The supermultiplier model
Slides 2, 3, 5, 8, 14,15
Michal Kalecki’s masterpiece paper on Tugan-Baranowski and Rosa Luxemburg (1967)
• Tugan-Baranowski shows that in principle a capitalist system can grow in equilibrium as far as capitalists employ all their savings to build new capital goods.
• the aim of capitalist production is not the satisfaction of human needs
• “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”
• Rosa Luxemburg correctly perceived the difficulty of capitalists to absorb the social surplus through their own consumption and
investment. Therefore the necessity of “external markets”, external to the capitalist income circuit, to absorb the surplus production. Typically these markets are funded by the capitalist system itself through the financial system.
• Kalecki includes in these markets exports to the underdeveloped
countries and government spending. We may usefully add consumers’
credit.
• We shall later call these external markets ‘non- capacity creating autonomous components of aggregate demand’.
From Kalecki to Serrano
• There are some ambiguities in Kalecki since he regards as external markets net exports and government deficit spending. The balanced budget multiplier shows that exports and gvmt spending are
expansionary even if fully compensated by, respectively, imports and taxes.
• Be this as it may, Kalecki suggests that to get out from Say-Tugan- Harrod’s knife edge problem, external markets must be taken into account as the ultimate explanation of investment, that cannot be, so to speak, a self-explanatory variable.
• Serrano approaches this question noting the surprising neglect of the autonomous/non-capacity creating components of AD (Z) in the post-Keynesian (and post-Kaleckian) literature.
• 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.
The way out proposed by Serrano consists of three steps: (i) consider investment as fully induced:
n e
ng X
v
I (1)
where X is the normal level of output and n g is the expected rate of growth of effective demand; e (ii) take into account the autonomous/non-capacity creating components of AD (Z); and (iii) anchor the formation of long-term demand expectations (ge) to the growth rate ( g ) of those components z (the idea is that this anchor permits a progressive adjustment of expectations to g ). z
Krugman believes in the accelerator but not
in textbooks
In his blog Krugman presents the figure in the right, and in another post he says that «it is a dirty little secret in
Economics that the interest rate does not influence non- residential investment but only housing (residential
investment).»
http://krugman.blogs.nytimes.com/2011/12/03/explaining-business-investment/
Serrano assumes, along the models reviewed above, that workers do not save while capitalists save all their earnings, so the marginal propensities to save of capitalists is sc = 1. Given that capitalists have a marginal propensity to consume equal to 1, the economy’s marginal propensity to consume is equal to the wage-bill share W on income wl
X wN X
W
n n
, where w is the given real wage, N is the number of workers and l is the labour input coefficient (quantity of labour for unit of output) l = N/Xn.
Income determination
AD = C + I + Z (where AD is aggregate demand) C = wlXn
I = vngeXn Z = Z
Xn = AD (that is output is equal to aggregate demand)
ge = gz (ge is expected aggregate demand growth, we assume perfect foresight, that is where gz is the rate of growth of autonomous demand).
In this model Z is autonomous spending of the capitalists (workers do not have access to consumption credit).
From these equations we get: AD = Z + vngeX + wlXn and, following the principle of effective demand, Xn = AD:
g Z v X wl
z n
n
) 1
(
1 (2)
The (multiplier and the) SM in most traditional terms
) I
) ( 1
( 1
1 C G E
m t
Y
Dc
a
) ) (
1 ( 1
1 C G E
m g
v t
Y c
z an
Limits of demand-led growth
Equation (A) provides economically meaningful solutions if:
1
vngz
wl [3]
and
Z > 0 [4]
if wlvngz 1, this means that the overall marginal propensity to spend is equal to one and this ‘is exactly what we mean by Say's Law’ (Serrano 1995a, p. 37). We have argued above that an Harrodian gw might indeed prevail if capitalists behaved according to Say’s Law. Of course, if the overall marginal propensity to spend is lower than one, the level of the autonomous components must be positive, as set by equation (4).
