Download On the Dynamics of Profit – and Wage

THE DYNAMICS OF DIFFERENT REGIMES OF DEMAND-LED EXPANSION.
by
Amit Bhaduri
Professor, Department of Economics,
University of Pavia
27100 Pavia, Italy
Any redistribution of income between profits and wages would have contradictory
effects in terms of aggregate demand, so long as the propensities to consume are
different for the two classes. For instance, the lowering of the real wage rate would tend
to depress total consumption expenditure by redistributing income against the wage
earners with a higher propensity to consume. At the same time, it might also encourage
investment by increasing the margin of profit per unit of sale. Depending on which
effect dominates quantitatively, two alternative regimes or paths both led by demand
emerge: the consumption- or wage-led path which has also been called ‘stagnationist’
,and the investment- or profit-led path called ‘exhilarationist’ (Bhaduri and Marglin,
1990; Marglin and Bhaduri, 1990).
The essential formalism is simple. With full capacity (potential) output normalised at
unity, the saving of the economy is written as,
(1) S= s.h.z , where is the saving propensity out of profit, and all wage is assumed to be
( ) = share of profit in output; and z
consumed for expositional simplicity; h = P Y


*
=  Y *  = degree of capacity utilization, with Y = 1 , i.e. the normalized level of full
Y


capacity output, 1≥ z , h≥ 0.
We assume investment depends positively on both capacity utilization (z) and
profit margin (m) or profit share (h) are by definition positively related as, h = m/(1+m).
Assuming for expositional simplicity, static expectation, the investment function is
written as
(2) I = I( z, h ) , Iz. >0, Ih >0.
From (1) and (2), the slope of the locus of saving – investment equality, the ISlocus, is derived through total differentiation as,
(3)
dz /dh = (Ih -sz) / (sh-Iz )
The positive slope of (3) indicates that a higher profit share (h) results in higher
capacity utilization (z), placing the economy in the exhilarationist regime. In this case
the stimulating effect of the higher profit share on investment expenditure outweighs its
depressing effect on consumption expenditure. When the slope (3) is negative, the
economy is said to be in the stagnationist regime the opposite reason. However, the two
regimes have normally been distinguished by assuming as valid the stability condition
of the one-variable income adjustment process through the Keynesian multiplier
mechanism. This requires saving to be more responsive than investment to changes in
income, making the denominator of the right hand side of expression (3) positive.
(4) Thus, assuming (sh –Iz )> 0,
1
(5) (Ih-sh)> 0, implies that investment is more responsive than saving to profit share,
setting the economy on an profit-led exhilarationist path;
if, on the other hand,
(6) (Ih –sh)< 0, the economy is on a wage led stagnationist path for the opposite reason.
However, this analysis remains valid only so long as the distribution of income (h)
is treated as an exogenous variable. In effect, this makes the underlying dynamical
system correspond to the usual single variable income adjustment process of Keynesian
theory with income distribution given, but capacity utilization (z) adjusting to excess
demand or supply in the product market. With capacity utilization (z) as the only
endogenous variable in the system, the dynamic adjustment equation, in view of (1) and
(2) becomes,
(7) dz /dt = α [ I( h,z) -shz ] , where α>0 is some arbitrary positive of adjustment.
However, the above argument could be reversed by
making income distribution (h) the endogenous variable adjusting to excess demand or
supply in the product market, while the degree of capacity utilization is assumed
exogenously fixed, say at the full employment or full capacity level. In this case an
excess of demand in the product market, would raise the price level; and, if the money
wage rate fails to keep pace in percentage terms, the real wage rate would fall, the
margin and share of profit would rise. This would tend to close the gap between
investment and saving at the exogenously given full employment or full capacity level
of output. This theory of distribution, sketched originally by Keynes (1930; see also
1936,p.vii), was developed later as the Keynesian theory of distribution (Kaldor, 1956;
Pasinetti, 1962; Robinson, 1962, Marglin, 1984). The theory presumes not only full
employment, but also ‘forced saving’ by the workers even in a situation of full
employment. On the other hand, if this latter assumption is abandoned, the possibility of
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a ’profit squeeze, rather than ‘forced saving’ by the workers, has to accommodated in
the analysis. In this case the money wage rate would rise faster than the price level, and
the share of profit would fall rather than rise in response to excess demand in the
product market. Thus, a more general version of the dynamic adjustment equation for
the ‘Keynesian’ theory of distribution might be written as,
(8) dh/dt= β [ I( h,z) -shz ] , where the speed of adjustment β >0 in case of ‘forced
saving’ by the workers, but β <0 in case of ‘profit squeeze’.
