[OPE-L:4190] RE: TSS transformation procedure

andrew klima (Andrew_Kliman@msn.com)
Wed, 12 Feb 1997 11:48:01 -0800 (PST)

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A reply to Jerry's ope-l 4187 and Allin's ope-l 41xcxc:

Jerry wrote: "What I find is 'odd' is that in Andrew's response to Allin's
#4180, he nowhere confronts what I read as the major point of Allin's post,
namely, that the Kliman-McGlone solution represents another 'iterative
approximation of the Bortkiewicz solution', that there is an 'arbitrary
variation in accumulation ratios across sectors', and that 'there is no
independent rationale for such differences [...] or in other words, they are

Actually, I did confront the point about equal rates of profit coexisting with
unequal rates of accumulation, in the passage you quoted. But what seems to
be bothering Jerry is the claim that we "cooked" the numbers and/or example.
Please don't be misled by the evil-sounding "cooked" and "arbitrary," Jerry,
or the important-sounding "no independent rationale for such differences."
The full quote from Allin is actually important: "There is no independent
rationale for such differences. THEY ARE SIMPLY MANDATED BY THE REQUIREMENT
THAT SIMPLE REPRODUCTION PROCEEDS -- or in other words, they are 'cooked'" (my

Yes, the differences in rates of accumulation are mandated by the
"requirement" that simple reproduction proceeds. That is precisely the case.
But who "requires" that the transformation preserve simple reproduction? Not
I. Not Ted. Not Eduardo. Not Marx. Who "requires" it is Bortkiewicz and
the whole simultaneist tradition, in the sense that they allege that Marx's
own account of the transformation is internally contradictory because it would
disrupt simple reproduction, or so they have wrongly claimed. So they have
"required" that a refutation show that *both* the transformation of values
into production prices and simple (or other balanced) reproduction can occur
when prices aren't stationary. And that's what we have shown.

Simple (or balanced) reproduction has absolutely nothing to do with the
transformation of values into production prices *per se*. It is an entirely
separate assumption that the simultaneists have imposed upon us, NOT in order
to show how the transformation itself can take place at nonstationary prices,
but to show that if transformation takes place at nonstationary prices, this
does not disrupt reproduction. (Actually, this is a reasonable requirement,
since rates of profit will not typically be equalized if supplies don't equal

Here is how Ted and I explained why we assumed simple reproduction:

"To illustrate this process [of 'input price transformation,' which is a
different matter from the transformation of values into prices of production],
some output-input relations must be assumed. For simplicity, we assume simple
reproduction ....

"We regard Marx's illustration of the value-price transformation as entirely
correct and complete, and modify it to account for simple reproduction ONLY to
defend it against the Bortkiewiczian critique. To defend it against the
charge of failing to transform input prices, another modification is also
made: we continue Marx's one period illustration into the next period.
Whereas the VALUE-PRICE transformation can be depicted in a single period, the
transformation of outputs into inputs, and thus the 'transformation' of OUTPUT
PRICES into INPUT PRICES, takes place between *one* period of production and
the *next* ("One System or Two," _Marx and Non-equilibrium Economics_, pp.
39-40, caps added).

So neither simple reproduction nor multiple periods is anything that *we*
"require." Marx's own one-period illustration is "entirely correct and
complete." Marx's simultaneist critics are the ones who have forced us to
introduce multiple periods in order to dispose of their idiotic charge that
"Marx failed to transform input prices" and their equally idiotic charge that
his account of the transformation would lead to a disruption of reproduction.

We have disposed of them. Everything the simultaneists now say implicitly
acknowledges this, because they drop the issue like a hot potato, act like it
never existed, the moment they see that we did refute these idiotic charges.
Why is this not acknowledged explicitly, unequivocally, and in print, none of
them will say. Why? Why? Why?

Instead, what we get are more and more stalling tactics. Another objection,
then another, then another. None of these objections are relevant, because
all of them are diversions from the original issue: can you have Marx's
transformation together with input price "transformation" and without
disrupting balanced reproduction?

