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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

**Next message:**Allin Cottrell: "[OPE-L:3158] Marx's commodity"**Previous message:**Duncan K. Foley: "[OPE-L:3156] Re: Re: RE: RE: Simple Commodity Production"**In reply to:**Paul Zarembka: "[OPE-L:2973] Re: Re: Need 1 and Luxemburg's *Accumulation of Capital*"**Next in thread:**Duncan K. Foley: "[OPE-L:3160] Re: Production for Production's Sake (was Need 1 and Luxemburg's *Accumulation of Capital*)"**Reply:**Duncan K. Foley: "[OPE-L:3160] Re: Production for Production's Sake (was Need 1 and Luxemburg's *Accumulation of Capital*)"**Reply:**Paul Zarembka: "[OPE-L:3287] Re: Production for Production's Sake (was Need 1 and Luxemburg's *Accumulation of Capital*)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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