Transcript Document

Lecture notes on accumulation theories
Heterodox Theories
Sergio Cesaratto
Professore ordinario di Politica economica
Università di Siena
Dipartimento di Economia Politica e Statistica (DEPS)
Piazza San Francesco 7
53100 Siena
338 1768793
[email protected]
http://www.econ-pol.unisi.it/cesaratto/
http://politicaeconomiablog.blogspot.com/
Growth course 3
Heterodox theories
• We shall consider 3 groups of theories:
• Cambridge equation (circa1950s-1970sKaldor, Joan Robinson,
Pasinetti)
• Neo-kaleckian models (circa 1980-2015 Rowthorn, Amadeo, Dut,
Lavoie, Marling and Bhaduri and many others)
• Sraffian authors (1990-2015) distinguished in: First Sraffian position
(FSP)  mainly at RM3; (b) the supermultiplier approach  Serrano
and others.
• Consensus on the Keynesian Hypothesis (Kaldor-Garegnani,
hereafter KH): investment is independent from saving both in the
short and in the long run (for the neoclassical/neo-keynesians
independence in the short run only)
• No consensus on specific models, but wide consensus in policy
issues: aggregate demand is the driver of growth.
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How to solve the Harrodian instability problem
• In Solow v adjusts through the neoclassical substitution
mechanisms in order that gA gw
• We shall review 4 heterodox attempts to solve the Harrodian
problem:
• Cambridge equation: s varies in order that gw -> gA (S adjusts to I)
• Neo-Kaleckians: va or, better, ua becomes the “new normal” so no
instability would arise (extra-saving comes from a higher degree of
capacity utilisation that becomes the “new normal”)
• FSP: extra-saving comes from a higher degree of capacity utilisation
and later from the new capacity created, but the FSP gives up the
idea of the economy converging to gw, so avoid the instability
problem
• Sraffian supermultiplier: reject the Harrodian context, make gross
investment (the source of troubles) induced by an external anchor of
growth (autonomous demand).
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Premise 1: Workers spend what they earn, capitalists earn
what they spend
• Heterodox models tend to share this Kalecki’s dictum.
• Capitalists decide their autonomous spending (investment and
luxuries)) by having access to credit (endogenous money  loans
create deposits). Through the multiplier (and supermultiplier)
process income X is created, part goes as wages W to workers that
can thus spend, and part as profits P to capitalists that can thus
return their loans to the banks.
• X = W + P = C + I + Z.
• Assuming cw = 1 and cc = 0, W = C (Workers spend what they earn)
• Then P = I + Z (capitalists earn what they spend)
Premise 2 - Normal degree of capacity utilisation: the
average degree of capacity utilisation desired by the
entrepreneurs
• We must distinguish between full, normal and (average) effective
degrees of capacity utilisation. The normal degree of capacity
utilisation is defined as
e
f
n
n
e
where Yn is the expected fnormal output when capacity is
originally installed [1] and Y is the capacity installed, with
(in general).
u Y Y
Yne  Y f
One main reason why entrepreneurs install additional capacity over
average expected output is to be able to meet sudden peaks of
demand and not let unsatisfied customers to turn to competitors.
Thus it depends both on expected normal output and on the
expected amplitude of the trade cycle peaks.
[1] Normal output is that forthcoming at normal prices with capacity
utilised at its normal level.
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Premise 2 (cont.)
un= Yn/Yf where Yf is the maximum physical output from a given
capacity K. In general Yn < Yf and un < umax.
When gA > gw, it means that s/va> s/vn,, that is
va = K/Ya < vn = K/Yn  Ya > Yn
or, in terms of degree of capacity utilisation u,
ua = Ya/Yf > un = Yn/Yf  Ya > Yn
Read in the opposite direction: whenever gA > gw, Ya > Yn  ua > un,
the actual degree of capacity utilisation ua is higher than normal
The opposite would of course happen when gA < gw (ua < un and
investment would keep falling to absorb the less-than-normal u).
In short:
if va < vn it means that the capital stock is overutilised, that is ua > un
if va > vn it means that the capital stock is sub-utilised, that is ua < un
Finally, if ua > un then ra > rn where rn is the normal profit rate.
A normal rate of profit prevails when, given the real wage and the
technical conditions of production, capacity is normally utilised (that
is ra = rn when ua > un.
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Premise 2 (cont.)
• Note that ua can alternatively be defined as ua = Ya/Yn
• so that un = Yn/Yn = 1
• We sometimes use this alternative definition.
The Cambridge equation and its critics
• The equations are
S = sc P = sc rn K
I=I
S=I
• where sc is the marginal propensity to save of capitalists (workers do
not save  classical hypothesis), P are profits, rn is the normal profit
rate
• Solving the system scrK=I  scr = I/K and recalling that I = K
we get the famous Cambridge equation
gK  scr
• Given vn = K/Y, gy = gK
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Observation
• Note that:
• gw = scrn = scP/K = sc(P/Xn)/(K/Xn),
where Xn is normal output.
• Reminding that:
• s = sc(P/Xn) + sw (W/Xn) and that sc = 1 and sw = 0
then scP/Xn = S/Xn = s, and that K/Xn = vn
we get: gw = s/vn
• It is important to note that in equilibrium Harrod’s warranted rate is
always respected, whatever the theory (it must, it is just a dynamic
expression of I=S). In equilibrium all cats are grey. Theories like
cats are, so to speak, visible only in disequilibrium. (Take another
example: competition prices are equal to production costs in all
theories, but they are not determined in the same way by, say, the
labour theory of value, Sraffa or the marginalists).
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Digression on grey cats
• Recall Solow’s fundamental equation y = sy – nk
• In the steady state equilibrium sy = nk, or sy/k = n, and given that
k/y = vn, s/vn = n. The warranted rate s/vn in Solow is a full
employment path equal to n.
• I want you to note that in any model the steady-state solution
“contains” (or “respects”) gw = s/vn
• In equilibrium all cats are grey (this is important to reject some FSP
criticism to the supermultiplier)
The main characteristic of the Cambridge equation is in the idea that
the rate of accumulation gk decided by the entrepreneurs influences the
normal income distribution[1] that thus becomes endogenous and
subordinated to the rate of accumulation
Assume that capacity is fully utilised  The CE does not distinguish
between uf and un.
Suppose that the entrepreneurs decide a higher level of investment
financed out of credit creation. The larger investment expenditure
would compete with the existing nominal consumption expenditure
out of the given nominal wages. The result is that capacity would be
transferred from the wage goods to the capital goods sector, wage
goods become more expensive and real wages fall. The larger
production of capital goods thus leads to a change in income
distribution from (real) wages to profits and to a saving supply
adequate to the larger level of investment. In terms of equation [1],
gk is the independent variable that, given sc, determines rn:
gk  r n
• [1] A said, the adjective ‘normal’ implies a situation where, given the
real wage and the technical conditions of production (including a
normally utilised degree of capacity utilisation), a normal rate of
profit prevails.
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A graphical representation: the wage-profit frontier on the left-hand side
and the CE gk = sc rn on the right-hand side
The idea is that because of the larger investment expenditure,
aggregate nominal demand and therefore, given full capacity utilisation,
prices will be higher. However, since the nominal wage bill and nominal
consumption expenditure are given, a real wages fall permitts to
capitalists to realise their desired investment.
• Let us try a simple way to show how in the CE context the investment
decisions by the entrepreneurs are able to divert resources from the
wage goods sector to the investment sector
• Corn economy, p = price of corn (in £), W = given nominal wage-bill, I
= investment, X = full capacity output
• W + Ip = Xp or W/(Xp) + I/X = 1
• Suppose capitalists decide to invest more I’ > I, and p  p’ (with p’ >
p)
• W + I’p’ = Xp’ or W/(Xp’) + I’/X = 1. Given that p’ > p then W/p’ < W/p
and I’/X > I/X.
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Criticism
• From an empirical point of view, the association of higher growth
rates to a change of income distribution in favour of profits is not
particularly robust. If anything, real wages would tend to rise during
periods of faster accumulation and higher labour demand as a
consequence of the greater workers’ bargaining power, and tend to
fall during downswings when the ‘industrial reserve army’ increases.
Not surprisingly, both neo-Kaleckian and Sraffian authors criticise
the Cambridge equation approach (Garegnani 1992: 63; Lavoie
2006: 111-2). In short, they both single out the capacity of capitalism
to accommodate an upsurge of capital accumulation by resorting to
a fuller rate of utilisation of productive capacity without the necessity
of changes in income distribution, as we shall explain below.