Note that from the investment function (1) we may obtain: I / Xn vnge. 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 of investment over the present normal output: ‘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 capacity-generating investment.’ (Serrano 1995a:
32; 37and ff; 1995b: 81-4).
A higher I / Xn implies a higher S / Xn.
Let us therefore determine S /Xn.
Recall that that s = scP/Xn + swW/Xn that, given that sw = 0 and sc = 1, simplifies in:
sXn = P.
Note next that since all savings come from profits, then:
S = P – Z
Recall that Z is autonomous spending which is “dissaving” (in practice capitalists spend Z at the beginning of the period financed by banks, and return Z to the banks at the end of the period once received theory profits, so S = P - Z). So
S = sXn – Z [5]
and finally
S/Xn = s – Z/Xn [6]
This expression shows the relation between the average and the marginal propensity to save.
Observe that now S / Xn is “flexible”. If Z = 0, S / Xn = s. This implies that if Z = 0 there is a unique
Xn
I = s consistent, given vn, with a normal growth rate. This is the Harrodian gw = s/vn.
With Z > 0, the average Xn
S changes when Z/Xn changes. We shall now show that Xn
S , the average
propensity to save, and not the inflexible marginal propensity to save s, appears in the SM’s warranted rate of growth.
The SM’s warranted rate of growth
In line with previous models and using equations (1) and (5), we can write a three equations system:
Z sX
S n (5)
n e ng X v
I (1)
I
S (7)
Substituting equations (5) and (1) in (7) and assuming that ge gz we obtain:
n n n
z v
Z X sX
g , and finally
n n
z v
X Z
g s / (8)
which is the normal path that assures the dynamic saving-investment equilibrium. 1 Using equation (6), the normal path can also be written as:
n n
w v
X g S /
(9).
1 Equation (8) can be directly obtained from equation (2).
Considering equation (8), we observe that if g rise, given s, then Z/Xz n must fall. How can this happen? Consider that 1 = I/Xn + C/Xn + Z/Xn. We already observed that whenever g rises, z then I/Xn must rise too. Since the share of consumption on normal output C/Xn 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. The economic reason is that in any period along a normal growth path, for the same given level of Z, a (say) higher expected g z (compared to a lower g ) is associated to a higher level of normal output Xz n – not surprisingly since a higher g implies higher current investment - such that it generates a share of capacity savings S/ z Xn adequate to the higher level of investment required by the higher g .z
What said so far has to do with an existence question, but it still leaves open the question of
stability, that is what happen during the transition from one normal path to another: are we sure that the faster growth of investment and above-normal degree of capacity utilisation stimulated by a higher growth rate of autonomous demand gz does not go-out-of control in an Harrodian fashion?
Synthesis: comparing normal paths
Harrod: gw s/vn: ‘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).
CE: gw rsc: changes in r provide flexibility and stability whenever ‘animal spirits’, the unexplained origin of growth, change.
NK:
a n
c
w v u
g s
or
nn c
w v
g s
where v is the ‘new normal’ capital coefficient: a nn
flexible u provides the necessary cushion against the instability due to changes in ‘animal a spirits’, the unexplained origin of growth; no clear role for economic policies (but support to cooperative capitalism).
SM:
n n z
w v
X g S
g /
: the endogeneity of S/X provides flexibility with respect to changes of gz;
the autonomous, non capacity-creating components of AD explain economic growth; economic policy, by acting on them, may stimulate growth.
Applications of the SM
• I suggest 2:
• The American pre-GFC experience & German neo-mercantilism
• In both cases growth led by, respectively, autonomous consumption and exports led to unsustainable debt of households or foreign
countries.
• So the SM model should not just be seen as a growth model, but also as a premise to a theory of the crisis.
• In addition, the SM is naturally complemented by the theory of
endogenous money: autonomous demand must be financed by an autonomous creation of purchasing power. Banks can do it through consumers credit. They can also finance foreign markets (vendor finance).
• According to MMT governments spend before taxing or issuing
public debt. This is correct in principle. The institutional mechanisms are still to be firmly assessed.
• NK (Hein et c.) contortions to explain these facts.