Allin's latest charge seems to be that there's no a priori reason we should
have unequal rates of accumulation. That is true. But it is a complete
diversion from the original issues. We have refuted the original idiotic
charges, and one might expect that we would be answered with gratitude for
having dealt a blow to Marx's critics, or with gratitude for having advanced
knowledge by showing a prevalent myth to be false, or even with grudging but
forthright acknowledgments that we have demolished a much-beloved myth.

In any case, why do we have unequal rates of accumulation? Simply because, if
one assumes simple reproduction and if prices aren't stationary, then rates of
accumulation can't be equal (except by some fluke). But again, WE have no
need to assume simple reproduction. We have put forth some ILLUSTRATIONS of
Marx's transformation in that context in order to refute an idiotic charge,
that is all.

But --- and this is the crucial point --- we can illustrate Marx's
transformation with nonstationary prices under an INFINITE number of contexts.
Among them is the case in with rates of accumulation are equal. It is
possible to infer from Allin's charge that the TSS transformation is
incompatible with equal rates of accumulation, but he certainly doesn't prove
it and, if one reads carefully, one will see that Allin actually does not say
it is impossible. The *only* thing that would make it impossible is the
assumption that simple reproduction takes place, or something similar, and
there is absolutely NO reason why that needs to be assumed.

To show conclusively that it *IS* indeed possible, indeed VERY EASY, to
illustrate Marx's transformation (as interpreted by TSS) with nonstationary
prices even when one assumes that rates of accumulation are equal, I have
constructed the following illustration.

Simplifying assumptions
(a) 2 sectors
(b) 750f each sector's total price is re-invested each period (Allin's
"accumulation percent" = 0.75 in each sector)
(c) only the output of sector 1 serves as means of production; it is
circulating capital
(d) only the output of sector 2 is consumed by productive workers
(e) other persons consume some of both goods;
(f) these other persons all consume the two goods in the same proportions
(g) unchanging technology in both sectors
(h) fixed coefficients technologies
(i) purchases and sales made at production prices, except that initial prices
are given
(j) $1 = 1 labor-year
(k) the money wage per unit of living labor extracted is constant

None of these assumptions is *necessary*. Again, I'm using them only to show
that there can be a transformation of values into production prices (and thus
equalized profit per unit of capital advanced), even though prices are
changing AND even though the accumulation rates are equal (b). If I were to
relax (c), (d), (f), (g), (h), or (k), or any combination thereof, that would
only make it EASIER to satisfy the requirements of the demonstration, because
that would give me MORE degrees of freedom. It is in this sense that the
assumptions are simplifying ones only. They are not meant to be realistic ---
they are NOT, in other words, a "model" of the economy.. They are indeed
"arbitrary," but so is *any* other assumption, because a contrary assumption
is always possible. But SOME particular assumptions need to be made in order
to generate any numerical or algebraic illustration.

TECHNOLOGY: in each period, 1/3 of a unit of good 1 and 2/3 of a labor-year,
is required to produce 1 unit of good 1. In each period, 1/5 of a unit of
good 1 and 4/5 of a labor-year, is required to produce 1 unit of good 2.

INITIAL INPUT PRICES: the unit input prices of both goods at the beginning of
the first period (period 1) are both 1.

INITIAL OUTPUT LEVELS: in the first period, 30 units of good 1 and 50 units
of good 2 are produced.

WAGES: the money wage per living labor-year extracted is a constant $0.50.
By assumption (j), this $0.50 is equivalent to 1/2 of a labor-year. Hence the
rate of exploitation is a constant 100%.

The above four specifications, together with the set of simplifying
assumptions and the TSS interpretation of Marx's own correct and complete
account of the transformation of values into production prices, yields the
following value/price tableau of the first three periods. p is the unit input
price of the sector's product (equal to its output price of the temporally
prior period). m is capitalists' revenue, i.e., their sales revenue from the
temporally prior period minus what they spend for C and V this period. TV and
TP are total value and total price. PR is profit. Rv is the "value" rate of
profit, S/(C+V). Rp is the "price" rate of profit, PR/(C+V). Both are
expressed as percentages. Figures for sector 1 are in the top row in each
year, figures for sector 2 are in the second row, and figures for the total
social capital are on the bottom.