Rowthorn (1981) has been particularly influential among the former
group of economists; Garegnani (1992) among the second.
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Neo-kaleckian criticism: the degree of capacity utilisation varies when
investment changes, neither prices nor real wages
• The underutilisation of capacity is explained by Rowthorn by
recalling Kalecki and Steindl idea of a ‘monopolistic economy which
is operating well below full capacity’ (Rowthorn 1981: 1). In such an
economy, ‘prices are relatively inflexible and firms respond to
change in demand by varying the amount they produce. When
demand is depressed 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 the
level of capacity utilization and the rate of profit' (ibid.).
Symmetrically, in the case of an investment upsurge, ‘there is no
need to reduce real wages, and the extra profits required to
stimulate investment can be generated simply by increasing output
and bringing idle capacity into use’ (ibid.). What is more, a fuller
capacity utilisation may accommodate both a rise in real wages and
of profits and ‘total profits may rise despite the fact that real wages
have increased’ (ibid.).
• You note that the (actual) profit rate depends on the degree of
capacity utilisation. As we have seen: if ua > un then ra > rn where rn
is the normal profit rate.
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The neokaleckians in brief
• So the neo-kaleckian idea is that given a capital stock, a higher rate
of accumulation is accommodated by a higher degree of capacity
utilisation and not by lower real wages, as in the CE.
• The higher saving provision becessary to accommodate the higher
investment derives from an higher actual profit rate (if ua > un then ra
> rn ).
• A higher actual profit rate is consistent with a given real wage rate.
Summing up what we have said so far
• Harrod: if, moving from a dynamic equilibrium in which S = I or gs =
gI , investment decisions vary, then no adjustment of S to I is
possible (or better, S adjusts to I through a higher ua, but the attempt
to restore un creates instability).
• CE: if, moving from a dynamic equilibrium in which S = I or gs = gI ,
investment decisions vary, then S adjusts to I through a change
income distribution (the normal profit rate rises) that affects s.
• NK: if, moving from a dynamic equilibrium S = I or gs = gI ,
investment decisions vary, then S adjusts to I through a higher
degree of capacity utilisation and the consequent rise in the actual
profit r, without affecting real wages). Instability seems to be avoided
by the NKs by neglecting the attempt by capitalist to return to un.
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Sraffian criticism to the CE (and to the NK)
• Sraffian authors are particularly keen on the distinction, met above,
between full, normal and (average) effective degrees of capacity
utilisation
• By contrast in Rowthorn and the NK we met full and actual degrees
only.
• So while Sraffian authors accept the idea that in the short-run the
flexibility of the degree of capacity utilisation consents a higher
accumulation rate at a given real wage rate, they also reject the NK
idea that the economy can rest in a position characterised by a not
normal degree of capacity utilisation and associated not normal rate
of profits
• The Sraffian position is a bit complicated.
• Step 1: normal prices would prevail even with a not normal degree
of capacity utilisation
• Step 2: there is some disagreement among Sraffians as to whether
the economy effectively tends to a normal degree of capacity
utilisation, so that it is useful to study normal accumulation paths
• We briefly dwell on the Sraffian position and then return on the NK
model.
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Step 1: normal prices would prevail even with a not normal
degree of capacity utilisation
• To begin with, according to Sraffian authors ‘long-period prices …are
the prices determined on the basis of conditions of production that
can be defined as normal, and hence a particular degree of
utilization of capacity, which we can also indicate as “normal”’
(Ciccone).
• What it is rejected is the claim that for pn to prevail the absolute size
of capacity must be fully adjusted to effectual or to effective
(aggregate) demand so to realise a normal degree of utilisation on
all plants.
For memory:
• Effectual demand (from Adam Smith) is defined as the demand that
is forthcoming in a single industry at the normal price.
• Effective demand is demand forthcoming at the aggregate level
when prices are normal in all sectors.
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When effectual demand varies pn may prevail through
variations in ua
• Assume that in one industry effectual demand (the demand of the
commodity at its normal prices) rises, so that pm > pn. Competition
leads firms in the industry to raise the degree of capacity utilisation
to meet the higher effectual demand and to re-establish pn.
• So precisely through a higher degree of capacity utilisation, output
rapidly adjusts to Effectual Demand and pm  pn (Ciccone)
• The adjustment of pm to pn takes place at a ua which is different from
un, so that ra would be different from rn: if ua > un then ra > rn
• At the same time (and given that ra > rn), a process of adjustment of
capacity to the new level of effectual demand would take place and
the rate of profit that firms expect on the newly installed equipment is
the normal rate of profits.
• So Sraffian economists may conclude that through variation of u, the
gravitation of pm  pn is quite a rapid and effective process while the
normal rate of profits (and related un) is prevailing or expected “at the
margin” (on gross investment) guiding the investment decisions of
firms.
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Step 2: normal positions and fully adjusted positions (cont.)
• So, although in the economy as a whole a tendency of aggregate
capacity to adjust to aggregate demand is always at work, with
respect to the gravitation of prices to their norma level it is not
necessary that capacity is fully adjusted, but only that “at the margin”
and in each industry a sufficient number of competing firms are
endeavouring such an effort to make the tendency to a normal profit
rate effective.
• The idea is that the effective (micro) gravitation of prices and
distribution towards the long period positions is less demanding and
faster than the (macro) full adjustment of aggregate capacity which
is more likely to be frustrated by the changes of long run aggregate
demand.
• These arguments are shared by all Sraffian economists. They
diverge, however, about how to treat accumulation (the divergence
is of method not of substance). We have a “first Sraffian position”
(Garegnani/Trezzini/Palumbo/Ciccone) and the followers of the
“Sraffian supermultiplier”.
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Difficulties with the first Sraffian position
• According to the FSP a (say) higher ga is accommodated by a higher
degree of capacity utilisation and ra (as in Rowthorn) , but it leaves rn
unaffected (as seen this may prevails “at the margin” even without full
capacity adjustment).
• But, having accepted the Harrodian framework, the FSP seems in
troubles to deal with the gravitation of the economy towards a normal
degree of capacity utilisation, which is however admitted.
• The escape this difficulty, they argue that the study of the normal path
of the economy (steady state paths) is useless.
• This view may appear as a post hoc ergo propter hoc argument due to
the difficulty of escaping from the dilemma between the CE which
respect the KH, is stable but violates Classical distribution theory; and
Harrod which is consistent with exogenous distribution, but is
unstable.
• Eventually the FSP is similar to the NK position: (i) exogenous
distribution (ii) surrender the study of growth with a normal degree of
capacity utilisation
• A “fourth way” is taken by the followers of the Sraffian followers of the
Supermultiplier that break the Harrodian framework.
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The inconsistent Harrodian Triangle
The canonical first-generation neo-Kaleckian model (a
very simple model)
• The first equation (similar to the CE), the saving equation, expresses
the rate of growth of the capital stock permitted by capacity saving for
given levels of the saving propensity – for simplicity profits are the
only source of savings - and of the actual profit rate.
Eq.1
gs  scra
The second equation expresses the rate of growth of K as a function of
the long term growth of sales expected by firms (animal spirits?).
Eq.2
gi  
The third equation states that the actual profit rate is a function of the
actual rate of capacity utilisation, given the actual profit share  and
the capital coefficient vn.
Eq.3

ra 
Eq. 4
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vn
ua
gs = gi (that is S/K = I/K)
24
Comparison with the CE model
•
•
•
•
Using the same presentation used
for the CE the NK model would
be:
It is enough to devide the first
three equations by K to obtain the
previous formulation.
the unknowns are g, ra, ua
let us derive the 3° eq. (which is
actually the differentia specifica
with the CE
S  sc P  sc rK
II
SI
r
vn
ua

