[OPE-L:4440] Re: Re: Re: Re: Re: 2 equalities, one invariancecondition

From: Ajit Sinha (ajitsinha@lbsnaa.ernet.in)
Date: Sat Nov 04 2000 - 05:14:52 EST

Rakesh Narpat Bhandari wrote:

> Ajit, you have not understood what I have proposed. So only a quick
> response to point out where you have not understood me.
> >
> >___________________________
> >Your first three equations will determine the relative prices of x, y, and the
> >third commodity z, and the rate of profits r.
> The set of equations can be solved for the absolute prices as well.


What do you mean by "absolute price"?

> >  Before I mention the problems with
> >your equations (4) and (5), let me first suggest to you that your
> >equations are
> >pure numbers. You consistently fail to mention the units in which
> >the variables
> >are measured.
> One money dollar represents one hour of social labor time. The value
> of money is held constant. So the total value of 875 is simply $875.
> In the initial tableau, the input means of production thus cost $375
> and the input wage goods $300. Etc.


The introduction of dollar in your system is illegitimate. And the stipulation that
"dollar represents one hour of social labor time" is doubly illegitimate. How can
you say a thing like that arbitrarily?

> >  As a matter of fact, the question of the unit of measure is the
> >crux of the transformation problem. So if you don't have the problem of unit
> >upper most in your mind, you cannot even begin to understand the nature of the
> >problem, let alone solving it. Now, my sense is that you would say,
> >the numbers
> >are given in money terms.
> Right. This is exactly how Marx proceeds.
> >Now, your world of equations have three commodities.
> >It appears that the first one is something like iron, second one is something
> >like wheat, and the third one could be gold.
> Nope it's a luxury good, let's say porcelain.  I am not letting the
> money commodity into this; the value of money is held constant. One
> labor hour is represented by $1. That's it. I have provided you with
> a long quote from Grossmann justifying this theoretical choice.


Who cares about Grossmann? This is simply illegitimate. So there is no need to go
any further with it. Cheers, ajit sinha

> >So let us say, gold is the money
> >commodity in your world,
> Nope won't allow it.
> >so the values/prices of x and y are given in terms of
> >gold. In that case, your third equation turns out to be
> >
> >50x + 90y + r(50x + 90y) = 200   (3').
> >
> >Now, the system of equations (1), (2), and (3') are in well defined units, and
> >they solve for x, y, and r. Given your unnecessary simple reproduction
> >constraint on the system, it must follow that:
> >
> >r(225x+90y)+r(100x+120y)+r(50x+90y) = 200.
> You just won't listen to what I am saying. The left hand is the sum
> of profits. I am saying that since the mass of surplus value is
> defined as total value minus cost price, the mass of surplus value
> can no longer on the right hand be the same 200 it was before cost
> prices were modified.
> The right hand is not 200--I was quite clear about this being the
> difference between me and Allin--but rather the equation which I have
> already provided you:
> 875-375x-300y (total value minus modified cost price=surplus value).
>   I am NOT postulating the mass of surplus value (or rate of profit)
> as invariant since I think that's impossible as we modify cost prices
> given Marx's definition of surplus value as total value minus cost
> price. Of course if the sum of surplus value changes as a result of
> the modification of cost prices, so must the rate of profit which is
> now modified sum of surplus value/modified cost prices.
> Below you take r as invariant. But r, as well as the sum of surplus
> value, is an unknown in my equations. It has to be solved for, and r
> and the sum of surplus value can be solved in absolute terms!
> >Here by design, total surplus value will always be
> >equal to total profits.
> That's absolutely correct.  I have written the set of transformation
> equations in such a way that Marx's two equalities not only both hold
> but also--it turns out to my surprise--are needed to determine the
> system.
> This is my point!
> The point is that with the two equalities,as I have them,  they  no
> longer overdetermine the system.
> You can be assured that I did not invent my equations 4 and 5 because
> I knew the system would not be overdetermined. I wrote equation 4
> exactly as I understood Marx. That is, I read Marx defining surplus
> value as total value minus cost price, so since you and Bortkiewicz
> wanted to modify the cost price by having the inputs transformed as
> well, I then wrote the left hand of the equation
> 875-375x-300y because that would now represent the new surplus value
> as cost price is modified
> and then I wrote the right hand
> as the sum of the branch profits
> Because that it is exactly what I understand the second equality to be.
> My fourth equation has never been proposed before. But it is exactly
> how I understand Marx.
> I think we are agreed that any changing of the outward appearance of
> the input and output prices of a system should not change the total
> value/price which the commodity output embodies.
> So that gave me my fifth equation which expresses both the invariance
> of total value/price and the determination of total prices (the right
> hand) by the invariant total value (the left hand).
> 875=375x+300y+r(375x+300y).
> It turns out that my fourth and fifth equations do not overdetermine
> the system.
> So what I am saying to you, Ajit, is that when I wrote down the set
> of input transformation equations for the scheme which Allin provided
> me, I was left with those five equations.
> And they do provide a solution not only for x/y and r but x, y, and
> r. This system is determined in absolute terms.
> I of course believe that I am the first to have correctly written the
> input transformation equations in Marx's own terms. The innovation is
> in my fourth equation, and it simply follows from my understanding of
> how Marx defines surplus value and what the second equality means.
> I am not trying to be cute. I am following Marx to the letter. And
> that's how the equations turn out on my reading.. I would have been
> disappointed if equations 4 and 5 overdetermined the system. But they
> do not.
> >   And if the gold sector is made of average organic
> >composition of capital, then total value will also be equal to total surplus
> >value. This is just one of those special cases.
> But my set of equations does not require any special assumptions
> about the organic composition of capital in the Div III, porcelain
> production. . Another virtue of equations is that no such assumptions
> are required.  In fact the tableau Allin gives us is exactly the one
> Sweezy uses when he relaxes the special assumptions about Div III. So
> your objection is misplaced.
> >  Mathematically,
> >your r has to be either known or unknown, they cannot be both at the
> >same time.
> Ajit, r is unknown in my set of equations.
> >In equation (4), on the right hand side you have r as an unknown variable,
> >whereas the left hand side 875 is derived by taking r = 8/27.
> That is not how the $875 is derived. $875 is simply the direct and
> indirect labor the commodity output represents. It is the value of
> the means of production+the direct labor embodied in the commodity
> output. This value cannot change simply by playing around with the
> outside price appearances of the system, which is what the
> transformation is about.
> r is not used to determine 875; in fact r is determined only by
> dividing that total value by cost price.
>   After my transformation the sum of surplus value and r will not
> remain invariant. But the  two equalities hold. In fact the two
> equalities are needed to solve the system to get a new sum of surplus
> value, rate of profit and prices of production.
> My equations then allow for a substantiation of Marx's intuition that
> if the cost prices are left unmodified, it is possible to go wrong...
> >  So this is simply
> >illegitimate. Same with equation (5). Whether you like it or not, you  have
> >presented a simultaneous equation system with three unknowns and
> >five equations.
> >If all your five equations are independent ones, then your system is
> >overdetermined (try solving for x, y, and r from your five
> >equations, which you
> >haven't done yet).
> Nope I really only have 4 equations. The fifth is a mathematical
> tautology (it is simply equation 3 and 4).
> >
> >On a general note: I would advise that a solution to the
> >transformation problem
> >does not lay in being cute by somehow showing that the two
> >invariance conditions
> >satisfy.
> Again, you have not understood me. I do not have two invariance
> conditions! Remember the slogan.
> All the best, Rakesh

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