[OPE-L:1634] Re: Temporality vs simultaneity

Allin Cottrell (cottrell@wfu.edu)
Fri, 29 Mar 1996 08:58:17 -0800

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This is not strictly speaking a reply to 1624, but it's in the
same domain. It's kind of long, so I won't be disappointed if it
takes a while to generate a response.

The following was sparked by the papers for one of the sessions at the EEA
in Boston. Since not everyone on OPE was there, I'll give a little context
to this posting. In one session David Laibman gave a paper criticizing
the approach to value theory favoured by Andrew Kliman, Ted McGlone, Alan
Freeman and others. Andrew presented a paper responding to David. I
wasn't able to attend the session, but I'd like to comment on one aspect
of Andrew's contribution, which I have now had time to read.

The paper has an appendix that discusses Bortkiewicz's critique of Marx's
transformation procedure. You'll recall that one criticism is that the
"post-transformation" situation set out by Marx does not allow for balanced
reproduction. Andrew tackles this point, drawing up a set of tables of
Marx's pattern in order to show that balanced (simple) reproduction _can_
occur, only it requires that output prices differ from input prices (i.e.
"nonstationary prices").

Tables 1 and 2 are reproduced from Andrew's paper. "m" stands for "revenue",
in a sense to be explained below. "vrate" and "prate" denote the rate of
profit, expressed in "value" and price terms respectively. "c+v+p" denotes
price. The other labels should be fairly self-explanatory.

Moving from table 1 to table 2 involves following certain rules, which I have
set out below. I continued applying the same rules until the numbers stopped
changing (to two decimal places, this occurs at table 21); and I have shown
tables 3 and 21 following Andrew's 1 and 2.

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

table 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

table 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

table 21 (after which there is no further change in the variables,
measured to 2 decimal places)

m c v s c+v+s prof c+v+p vrate prate
I 43.95 188.99 37.05 22.95 248.99 43.95 269.99 10.15 19.44
II 20.10 54.00 49.40 30.60 134.00 20.10 123.50 29.60 19.44
III 12.45 27.00 37.05 22.95 87.00 12.45 76.50 35.83 19.44
Tot. 76.50 269.99 123.50 76.50 469.99 76.50 469.99 19.44 19.44

Rules (uppercase refers to totals, lowercase to sectoral figures):

1. Simple reproduction, no technical change.

2. Total living labour per period = constant = 200.

3. S + V = 200 by hypothesis, so S(t) is a residual = 200 - V(t).

4. Total profit for period t = S(t) by hypothesis.

5. Output prices in each period formed by adding an aliquot share of profit
to c+v.

6. Output prices at t = input prices for t+1.

7. C(t) = c(I,t-1) + v(I,t-1) + p(I,t-1).

8. V(t) = c(II,t-1) + v(II,t-1) + p(II,t-1).

[7 and 8 are in the nature of intersectoral balance conditions.]

9. c(i,t) = w(c,i)*C(t) and v(i,t) = w(v,i)*V(t), where the w's are weights
that sum to unity across the sectors for both c and v.

11. The "c+v+s" column is taken as giving the "value" of the output for
department in question. That is, "value" = price of means of production used
up, plus living labour-time applied.

12. The "m" figures represent "revenues", in the sense of what is left over
out of the aggregate price of the output of that sector after the purchase of
means of production and labour power for the following period. Aggregate
revenue for each period equals the aggregate price of the output of
Department III in the previous period, or M(t) = c(III,t-1) + v(III,t-1) +

Contention: The rules above ensure that agregate price equals aggregate
"value" in each period; and that aggregate profit = aggregate "surplus
value". But "value" is thereby disconnected from its original definition
as labour-time embodied (or required for reproduction).