P
/
Y
P
/
Y
f
a
r

P
/
K


Y
/
Y
u
a
a
f
a
Y
K
/
Y
v
n
a
K
f
Y
Y
f
a
Solving the model
• By simple substitutions we obtain:
eq.4
gs 
sc
ua
vn
• The long run goods market equilibrium is
where:
g s  gi
• So we obtain:
eq.5
ua 
vn
sc
• Equations [2] and [4] can be drawn in the
space g-u, as shown in the top part of figure
(1). Equation (3) is drawn in the lower part
(as profit curve PC): a higher ua implies a
higher ra.
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The capacity-saving growth function (4), indicated as gs, is an increasing function of u. This is so
because a higher u increases the amount of profits extracted by any given level of K, raising the actual
r and the capacity-saving supply. In drawing the picture we supposed that at the intersection A the
equipment is normally utilised (“old normal”), but this is a fluke since this is not typical of this genre of
models. In the lower part of the figure we drew equation [3] indicating that in correspondence to un we
find the normal profit rate. Figure 1 then shows the case in which long term growth expectations grow
from  to ’. The consequence would be a higher u, that in this model can be taken as the ‘new
normal’.
g
gs
'
g i'
B
A

gi
u a  u 1n
un0
u
r
PC
ra  rn1
rn0
B
A
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u n0
u a  u 1n
u
Notably, the higher capacity savings corresponding to the new
accumulation pattern are brought about by the higher actual profit rate
corresponding to the higher utilisation rate. But how is the instability
problem removed? What is actual is normal: the new normal
• From eq. 5 we get eq. 6:  = sc/(vn/ua)
• Note that in point A (old normal):
 = sc/(vn/un) = s/(vn/un)
And defining un = Yn / Yn, we have un = 1, then  = s/vn
The old normal had necessarily to be an Harrodian equilibrium in which
all savings are systematically invested (either because there is
economic planning or because capitalists collectively decide so
[which is the same], or because we were there by fluke)
Be this as it may, in A it is s/vn that dictates .
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What is actual is normal: the new normal
• Look now at point B where the animal spirits dictate a higher
accumulation rate ’
• According to the NK entrepreneurs are content with any actual capital
coefficient it happens to be, and the actual ua can therefore be usefully
defined as the ‘new normal’ ua = unn.
• We may similarly define a “new normal” capital coefficient:
’ = sc/(vn/ua) = sc/(vn/unn)
The term vn/ua = vn/unn) can be defined as the “new normal” capital
coefficient:
vnn = vn/ua= (K/Yf)/(Ya/Yf) = K/Ya
so that ’ = sc/vnn = s/ vnn
• We thus obtain a “flexible” Harrodian gw = s/va = s/vnn
Whatever is real is rational, or better, whatever is actual is normal what
is normal is endogenous (very funny)
What is actual is normal: the new normal
• As observed, the initial equilibrium in A is an Harrodian equilibrium,
i.e.  is the only growth rate consistent with growth with a normal
capacity utilisation (“normal growth”). So to abandon the concept of
normal growth is essential for the NK to sustain the KH (that is a
“freedom” of capitalist to decide the accumulation rate).
• But, as we shall see, they cannot abandon it completely.
• In Harrod: if ga > gw, ua > un. The attempt by the entrepreneurs to
restore un determines instability: recall, if they expect ge>gw, then
ga>ge and they expect an even larger ge.
• NK: if ga > gw, ua > un, but ua becomes the ‘new normal’ ua = unn.
• So no instability (recall that the harrodian instability depends of the
attempt to restore a normal exogenous degree of capacity
utilisation). Here un is endogenous and equal to the actual rate. Very
ad hoc.
By comparison, it might be useful to illustrate what would happen in the CE
model where the corresponding equations would be (they are derived dividing
the equations by K)
•
Eq. 1
gs  scrn
•
Eq.2
gi  
•
Eq.3
rn 

vn
•
Eq. 4
•
•
For memory, eq. (3) in the NK was
In the CE ua = un = Yn/Yf = 1,
there is a unique normal degree of
capacity utilisation equal to full
gs = gi
rn 

vn
ua
capacity
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A rise in the long run expectations from  to ’ causes a change in income distribution, a rise of the
profit share  in equation [3] and an upward rotation of the corresponding PC and gs curves, as shown
by figure 2. The new equilibrium is thus again characterised by a higher normal profit rate set in
correspondence to a normal degree of capacity utilisation. (in a sense, in the CE we have a “new
normal” profit rate.
g s'
g
gs
'
B
g i'

A
gi
un  u f
u
r
PC’
PC
'
n
r
rn
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A
B
un  u f
u
Figure 2
32
Again as a comparison with the CE, note first that we have different
wage-profit curves each for any different degree of capacity utilisation
In the NK case, a higher growth rate (gs = scr in the right-hand side) is
accommodated not by a change in income distribution (as in the CE) but
by a change in the degree of capacity utilisation, from old to new normal.
The absence of the thrift paradox in these models and how
to amend it
It can be noted that in both approaches as presented in figures 1
and 2, a lower marginal saving propensity has no positive effect of
long run term growth, although it affects, respectively, the normal
profit rate (rising it since a higher profit share is required to generate
capacity savings equal to investment) or the degree of capacity
utilisation (rising it through the effect of the higher s on the standard
Keynesian multiplier).
So, unless we assume that these two effects positively influence
investment, there is no ‘thrift paradox’ as one might presumably
expect from Keynesian or Kaleckian models.
“Might”, because this “thrift paradox” is wrong: empirically, a higher g is
associated to a higher I/K = S/K, not the opposite as the NKs would
like. This is why neoclassical theorists try to endogenize growth
sg. This does not imply that we think that sg is true. But we
believe that I/K  g.
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Normal profit and investment decisions I (a digression on
an alternative way to demonstrate the thrift paradox)
• Lavoie reports that Joan Robinson assumed that investment is
sensible to the level of the normal profit rate – so that if sc falls , given
, rn rises, and consequently I and then Y rise (another way to show
the thrift paradox)
• However, the influence of the normal profit rate on investment raises
perplexities. Given rn, investment depend on expected effective
demand (that forthcoming at the normal profit rate).
• Given rn (whatever it is) competition leads entrepreneurs to satisfy all
expected demand at that rate.
• Variations of rn have to do with income distribution and only through
this they may affect expected effective demand and investment.
• A rise/fall of rn may negatively/positively affect investment if expected
demand is negatively affected by lower/higher wages.
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Normal profit and investment decisions II
• Therefore, a rise of rn, as such, for no reason would positively affect
investment.
• Likewise, a lower rn will in general leave gross investment unaffected
as long as capitalists fear to leave market shares to competitors:
each capitalist is homo homini lupus with respect to her classmates.
• Ça va sans dire that a rise/fall of ra above/below rn will just signal that
ua is above/below un. In both cases gross investment will vary in
order to readjust the degree of capacity utilisation and normal
profitability (while the long trend of investment is still set by demand
for products associated to normal profitability).
• As Serrano sums up: “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 is met, irrespectively if this
normal rate is high or low‘.
Normal profit and investment decisions III
• It can finally be thought that a lower rn is not accepted by capitalists
that might recur to an “investment strike”
• A lower rn does not discourage investment since capitalists do not
invest as a class (as perhaps Marx and Vianello tend to think), and
they do not want to risk loosing market shares by starting an
individual “investment strike” (they would be afraid to lose market
shares to competitors if they do this)
• However, recalling Marx’s dictum “The executive of the modern
state is nothing but a committee for managing the common affairs of
the whole bourgeoisie”, a lower rn might induce the government to
adopt deflationary economic policies to re-create the industrial
reserve army.
Full ‘canonical’ NK model: to demonstrate the thrift paradox, the NK
model introduces the dependence of investment on the degree of
capacity utilisation – so that if a lower s raises ua, gi would rise
• A full ‘canonical’ neo-Kaleckian model (Lavoie 2006) does thus
contemplate the attempt by firms to adjust capacity to the desired,
normal level. The model:
• Eq.1 g  s r
s
• Eq.2
c a
g



