Lecture Notes: Maturity and Stagnation
Josef
Steindl
AC14446155
LECTURE NOTES: MATURITY AND STAGNATION
J^^Sir Roy^ Harrods theory is a good starting point for an explanation
of maturity. aigebra
In the following his XKMXjf is a tiny bit complicated by introducing
the concepts of capacity and NKX utilisation.
* . V
We define: Y output volume (i.e. its value in constant prices)
K capacity output ( as above)
2 u= Y /K degree pf utilisation
^ v= I/A K marginal capital coefficient ^<zZ-cofr&t*
Writing each variable with a subscript t we make them all depend on time.
We £btain
+ K*Aut (-,)
XK%
k Kt = (1/Ut (A ut/ut ) K| (£)
It = v^K|
it = fv/ut )^Xf " V(A ut/ut^ Kt
It = st = sY^
T^jh propensity to save s and the capital coefficient v are assu med
to be constants, dividing the last *wo equations we obtain
(v/s ut )(A^t) = 1 + (v/s)^ut/ ut ^
A Yt/ ^t =(f/v) ut + A Vut (4)
It follows that if the actual growth rate (left side)
is smaller than the warranted growth rate^s/v^u^. at a given rate of
utilisation - say, at the normal or desired rate - than the rate of
utilisation will hatre to decline. Harrod deals with the case where
the rate of growth cannot surpass a certain level for lack of manpower
-the so-called natural rate of growth - and where consequently
and unemployment
the system is driven into dBpression^because the low rate of
utilisation will discourage private investment.
This is a description of maturity even though this term
is not used by Harrod .
Harrod no doubt was strongly influenced by the experience of
the nineteen thirties. His case of a high warranted rate of
growth exceeding the natural rate might be interpreted as follows
( the responsibility for this explanation feeing mine):
Our system is still adapted to the high rates of growth which
obtained in earlier stafees of capitalism in so far as its
saving propensities are high in relation to its requiremunts of
capital as determined by(_demographig and technical conditions.
A high saving propensity ,however, means a high share of profits
in the national income . Thus the implication is that the
distribution is adapted to the high rates of growth *fc±sc±HXgH
characteristic early capitalism, but ill-suited to a modern
- a mature - economy.
While Harrod assumed a very high degree of rigidity of the
saving ratio, and therefore, in my view implicitly also of the
distribution of income, the ppposite is assumed by neo-classical
theory, but also by the so-called Cambridge theory of long run
income distribution as represented by Kaldor. My own theory is
in the middle of these extremes: I assumed ^possibility of
adaptation.in principle^of the distribution to the requirements of
growth, but I realised that its practical importance in a modern
ecomomy dominated by oligopolies is limited, and therefore
there is a rigidity of distribution, though not absolute, still
sufficiently great to bring about the same result as in Harrods case:
A tendency to long run unemployment which persists even if it is
overlaid by bompensating factors like armaments and other public
expenditure financed by taxes on profits.
or ft) '
Ma*- Ift) (
THE PROFIT FUNCTION
111
to explain the interaction of distribution and a<Si£umula±ion
we need the profit function^which enables us to distinguish
between changes in the profit rate due to a change in utilisation
and changes in the profit rate taking place at constant utilisation .
The profit function is inspired by Kalecki, but in using it
I follow my own wa^s.
[the profit function plays a role similar to the production function
4 H 6 O i
iiTjclassical theory: It replaces it, in a sense.
Let us define
h direct labour iput in hours
hQ overhead labour in hours
w wage per hour
’ff price of output
T„ , , P profits K capital, both in
W wage and salary bill current prices -------£1_______—_-----
We adopt now the theory that the wage and salary bill
depends on output and on capacity; it is assumed that the capacity
dH±BrmiHSs of the equipment determines the amount of overhead labour.
W = hw Y* + hQw K*
P = IT Y* - W = Y*( IT -hw ) - hQw K* ( 6 )
We may now express the profits as a ration of income,
or as a ratio of capacity income, or as a ratio of capital, i.e.
as a profit rate:
xxxxxx mIxx
xxxxxxxxxxxxxxlxxxxxxxffxxxxxxxx-x-xx-xx
Q / .
rr ^
P
TTr*
p
K
(l - ~r)^
7r *
ax ow ^ *
^f*' ^
pr
i
j
As a short hand expression we can write for the last equation:
P - Au - B
T he neatness of this expression is of course due to the
drastic simplifications we have made:
1) Linearity of t|ie function
2) Overhead cost are assumed to he a constant ratio of
the capacity output (at prices of the basis year ).
