[OPE-L:4362] Re: Re: Re: Technical change and general truths

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Mon Oct 30 2000 - 02:56:32 EST

>On Sun, 29 Oct 2000, Andrew_Kliman wrote:
>>  The following, which Steve Keen wrote in OPE-L 4349, is false:
>>  "The TSS approach to this is to dismiss consideration of a state in which
>>  rates of [technical] change equal zero, and provide numerical examples
>>  where the twin propositions above cannot be contradicted.
>I think you have to cut Steve a little slack here, given that he
>was engaging with Rakesh, whose special version of TSS (if it is
>a version of TSS; maybe it isn't) does insist upon technical
>change as a condition of maintaining Marx's two equalities...
>except that it turns out that technical change is not in fact
>sufficient to do the trick... (I feel saner since I withdrew
>from that debate.)

I am not sure why you don't think it did the trick.

But let's play the game of simple reproduction. Let me ask that you 
or Steve consider this one last reply before finally withdrawing; of 
course if your sanity is at stake, please ignore this.  Of course I 
have already suggested this repsonse to you in private 
correspondence, so you can voice the same objection which you have 
already expressed.

take the traditional approach to the problem. No technical change at all!

  The only difference is that I am keeping one invariance condition: 
the total value/price remains the same in the unmodified and modified 

  The changing of the price of the inputs should  have no effect on 
the *value of the means of production consumed* in the ouput or the 
new value added by labor since we are maintaining the same number of 
workers (the quantity of wage goods used as inputs to hire workers is 
not changed by the transformation of the price of the input wage 

So total value/price remains 875 after the transforming of the inputs.

The initial value table for Bortkiewicz-Sweezy-Cottrell:

	  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

A transformed scheme with a uniform profit rate in simple reproduction will be

(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)

That is, the first three equations set the system in simple reproduction.

but here's my innovation:

The fourth equation says that the mass of surplus value [total value-(modified)
  total cost price] does not equal but DETERMINES WHAT THE BRANCH PROFITS ADD UP

This is the meaning of the second equality: the mass of surplus value 
determines  the sum of the branch profits. This is the macro part of 
Marx's value theory.

As Fred says, the macro magnitudes are determined  prior to, and are 
determinative of, the micro magnitudes of the rate of profit and the 
prices of production (see also Blake, 1939; Mattick, 1983).

The iteration now follows as such:

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

Keeping total value/price the same (875), we apply the PV ratios to the inputs

	  c	  v   profit    price   pvratio
    I  245.00   85.56   86.60     417.  1.112
   II  108.89  114.07   58.41     281   .9379
  III   54.44   85.56   36.68     177   .885
Tot.  408.33  285.19   181.5     875   1.0

Then, following your lead,  we keep iterating until we arrive at 
simple reproduction or the equilibrium state in which the economists 
are so interested (how would I solve the above equations 
simultaneoulsy? I don't have time for 45 or so iterations nor the 
computer skills to write the algorithm.)

  It is obvious that the mass of surplus value and the average rate of 
profit will have changed from the value scheme. Only the total in the 
value/price column will remain the same (875).

The break with the Bortkiewicz-Sweezy-Cottrell tradition here is in 
the so called equality I have decided to break. Unlike them, I am 
keeping the total value/price sum the same in the unmodified and 
modified schemes (875).

*I do not understand the second equality to be an invariance 
condition, so I am not breaking it.*

So even if we transform the inputs into the same prices of production 
as the outputs (if this is the kind of thing one has to do to solve 
the transformation problem), one can still get a modified scheme in 
simple reproduction (if this is what has to be demonstrated to 
silence the critics).

Total value remains the same (875), and the sum of surplus value 
(total value- total cost price) DETERMINES the sum of the branch 

In the iteration, this is simply done by modifying the inputs on the 
basis of the PV output ratios and then subtracting the sum of these 
new modified inputs from total value/price of 875. This gives the 
bottom of the total profit column, which is then divided by the 
modified cost prices to yield r (average rate of profit) which is 
then applied to the modified cost prices in each branch to generate 
new branch prices of production and PV ratios which are again applied 
to the inputs. This is continued until the system settles into simple 

If we hadn't modified the inputs, we would have gone wrong in the 
determination of the rate of profit and the prices of production. 
Marx was right about this.

My simple solution can only be had if we maintain the second equality 
as I define it. So not only have I maintained both equalities. I have 
shown why they must be maintained in order to carry out the 
transformation in an iterative manner.

I know that I have defined the second equality in a radically 
different manner than all commentators on the transformation problem. 
But this seems to me exactly what Marx meant by the sum of the branch 
profits being determined by the mass of surplus value.

If we want to stick to simple reproduction/equilibrium prices, then 
the entire transformation debate has been conducted on a 
misunderstanding of the meaning of second equality, which is 
correctly expressed in equation (4)

The only way to defeat my argument is to show that I have 
misinterpreted what Marx meant by the sum of surplus value equaling 
the sum of the profits in the different branches. Was it meant as 
invariance condition between the unmodified and modified scheme  or 
is the mass of surplus value determined after the modified cost 
prices have been subtracted from total value?

If it's the former, the transformation problem remains; if it's the 
latter, then I have presented a reasonable solution of the 
transformation problem under the static conditions which resemble 
general equilibrium theory. Of course I think such a solution is of 
absolutely no real interest in the understanding of capital anyway.

All the best, Rakesh

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