**Next message:**Paul Zarembka: "[OPE-L:3288] Dunayevskaya on Luxemburg"**Previous message:**Paul Zarembka: "[OPE-L:3286] Re: Re: Two prefaces"**In reply to:**Andrew_Kliman: "[OPE-L:3157] Production for Production's Sake (was Need 1 and Luxemburg's *Accumulation of Capital*)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

[ show plain text ]

"Andrew_Kliman" <Andrew_Kliman@email.msn.com> said, on 05/12/00 in 3157:

*>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).
*

Thanks and noted.

*>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.
*

Good -- c/v constant as in all of Marx's schemes.

*>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.)
*

...

*>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.
*

Andrew's model follows below (for those who deleted it). He claims that

from an initial point of simple reproduction into the TRANSITION from a

steady-state growth path of 10%, Dept. I will grow faster than Dept. II,

seemingly to disprove Luxemburg and defend Marx (who holds c/v in each

sector constant).

An examination of Andrew's model reveals that capitalist consumption is a

residual after requirements means of production and requirements for

workers' survival. Therefore, when we MOVE from a 0 0rowth path to a 10%

growth path, the capitalist consumption takes a hit which means Dept. II

takes a hit. The hit persists until we reach the 10 0rowth path.

I believe this is the economics of what is going on and doesn't mean

anything for Luxemburg's case, one way or another, nor Dunayevskaya's, for

that matter. All that is happening is a change in the capitalist choice

of their proportions between accumulation (initially zero in the proffered

example) and their consumption. Put another way, Luxemburg (or I) can

concede this example.

I would also call attention to a similarity between both Andrew's model

and Bauer's. Both have hours of labor power continually increasing, and

thus both include "accumulation" under the definition I have proposed in:

"Accumulation of Capital, its Definition: A Century after Lenin and

Luxemburg": http://ourworld.compuserve.com/homepages/PZarembka/len-lux.htm

*>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.
*

OK, we'll be "on hold" on this issue.

Paul Z.

***********************************************************************

Paul Zarembka, supporting RESEARCH IN POLITICAL ECONOMY

******************** http://ourworld.compuserve.com/homepages/PZarembka

*>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.
*

**Next message:**Paul Zarembka: "[OPE-L:3288] Dunayevskaya on Luxemburg"**Previous message:**Paul Zarembka: "[OPE-L:3286] Re: Re: Two prefaces"**In reply to:**Andrew_Kliman: "[OPE-L:3157] Production for Production's Sake (was Need 1 and Luxemburg's *Accumulation of Capital*)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*
This archive was generated by hypermail 2b29
: Wed May 31 2000 - 00:00:11 EDT
*