Note the central difference between adjustment equations (7) and (8).In the former, the
profit margin as well as profit share are given which makes the real wage inflexible so
that the entire burden of adjustment falls on capacity utilization (Kalecki, 1971). In the
latter case, the margin is flexible but capacity utilization is fixed by assumption, making
adjustment work exclusively through the real wage rate, i.e. income distribution.
Consequently in a more general case in which neither the profit margin and share (h)
nor the degree of capacity utilization(z) is treated as exogenous , and both
are
endogenous variables reacting simultaneously to an excess demand or supply in the
product market , we have a coupled dynamical system consisting of (7) and (8). The
product market clearing, equilibrium path of the system depicted by the IS-curve with
its slope given in (3) still remains the same. However, the stability property of this two
variable dynamical system need no longer correspond to the one- variable stability
condition (4) of the usual Keynesian system. Moreover, since both z and h are assumed
to be endogenous, a positive relation between z and h placing the economy on the
profit- led exhilarationist path must hold, if both α and β are positive. This means that
‘forced saving’ by the workers necessarily implies that the economy is necessarily on
an exhilarationist path, when both z and h are endogenous. Obversely, with α>0, but
β<0 in the ‘profit squeeze’ case the economy is necessarily placed on a wage-led
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stagnationist path. This can seen easily from dividing (7) by (8) to obtain the integral
curve determining the sign of the slope of the IS locus as,
(9) dz /dh= α / β, where α >0 but β can be positive or negative. .
The stability of the dynamical system (7) and (8) may be examined by
considering the function,
(10)
V (t ) =
1
[ I ( h, z ) − shz ]2
2
The function V is a Liapunov function with all the desirable properties for stability in
the large, i.e. positive definiteness and unboundness as (I-S) tends to infinity, provided
also dV/dt <0 (e.g. LaSalle and Lefschetz, 1961; Minorsky, 1962; Gondolfo,1995), .
This last condition can be checked by differentiating (1) and (2) with respect to time,
and substituting from (7) and (8) to obtain,
(11)
dV
2
= [ I − S ]  β ( I h − sz ) − α ( sh − I z )  < 0
dt
Therefore, global stability requires,
(12)
β (I h − s p z ) < α (s p h − I z ) .
Using (3) and (12), a complete classification of the various cases of profit-led or
exhilarationist as well as wage-led or stagnationist sub-regimes according to their
stability property becomes possible. Note however that this classification is done in two
successive steps to highlight the difference between a single endogenous variable
stability analysis given by conditions (3) to (6), and the stability analysis in the case of
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the dynamical system (7) to (9) when both the variables, h and z are
endogenous.Classification (α > 0; β ⊕ 0)
Sign of
Cases
dz / dh
from (3)
A.1
(s ph − I z ) > 0
Positive
Nature of
Regime
Profit-led
Stability
Unambiguously
larger is α
Negative
Wage-led
β
Unambiguously
from
(9),since z and h
are endogenous
Stability
stable, but not ambiguous;
possible
and
(I h − s p z ) < 0
B.1
for β < 0
more likely the possible
(I h − s p z ) > 0
(s p h − I z ) > 0
for β > 0
ambiguous, and stable, but not
and
A.2
Stability Property from (11)
from more likely to
(9),since z and h be stable larger
Negative
Wage-led
are endogenous.
α
Unambiguously
Stability
β
(s p h − I z ) < 0
unstable, but not ambiguous.
and
possible
(I h − s p z ) > 0
(9),since z and h likely, the larger
B.2
Positive
Profit-led
from Stability
less
are endogenous.
