[OPE-L:4404] Re: Re: Re: Technical change and general truths

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Wed Nov 01 2000 - 14:11:54 EST

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 

  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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