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Rosa Luxembourg in The Accumulation of Capital describes & investigates the constant and fixed capital of Marx & Smith respectively.

With Marx, she says Constant capital is the value invested in the means of production.

In Chapter 2, she writes:

There is a fixed capital of society, no part of which enters into its net revenue. This fixed capital consists in ‘the materials necessary for supporting their useful machines and instruments of trade’ and ‘the produce of labour necessary for fashioning those materials into the proper form’.

and then:

By singling out the production of such fixed capital as of a special kind, and explicitly contrasting it with the production of consumer goods, Smith in effect transformed fixed capital into what Marx calls ‘constant capital’ – that part of capital which consists of all material means of production, as opposed to labour power.

It appears, that she means that constant capital refers to that value embodied in the means of production whether they produce consumer or non-consumer goods; where consumption means consumed by the labouring class. So a non-consumer good could be the production of iron girders, which though, consumed in the production of sky-scrapers, are not consumer goods in her sense.

This is not the fixed capital of Smith, but she is able to draw some relation with the constant capital of Marx.

What is fixed capital, and what is this relation?

(I had thought that it was that part of constant capital embodied in the means of production, whose produce is non-consumer goods. But I don't think this is right).

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Let's examine the description of fixed capital more closely.

First,

no part of which enters into its net revenue

This is important, because it means that fixed capital cannot be a part of final goods and services. So for example, if there is a machine that builds consumer goods, but that machine is bought and sold, then that machine is not a part of fixed capital, as it adds to net revenue.

But wait!

This fixed capital consists in ‘the materials necessary for supporting their useful machines and instruments of trade'

We now know both what isn't part of fixed capital, but also that fixed capital is not equivalent to the null set (unless, of course, there is no production in this theoretical society).

Perhaps cleanliness of the air, for example, which is not considered in net revenue may be a portion of fixed capital. If the aforementioned machine is coal burning, the particulate matter expelled confers increased output (over using, say, a solar ray in climate that sometimes experiences cloudy days) but does not in any way affect net revenue. In this case then, clean air may be a form of fixed capital.

‘the produce of labour necessary for fashioning those materials into the proper form’.

To continue with the coal burning example, clean air can be generated by breathing in particulate-inundated air and filtering it with lungs. In this case, clean air is also a produce of labour, and is necessary, full particulate atmosphere would restrict the ability of other capital to function.

But what is constant capital?

that part of capital which consists of all material means of production, as opposed to labour power.

Oh! So constant capital is permitted to enter into net revenue but is not permitted to consist of labor. So the portions of clean air generated from other sources (we probably don't count trees as members of the labor force, and they also clean air), but not the portions cleaned by labor force lungs are counted in constant capital, as is our coal burning machine, for the fact that it may be bought or sold in no way affects its ability to be capital in the Marxist sense.

Summary:

Fixed capital: Not counted in revenue, may include labor.

Constant capital: Anything contributed to output that isn't labor.

I think it would fair to call the overlap something like "pure capital," as it is pure of both being output and of being labor, and say that this is the relation being drawn. The theoretical value embodied in capital suggested would be equivalent to this "pure capital."

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This should be reduced to a comment, but I will say that I find Luxembourg very good in general, but sometimes bewildering in detail.

This being Luxembourg, I suspect that we may be dealing here with questions of raw materials extracted through colonized labor and embedded in the material structure of a society, but not entering into values derived from "production." In other words, the the abiding remnants of "merchant capital."

While this is pure speculation, she may be criticizing Smith for collapsing merchant capitalism into the "pure critical logic" used by Marx to analyze industrial capitalism. Of course, Smith would be right to do so, but he wouldn't know it.

Since Luxembourg devoted herself to Volume Two, we are dealing with very complex second-order "motions" of capital. These would include the remnants of "merchant capital" that appeared even less relevant to Marx than to Smith. Marx may conceive of "constant capital" narrowly in the production process (for theoretical reasons), where a social "fixed capital" must widen the view to those institutions materialized out of international trade.

