Value loops

[Comrade #138672]

How do you determine, or rather approach, the value of a commodity, when its value is dependent on... itself?

Let's say there are two commodities: wood and axes. I know this is a very simple situation and very primitive for capitalist production, but it should be sufficient in order to illustrate the problem of "value loops". We assume that axes are made completely out of wood and that wood is produced by applying axes.

We know that W = c + L, with c being the productively consumed constant capital, and L being the newly added value (disregarding the distinction between v and s).

W(wood) = c(wood) + L(wood);
The value of wood is determined by the constant capital c advanced and the newly added value L.

c(wood) = x * W(axe);
Here x is equal to the part of the axe consumed productively, by its wear and tear, to produce one quantum of wood.

W(axe) = c(axe) + L(axe);
c(axe) = y * W(wood);
Here y is equal to the part of the wood productively consumed for the production of the axe.

We can now see that the value of wood depends on the value of axes, which depends on the value of wood again, etc. This means that we can expand this formula infinitely, without a possible solution.

W(wood) = x * W(axe) + L(wood);
W(wood) = x * (y * W(wood) + L(axe)) + L(wood);
W(wood) = x * (y * (x * (y * W(wood) + L(axe)) + L(wood)) + L(axe)) + L(wood);
etc...

At best we can approach it, but how?

One thing seems obvious: the indirect productive consumption of wood, by itself, is always a fraction of the produced wood (so x < 1). Otherwise, wood could not be produced and its value would be equal to infinity. This means that the further you expand on the formula, the smaller the contribution of each subsequent x is. At some point, it should be possible to ignore every subsequent x and treat it as 0, but at which point would this be?

Another question, how many of these value loops would there be in real-life capitalism and (how) do they complicate a more in-depth analysis of capitalism and LTV?

[Hit The North]

I don't pretend to follow your schema here, but your first premise that a commodity's value is dependent only on itself is incorrect because value is relational and socially determined. Also, if you're chopping wood with an axe made only of wood, you are not going to be doing much chopping. If a commodity's value depends on its socially necessary labour time then your wood will be very expensive (and uncompetitive as a commodity) compared to the wood chopped by a woodsman using a stone or metallic axe head.

I'm sorry if I've completely misunderstood the point, but what is a 'value loop' anyway?

[The Garbage Disposal Unit]

This reminds me of the time I got too high and thought I saw a contradiction in Kitty and Mimmy.
http://autumnsunshineandgabrielleangel.files.wordpress.co m/2011/11/hello-kitty002.gif?w=300&h=239

Anyway, you seem to be missing some pretty crucial steps here, even assuming, for simplicity's sake, an axe that is made entirely from wood.

1) In understanding the value of the wood, we have to understand all of the re/productive labour necessary to realize the axe as a commodity, which includes not only the axe and the labour of chopping the wood, but also the reproduction of the worker (food, sex, shelter), the organization of the chopping (leases, etc., or at the very least, the necessity of hiking out to the forest), etc.

2) The axe needs to be understood this way too - which means when we talk about the influence of the axe on the value of the axe, we're not talking about the axe-itself as an individual axe, but the relationship of the axe to axes generally, and the totality of capitalist relations in which the axe is either a commodity or capital (as the particular case may be).

Thus, the axe does not determine its own value - there's no contradictory "loop" at play.

[Comrade #138672]

Btw, I stumbled upon this problem, because I tried to write a simple Prolog program that would be able to calculate and compare values of commodities in different situations. It was never meant to be exhaustive or anything. I just wanted it to give a decent and modest impression of what is at play. However, I quickly found out that my value definitions created an infinite "loop" in my program and that I had to somehow approach it differently.


I don't pretend to follow your schema here, but your first premise that a commodity's value is dependent only on itself is incorrect because value is relational and socially determined.I'm not saying that the commodity's value is only dependent on itself. I'm saying that it's also dependent on its own value. I don't deny that the value is socially determined and relational. I'm merely adding to it that the axe's value is also related to itself.


Also, if you're chopping wood with an axe made only of wood, you are not going to be doing much chopping.I know. It's merely for simplicity's sake.


If a commodity's value depends on its socially necessary labour time then your wood will be very expensive (and uncompetitive as a commodity) compared to the wood chopped by a woodsman using a stone or metallic axe head.I realize that. I lack the imagination to think of a more realistic scenario that involves "value loops".


I'm sorry if I've completely misunderstood the point, but what is a 'value loop' anyway?Value defined in such a way that its definition connects back to itself, to form a loop. I couldn't think of a better term. You could also call it "value recursion" or something.


This reminds me of the time I got too high and thought I saw a contradiction in Kitty and Mimmy.
http://autumnsunshineandgabrielleangel.files.wordpress.co m/2011/11/hello-kitty002.gif?w=300&h=239

Anyway, you seem to be missing some pretty crucial steps here, even assuming, for simplicity's sake, an axe that is made entirely from wood.