Year p m C V S TV TP PR
Rv Pp
1 1 -- 10 10 10 30 32 12
50 60
1 -- 10 20 20 50 48
18 66.7 60

20 30 30 80 80 30 60 60

Year p m C V S TV TP PR
Rv Pp
2 1.067 8 12.4 11.6 11.6 35.6 38.0 14.0
48.4 58.5
.960 12 12.5 23.5 23.5 59.5 57.1 21.1
65.2 58.5

20 24.9 35.1 35.1 95.1 95.1 35.1
58.5 58.5

Year p m C V S TV TP PR
Rv Pp
3 1.092 9.5 14.9 13.6 13.6 42.2 45.1 16.5
47.8 57.9
.972 14.3 15.1 27.7 27.7 70.5 67.6 24.8
64.7 57.9

23.8 30.0 41.3 41.3 112.6 112.6 41.3 57.9 57.9

Checking the accumulation percentages, we can verify that (12.4+11.6)/32 =
(12.5+23.5)/48 = (14.9+13.6)/38.0 = (15.1+27.7)/57.1 = 0.75. (Of course,
you'll find errors due to rounding; I rounded to the nearest $0.10 in the hope
of making the numbers fit on your screens in the appropriate lines.) So we

I. the transformation of values into production prices taking place in exact
conformance with Marx's own account.
II. the "transformation" of input prices.
III. nonstationary prices
IV. equal rates of accumulation (in Allin's sense)

So that people can verify the value/price figures, let me provide the
corresponding physical numbers. Again, sector 1 numbers are on top, sector 2
numbers below.

Year Means Living Labor Output
1 10 20 30
10 40 50

2 11.613 23.226 34.839
11.739 46.957 58.696

3 13.638 27.276 40.913
13.840 55.361 69.201

One can verify from these figures that the technology is unchanging and that
fixed coefficients prevail. Multiplying "Means" by the input price of sector
1, one gets the "C" figures. Multiplying "Living Labor" times the money wage
($0.50) gives the "V" figures. Subtracting V from Living Labor gives the "S"
figures. Dividing each sector's total price by its "Output" yields the unit
input price of the following year.

Since workers are assumed to consume only good 2, the unit input price of good
2 times the quantity of the good they consume must equal their money wages.
Hence, money wages divided by the input price of good 2 gives the amounts they
consume. These are

Year Workers' Consumption of Good 2
Sector 1 Sector 2
1 10 20
2 12.097 24.457
3 14.030 28.477

The capitalists' revenue, m, is spent on good 1 and good 2. Above, I assumed
that all persons other than productive workers divide their consumption
between the two goods in the same way. For all of both products to be sold,
it turns out that this assumption concerning unproductive consumption implies
that sector 1 must purchase 40%, and sector 2 must purchase 60%, of the output
of the temporally prior period that remains after sales of means of production
and workers' consumption. This is true for m in both period 2 and period 3.
In other words, the m of sector 1 purchases 400f the part of output of good
1 that remains and 400f the part of output of good 2 that remains, and the m
of sector 2 purchases the rest. Thus we get the following physical quantities
consumed unproductively:

Year Unproductive Consumption
Sec1, G1 Sec1, G2 Sec2,G1 Sec2, G2
2 2.6952 5.3787 3.9888 8.0680
3 2.9443 6.4756 4.4164 9.7134

Multiplying these figures by the appropriate input prices, one can verify that
the spending on these goods equals the money figures for m, in both sectors,
in both year 2 and year 3. One can also use these figures together with the
Output, Means, and Workers' Consumption figures to verify that all output of
both goods is indeed always sold.

So now, how about an unequivocal, public, published statement of concession
from our simultaneist friends? How many rivers do we have to cross?

Andrew Kliman