Petri, Anwar Shaikh and two referees for numerous usefulsuggestions.

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