1) In understanding the value of the wood, we have to understand all of the re/productive labour necessary to realize the axe as a commodity, which includes not only the axe and the labour of chopping the wood, but also the reproduction of the worker (food, sex, shelter), the organization of the chopping (leases, etc., or at the very least, the necessity of hiking out to the forest), etc.

2) The axe needs to be understood this way too - which means when we talk about the influence of the axe on the value of the axe, we're not talking about the axe-itself as an individual axe, but the relationship of the axe to axes generally, and the totality of capitalist relations in which the axe is either a commodity or capital (as the particular case may be).

Thus, the axe does not determine its own value - there's no contradictory "loop" at play.I agree with you that determining the value is incredibly complex, and that the value of an axe is determined by the capitalist production of axes generally and the totality of capitalist relations, but this doesn't mean that there are no "value loops". Actually, I think it means that there are many of these hidden "value loops", because everything depends on each other.

Also, it's not necessarily a contradiction. It just makes it more complicated.

[Hit The North]

I'm not saying that the commodity's value is only dependent on itself. I'm saying that it's also dependent on its own value. I don't deny that the value is socially determined and relational. I'm merely adding to it that the axe's value is also related to itself.


Isn't that just its use value? In fact, that the axe's value is related to its use rather than its self.


Value defined in such a way that its definition connects back to itself, to form a loop. I couldn't think of a better term. You could also call it "value recursion" or something.

But can you point to an actual case of this within capitalism?

[Comrade #138672]

Isn't that just its use value? In fact, that the axe's value is related to its use rather than its self.Well, of course use-value is relevant (otherwise the product could not be productively consumed), but a part of the (exchange-)value of the axe is actually transferred, by its wear and tear (productive consumption), to the production of wood. When axes are produced, the wood that is consumed in the process, surrenders its value to the produced axes. According to this scenario, the value of wood is dependent on the value of axes, which is dependent on the value of wood. Thus, the value of wood is indirectly dependent on the value of wood, i.e. its own value.


But can you point to an actual case of this within capitalism?Let me think about this for a bit.

[cyu]

"The more you exercise, the longer you live. The longer you live, the more you exercise." -Hefty Smurf :laugh:

[reb]

different types of labor, making axes and chopping trees are different labor processes

[Five Year Plan]

How do you determine, or rather approach, the value of a commodity, when its value is dependent on... itself?

Let's say there are two commodities: wood and axes. I know this is a very simple situation and very primitive for capitalist production, but it should be sufficient in order to illustrate the problem of "value loops". We assume that axes are made completely out of wood and that wood is produced by applying axes.

We know that W = c + L, with c being the productively consumed constant capital, and L being the newly added value (disregarding the distinction between v and s).

W(wood) = c(wood) + L(wood);
The value of wood is determined by the constant capital c advanced and the newly added value L.

c(wood) = x * W(axe);
Here x is equal to the part of the axe consumed productively, by its wear and tear, to produce one quantum of wood.

W(axe) = c(axe) + L(axe);
c(axe) = y * W(wood);
Here y is equal to the part of the wood productively consumed for the production of the axe.

We can now see that the value of wood depends on the value of axes, which depends on the value of wood again, etc. This means that we can expand this formula infinitely, without a possible solution.

W(wood) = x * W(axe) + L(wood);
W(wood) = x * (y * W(wood) + L(axe)) + L(wood);
W(wood) = x * (y * (x * (y * W(wood) + L(axe)) + L(wood)) + L(axe)) + L(wood);
etc...

At best we can approach it, but how?

One thing seems obvious: the indirect productive consumption of wood, by itself, is always a fraction of the produced wood (so x < 1). Otherwise, wood could not be produced and its value would be equal to infinity. This means that the further you expand on the formula, the smaller the contribution of each subsequent x is. At some point, it should be possible to ignore every subsequent x and treat it as 0, but at which point would this be?

Another question, how many of these value loops would there be in real-life capitalism and (how) do they complicate a more in-depth analysis of capitalism and LTV?

Value refers to a 'third thing' (socially necessary labor time) that connects commodities of intractably different use values, so that they can be measured quantitatively by a shared standard. By definition, this means that it is not possible to have a 'loop' of the kind you mention, unless you are selling socially necessary labor time in some kind of pure abstract form. That is a non-sensical idea, however, since it is so abstract that it must take some phenomenal form in order to acquire a kind of usefulness.

