Jerry, let me make the point even clearer. Basically what I am saying
that both equalities can be maintained even if one so called
invariance condition is given up. This is the logical possibility
which I demonstrate here.
Let me show this:
We are all agreed that there are two equalities:
(1)sum of value=sum of prices of production
(2)sum of surplus value=sum of profits.
We have Marx's transformation procedure:
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
Marx's first-step transformation takes the given total s
and distributes it in proportion to (c+v). Thus:
c v profit price pvratio
I 225.00 90.00 93.33 408.33 1.0889
II 100.00 120.00 65.19 285.19 0.9506
III 50.00 90.00 41.48 181.48 0.9074
Tot. 375.00 300.00 200.00 875.00 1.0000
Marx argues that unless the inputs are transformed as well,it is possible to
go wrong.
So we have to transform the inputs.
We will be changing *the prices* at which the inputs represented in
the c and v column will sell. I will accept the backwardly causal
method of applying the output PV ratios on the inputs.
Now we are NOT changing the indirect and direct labour embodied in
the output whose value will thus remain invariant (875); this total
value will continue to determine the sum of the prices of production
in the transformation or throughout the iteration.
However, the point of this exercise is to modify the cost prices or
the quantity of the capital advanced and to see how this changes our
results.
Marx defines surplus value as total value minus cost price or total
capital advanced, i.e., the money paid for the direct and indirect
labour embodied in the commodity (see Capital 3, ch 2). Since we are
modifying cost prices, the sum of surplus value and the rate of
profit determined in terms of it cannot remain invariant.
Of course the sum of surplus value as changed by subtracting from the
invariant total value modified cost prices must still equal the sum
of branch profits. We have to preserve the second equality.
So the logic of Marx's argument about the need to transform the
inputs implies that both equalities remain intact but the second so
called invariance condition is given up: The mass of surplus value
simply change because from total value modified cost prices are being
taken, as shown in equation 6 below.
So we have the following transformation equations:
(3) 225x+90y+r(225x+90y)=225x+100x+50x
(4) 100x+120y+r(100x+120y)=90y+120y+90y
(5) 50x+90y+r(50x+90y)=r(225x+90y)+r(100x+120y)+r(50x+90y)
(6) 875-(225x+100x+50x+90y+120y+90y)=r(225x+90y)+r(100x+90y)+r(50x+90y)
(7) 875=375x+300y+r(225x+90y)+r(100x+90y)+r(50x+90y)
If I take the (rate of profit + 1) to be m, I have these equations
(8) m(225x+90y)=375x
(9). m(100x+120y)=300y
(10). m(50x+90y)=(m-1)(375x+300y)
(11) 875-375x-300y=(m-1)(375x+300y)
which implies
(12) m(50x+90y)=875-375x-300y
As Andrew tells me, m and x/y can be solved for by (10) while (11)
allows me to determine the absolute levels of x and y as well.
So we have the transformation in which both equalities (1) and (2)
are indeed maintained in equations the (6) and (7).
Now Allin objects that I have preserved the two equalities by
trickery. But it makes no sense to read the second equality as also
an invariance condition.
It would make no sense to keep the mass of surplus value invariant
with total value as we modify the cost prices since Marx defines
surplus value as total value minus cost price. It would also make no
sense not to treat total value as invariant since we are only
changing the prices of inputs and outputs, not the quantity of direct
and indirect labor in this single system.
So the breaking of an invariance condition is the not the breaking of
either of the two equalities.
Moreover, I do not think the point of this exercise is to provide
additional warrant for the two equalities. The point is to show that
since the average rate of profit and prices of production do change
when we transform the inputs, Marx was correct to conclude that it is
possible to go wrong if the cost prices remain unmodified.
all the best, Rakesh
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