α
Stability
Unambiguously
β
(s p h − I z ) < 0
ambiguous, and unstable, but not
and
less likely the possible
(I h − s p z ) < 0
larger is (α β ). .
from
(9),since z and
hare
endogenous.
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In the case of the general dynamical system with both variables endogenous, it
emerges as a general result that the stability of the neither the profit-led nor the wageled path of expansion is unambiguously stable. The stability depends critically on the
relative magnitudes of the speeds of adjustment, i.e. the absolute value of the ratio
(α / β). Thus, when β>o i.e. the case of ‘forced saving’ by the workers, only the profitled path is relevant, and the usual one variable Keynesian stability condition (4) may or
may not matter in determining the stability of this profit- led regime depending on the
ratio of the relative speeds of adjustment. The higher (lower) is the ratio, implying
faster (slower) speed of adjustment of capacity utilization relative to that of income
distribution, the more (less) likely is the stability of the profit –led regime, depending
on whether the sensitivity of saving is more (less) than that of investment to changes in
income (i.e.condition 4 satisfied or not). In a similar manner, in the case of ‘profit
squeeze’ i.e.β < 0, leading to wage- led expansion, again the Keynesian stability
condition may or not be relevant depending on the (absolute) value of the relative
speeds of adjustment. It follows the Keynesian stability condition is neither necessary
nor sufficient without considering simultaneously the relative speeds of adjustment of
capacity utilization and, of income distribution.
The critical role played by the relative speeds of adjustment points towards an
interesting possibility of extending this analysis. It is often argued that Keynesian
analysis neglects the ‘supply side’. One way of reckoning with the supply side would be
to incorporate into the analysis the fact that the speed of adjustment of capacity
utilization tends to decrease as the degree of utilization increases, and various
bottlenecks begin to appear on the supply side. This means α can be treated as a
decreasing function of z to incorporate partly considerations on the supply side. This
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would lead non-linearities which we have avoided dealing with in this paper, and must
remain a matter of future research.
AMIT BHADURI
Department of Economics
University of Pavia, Italy
e-mail [email protected]
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References
Bhaduri, A. and Marglin, S. 1990. ‘Unemployment and the real wage: the economic
basis for eontesting political ideologies,’ Cambridge Journal of Economics,
14: 375-93.
Kaldor, N. 1956. ‘Alternative theories of distribution,’ Review of Economic Studies, 23:
83-100.
Kalecki, M. 1971. Selected Essays in the Dynamics of the Capitalist Economy,
Cambridge, Cambridge University Press.
Keynes, J. M. 1936. The General Theory of Employment, Interest and Money, London,
Macmillan.
Marglin, S. A. 1984 Growth, Distribution and Prices, Cambridge, Mass; Harvard
University Press.
Pasinetti, L. L. 1962. ‘The rate of profit and income distribution in relation to the rate
of economic growth’, Review of Economic Studies, 29: 267-79.
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The “Profit Squeeze” Case (Appendix)
[
]
[
z& = α I (h, z ) − s p hz ; h& = − µ I (h, z ) − s p hz
V (t ) =
1
(I − S )2
2
dV
dt
= (I − S ) I h h& + I z z& − s p zh& − s p hz&
[
]
[
]
= (I − S ) (I h − s p z )h& + (I z − s p h )z&
]
= (I − S ){(I h − s p z )[− µ (I − S )] + (I z − s p h )α (I − S )}
[
]
= (I − S ) − µ (I h − s p z ) + α (I z − s p h ) < 0
2
For
dV
<0 ⇒
dt
− µ (I h − s p z ) + α (I z − s p h ) < 0
− µ (I h − s p z ) < −α (I z − s p h )
or µ (s p z − I h ) < α (s p h − I z )
(11A) i.e. instead of (11) α (s p h − I z ) > µ (s p z − I h ) ; β = µ > 0 .
Case
A.1 αH.S.>0; R.H.S.<0 ∴unambiguously stable
α 
A.2 αH.S.>0; R.H.S.>0 ∴stability ambiguous; larger   more likely stability
µ
α 
B.1 αH.S.<0; R.H.S.<0 ∴stability ambiguous, larger   stability less likely
µ
B.2 αH.S.<0; R.H.S.>0 ∴unambiguously unstable
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