[Comrade #138672]

Value refers to a 'third thing' (socially necessary labor time) that connects commodities of intractably different use values, so that they can be measured quantitatively by a shared standard. By definition, this means that it is not possible to have a 'loop' of the kind you mention, unless you are selling socially necessary labor time in some kind of pure abstract form. That is a non-sensical idea, however, since it is so abstract that it must take some phenomenal form in order to acquire a kind of usefulness.Yes, value = socially necessary labor-time. I get that. A given quantity cannot be in a "loop" with itself, and, even if it was, then it has already been resolved, because it is given. I agree with that. However, the problem arises when dealing with value definitions, so "value definition loops" or "recursive value definitions" would probably be more appropriate terms.

I have been able to resolve this problem, though. At least approximately. I have introduced a limit that treats the n'th self-referencing c as 0. The program now produces more or less satisfactory results. This is enough for an amateur like myself.

Before:

?- w(wood, W).
ERROR: Out of local stack

After:

?- w(wood, W).
W = 0.20110055027513757.

If anybody is interested in it, here is the code in a spoiler (Prolog (http://www.swi-prolog.org/) is necessary, though):
% Value recursion limit.
value_recursion_limit(6).

% Value composition definitions.
% v(Commodity, ConstantCapital, SociallyNecessaryLaborTime)
v(wood, [0.001 * axe], 0.2).
v(axe, [0.5 * wood], 1).
v(pick_axe, [0.3 * iron, 0.4 * wood], 1).
v(iron, [0.001 * pick_axe], 0.5).
v(grain, [], 1).
v(flour, [5 * grain], 0.5).
v(bread, [0.2 * flour], 1).
v(machine_component, [30 * iron, 2 * wood], 10).

% Generalized rule for constant capital and productive consumption.
% Calculate the productively consumed constant capital W for the production of commodity X.
c(_, [], 0, _).
c(X, [Head | Rest], W, Visited) :-
Head = L * Y,
w(Y, L, WHead, Visited),
c(X, Rest, WRest, Visited),
W is WHead + WRest.

% Calculate the value W of a given commodity X.
w(X, W) :-
w(X, 1, W),
!.
w(X, N, W) :-
w(X, N, W, []).
w(X, N, W, Visited) :-
v(X, C, WOfL),
NewVisited = [X | Visited],
count(X, NewVisited, RCount),
value_recursion_limit(RCountLimit),
(
RCount > RCountLimit,
WOfC = 0;

RCount =< RCountLimit,
c(X, C, WOfC, NewVisited)
),
W is N * (WOfC + WOfL).

% Count the frequency N of element E in list L.
count(_, [], 0).
count(E, L, N) :-
L = [Head | Rest],
(
Head = E,
Match = 1,
!;

Head \= E,
Match = 0
),
count(E, Rest, Count),
N is Count + Match.

Anyway, thanks for your time. :)

[Five Year Plan]

Yes, value = socially necessary labor-time. I get that. A given quantity cannot be in a "loop" with itself, and, even if it was, then it has already been resolved, because it is given. I agree with that. However, the problem arises when dealing with value definitions, so "value definition loops" or "recursive value definitions" would probably be more appropriate terms.

I have been able to resolve this problem, though. At least approximately. I have introduced a limit that treats the n'th self-referencing c as 0. The program now produces more or less satisfactory results. This is enough for an amateur like myself.

Before:


After:


If anybody is interested in it, here is the code in a spoiler (Prolog (http://www.swi-prolog.org/) is necessary, though):
% Value recursion limit.
value_recursion_limit(6).

% Value composition definitions.
% v(Commodity, ConstantCapital, SociallyNecessaryLaborTime)
v(wood, [0.001 * axe], 0.2).
v(axe, [0.5 * wood], 1).
v(pick_axe, [0.3 * iron, 0.4 * wood], 1).
v(iron, [0.001 * pick_axe], 0.5).
v(grain, [], 1).
v(flour, [5 * grain], 0.5).
v(bread, [0.2 * flour], 1).
v(machine_component, [30 * iron, 2 * wood], 10).

% Generalized rule for constant capital and productive consumption.
% Calculate the productively consumed constant capital W for the production of commodity X.
c(_, [], 0, _).
c(X, [Head | Rest], W, Visited) :-
Head = L * Y,
w(Y, L, WHead, Visited),
c(X, Rest, WRest, Visited),
W is WHead + WRest.

% Calculate the value W of a given commodity X.
w(X, W) :-
w(X, 1, W),
!.
w(X, N, W) :-
w(X, N, W, []).
w(X, N, W, Visited) :-
v(X, C, WOfL),
NewVisited = [X | Visited],
count(X, NewVisited, RCount),
value_recursion_limit(RCountLimit),
(
RCount > RCountLimit,
WOfC = 0;

RCount =< RCountLimit,
c(X, C, WOfC, NewVisited)
),
W is N * (WOfC + WOfL).

% Count the frequency N of element E in list L.
count(_, [], 0).
count(E, L, N) :-
L = [Head | Rest],
(
Head = E,
Match = 1,
!;

Head \= E,
Match = 0
),
count(E, Rest, Count),
N is Count + Match.

