[OPE-L:4374] Re: Re: Re: Re: Re: Re: Re: Technical change and general truths

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Mon Oct 30 2000 - 18:20:15 EST

Re 4373

>Marx used it to "collectivise" surplus before undertaking the
>transformation, Rakesh. That, to my mind, is a kludge.

Steve, you first argued that Marx assumed that capitalists operated 
as a true collective which decided to share surplus value equally 
among themselves. As a Marx expert you were not embarrassed by this 
characterization. I reminded you that Marx assumed that as 
capitalists seek to make the maximum profit, their *competitive* 
behavior would engender a tendency towards the equalisation of profit 
rates. The question for Marx was what the magnitude of that equalized 
profit rate would be. As a Marx expert you have doubtless heard it 
said that Marx criticized Smith and Ricardo for failing to understand 
that competition itself could not explain said magnitude.

Now you do not blame the capitalists but Marx for collectivizing 
surplus value. Do note the unsubtle shift in your position.

Yes, this is exactly what Marx does. Now *why* is it a kludge, 
whatever that means? Marx's argument is that the individual 
capitalists cannot be concerned with the total surplus value in the 
system; they are only concerned with making the greatest profit on 
their capital investments. This will lead to an equal apportioning of 
the total surplus value.

But why is it a kludge for Marx to define that mass of surplus value 
as total value-total cost price/total cost price?

Are you suggesting that there is some sort of illicit holism in 
Marx's method? If so, this is indeed an interesting criticism, and 
leads us to the heart of the macro part of Fred's method.

>As for your arithmetic, if you want to get my interest and undertake the
>intellectual task to which you seem to aspire, restate your entire system
>as a set of ordinary differential equations, and then I will take an interest.

My goodness, Steve, you just told me that transformation has to be 
generalized to cases with zero rates of change. So then I try to do 
it, and now you tell me to put it in differential equations.  Wow!

If I were still trying to convince you that inputs should be 
transformed into different unit prices of production than the 
outputs, then I would need to do this. But you have closed your ears.

So I am making another criticism in terms of simple reproduction.

The transformation debate has been conducted on a misunderstanding of 
the two equalities which need to hold from the unmodified so called 
value scheme to the modified so called price scheme.

the first equality is that the sum of the output prices in both the 
unmodified and modified scheme should equal the same total value 
(which is 875 in the bort-sweezy-cottrell scheme).

the second equality is not an equality but a determination: the mass 
of surplus value determines the sum of the branch profits.

Since the mass of surplus value is defined by Marx--as I have 
shown--as total value, less cost price, the modification of cost 
prices due to the transformation of the inputs means that the mass of 
surplus value and thus the average rate of profit and branch profits 
will indeed be different in the transformed so called price scheme 
than in the unmodified so called value scheme.

One will indeed go wrong if one does not transform the inputs and 
thereby modify the cost prices.

Now take what Allin has given us:
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
Now what I am saying is simple.

1. Apply the PV ratios to the inputs.
2. Sum the new modified cost prices, the new totals in the c and v columns.
3. Subtract the total modified cost prices from the same total value of 875
4. Divide this sum of modified SURPLUS VALUE by the modified total cost prices,
     given in the second step, to arrive at r
5. Multiply the branch cost prices by this new r to arrive at branch profit.
6. Add each branch profit to each branch cost price to arrive at prices of
     production for each branch.
7. Determine new PV ratios on that basis.
8. Apply the PV ratios to the inputs.
9. Iterate until you arrive at equilibrium.

the final tableau will have the new output prices equal the same 
total value in the unmodified scheme of 875.

the sum of surplus value will determine the sum of the branch 
profits. This is implied in steps 4 and 5.

Both equalities as Marx, not Bortkiewicz and almost everyone, meant them!

the same procedure can be put in simultaneous equations.

(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)

the invariance condition is that the sum of output prices remains 
determined by the total value in the system of 875.

I have shown that the transformation debate has been conducted on one 
questionable assumption (the inputs should be transformed into the 
same prices of production as the outputs) and a misinterpretation of 
what Marx meant by the sum of surplus value equalling (DETERMINING!) 
the sum of branch profits.

All the best, Rakesh

>At 10:11 AM 10/30/2000 -0800, you wrote:
>>re 4371
>>>Sorry Rakesh,
>>>But I regard this particular argument of Marx's:
>>>"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)."
>>>(for once I can't quickly locate the original by Marx, but I do know it)
>>>as one of the greatest kludges he ever attempted to pull. That capitalism,
>>>which is inherently a competitive class system, should somehow operate as a
>>>true collective of capitalists as to the division of surplus-value, I
>>>regard as pure nonsense.
>>Steve, Marx is saying that it is exactly by inherent competition in
>>search of the maximum profit that capitalists tendentially come to
>>share equally in the mass of surplus value which the working class as
>>a whole produces (there are of course tendencies working towards the
>>disruption of equalisation from which we abstract at this point.)
>>It is the linchpin of Marx's critique of Smith and Ricardo of course
>>that competition itself cannot determine the magnitude of the
>>resultant average rate of profit .  This is determined behind the
>>backs of the capitalists in terms of the total value produced, less
>>total cost price/total cost price.
>>The macro part of Fred's method is perfectly sound.
>>Now note what happens when we keep to Marx's definition of surplus
>>value: total value-total cost price. I have already provided the
>>It becomes impossible to maintain that the mass of surplus value will
>>remain the same after the inputs are transformed into prices of
>>production and cost prices modified thereby. It becomes impossible to
>>assume that Marx meant for there to be an invariance condition such
>>that the same mass of surplus value will determine the sum of branch
>>profits in both the unmodified so called value scheme and the
>>transformed so called price scheme.
>>What then is the meaning of the so called second equality?  It means
>>that the sum of surplus value not only has to be determined prior to
>>but also itself determines the sum of branch profits.
>>Once one understands the second equality in such terms, it's a matter
>>of solving the following set of transformation equations.
>>And here are the transformation equations for the
>>bort-sweezy-cottrell value scheme:
>>(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)
>>The left hand in the 4th equation gives us the mass of surplus value
>>(total value, less modified cost price); the right hand of this
>>equation has the mass of branch profits set equal to it. The second
>>equality is maintained. total value has been held invariant.
>>solve for x, y, and r. I took a few steps via an iterative method.
>>How would one do it with the less cumbersome method of matrix algebra?
>>all the best, r
>Dr. Steve Keen
>Senior Lecturer
>Economics & Finance
>University of Western Sydney Macarthur
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