3) We consider only price of output and wage, but do not
introduce rq.w materials, which according to Kalecki ought to have
an influence on the profit margins.
In fact, if the constants in the equation are constant
then the direct labour cost are a constant share of the price of
the output. From Kaleckis point of view this would bejtrue only
if the proportion of rqw material dnd direct wage cost were
constant, and if the mark up was constant too.
It appears that a change iin the mark-up
—
implies a proportionate change in the coefficient A of utilisation
in equation Oo). ( assuming either the proportionality of
raw material cost or that the mark-up is/calcultated on direct labour
alone).
ad 2) The assumption about overhead cost implies that there are
no economies or diseconomies of scale in overhead labour .
The last mentioned assumption particularly is probably quite
unrealistic. It is to be understood merely as a simplification.
In the general case we should habe a function f ( K* ) which
will presumably be non-decreasing. Changes taking\ place in this
function or in hQ in the course of time are a different matter:
they will be due to technical progress.
What can we do with the profit function?
In the short run, if profits haave to he adjusted upwards or
downwards becaus e there is a boom in or a slump in investment,
and the saving mainly comes out of profits, then the utilisation
will vary and all the other quantities will stay constant,
these other quantities being rather rigid in the short run.
In the long run we cannot take the constancy of these
factors for granted. First , they will chagge in the course of
technical ( h,hQ) and economic ( Tf ,w ) develppment. uecond,
they may haveeto change, if the utilisation is not any more a
passive factor, and therefore the adjustment of savings and profits
can not rely on the fluctuations in utilisation any more.
This second caae is relevant for my theory: I assume
that firms are in principle concerned with establishing in the long
run, that is on the average over boom and slump, a normal or
desired degree of utilisation. This is done by varying the pressuce
of competition in such a way that either more or less hxekssx
capaaity is eliminated in a given year. The variation in competitive
pressure involves a ahift, or change in xhajsax the parameters,
of the profit function. Thus, in the long run, an increase in
profits and savings may be brought about by an increase of the
-fr* — hw
mark-up —2------------ rather than an increase in utilisation,
7T
and mutatis mutandis the same is true for a decrease in profits.
In this sense the long run distribution pattern will change aas
a result of a change in the speed of accumulation (rate of investment).
In connection with this we have now to eexplain a technical
point. If the increase in prdducktivity affeet^variable and
overhead cost in the same proportion ( if h and ho ^.s reduced in
the same porportion) then a corresponding increase in w/ir
may compensate it so that the parameters of equation (lo) rremain
unchanged. In the al&erhative case/of a non-ppoportionate movement
- for example, if the direct cost decrea:se and the overhead cost
are constant or even increase, a compensating movement of the
wage-price ratiowill not restore the original values of the
parameters: the shape of the function will not he the same as
before, and the amount of compensating movement rquired to keep
the rate of profit unchanged will depend on the existing degree of
utilisation.
A decline in direct cost will increase the slope of the profit
function; an increase of overhead cost willshift it downwards.
^learly the balance of the two forcggg wilj^ege^d on the
utilisation: at a low utilisation j will be decreased, at a high
one it will Ibe increased. w. ,, „„„ +
Wfljoxi const£int cost
Again, a change in the wage-price relatipn^will chagge the
shape of the profit function ; a relative decrease of wages for example
/ynA/i/k - ujo
will increase the profmar^g-i-n- the slope- and at the same time
shift the curve upward; the new jHapfx profit will be superior
at any utilisation, but the eaact amount will depend on
the utilisation.
Since in my theory there is always talk about the balance of
the two forces, cost reductions through technical progress and
wage-price ratio increases through cmmptition, we must
refer to a certain degree of utilisation in order to state
unambigously what the balance is. It is natural to choose the
planned or desired degree of utilisation for the purpose.
( It is true that the desired utilisation may itself change in the
process, but then we have the problem of ind/ces with different
bases which hah have to be linked.).
Graph: iechnical innovation ledding to decrease in marginal cost and
increase in overhead cost, compensation by an increase in wage-profit
ratio.