# [OPE-L:4418] Re: Re: 2 equalities, one invariance condition

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Fri Nov 03 2000 - 02:15:49 EST

```>
>Rakesh, I think you have found the right vocation for yourself
>finally! Now, my
>advise would be to put all your energy into t-shirt business. All the best!
>Cheers, ajit sinha

Glad you're back, Ajit. Truly. My joke was made at the end of the

Remember you said that the two equalities overdetermine the system. I
am saying that this is not true. We can have total value=total price
and mass of surplus value=sum of profits as long as surplus value is
defined,as Marx explicitly does,  as total value minus cost price
(instead of value of inputs) which allows for the modification of the
latter to change the mass of surplus value. The two equalities do not
then overdetermine the system of transformation equations. I am the
first to argue that the problem of overdetermination disappears once
we use Marx's definition of surplus value. So I can understand why
you may not have got the point.

To see this, I'll have to copy this again:

_______________________
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
_________________

I propose these input transformation equations in which total
value/price is invariant from the original tableau (equation 5) and
the sum of surplus value equals (determines) the sum of profits
(equation 4).

(1) 225x+90y+r(225x+90y)=225x+100x+50x
(2) 100x+120y+r(100x+120y)=90y+120y+90y
(3) 50x+90y+r(50x+90y)=r(225x+90y)+r(100x+120y)+r(50x+90y)
(4) 875-(225x+100x+50x+90y+120y+90y)=r(225x+90y)+r(100x+90y)+r(50x+90y)
(5) 875=375x+300y+r(225x+90y)+r(100x+90y)+r(50x+90y)

Allin proposes that the transformation should keep the mass of
surplus value invariant even as cost prices are modified :

(6) 225x+90y+r(225x+90y)=225x+100x+50x
(7) 100x+120y+r(100x+120y)=90y+120y+90y
(8) 50x+90y+r(50x+90y)=875-375-300 (200)
(9) 875-375-300 (200)=r(225x+90y)+r(100x+90y)+r(50x+90y)
(10)875=375x+300y+r(225x+90y)+r(100x+90y)+r(50x+90y)

My set of equations has a determinate solution for x,y and r; this
much you will have to grant.

Now tell me why my equation 4 is the incorrect expression for mass of
surplus value=sum of profits. I have responded to Allin's criticism.

What's yours? It would be truly appreciated.

All the best, Rakesh
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