Pure gibberish, for what it's worth.

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(I had thought that it was that part of constant capital embodied in the means of production, whose produce is non-consumer goods. But I don't think this is right).

from pretty much just what you posted: constant capital - capital invested in non labouring productive forces; fixed capital - the above including reference to the labour power needed to maintain them.

[by] explicitly contrasting it with the production of consumer goods, Smith in effect transformed fixed capital into what Marx calls ‘constant capital'

if Smith defines the labour power spent in maintaining these items in terms of the reproduction of the labourer [and concomitant consumer goods], and then excludes that from "fixed capital" then he has done away with the term

for him, fixed capital is the same as constant capital in marx; but lux. claims that his analysis makes constant capital disappear [quite how, i don't know]

As the machines and instruments of trade, etc which compose the fixed capital either of an individual or of a society, make no part either of the gross or the neat revenue of either, so money, by means of which the whole revenue of the society is regularly distributed among all its different members, makes itself no part of that revenue.’(6)

Constant capital, the fixed capital of Adam Smith, is thus put on the same level as money and does not enter into the total produce of society, its gross revenue. It does not exist within this total product as an element of value.

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For Marx, capital invested in production comprises variable capital, which buys labour-power, and constant capital, which buys all other components of production. The text to start with here is "Constant Capital and Variable Capital", which is Chapter 8 of Capital, Volume 1.

The means of production on the one hand, labour-power on the other, are merely the different modes of existence which the value of the original capital assumed when from being money it was transformed into the various factors of the labour-process. That part of capital then, which is represented by the means of production, by the raw material, auxiliary material and the instruments of labour does not, in the process of production, undergo any quantitative alteration of value. I therefore call it the constant part of capital, or, more shortly, constant capital.

On the other hand, that part of capital, represented by labour-power, does, in the process of production, undergo an alteration of value. It both reproduces the equivalent of its own value, and also produces an excess, a surplus-value, which may itself vary, may be more or less according to circumstances. This part of capital is continually being transformed from a constant into a variable magnitude. I therefore call it the variable part of capital, or, shortly, variable capital. The same elements of capital which, from the point of view of the labour-process, present themselves respectively as the objective and subjective factors, as means of production and labour-power, present themselves, from the point of view of the process of creating surplus-value, as constant and variable capital.

Constant capital comprises fixed capital, which is that part of it invested in machinery and equipment that outlast one production cycle, but which during the cycle are subject to wear and tear, amortisation, and therefore transfer some of their value to the product; and circulating capital, that part of it invested in raw materials and other items that are used up within such a cycle.

See in particular "Fixed Capital and Circulating Capital", which is Chapter 8 of Capital, Volume 2.

A part of capital has been advanced in the form of constant capital, i.e., of means of production, which function as factors of the labour-process so long as they retain the independent use-form in which they enter this process. The finished product, and therefore also the creators of the product, so far as they have been transformed into product, is thrust out of the process of production and passes as a commodity from the sphere of production to the sphere of circulation. But the instruments of labour never leave the sphere of production, once they have entered it. Their function holds them there. A portion of the advanced capital-value becomes fixed in this form determined by the function of the instruments of labour in the process. In the performance of this function, and thus by the wear and tear of the instruments of labour, a part of their value passes on to the product, while the other remains fixed in the instruments of labour and thus in the process of production. The value fixed in this way decreases steadily, until the instrument of labour is worn out, its value having been distributed during a shorter or longer period over a mass of products originating from a series of constantly repeated labour-processes. But so long as they are still effective as instruments of labour and need not yet be replaced by new ones of the same kind, a certain amount of constant capital-value remains fixed in them, while the other part of the value originally fixed in them is transferred to the product and therefore circulates as a component part of the commodity-supply. The longer an instrument lasts, the slower it wears out, the longer will its constant capital-value remains fixed in this use-form. But whatever may be its durability, the proportion in which it yields value is always inverse to the entire time it functions. If of two machines of equal value one wears out in five years and the other in ten, then the first yields twice as much value in the same time as the second.

