I'm striving to understand your view. Let's see if this
argument works better.
Start with what we agree on (I think). Marx's transformation,
in itself, is an atemporal comparison of two possible states of
a single economy, states which differ in respect of the pricing
of commodities (according to values in the one case, in such a
manner as to generate an equalized rate if profit in the other).
Marx had a table which showed the inputs being purchased at
prices equal to values and the output selling at prices that
equalize profits. This is fine as a starting point, (a) because
Marx wanted to root prices of production in values, so it makes
sense to have the inputs at prices equal to values in the first
instance, and (b) because -- as you say -- Marx hasn't yet
developed the concept of price of production when he first draws
up the table.
Fine as a starting point, but it looks as if some more work is
needed. The next question that suggests itself is: what would
things look like if the inputs were purchased at prices of
production too? (Marx only got as far as asserting that this
would make no material difference.)
So how are we going to examine the situation where the inputs
are at prices of production too? To get at this we need a
little model system that represents a complete economy (with its
interdependencies), not just a few industries drawn from a
larger economy.
Agreed so far?
Bortkiewicz offered one such little system, with 3 departments.
He conceived of his system as a "time-slice" of an economy
undergoing simple reproduction -- because this was the simplest
assumption, and because it seemed adequate to test Marx's claim
concerning the two equalities, total price = total value and
total profit = total surplus value. Marx's claim being
perfectly general, if it was shown to fail in the case of simple
reproduction, it would be shown to be false.
OK, I understand that you don't want to have anything to do with
the assumption of simple reproduction, constant technology, and
an equilibrium where input prices equal output prices. So let's
reinterpret Bortkiewicz's table as representing a time-slice
from an economy where labour productivity is increasing at 5
percent per period. Let's say the slice is at period t, with
certain means of production coming forward from t-1 as inputs,
and certain means of production being produced during t, for
carrying forward to t+1.
The initial value table:
c v s value
I 225.00 90.00 60.00 375.00
II 100.00 120.00 80.00 300.00
III 50.00 90.00 60.00 200.00
Tot. 375.00 300.00 200.00 875.00
Where B. would assume that the physical quantities and unit
values of the means of production coming forward from t-1 are
same as those of the means of production going forward to t+1,
we'll assume that the physical quantity going forward to t+1 is
5% greater than the quantity coming from t-1, while the per-unit
value is 5% smaller on the output side than on the input side.
Now we do the iteration, as I suggested before. Start with
Marx's stage 1 transformation:
c v profit price
I 225.00 90.00 93.33 408.33
II 100.00 120.00 65.19 285.19
III 50.00 90.00 41.48 181.48
Tot. 375.00 300.00 200.00 875.00
I observed that the aggregate price of output of Department I
stood here in a ratio of 1.0889:1 (408.33/375) to the value of
that output, and proposed to revalue the means of production as
inputs by the same factor (i.e. I was supposing that their price
as inputs at the beginning of t "ought to be" the same as their
prices as outputs at the end of t).
Let's correct that. My next-round figure for the aggregate
price of the means of production as inputs (408.33) has to be
adjusted in two ways:
1) By assuming that the quantities are the same on the input and
output sides, I have overstated the quantity of inputs by 5
percent, and hence overstated the aggregate price accordingly.
Thus we need to divide my figure by 1.05.
2) We assume the value of money is constant (as you said).
Therefore, aside from any adjustment due to equalization of
profit, the unit price will be 5 percent lower on the output
side than the input side, due to the 5 percent drop in per-unit
value. My initial calculation ignored this, "carrying back" the
output price unaltered. To correct for the drop in unit prices
from inputs to outputs, we have to multiply my figure for the
aggregate input price by 1.05.
Thus the combined correction factor is 1.05/1.05 = 1. In other
words, no correction to my figures is needed after all. The
next table looks like this, if we take a total profit equal to
the total surplus value from the original value table (200) and
distribute it in proportion to capital advanced:
c v profit price
I 245.00 85.56 95.33 425.88
II 108.89 114.07 64.30 287.26
III 54.44 85.56 40.37 180.37
Tot. 408.33 285.19 200.00 893.52
As I said before, total price (893.52) has come unstuck from
total value (850). Hold to one of Marx's equalities and you
break the other one.
What happened? Well, it shouldn't really be a surprise. A
difference in physical quantities between outputs and inputs
makes no difference to the value or price of production tables,
in aggregate terms, since it is completely offset by the change
in unit values (and prices, given a constant value of money).
There _is_ a difference, but it's invisible in the aggregate
tables: the _unit_ prices of production are no longer the same
for inputs and outputs. As you wished, unit output prices are
lower.
What do I conclude from this? "Aha, so Marx was completely
wrong. We can forget about exploitation of labour as the source
of profit. Capitalism is fine and just after all"? Of course
not. With this loophole opened, it's possible to cook up
examples a la Steedman where profit and suplus value do not just
diverge by a few percentage points, but have nothing to do with
each other. But as Paul C has repeatedly said, we have to
subject this sort of thing to sensitivity analysis -- to get a
feel for what are plausible numbers for real capitalist
economies. Steedman's examples are theoretical freaks, of no
practical significance.
Allin Cottrell.
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