# [OPE-L:4180] TSS transformation procedure

Allin Cottrel (cottrell@wfu.edu)
Sun, 9 Feb 1997 16:48:44 -0800 (PST)

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I'd like to put the following back into the context of a
debate from last year, concerning Andrew's (and Ted's) claim
to have set out a "transformation" which validates all
Marx's propositions while escaping the Bortkiewicz critique,
the "catch" being that prices are non-stationary.

After Andrew presented a paper on this point to the Value
Theory conference last spring, I offered a critique, arguing
that Andrew's procedure can and should be thought of as
nothing other than an iterative approximation to the
Bortkiewicz solution. Andrew's response was (something
like), "You can iterate my procedure if you want to, but my
point is that each table represents a perfectly good
equalized-profit state in its own right; there's nothing
inherently 'incomplete' about the first few rounds."

Now some of us thought this claim was mistaken (Fred Moseley
has made a similar complaint), but what *exactly* is wrong
with it? It won't do simply to say, "the transformation is
incomplete because prices are changing", since that begs the
question Andrew is tackling. Recently I have tried to
identify what I thought was wrong in terms of the "release
of fixed capital", but on reflection I'm not sure that's the
most enlightening angle. In this post I try a different
tack.

Here's a reminder of Andrew's tableaux ("periods" 1 and 2
are in his 1996 conference paper; 3 is my extrapolation).
["m" = revenue; "vrate" = rate of profit in value terms,
"prate" = rate of profit in price terms, as on Andrew's
definitions; other notation presumed obvious.]

period: 1
m c v s c+v+s prof c+v+p vrate prate
I 0.00 140.00 36.00 24.00 200.00 44.00 220.00 13.64 25.00
II 0.00 40.00 48.00 32.00 120.00 22.00 110.00 36.36 25.00
III 0.00 20.00 36.00 24.00 80.00 14.00 70.00 42.86 25.00
Tot. 0.00 200.00 120.00 80.00 400.00 80.00 400.00 25.00 25.00

period: 2
m c v s c+v+s prof c+v+p vrate prate
I 33.00 154.00 33.00 27.00 214.00 51.00 238.00 14.44 27.27
II 22.00 44.00 44.00 36.00 124.00 24.00 112.00 40.91 27.27
III 15.00 22.00 33.00 27.00 82.00 15.00 70.00 49.09 27.27
Tot. 70.00 220.00 110.00 90.00 420.00 90.00 420.00 27.27 27.27

period: 3
m c v s c+v+s prof c+v+p vrate prate
I 37.80 166.60 33.60 26.40 226.60 50.34 250.54 13.19 25.14
II 19.60 47.60 44.80 35.20 127.60 23.23 115.63 38.10 25.14
III 12.60 23.80 33.60 26.40 83.80 14.43 71.83 45.99 25.14
Tot. 70.00 238.00 112.00 88.00 438.00 88.00 438.00 25.14 25.14

Now here's a new perspective on what's wrong with the above.
The supplementary figures below were calculated on exactly
the same basis.

The column headed "init_v" shows the *initial* investment
(c+v) in each of the sectors (so this, of course, does not
change from period to period). The column headed "c+v+p" is
just a transcription, from above, of the total price of each
sector's output in each period. And the column headed
"ratio" is the ratio of c+v+p to init_v. Now notice that in
this circulating-capital system the "value of the firm" in
any period is just equal to the value of its current output.
There is no fixed capital to reckon with. So here's
something odd: although the rate of profit is equalized in
every period, nonetheless the rate of expansion of the value
of the firm is *not* equalized. For instance, by period 3
the initial capital invested in sector I has expanded by 42
percent ("ratio" = 1.42) while that in sector II has
expanded by only 31 percent ("ratio" = 1.31) and that in
sector III by 28 percent.

What's going on? This is revealed by reference to the
remaining columns of the tables below. That headed "accum"
shows the amount that will be laid out as c+v in the *next*
period, and that headed "percent" shows "accum" as a
percentage of current income (c+v+p). Notice that the
accumulation percentage varies arbitrarily across the
sectors. At the end of period 1, sector I devotes 850f
income to accumulation, but sector III only 79%. 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". By
contrast, there is no such arbitrary variation in
accumulation ratios across sectors (nor the corresponding
arbitrary variation in rates of expansion of the value of
the capitals) in the "standard" Bortkiewicz-style
transformation -- which is also the point on which the
Kliman-iteration converges. This bolsters my point that the
Kliman tables must be conceived merely as iterative
approximations to a transformation, and not as representing
"perfectly good" equalized-profit states in their own right.

period: 1
init_v c+v+p ratio accum percent
I 176.00 220.00 1.25 187.00 0.85
II 88.00 110.00 1.25 88.00 0.80
III 56.00 70.00 1.25 55.00 0.79

period: 2
init_v c+v+p ratio accum percent
I 176.00 238.00 1.35 200.20 0.84
II 88.00 112.00 1.27 92.40 0.83
III 56.00 70.00 1.25 57.40 0.82

period: 3
init_v c+v+p ratio accum percent
I 176.00 250.54 1.42 210.06 0.84
II 88.00 115.63 1.31 96.36 0.83
III 56.00 71.83 1.28 59.74 0.83

(after a few more iterations we get a good approximation to
the Bortkeiwicz-style solution, in which all sectors are
accumulating 84 percent of income.)

The numbers above were derived from a simple C program
embodying the Kliman-McGlone algorithm as I understand it,
and I'll be happy to post the program if anyone's
interested.

Allin Cottrell