This portion of the capital-value fixed in the instrument of labour circulates as well as any other. We have seen in general that all capital-value is constantly in circulation, and that in this sense all capital is circulating capital. But the circulation of the portion of capital which we are now studying is peculiar. In the first place it does not circulate in its use-form, but it is merely its value that circulates, and this takes place gradually, piecemeal, in proportion as it passes from it to the product, which circulates as a commodity. During the entire period of its functioning, a part of its value always remain fixed in it, independently of the commodities which it helps to produce. It is this peculiarity which gives to this portion of constant capital the form of fixed capital. All the other material parts of capital advanced in the process of production form by way of contrast the circulating, or fluid, capital.

Some means of production do not enter materially into the product. Such are auxiliary materials, which are consumed by the instruments of labour themselves in the performance of their functions, like coal consumed by a steam-engine; or which merely assist in the operation, like gas for lighting, etc. It is only their value which forms a part of the value of the products. The product circulates in its own circulation the value of these means of production. This feature they have in common with fixed capital. But they are entirely consumed in every labour-process which they enter and must therefore be wholly replaced by new means of production of the same kind in every new labour-process. They do not preserve their independent use-form while performing their function. Hence while they function no portion of capital-value remains fixed in their old use-form, their bodily form, either. The circumstance that this portion of the auxiliary materials does not pass bodily into the product but enters into the value of the product only according to its own value, as a portion of that value, and what hangs together with this, namely, that the function of these substances is strictly confined to the sphere of production, has misled economists like Ramsay (who at the same time got fixed capital mixed up with constant capital) to classify them as fixed capital.

That part of the means of production which bodily enters into the product, i.e., raw materials, etc., thus assumes in part forms which enable it later to enter into individual consumption as articles of use. The instruments of labour properly so called, the material vehicles of the fixed capital, are consumed only productively and cannot enter into individual consumption, because they do not enter into the product, or the use-value, which they held to create but retain their independent form with reference to it until they are completely worn out. The means of transportation are an exception to this rule. The useful effect which they produce during the performance of their productive function, hence during their stay in the sphere of production, the change of location, passes simultaneously into the individual use in the same way in which he pays for the use of other articles of consumption. We have seen that for instance in chemical manufacture raw and auxiliary materials blend. The same applies to instruments of labour and auxiliary and raw materials. Similarly in agriculture the substances added for the improvement of the soil pass partly into the plants raised and help to form the product. On the other hand their effect is distributed over a lengthy period, say four or five years. A portion of them therefore passes bodily into the product and thus transfers its value to the product while the other portion remains fixed in its old use-form and retains its value. It persists as a means of production and consequently keeps the form of fixed capital. As a beast of toil an ox is fixed capital. If he is eaten, he no longer functions as an instrument of labour, nor as fixed capital either.

What determines that a portion of the capital-value invested in means of production is endowed with the character of fixed capital is exclusively the peculiar manner in which this value circulates. This specific manner of circulation arises from the specific manner in which the instrument of labour transmits its value to the product, or in which it behaves as a creator of values during the process of production. This manner again arises from the special way in which the instruments of labour function in the labour-process.

We know that a use-value which emerges as a product from one labour-process enters into another as a means of production. It is only the functioning of a product as an instrument of labour in the process of production that makes it fixed capital. But when it itself only just emerges from a process, it is by no means fixed capital. For instance a machine, as a product or commodity of the machine-manufacturer, belongs to his commodity-capital. It does not become fixed capital until it is employed productively in the hands of its purchaser, the capitalist.