(
u
u
)
i
a
n

ra  ua
• Eq.3
vn
• It looks more than suspicious that long run effects of variations of
the saving propensity on accumulation relies on what should be
regarded as short-run adjustments to restore a normal degree of
utilisation
27/03/2016
39
By substituting equation [3] in [1], we get Eq.4:
gs 
• The long run goods market equilibrium is where
sc
ua
vn
g s  gi
un
scvn
• that is where, equating equations [4] and [2]: u
a
• Equations [4] and [2] can now be drawn in the space g-u, as shown
in the top part of figure 3. Also the investment growth function [2] is
now an increasing function of u. This is so because a higher degree
of capacity utilisation induce firms to invest in order to obtain the
desired degree of capacity utilisation. In drawing the picture we
supposed again, for the sake of the argument, that at the initial
equilibrium A the equipment is normally utilised. Reconsider now the
paradox of thrift.
27/03/2016
40
Suppose that a rise in real wages causes a fall of the profit share . This causes a rightward rotation of
the gs and PC curves in figure 3, respectively. At the initial growth rate g = , the lower capacity
savings determine a higher ua0. The higher rate of extraction of profits out of a given capital stock
compensates the fall in the profit share, so that the resulting r is to the initial one. The higher u leads
then to a higher growth rate of investment and to an even higher rate of utilisation until a new
equilibrium is reached in correspondence to ua1.
g
gs
g s'
g’
gi
C
g= 
A
B
un
u a0
u 1a
u
r
PC
ra
rn
27/03/2016
C
A
B
un
u a0
u 1a
PC’
u
41
The neo-kaleckian Wage-led growth and the classical
wage-profit rate relation
• The paradox of thrift is proved, in a growth context, since a lower
saving rate leads to a higher growth rate.
• These economists also speak also of a ‘paradox of costs’: ‘A higher
real wage, and therefore higher costs of production, leads to a
higher long-period profit rate. In other words, a reduction in the
gross costing margin of each individual firm ultimately leads to a
higher profit rate for the economy as a whole’ (Lavoie).
• These results, the possibility of wage-led growth accompanied by a
higher profit rate, is considered particularly important by neoKaleckian authors since it is in sharp contrast not only with the CE
inverse relation between real wages and growth rates, but also with
the Classical economists inverse relation between real wages and
the profit rate.
27/03/2016
42
What is actual is normal: the ‘new normal’
Similarly to above, from eq. [2]
and [4] we get:
Redefining ua as the ‘new normal’
unn, the denominator on the righthand side becomes the “new
normal” capital coefficient
s

c



(
u
u
)
a
n
v
nu
a
vn
vnn 
unn
we may obtain a warranted growth
rate equal to
sc π
gW =
= α + β(u a  un )
vnn
27/03/2016
43
The NK warranted rate
The growth rate is determined by the ‘animal spirits’ a plus an endless
attempt (un – ua) by the entrepreneurs to recover the normal
utilisation rate, a never completed attempt that becomes a stable
component of the growth rate that might usefully re-defined

'

