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This is a response to Paul Zarembka. I realize there are others to whom
I owe replies. I apologize for the delay. The usual end-of-semester
crunch came.
I have re-read a couple of times the sections of Paul's paper dealing
with the issue of definitions, as well as his posts about this, and I
still don't get what's at issue. I'll just note that Marx's usage
depends in part on context. In light of our discussion I happened to
note that he identifies "real accumulation" as "an expansion of
production" (middle of 2d para. of Ch. 21, Vol. II).
What interests me more is the supposed impossibility of "realizing" all
surplus-value in a closed, 2-class capitalist nation. "[S]urplus value
cannot be realized by sale either to workers or to capitalists, but only
if it is sold to such social organizations or strata whose own mode of
production is not capitalistic" (Luxemburg, _Accum. of Capital_, pp.
351-52, quoted in Paul's paper, section III). I want to approach this in
terms of the analytical and theoretical issues, rather than the history
of thought, because
(a) I do not understand the critique of Bauer (at one point I thought I
did, and thought Paul was right, but now I'm back to being confused),
(b) Bauer's introduction of technological change complicates matters and
distracts from the basic issue, and
(c) I think the Bauer-Grossmann scheme is ludicrous. It assumes
*constant* rates of increase in c and v even though values are *falling*,
which implies that demand for the material components of c and v grows at
an ever-accelerating rate and eventually outstrips supply. This excess
demand is in fact what leads to the "breakdown" of capitalism!
So I want to deal with the issue by assuming, as Marx did, that values
and techniques are unchanging. It is easy to generalize beyond this.
I will show that all of the surplus-value can be "realized" internally,
in a closed, 2-class capitalist nation. I will also substantiate
Dunayevskaya's argument that all surplus-value can be "realized" even
when growth is *unbalanced*, i.e., when the supply of means of production
(MP) continually grows faster than the supply of articles of consumption
(AC). In other words, Dept. I continually grows faster than Dept. II.
(If all surplus-value is to be "realized," supplies must match demands,
and so it is likewise necessary that I show that *demand* for MP can
continually grow faster than *demand* for AC. I will do so.)
My argument will also show that an expansion of credit is *not* necessary
for expanded reproduction to occur. (Many authors, especially
post-Keynesians, have claimed incorrectly that it is necessary.) I will
assume that there is *no* credit.
The argument will also demonstrate that Department I can continually grow
faster than Department II even if -- as I will assume -- the ratio of
means of production to living labor (and the ratio of means of production
to real wages) is not changing, neither in the aggregate nor in either
department.
I'll examine a particular numerical example, although it is possible to
generalize the results much further.
I realize that there is another issue involved in the debate,
historically and currently, namely whether capitalists lack an
"inducement" (Joan Robinson) to invest in the manner depicted below.
I'll have to tackle that in another post. The following shows that they
*could* invest in this manner and that, if they did so, this would solve
the alleged "realization problem." Before dealing with behavioral
issues, I think it is helpful at least to reach agreement on the
analytical ones.
Assumptions:
============
Annual cycle of production in both depts.
Dept. I produces one good; it serves as the sole MP for both depts.
The MP are fully used-up in production each year.
Each dept. uses 1/2 unit of the MP per unit of output.
Each dept. also requires 1/2 unit of living labor per unit of output.
Hence the unit values, in terms of labor-time, are P1 = P2 = 1.
If we further assume that 1 unit of living labor = $1, then all of the
numbers will refer equally to physical units, labor-time, and dollars.
Dept. 2 produces one good; it serves as the AC for the workers and the
moneybags.
Each worker, in both depts., receives an annual wage that enables him/her
to acquire 1/2 unit of the AC.
Each worker performs 1 unit of living labor per year.
Finally, supplies are "realized" immediately (no credit). Goods produced
at the end of year t-1, the supplies, are supplied immediately at the
start of year t, and are "realized" by means of demands at the start of
year t.
Demands
=======
Denoting the output of each dept. as Xj,
Dept. I's demand for MP at the start of year t is
DMP1[t] = (1/2)X1[t]
and Dept. II's demand for MP at the start of year t is
DMP2[t] = (1/2)X2[t].
