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Ajit, thanks for your latest post (3741). Because of the number of points
raised, I will respond in two or three posts. This first post focuses on
the middle parts of Ajit's post, from the introduction of his equation
(1) through his reply to my previous #2 ("no problem to solve").
In order to clarify and economize my responses below, I will very briefly
summarize my understanding of the logical relation between Volume 1 and
Volume 3 of Capital (in half a page!), which I have presented in several
papers, but which Ajit chooses to ignore.
There are two main points:
1. Volume 1 is mainly about the determination of dM (for the economy as a
whole). Marx's theory of dM in Volume 1 can be concisely summarized by
the following simple equations:
(1) dM = S = NV - V
= m (L - Ln)
where m, L, and V are taken as given and Ln = V/m.
Please notice that these equations for the determination of dM do not
include prices of production in any way. In other words, the
determination of dM is prior to and independent of the determination of
prices of production.
2. In Volume 3, prices of production are determined (along with other
forms of the distribution of surplus-value) according to the equation:
(2) ppd = (Ci + Vi) (1 + r)
where r = dM / M, or = S / (C + V), and Ci and Vi are taken as given
(and ignoring the difference between fixed and circulating capital.
In other words, the dM determined in Volume 1 becomes one of the
determinants of ppd in Volume 3.
Now, within that context, let us turn to Ajit's latest post, starting with
his equation (1).
On Thu, 31 Aug 2000, Ajit Sinha wrote:
> ... Anyway, let's move on, this
> disaggregated $x, say $x(i) for sector (i) is supposed to stand in a
> particular relation with the total revenue earned after sales of the ith
> sectors final outputs. And this particular relationship is like this:
>
> $x(i) + $x(i) r = $y(i) -- eq. (1);
>
> where r stands for the rate of profit and
> y as the total gross revenue. (Of course, Fred has forgotten the variable
> capital here in this equation, but since he takes that as given too, that's
> not much of a problem at this stage.)
Ajit, this is your equation, not mine! My equation for prices of
production (see above) always includes variable capital. But you are
right that variable capital is also taken as given in my interpretation,
along with constant capital.
> Now, in the above equation, either we must know the r to solve for y(i) or we
> must know y(i) to solve for r. So up till now, Fred's system is indeterminate.
> He has not told us whether he takes y(i) or r as given in his system.
Ajit, again!! I have said repeatedly in papers and posts that the rate of
profit is determined prior to the determination of prices of production by
the analysis of capital in general in Volume 1, as the ratio of the total
surplus-value to the total capital invested. The rate of profit is then
taken as given in the determination of prices of production (analogous to
your equation (1)). Please see my summary above.
> Fred says, "Unit prices could be determined on the basis of Marx's theory by
> dividing
> the prices of production (or total industry revenues) by the industry
> quantities." So now, do we have y(i's) as given too? How did we get that? And
> how did we get the physical quantity of total output of sector i? In any case,
> I would like the reader to take a serious note of this.
Again, the y(i)'s (or prices of production) are determined by my equation
(2) above.
Unit prices play no essential role in the three volumes of Capital, as
summarized above. In one place (that I know of) Marx discussed briefly
the determination of unit prices, as I mentioned in my last post, in the
"Results" manuscript (C.I: 957-67), which was intended as a transition
from Volume 1 to Volume 2. So prices of production have not yet been
determined and the discussion is in terms of the value of commodities
(i.e. the price that would obtain if prices were proportional to their
labor-times). Marx argued that unit prices are derived from total
industry value, by dividing the total industry value by the quantity of
output, NOT the other way around; i.e. the industry totals are NOT
determined as the product of unit prices and the quantity of output. The
same point would apply after prices of production are determined. The
quantity of output is simply assumed for the purpose of this minor point.
> Still no answer to our problem. Now we are told that the main problem he is
> concerned with is to show where does dM come from. From our equation (1)
> above, we don't know whether there is any dM in the system unless we take that
> either r or y(i) is given.
Here is a fundamental confusion, mixing up different levels of abstraction
in Marx's theory: the theory of dM in Volume 1 and the theory of prices
of production in Volume 3. As discussed above, prices of production
(Ajit's y(i)'s) have nothing to do with Marx's theory of dM; therefore, it
is not necessary to take the y(i)'s (or r) as given in order to explain
dM. Rather, dM is explained prior to the determination of the y(i)'s and
then used to determine the y(i)'s.
Ajit appears no have no understanding of Marx's logical method of the
determination of different sets of variables at different levels of
abstraction. For him, all variables are determined simultaneously within
one system of equations. The latter is not Marx's method.
> From the above statement, it appears that Fred
> takes y(i's) as given. In this case, as i had suggested in my earlier post,
> the dM is simply determined by taking [sumof y(i's) - (C + V)], all of which
> is taken as given by Fred. Thus dM can be determined in his system without any
> regard to L.
As explained above, dM is determined in Volume 1 by the equation:
dM = m (L - Ln)
and therefore dM depends clearly and crucially on L. Why is this so hard
to understand?
> Otherwise, he has to give up that y(i's) are given. Then in that
> case, he has no way of determining the prices of production as he had
> suggested above.
More confusion. As explained above, the y(i)'s (i.e. prices of
production) are determined by equation (2) above and then taken as given
in the determination of unit prices. No problem.
Further responses to the remaining points in Ajit's post to follow. Ajit,
thanks again for the discussion.
Comradely,
Fred
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