(
u
a u
n)
so that
sc π
gW =
= α + β(u a  un ) α '
vnn
In the words of Lavoie:
27/03/2016
44
This is clearly said by Lavoie*
• “what this really means in terms of our … Kaleckian
model is that the parameter  gets shifted as long as the
actual and normal rates of capacity utilization are
unequal: The reason for this is that … the  parameter
can be interpreted as the assessed trend growth rate of
sales, or as the expected secular rate of growth of the
economy. When the actual rate of utilization is
consistently higher than the normal rate (ua>un), this
implies that the growth rate of the economy is
consistently above the assessed secular growth rate of
sales (ga>). Thus, as long as entrepreneurs react to this
in an adaptive way, they should eventually make a new,
higher, assessment of the trend growth rate of sales,
thus making use of a larger parameter in the investment
function.”
27/03/2016
45
A Karamazovian theory
• We observed above that the initial equilibrium in A is an Harrodian
equilibrium, i.e.  is the only growth rate consistent with growth with
a normal capacity utilisation (“normal growth”). So to abandon the
concept of normal growth is essential for the NK to sustain the KH.
• But, we see now that they cannot abandon it completely. A term (ua
– un) must be retained (that is the term un must be retained) in the
“new normal” growth rate since this serves to show the ‘thrift
paradox’.
• So we cannot let the attempt to re-establish a normal path to go on
since this means a return to the Harrodian instability; so we
redefine a “new normal path” that, however, contains an endless
attempt to re-establish the old normal path. Moreover, this is
essential to show the thrift paradox.
• As we shall see, Vianello recourses to the Faust to describe this NK
tormented soul, I may recur to the Karamazovian equally divided
spirit: the economy must at the same time escape from point A,
where Harrod prevails and the KH is not proved, but also try to
return to it (the term (ua – un)), in order to show the saving paradox.
The result of this drama is that the economy stays in C.
The literature has pointed out a number of unsatisfactory
aspects of this canonical model.*
• Core-Sraffian authors (and others) have indicated two: (a) the
inconsistency of a steady state model characterised by a not-normal
degree of capacity utilisation; (b) the confusion, in dealing with
income distribution, between the normal and the actual profit rate
(for a given real wage).
• I suggested a third substantial weakness: (c) it is surprising that in
the neo-Kaleckian canonical model the long-term role of effective
demand relies on the firms’ effort to obtain a normal degree of
capacity utilisation. This process is, presumably, a short run process
that, however, in the neo-Kaleckian view must never be completed
in order to have a lasting effect on the accumulation rate (Achilles
must never chase the tortoise). Indeed, the capacity adjusting term
in the investment function [2] is not just a due addition in order to
testify the attempt by firms to adjust capacity, but all the model
desired results bear on their long-run failure to do so.
• Let’s begin from (c).
27/03/2016
47
Lavoie admits instability*
• “Once the economy achieves a long-run solution with a higher than
normal rate of utilization, say at u0 > un , (after a decrease in the
propensity to save …), the constant in the investment function
moves up …, thus pushing further up the rate of capacity utilization
to u1 and u2, with accumulation achieving the rates g1 and g2, and so
on. Thus, according to some of its critics, the Kaleckian model gives
a false idea of what is really going on in the economy, because the
equilibrium described by the Kaleckian model (point (C)) will not be
sustainable and will not last.” (2008: 7).
• Below Lavoie’s figure, but I prepared an improved description
g
gs
g s'
D
g2
C
g1
g0
g
gi
B
A
un
ua0
u 1a
u a2
u
This is the key Lavoie’s passage (worth repeating)*
• “what this really means in terms of our … Kaleckian
model is that the parameter  gets shifted as long as the
actual and normal rates of capacity utilization are
unequal: The reason for this is that … the  parameter
can be interpreted as the assessed trend growth rate of
sales, or as the expected secular rate of growth of the
economy. When the actual rate of utilization is
consistently higher than the normal rate (ua>un), this
implies that the growth rate of the economy is
consistently above the assessed secular growth rate of
sales (ga>). Thus, as long as entrepreneurs react to this
in an adaptive way, they should eventually make a new,
higher, assessment of the trend growth rate of sales,
thus making use of a larger parameter in the investment
function.”
NK instability: an improved representation (next slide the complete
figure)*
g
gs1
gi3
gi2
gs0
D
gi1
C
gi0
A
un
gi0
B
u0
u1
u2
u
g
gs1
gi3
gi 2
gs0
D
gi 1
C
gi0
A
B
un
ua0
gi0
u1a
ua2
u
ua2
u
r
ra1
C
rn  ra0
A
un
B
ua0
u 1a
. The economy starts from point A where g s0  g i0 and g i0   . As before, for the sake of
the argument, we assume that in A un and rn prevail (what is to say that an Harrodian warranted rate
rules there). After a decrease in the propensity to save the gs function shift downwards and the
economy provisionally goes to B. In B the higher demand for wage-goods is satisfied by a higher
ua, while the accumulation rate is still g i0   . Supposing that capitalists try to restore un, the
economy moves along a new investment function g 1i     (u a0  u n ) to reach point C. Following
Lavoie’s suggestion that “entrepreneurs … make a new, higher, assessment of the trend growth rate
of sales, thus making use of a larger  parameter in the investment function” (re-read the above
quotation), the new investment function becomes g i2   '  (u 1a  u a0 ) , where  '     (u a0  u n ) ,
and a new provisional equilibrium is reached in D. There, though, a new investment function
g 3i   ' '  (u a2  u 1a ) prevails, where  ' '   '  (u 1a  u a0 ) , and so on and so forth.
Final strike to the NK models*
• We may ask ourselves where Lavoie would put its “new normal”
growth path. Natural would be to put it in B: entrepreneurs take as
“normal” whatever the rate of capacity utilisation happens to be.
Indeed if we let them to adjust capacity to restore the “old normal”
un, there is no reason why they should stop in C, or D etc. The NK
have a problem here, however. If the economy stops in B, a fall 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. So, Lavoie would likely have the economy stop in C. In a
Karamazonian way, capitalists are trapped between the will to
restore normal capacity utilisation – that leads them in C, D etc –
and that to take for normal whatever ua the experience. So they stop
in C. The ad hocery of this way of reasoning is patent
• This is a very weak growth theory. So two pigeons with one seed: a
“new normal” function ’ =  + (ua-un) serves the purpose of
showing the thrift (and cost) paradoxes and avoids the Harrodian
instability.
Well, not the final strike: ad hoc new normal*
• Rationalisations of the endogenity of the degree of capacity
utilisation (see Hein & Lavoie).
• ‘provisional equilibrium’ (when ua<> un) (Chick, Caserta, Dutt):
‘Hence … firms may be quite content to run their production capacity
at rates of utilization that are within an acceptable range of the
normal rate of utilization. Under this interpretation, the normal rate of
capacity utilization is more a conventional norm than a strict target.’
• ‘managers are satisficers, rather than maximizers’ (Park, J.Robinson
and Koutsoyiannis ).
• These arguments simply forget that the tendency to a normal degree
of capacity utilisation (and to a normal profit rate) takes place ‘at the
margin’ on new gross investment (while a quasi rent is yield on the
existing capital stock). This is the traditional method shared both by
Marx and Marshall (Cesaratto 1995). To argue that: ‘if goals are not
met the firm readjusts downwards its aspiration levels’, is simply ‘not
credible’ (Hein et al). On new investment firms expect un, unless they
deliberately make wrong investment decisions to perpetuate
• ua >< un!
Origin of the NK contortions
• The economic explanation of the NK contortions is that wages are
an induced component of aggregate demand, and as such they
cannot be the primum movens of growth. By creating a never
adjusted discrepancy between ua and un, however, a rise of real
wages may affect growth; but the weakness of the trick is patent (it
can be seen that in the SM approach higher wages have a level
effect only)
• For a correct analysis of the (level and not growth) effects of a rise
of wages see Serrano’s Ph.D. dissertation Chapter 3.
The inconsistency triangle: a new look
un
Harrod
CE
exogenous distribution
KH
NKs/FSP
The neo-marxists or second generation- neoKaleckians
• Model by Marglin and Bhaduri, very
popular since the1990s, not discussed.
27/03/2016
58
All Harrodians now?
• As seen, behind all the steady state growth equations there is (after
some easy manipulation) Harrod’s gw:
• Solow: gw = n = sy/k  gw = s/vn (with n as the independent variable,
vn as the adjusting variable)  stable, but problems with K theory
• CE: gw = scrn  gw = s/vn (with gk = gg as the independent variable,
and with rn as the adjusting variable)  stable, but not empirically
robust
• NK: gw =  = sc/(vn/ua), where ua = unn can be defined as the “new