Argument: Simple reproduction is assumed. Let us suppose that the table 1
figures for c, v, and s represent values in the standard sense: the sum of
direct and indirect labour-time actually required to reproduce the
commodities. By assumption, no change occurs in the labour-input
coefficients or the quantities of means of production required in each
sector. Yet once the transformation is complete -- in the equilibrium
achieved in table 21 -- the "value" magnitudes look quite different. The rate
of profit = 19.44%, as opposed to the value rate of profit in the standard
sense of 25%. Total "values" = 469.99, as opposed to the standard total of
400; and total "surplus value" = 76.50, as opposed to the standard figure of

Less immediately obvious value magnitudes are not preserved either. The
relative values of the outputs of the three sectors stand in the ratio
2.5:1.5:1.0 in the original situation; but the "values" shown in the
equalized profit state stand in the ratio 2.86:1.54:1.0. The rate of surplus
value is 67 percent in the original situation; it appears to be 62 percent in
terms of the "value" magnitudes of the equalized-profit equilibrium.

These "value" figures are of course the Bortkiewicz "price" figures,
i.e. precisely the figures that most people take to show that Marx's
invariances are _not_ preserved. [The exception to this statement is that
the figures Andrew gives for "c+v+s" (as opposed to c+v+p) have no
counterpart in the Bortkiewicz tables. The "c+v+s" numbers are a
hybrid, consisting of the sum of (a) the cost-price, measured at prices of
production and (b) a share of the total profit allocated in proportion to the
variable capital (again measured in terms of prices of production) used in
each sector.]

To be precise, the figures at which we arrive by iterating Andrew's procedure
differ from those arrived at by Bortkiewicz's own method by a scalar. The
Bortkiewicz procedure has one degree of freedom: he closes the system by
assuming that the product of Department III serves as the money-commodity and
therefore has a price of unity (i.e., it serves as numeraire for the
price-of-production system). Andrew, on the other hand, uses the degree of
freedom to set V+S in the price system equal to V+S in the value system.

If we assume, with Bortkiewicz, that Dept. III produces the money commmodity,
Andrew's use of the degree of freedom amounts to choosing a standard of price
other than one unit of money. In this particular numerical example, it turns
out that the standard of price has to be 1.05 units of money to hold S+V
constant between table 1 and table 21. (Under the Bortkiewicz solution the
total of S+V in price terms is 209.15 as opposed to 200 in the original value
terms; B's method preserves the figure for total S rather than for S+V.)

What is going on here? Andrew [not just Andrew, of course] has simply
redefined "value" in such a way that his aggregate value magnitudes
"shadow" whatever aggregate price magnitudes may happen to be thrown up in
the process of calculating the price vector that ensures a uniform rate of
profit. The resulting figures bear little relationship to the
direct-plus-indirect labour-time numbers shown (by assumption) in the
first table.

The question of dynamics: I think Andrew will agree that that a set of
tables of this sort does not constitute a dynamic analysis. It is simply a
"logical-time" iterative calculation. (For one thing, if it were intended as
an actual dynamic analysis there would be no justification for imposing a
uniform rate of profit in each "period". Presumably the system would take
many periods to converge on a uniform rate of profit, as in the dynamic
simulations of Dumenil and Levy.) Given this, there is no real argument for
"stopping the calculation short" at step 2; one should proceed until
calculation is done, that is, until a consistent set of prices is achieved
(step 21).

Note there is a clear sense in which the calculation is truncated if we stop
at step 2. The ("backward-looking") rate of profit is equalized, and
balanced reproduction is possible, as Andrew says, if we allow output prices
to differ from input prices. But the disposable profits available to the
capitalists in each sector after they have met the requirements of
continuing production in the following period -- i.e. the resources available
for consumption or accumulation, if each sector is viewed as a going concern
-- do not stand in a common proportion to their outlays. Take tables
2 and 3 for instance.

(1) (2)
outlay (c + v) disposable profit
Dept. in period 2 available for expenditure (2)/(1)
in period 3
I 187 37.80 20.21%
II 88 19.60 22.27%
III 55 12.60 22.91%

Rates of return in this sense are equalized only once input and output prices
converge, and from this point of view "stationarity" of prices should be
seen as part of the specification of equilibrium.

Allin Cottrell