Employment in Dept. I in year t is (1/2)X1[t], and the real wage rate is
(1/2), so the demand by Dept. I's workers for AC, at the start of year t,
is
DW1[t] = (1/2)(1/2)X1[t]
and analogously, the demand by Dept. II's workers for AC, at the start of
year t, is
DW2[t] = (1/2)(1/2)X2[t].
Any sales receipts from the outputs produced at the end of year t-1
(received at the end of year t-1 = start of year t) that are not used to
buy MP or pay wages are used to purchase AC for the moneybags'
unproductive consumption. Hence Dept. I's unproductive demand at the
start of year t is
DU1[t] = P1*X1[t-1] - P1*(1/2)X1[t] - P2*(1/2)(1/2)X1[t]
= X1[t-1] - (3/4)X1[t]
(since P1 = P2 =1)
and Dept. II's unproductive demand at the start of year t is
DU2[t] = P2*X2[t-1] - P1*(1/2)X2[t] - P2*(1/2)(1/2)X2[t]
= X2[t-1] - (3/4)X2[t].
To sum up, total demand for the output Dept. I has produced at the end of
year t-1 is
DMP[t] = DMP1[t] + DMP2[t] = (1/2)X1[t] + (1/2)X2[t];
and total demand for the output Dept. II has produced at the end of year
t-1 is
DAC[t] = DW1[t] + DW2[t] + DU1[t] + DU2[t]
= (1/2)(1/2)X1[t] + (1/2)(1/2)X2[t] + {X1[t-1] - (3/4)X1[t]} +
{X2[t-1] - (3/4)X2[t]}
= {X1[t-1] - (1/2)X1[t]} + {X2[t-1] - (1/2)X2[t]}.
Supplies
========
The supplies at the start of a year are simply the outputs produced at
the end of the preceding year. The supply of MP at the start of year t
is
SMP[t] = X1[t-1]
and the supply of AC at the start of year t is
SAC[t] = X2[t-1].
Supply-demand balance
=====================
If all surplus-value is to be "realized," supplies and demands must be
equal. For Dept. I, this requires that
SMP[t] = DMP[t], i.e.
X1[t-1] = (1/2)X1[t] + (1/2)X2[t].
We must also have, for Dept. II,
SAC[t] = DAC[t], i.e.,
X2[t-1] = {X1[t-1] - (1/2)X1[t]} + {X2[t-1] - (1/2)X2[t]}
but this reduces to
X1[t-1] = (1/2)X1[t] + (1/2)X2[t],
the same condition as above.
Solution
========
The whole problem of "realizing" all surplus-value in a closed, 2-class,
capitalist nation, without credit, while Department I continually grows
faster than Department II, thus reduces to the following question. Do
there exist time paths for X1 and X2 that:
(1) satisfy X1[t-1] = (1/2)X1[t] + (1/2)X2[t], while also
(2) ensuring that X1 continually grows faster than X2, i.e., that X1/X2
rises continually?
In fact there exist an unlimited number of such sets of paths, but I'll
just present one. Let's assume the initial set-up satisfies simple
reproduction: X1[t-1] = X1[t]. Then, using condition (1), we must
initially have X1 = X2. Starting the years at t = 0, we then have the
initial condition X1[0] = X2[0].
Now let X1 grow as follows:
X1[t] = (11/110)X1[0]*(1.1)^t + (99/110)X1[0]*(.99)^t
and let X2 grow as follows:
X2[t] = (9/110)X2[0]*(1.1)^t + (101/110)X2[0]*(.99)^t .
These paths satisfy condition (1). They also satisfy condition (2);
X1/X2 increases continually over time. This ratio starts at X1[0]/X2[0]
= 1 and gradually approaches X1/X2 = 11/9 > 1 as time proceeds.
The growth rate of the economy, which was initially 0%, eventually
approaches 10% (= 1.1 - 1). In the *limit*, both departments grow at 10%
p.a. But Dept. I's growth rate in any *actual* year always exceeds Dept.
II's.
Andrew Kliman
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