normal” u so that vnn = vn/unn  gw = s/ vnn (with gw =  +  (ua – un)
as the independent variable, and with unn as the adjusting variable)
 ad hoc stability
• FSP: difficult to say since they bypass problems by avoiding a
model.
• All the adjustment processes are unsatisfactory
• We must break with the Harrodian context
We were all Harrodian
• The Warranted Growth equation gw = s/vn is behind any growth
model since it is an equilibrum condition that dictates the rate of
growth consistent with I = S given s and vn.
• There is stability if competition leads to an adjustment either of s,
given vn, or of vn given s.
• No flexibility of both parameters in Harrod
• In Solow it is vn that changes via change of techniques (of k = K/L)
• In the NK it is vn that changes via the re-definition of the normal
degree of capacity utilisation: vnn = vn/unn where unn = ua.
• In the CE it is s that changes given vn.
• But all this adjustments are unsatisfactory for one reason or the
other.
• The FSP avoids the problem
• We must break with the Harrodian context
The supermultiplier approach (the Sraffian Kaleckians):
Growing with autonomous components of aggregate
demand. The problem with Harrod SEE THE OTHER
PRESENTATION IN MY WEB PAGE
• Serrano (1995a: 47) points the problems with Harrod out very
effectively:
“On the one hand – he argues – the accelerator relation I = vngeX*
[where, ge = expected income growth, X* normal capacity output]
uniquely determines the required share of investment in capacity for
any given expected rate of growth … . On the other hand,
completely different factors such as the distribution of income …
uniquely determine the average propensity to save … Only by a
complete fluke will the marginal propensity to save exactly coincide
with the required share of investment”
• That is only by fluke: sX* = I/X* = vnge so that
ga = gw = ge = s/vn
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61
Serrano also points out the surprising absence of the autonomous
components of aggregate demand (Z) in the post-keynesian (and postKaleckian) literature. Criticism to investment as the independent
variable.
• The NK approach (as well as the CE) seems to neglect the analysis
of the determinants of long run expectations captured by the term 
in the investment functions which, one would expect, is the relevant
research issue (unless we really believe that talking of ‘animal
spirits’ is a serious investment theory).
• Eatwell: investment should not be taken as the independent
variable, long-term expectations are the independent variable, but
anchored to what?
• Similarly, Serrano points out that 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 …
investment is the key independent variable.’ Investment is often
explained by evoking the ‘animal spirits’. Leaving aside the
vagueness of this explanation, the conceptualisation of investment
as autonomous appears inconsistent with its induced nature, as the
adjusting force of capacity to demand.
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62
We must change the framework: enter the autonomous
components of aggregate demand
• These components are defined as those that (a) do not depend on
produced or expected income (as induced consumption and induced
investment, respectively) and (b) do not create capacity.
• Examples are: government spending, autonomous consumption,
exports, [autonomous investment]
• Their absence in previous post-keynesian models is even more
surprising if we recall the role that government spending plays in
Keynes’s theory and “external markets” in Kalecki (on which we
shall shortly return). Garegnani (1962) has a similar expression “final
demand”.
• In a late paper, Kalecki seems to present the “external markets”
(already introduced in the eary 1930s) as a way out from the
Harrodian troubles
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63
Kalecki on Harrod - To my knowledge, it has not yet been noticed that
Michal Kalecki’s masterpiece paper on Tugan-Baranowski and Rosa
Luxemburg (1967) is a contribution on how to overcome the problems
with Harrod.
• The argument of the paper can be so summed up. TuganBaranowski shows that in principle a capitalist system can grow in
equilibrium as far as capitalists employ all their savings to build new
capital goods. Tugan thus shows a distinctive characteristic of
capitalism, that the aim of production is not the satisfaction of human
needs, but it can well be the production of means of production
useful to produce further means of production and so on and so
forth
• In order to be so, a tacit pact among capitalists should be stipulated
in order that all the social surplus, if not consumed, is invested so
that all production is sold. The problem with this view is that we
cannot expect capitalists to blindly or deliberately follow Say’s Law,
since “capitalists do many things as a class but they certainly do not
invest as a class. And if that were the case they might do it just in
the way prescribed by Tugan-Baranowski”
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64
Rosa Luxemburg, on the other hand, correctly perceived the difficulty of
capitalists to absorb the social surplus through their own consumption
and investment. Recall the surplus equation Surplus = Social product Necessities
• Therefore the necessity of “external markets”, external to the
capitalist income circuit, to absorb the surplus production (this view
was taken up in Kalecki 1934). Typically these markets are financed
by the capitalist system itself through the financial system . Kalecki
includes in these markets (net) exports to the underdeveloped
countries and government (deficit) spending. We may usefully add
consumers’ credit. We shall later call these external markets ‘noncapacity creating autonomous components of aggregate demand’.
Think of the housing bubbles in the US (consumers’ credit) and in
Spain (Germany financed consumers’ credit in an (relatively)
underdeveloped country).
• The numerical example used by Kalecki (shown later) to illustrate
the difficulties with Tugan is very clearly intended to show the
problems of Harrod’s model.
• Kalecki’s paper is quite relevant since it relates in a Marxian fashion
the Classical surplus theory to the theory of capitalist accumulation.
Just stop a little on Rosa Luxemburg.
27/03/2016
65
See this summary from Brewer A.,Marxist theories of imperialism : a
critical survey, 1990.
• “In Marxist theory, surplus value originates in production, where the
value produced by a worker exceeds the value of his labour-power.
The value created is embodied in a product, which must be sold to
‘realize’ the value in money terms, before the capitalist can buy fresh
means of production and labour-power to start the process again.
Marx analysed the realization of the product, and the reproduction of
the system as a whole, in a purely capitalist economy, containing
only workers and capitalists, plus hangers on (priests, prostitutes,
etc.) who derive their incomes from the capitalists. Luxemburg
argued that expanded reproduction is impossible in this context. ...
For reproduction to continue smoothly, the entire product at the end
of a period of production must be realized, i.e. sold to someone.”
66
Luxemburg wrote: ‘Perhaps the capitalists are mutual customers for the
remainder of the commodities [the social surplus] – not to use them
carelessly, but to use them for the extension of production, for
accumulation’ (Anti-Critique: 56-7).
She, however, rejected the possibility: ‘All right, but such a solution
only pushes the problem from this moment to the next . . . the
increased production throws an even bigger amount of commodities
onto the market the following year . . . [will] this growing amount of
goods again be exchanged among the capitalists to extend
production again, and so forth, year after year? Then we have the
roundabout that revolves around itself in empty space. That is not
capitalist accumulation i.e. the amassing of money capital, but its
contrary: producing commodities for the sake of it; from the
standpoint of capital an utter absurdity.’ (Anti-Critique: 57)
From this she drew the conclusion that there must be buyers outside
capitalist relations of production.
27/03/2016
67
External markets because “capitalist do not invest as a
class”
NOTE that Kalecki approves T-B in saying that “producing
commodities for the sake of it; from the standpoint of capital IS NOT
an utter absurdity.’ The question seems rather that of the instability
of the T-B-Say-Harrod model – unless capitalists “invest as a class”.
Kalecki suggests that to get out from Tugan-Harrod’s knife edge
problem, Luxemburg’s external markets must be taken into account
as the ultimate explanation of investment. Investment cannot be, so
to speak, a self-explanatory variable. Thus, both Kalecki (and
Eatwell) suggest that investment should not be taken as the
independent variable in growth theory.
In the paper under examination Kalecki rejects the idea that the
economy might stabilise along a growth path characterised by a belownormal capacity utilisation rate
• In MK’s view, only two alternatives are present: growth with normal
capacity utilisation, which is however unstable, and the stationary
state (not in the neoclassical sense)*, where the instability of
capitalism without external markets might lead the economy. So,
Kalecki does not find a way out from Harrod’s problems in