Anyway, thanks for your time. :)

No, I don't think you do understand. The value of wood, grain, or anything else is not intrinsic to the nature of the objects themselves. They are measurements assigned on the basis of socially necessary labor time, and will exchange with other objects according to that property. Even when grain acts as a currency, it is not grain qua grain that is the currency, but rather the value that X amount of grain represents that acts as the mechanism of exchange. Grain is merely the phenomenal form. Grain by itself is not a third thing, and therefore can not loop back on itself as a basis for measurement. Neither can any of the other objects you mention.

[Comrade #138672]

No, I don't think you do understand. The value of wood, grain, or anything else is not intrinsic to the nature of the objects themselves.Oh, you're right about that. I did not actually think that, though. I'm talking about specific commodities in a specific capitalist context. I realize that they are not intrinsic properties.


They are measurements assigned on the basis of socially necessary labor time, and will exchange with other objects according to that property.Yes. This is what I'm trying to do: measuring that value by applying LTV.


Even when grain acts as a currency, it is not grain qua grain that is the currency, but rather the value that X amount of grain represents that acts as the mechanism of exchange. Grain is merely the phenomenal form. Grain by itself is not a third thing, and therefore can not loop back on itself as a basis for measurement. Neither can any of the other objects you mention.Sorry, but I still don't know what I'm not understanding.

The value of a commodity depends on its socially necessary labor-time, right?

The socially necessary labor-time embodied in, for example, flour, as a commodity in capitalism, doesn't depend only on the labor-time socially necessary to convert the grain into flour, but also on the socially necessary labor-time embodied in grain, as a commodity in capitalism. Do you agree with this?

Thus, W = c + L. The value that flour represents (W) is not just the labor-time socially necessary to transform the grain into flour (L), but also the labor-time socially necessary to produce grain (c). This is, of course, a very simplified situation, but the relationship is correct, no?

Then all I did was constructing a loop by connecting the dependencies, in order to measure the value that certain commodities represent in specific simplified situations in a capitalist context.

So where did I go wrong, aside from being very simplistic?

[Vladimir Innit Lenin]

Of course, this loop is merely a means to an exercise in theoretical uselessness. Whilst it makes for an interesting mathematical problem, we would not rely on solving this (abstract mathematical) problem to solve the (real world) problem of ascribing a proper value IRL to wood, and on its productive uses.

We would merely decide that the axe is, in general, the means, with the wood (in finished good form) being the ends. So rather than setting up the production related to the wood and the axe as a loop, we would decide what finished goods we want to produce using the natural resource (wood), and produce enough axes accordingly, taking into account the variables you mention (depreciation of the capital stock being the most important with 'machinery' like an axe) to find the most efficient production level for axes, for the given level of wood being transformed from natural resource to finished good.

Problem solved, let's eat some pie.

[Five Year Plan]

The socially necessary labor-time embodied in, for example, flour, as a commodity in capitalism, doesn't depend only on the labor-time socially necessary to convert the grain into flour, but also on the socially necessary labor-time embodied in grain, as a commodity in capitalism. Do you agree with this?

Yes. Grain would be an input in the labor process of producing the commodity flour. So the labor time required to produce flour will be added to the labor time already necessary to harvest the flour-producing grain.


Thus, W = c + L. The value that flour represents (W) is not just the labor-time socially necessary to transform the grain into flour (L), but also the labor-time socially necessary to produce grain (c). This is, of course, a very simplified situation, but the relationship is correct, no?

Correct.


Then all I did was constructing a loop by connecting the dependencies, in order to measure the value that certain commodities represent in specific simplified situations in a capitalist context.

So where did I go wrong, aside from being very simplistic?

Where you are wrong in your "loop" is by saying that "We can now see that the value of wood depends on the value of axes, which depends on the value of wood again, etc."

The value of wood is not dependent on the value of axes. Axes are merely one thing that wood can be made into. There are many other things that wood can be made into. Conversely, there are other ways to harvest trees and transform them into a salable commodity apart from the use of an axe Otherwise, it would have been impossible to build an axe in the first place, since the axe would have required the use of wood, and the wood would not have been producible without the axe.

Now it is true that a wood-formed axe might make more efficient, and reduce the socially necessary labor time required in, the process of producing salable wood, just as certain equipment made of steel makes more efficient the process of mining for the iron ore necessary to produce steel. But that is different than the abstract infinite loop you are trying to model. Even there, the labor time saved by the use of the axe *affects* the value in the commodity wood. It doesn't determine it. What always determines it is the socially necessary labor time in total, not some adjustment in it brought about by a productivity increase. It is an example of complex systems in which one element transforms into another and then reacts back upon other elements of the first kind.