All other circumstances being equal, the degree of fixity increases with the durability of the instrument of labour. It is this durability that determines the magnitude of the difference between the capital-value fixed in instruments of labour and that part of its value which it yields to the product in repeated labour-processes. The slower this value is yielded — and value is given up by the instrument of labour in every repetition of the labour-process — the larger is the fixed capital and the greater the difference between the capital employed in the process of production and the capital consumed in it. As soon as this difference has disappeared the instrument of labour has outlived its usefulness and has lost with its use-value also its value. It has ceased to be the depository of value. Since an instrument of labour, like every other material carrier of constant capital, parts with value to the product only to the extent that together with its use-value it loses its value, it is evident that the more slowly its use-value is lost, the longer it lasts in the process of production, the longer is the period in which constant capital-value remains fixed in it.

If a means of production which is not an instrument of labour strictly speaking, such as auxiliary substances, raw material, partly finished articles, etc., behaves with regard to value yield and hence manner of circulation of its value in the same way as the instruments of labour, then it is likewise a material depository, a form of existence, of fixed capital. This is the case with the above-mentioned improvements of the soil, which add to it chemical substances whose influence is distributed over several periods of production or years. Here a portion of the value continues to exist alongside the product, in its independent form or in the form of fixed capital, while the other portion of the value has been delivered to the product and therefore circulates with it. In this case it is not alone a portion of the value of the fixed capital which enters into the product, but also the use-value, the substance, in which this portion of value exists.

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The simplest answer would be:

  • Fixed capital = machinery and facilities, as opposed to

  • Circulating capital = raw materials and labour power.

On the other hand,

  • Constant capital = machinery, facilities, and raw materials, as opposed to

  • Variable capital = labour power.

Each disjunction serves different purposes, but the first one plays a secondary role within Marxist theory, and is more or less consensual among Marxists and non-Marxists. The second one, on the other hand, is central to Marxist theory, but its significance would be, I suppose, disputed by non-Marxists.

Luxemburg claims that Smith confuses the distinctions, making fixed capital = constant capital, and she might be correct about that. Thence "for [Smith], fixed capital is the same as constant capital in [M]arx; but [L]ux[emburg] claims that [Smith's] analysis makes constant capital disappear". If I correctly remember, she does make that exact claim, but I am not sure it is in the context of the confusion between fixed capital and constant capital. The argument would rather be that Smith enters into a kind of unwarranted regression, in trying to establish the principle that all value is a product of labour: instead of considering, like Marx, that constant capital is dead labour, and that its value is merely transferred into the new products, he attempts to explain that the items consisting in constant capital are themselves the product of labour, so that the value created by them is also indirectly produced by labour. In this way, he annuls the concept of constant capital; all capital is variable because all capital is ultima ratio reducible to labour. And, with even more reason, "capital" becomes an a-historical entity; the fact that fixed capital, at some point in the past, consisted in goods that were not produced within capitalist relations is lost, as is the distinction that Marx underlines in his critique of the Gotha program: value is not wealth, and wealth is not value, even though they largely intersect in a capitalist society.

That might be related to Smith's confusion of constant and fixed capital (if he misses fixed capital's specificity, which is to transfer its value to new products only gradually and along the duration of several sucessive production cycles, he might think of facilities and machineries as merely another kind of raw material in production, and this might be tied to his confusion between dead labour and live labour - in reducing all capital to labour, the specificities of each kind of capital are possibly lost). But then I am no specialist in Smith, and might be getting the finer distinctions wrong here.

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Fixed capital is means of labor. Now in production there is fixed capital as well as fluid or circulating capital. These are different in how they transfer value to the product, fluid capital transferring its value all at once, fixed only bit by bit. Fluid is the objects of labor and variable capital. These transfer their value at once, while fixed over many turnovers of the fluid capital. Fixed capital and fluid are different categories from constant and variable. I don't remember Smiths argument very well but Marx writes about it in detail in vol 2 of capital. You could probably jump in and understand it right at that chapter.

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