abandoning the notion of normal growth, but suggests the stabilising
force of “external markets”. Most of the heterodox literature of any
orientation has, however, so far taken investment as the
independent variable.
*“we have shown that the development of capitalism which does not
encounter the problem of effective demand, even if possible, is unstable.
…it may be said that an expanded reproduction will take place if there exist
factors that simply do not permit the system to remain in the state of simple
reproduction… Rosa Luxemburg considers expanded reproduction in the
long run without the existence of ‘external markets’ to be not only far from
obvious but outright impossible” (Kalecki 1967: 150-1).
• Let us now go back to Serrano
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69
The way out from Harrod’s trouble proposed by Serrano consists of
three steps:
• (i) consider investment as fully induced, (ii) take into account the
autonomous component of aggregate demand (Z), and (iii) anchor
long-term demand expectations to the growth rate (gz) of those
components. We shall discuss later if a Schumpeterian explanation
of investment as a component of those autonomous components is
acceptable. The presence of Z allows the existence of a plurality of
demand-led normal growth rates.
• Once we introduce Z we must distinguish between the marginal and
the average propensity to save, and it is precisely this distinction
that gives more flexibility to the approach.
• Historical note: SM comes from J.Hicks 1951; recovered by (the
late) Kaldor; independently developed by Bortis, De Juan, Serrano.
Allen, a French economist close to the NK must now be added to
the list.
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70
Paul Krugman admits in a post, we do not need “some kind of special
factor aside from the depressed economy to explain low business
investment” presenting a chart that shows the association between
business investment and what can be taken as a proxy of u
Serrano proposes a very simple model of a single-commodity
economy with circulating capital only
•
•
•
•
•
•
Eq.1 X* CIZ
Eq.2 I = vng e X
n
Eq.3 C = wlX n
Eq.4 Z  Z
Eq.5 g e  g z
Where Xn is the normal level of output, Z is autonomous spending of
the capitalists, vn is the normal capital/output ratio, w is the given
real wage, l is the labour input coefficient l = N/Xn, and ge is the
expected rate of growth of effective demand.
• In equation 5 we are provisionally assuming that firms form their
growth expectations and investment decisions on the basis of a
known rate of growth of Z.
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Workers do not save and capitalists save all their profits
• Workers do not save sw =0 and capitalists save all their revenues
sc= 1.
• c = marginal propensity to consume = wage share wl=wN/Xn
• s = marginal propensity to save (1-wl) = profit share = 
From these equations the level of income is easily determined:
The supermultiplier: X =
1
Z
( 1  wl)  vng z
Equation provides economic meaningful solutions if
1) wl  vgz < 1
2) Z > 0
The former condition says that the marginal propensity to spend (which is
the summation of induced consumption and induced investment) must
be lower than 1 or s/vn > gz
If the marginal propensity to spend is equal to 1 we are back to Say’s
Law and to Harrod’s Warranted Growth s/vn > gz with no space for the
autonomous components of demand
In Serrano's words: if wl + vngz = 1 if the marginal propensity to
spend is equal to one: “that of course is exactly what we mean by
Say's Law, i.e., any increase in capacity output would automatically
generate an equivalent demand (counting both induced investment
and induced consumption for it)”
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74
The (multiplier and the) SM in most traditional terms
1
YD 
(C a  I  G  E )
1  c(1  t )  m
1
Y
(C a  G  E )
z
1  c(1  t )  v n g  m
Kalecki/Serrano: workers spend what they earn,
capitalists earn what they spend
•
•
•
•
•
•
Z + I total expenditure of capitalists financed by credit creation: they
can spend (ex ante) before receiving profits.
Their profits are then equal to Z + I  Xn - wlXn = Z + I
Also Xn = sXn = Z + I
When they get their profits, capitalists return the loans to the banks
(so, not surprising they do not spend their profits sc = 1)
Indeed, while post factum capitalist do not spend what they earn, they
have consumed and invested ante factum (indeed they earn what
they spend).
The fact that capitalists consume (Z = luxuries) is shown by the fact
that with autonomous consumption marginal and average
propensities to save are different. This has a key role.
Marginal and average propensities to save
• Marginal propensity to save s = sc P/Xn where sc = 1
• Average propensity to save:
S = Xn - wlXn - Z = (1 – wl)Xn - Z = Xn - Z
or S/Xn = s – Z/Xn
- Although capitalists ex post do not spend what they earn (sc = 1), the
average propensity to save depends on the autonomous
consumption decisions of the entrepreneurs (so part of ex-post
capitalists’ saving is just a redemption of former consumption-loans).
Another expression for the average propensity to save
• From S = I. Recall that sXn = Xn = Z + I.
• S/(sXn) =I/(Z + I)
• Note that since I+Z are profits, I/((I+Z)) is the share of profits sp that
capitalists invest.
sp 
I
I Z
• So the average propensity to save is also equal to
S/Xn = sp s.
The SM normal (warranted) growth path
Recall that
S/Xn = s –Z/Xn this is the average propensity to save
• We may derive Serrano’s gw using the three equation system (we
assume gw = gz = ge, we shall return on this):
Eq.1
S = s Xn – Z
Eq.2
I = vngzXn
Eq.3
S=I
So:
vngzXn = s Xn –Z,
that is:
gz = gw = (s –Z/Xn)/vn
finally:
gw = (S/Xn)/ vn .
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Understanding Serrano’s gw (I)
• gw = (S/Xn)/ vn can be rewritten as
gw = (s –Z/Xn )/vn
With Z = 0, gw = s/vn, back to Harrod.
• Compare two normal paths with different levels and growth rates of Z.
If gw’ > gw, then (S/Xn)’/ vn>(S/Xn)/ vn or (sc–Z/Xn )’/vn > (sc–Z/Xn )/vn
• So if gw = gz rises, the share of S/Xn = I/Xn must also rise and so Z/Xn
must fall (given the marginal propensity to save s = 1-wlXn).(Note that
C/Xn is given and equal to the wage share – wages are proportional to
income)
Intuitively, when gz rises, I/Xn must rise since investment must be
higher now to meet higher demand tomorrow: ‘given the capital-output
ratio, a higher rate of growth of capacity will necessarily require that a
higher share of current level capacity output be dedicated to capacitygenerating investment.’ (Serrano)
• This can be viewed also from the accelerator I = vngzXn that implies:
I/Xn = vngz
Understanding Serrano’s gw (II)
• Thus, if rises, in the new normal path the ratio I/Xn must be larger
and the ratio Z/Xn lower (for a given s). Since the share of
consumption on normal output is constant – it is indeed equal to the
wage share which is also constant: W/Xn = wl – then in the new
steady state by necessity the higher 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 (compared to a
lower ) is associated to a higher level of normal output Xn – not
surprisingly since a higher implies higher current investment - such
that it generates a share of capacity savings S/ Xn adequate to the
higher level of investment required by the higher .
• (see the example)
Understanding Serrano’s gw (III)
Recalling that the average propensity to save is also equal to
S/X = sp s
where sp = I/(I + Z), alternatively the normal growth path can be
written as
gw = sp s/vn
Note that since I+Z are profits, I/((I+Z)) is the share of profits that
capitalists invest. So in a normal growth path with an higher gz,
capitalist will invest a higher proportion of their profits.
(Note that with Z = 0, gw = s/vn, back to Harrod)
A higher gz, given s, implies a higher sp = I/(I + Z), that is that in the
new normal path a larger share of profits is invested. The idea is
again that a higher (compared to a lower ) for a given Z, implies
higher current I, Xn and level of profits.
A stylised fact of growth
• Observe that a positive relation between gw and S/X* = I/X* is a
stylised fact of economic growth, a widely (although not
unanimously) recognised fact. The causality, whether from output to
investment, as in the accelerator-based theories, or from investment
to output as in other theories (included the neoclassical) is also, of
course, matter of controversy.
• [The lack of this association in theory was a problem also for Solow,
see my paper on EGT]
• The association between gw and I/K might suggest that higher
growth requires a fall in consumption, re-proposing the
Samuelsonian choice between butter and guns. This is not so. The
larger output accommodates larger Z, C and I.
• Indeed, a higher gz is associated to higher S/Xn = I/Xn since it
generates a higher level of normal output capacity - as it must be in
a demand-led growth model  by comparison, in the CE model,
saving adjusts to investment through variation of distribution given
normal output.
Understanding Serrano’s gw (IV)
•
•
•
•
•
•
•
•
•
•
•
•
Suppose Z = 100, s = 0.5, vn = 2, and gz = 0.05.
Xn = 250 , P = Z + I =125, W = C = 125,
I = vnXngz = 2*250*0.05 = 25
gz = (s – Z/Xn)/vn = (0.5 – 100/250)/2 = 0.1/2 = 0.05
S/Xn = 0.1
sp = 0.2.
If gz = 0.02.
Xn = 217
P = Z + I =108.5, W = C = 108.5.
gz = (s – Z/Xn)/vn = (0.5 – 100/217)/2 = 0.04/2 = 0.02
S/Xn = 0.04
sp = 0.08.
When the expected rate of growth of AD rises, I rises, and the share
