**Next message:**Ajit Sinha: "[OPE-L:4441] Re: Re: What is Volume 1 about?"**Previous message:**Rakesh Narpat Bhandari: "[OPE-L:4439] Re: Re: what is Volume 1 about?"**In reply to:**Rakesh Narpat Bhandari: "[OPE-L:4421] Re: Re: Re: Re: 2 equalities, one invariance condition"**Next in thread:**Rakesh Narpat Bhandari: "[OPE-L:4444] Re: two schemes?"**Reply:**Rakesh Narpat Bhandari: "[OPE-L:4444] Re: two schemes?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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

**Next message:**Ajit Sinha: "[OPE-L:4441] Re: Re: What is Volume 1 about?"**Previous message:**Rakesh Narpat Bhandari: "[OPE-L:4439] Re: Re: what is Volume 1 about?"**In reply to:**Rakesh Narpat Bhandari: "[OPE-L:4421] Re: Re: Re: Re: 2 equalities, one invariance condition"**Next in thread:**Rakesh Narpat Bhandari: "[OPE-L:4444] Re: two schemes?"**Reply:**Rakesh Narpat Bhandari: "[OPE-L:4444] Re: two schemes?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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