of profits which is invested sp rises or, which is the same, the average
propensity to save rises.
S, I
sXn
I1
S/X
I
0
0
Z
X
Comparison with the NK wage-led growth: growth and level
effects of a rise of real wages
• In the SM framework, an increase in real wages, and the
consequent lower profit share and marginal propensity to save, have
a positive level effects, but not the growth effects alleged, with
unconvincing arguments, by the NK model.
• The lower marginal propensity to save (1 – wl) will increase the
value of the SM in equation and thus the level of induced
consumption investment leading to a higher long-period level of
productive capacity. There might therefore be a temporary faster
growth, but once capacity has adjusted to the new higher level of
effective demand entailed by the stronger SM, the economy will
return to the former normal growth rate determined by the growth
rate of autonomous expenditure
• As said, being an induced component of income, real wages cannot
lead growth. However, during the transition they affect growth, and a
slow decline in the wage share, as it happened in the last decades,
would have serious negative growth effects.
Summing up: Warranted rates compared
Harrod: g w  s / vr : ‘strict uniqueness’ and instability. Economic policy may stimulate growth
by increasing s and keep instability at bay through economic planning.
CE: g w    rnsc : changes in r provide flexibility and stability if ‘animal spirits’, the
unexplained origin of growth, change. No clear role for economic policies (but support to
cooperative capitalism).
NK: g w   
s c
s
or g w    c where v nn is the ‘new normal’ capital coefficient: a
vn u a
vnn
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.
SM: g w  g z 
S / Xn
: the endogeneity of S/X provides flexibility with respect to changes of
vn
g z ; the autonomous, non capacity-creating component of aggregate demand explain economic
growth; economic policy, by acting on them may stimulate growth.
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Advancements by Serrano and open questions:
existence and stability of the SM normal growth path
• We have now the existence of a variety of normal paths that depend
on gz and that are not distinguished by a different normal distribution
(as in the CE) or by different un (as in the NK models)
• Give the real wage w, rn, vn and therefore , given also s, there are
infinite gw depending on gz (there was just one in Harrod)
• Up to now we have assumed that I is decided on the basis of
expected ED ge with ge = gz. We must now see what happen if gz
changes
• An open question concerns the transition between a normal path to
another, the stability issue: does ge adjusts to the new gz (or
perhaps we meet the Harrodian instability again?).
• When gz rises, ua > un, so entrepreneurs not only invest to deal with
the higher expected g, but also to restore un. Does the process
“overshoots” in the sense that investment determines a self-fulfilling
explosive dynamics?
Freitas and Serrano put forward a stability argument that
I will verbally summarise here.
Suppose that, moving from a fully-adjusted position g z rises. The actual growth rate g a of
aggregate demand and output also goes up and, as a consequence, induced consumption and
investment will also grow. The degree of capacity utilisation becomes higher than normal. The rise
in the induced components generates, in turn, a further augment of g a , a further climb in the
induced components and so on and so forth. The fact, however, that g a is anchored to g z means
that g k > g a > g z (where gk is rate of growth of the capital stock). Therefore, in spite of the fact that
the attempt by firms to adjust the capital stock is an additional stimulus to aggregate demand, the
capital stock and capacity are rising more rapidly than aggregate demand and output, so that
capacity utilisation ua is falling and tending to normality. The fact that ua tends to normality means
that the escalation of g k is slowing down. This implies that also the rise of g a is slowing down,
and that g k tends to g a , that in turn tends to g z
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Comparison with Harrod: we have an attractor now
In a normal position we have: g k  g w  g a . Suppose then that in a Harrodian context g a  g w .
This means that g k  g a  g w . But this leads to g a'  g a  g w , the well known Harrodian
instability result. In the SM context productive capacity benefits from the positive effects of a
higher g k in adjusting the capital stock to the higher g a . The fact that the latter rate is anchored to
g z limits the effects of the higher g k on g a . In a nutshell, in the SM context the effects of
investment on the supply side are faster than those on the demand side. In Harrod, before that g k
has time enough to affect capacity, it spurs g a , since g k is the exclusive determinant of the latter
(given sc). In this case the effects of investment on the demand side are faster than those on the
supply side generating instability.
Synthesis and necessary condition
• In synthesis, while in Harrod investment is both the engine both of
demand and of the adjustment of capacity, and the two roles may
compound spiralling instability (unless capitalists invest according to
gw = s/vn), in the SM approach aggregate demand is anchored to gz,
a variable that it is not affected by the adjustment process. Therefore
this adjustment does not create instability.
• F&S argue that a sufficient condition for stability is that the reaction
of investment must not be ‘too strong’. In intuitive terms, if gk reacts
too strongly to the fall in gz and gx, then the fall in gk would pull
(drag) gx with it in its plunge, and more and more far away from the
anchor gz. Using a metaphors, the storm on investment must not be
so strong that the chain that links aggregate demand to autonomous
demand breaks.
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Summing up
• Since Harrod’s contribution, followers of Keynes and Kalecki have
taken investment as the independent variable and neglected
“external markets”. This has been the source of analytical and
substantial troubles.
• Post-keynesian authors have overcome Harrod’s troubles by giving
up exogenous distribution; neo-Kaleckian models by giving up the
concept of long-run full (normal) capacity utilisation, while coreSraffians have given up the formulation of an analytical model of
accumulation.
• On the opposite, the supermultiplier approach combines (Eatwell’s
and) Kalecki’s suggestions by anchoring long-term expectations to
the growth rate of ‘external markets’ or non capacity-creating
autonomous components of aggregate demand. Thus, it has been
able to provide a formal model of demand-led growth with full
capacity utilisation.
• This solves the puzzles that gripped the Harrodian, neo-Kaleckian
and the FSP literature, and by providing a theory more suitable to
the analysis of the real economy where, as it is widely
acknowledged in practice, the autonomous components of demand
are the determinants of long-run growth. In the final part of the
presentation we point out that this model of capitalist growth might
contains the germs of its crisis.
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The instability of capitalism
• We have rather moved from one basic contradiction of capitalism,
that 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 purchasing power creation, and we may find here an
important field of convergence with the literature on ‘endogenous
money’. Purchasing power creation finances the external markets
that absorb the capitalists’ surplus and return to the capitalists’
hands as profits. Capitalists thus become creditors of those
‘markets’. We may find here a main source of instability in the
building up of unsustainable imbalances between core-capitalism
and the external markets in what sounds, after all, a debt-driven
model of capitalism both the US and the Eurozone have played with
(Cesaratto and Stirati 2011), perhaps the only game in town for
market economies. In this regard, convergences can be found with
the emphasis of the ‘Stock-Flow consistent model’ on the building
up of the mentioned imbalances (Zezza 2009) and with the
emphasis laid by Minskian scholars (e.g. Wray 2011) on the ensuing
financial fragility of capitalism.
Limits of steady state analysis and the instability of
capitalism
• This also shows the limits of steady state analysis (Garegnani’s
scepticism is not unjustified from this point of view).
• SM analysis is useful to investigate certain phases of growth (and
decline), but it is not meant to entail that capitalism evolves
according to some natural secular trend (as neoclassical economists
sometimes maintain).
• Inequality of income distribution and the fact that, to compensate
this, demand from external markets is linked to purchasing power
creation and debt creates an inherent instability of capitalism and
cycles (that, however, are not around a natural trend).
• The idea of a natural trend is perhaps associated to that of a natural
and exogenous trend of potential output (given by population
growth, institutions and habits, technical change). This is not the
view of Modern Classical Theory that regard all these factors
endogenous to the historical vicissitudes of different periods and
regimes of accumulation.
Y
1
Z
1  c(1  t )  d  m