# Rough Theory

Theory In The Rough

## The Quantitative Indeterminacy of Value

Completely exhausted at the moment – just tossing some quick and probably very ill-thought notes onto the blog for future development. I keep meaning to say something about the curious way that Marx often uses simple mathematical relations to talk about value in the first volume of Capital. What interests me specifically is the way in which these passages – due to the mathematical form in which they are written – could seem to suggest that value is something one could potentially calculate. Yet the actual substance of the passages actually undermines any ability to get back “behind” the flux of the proportions in which goods exchange, to determine anything about the amount of “value” that is expressed through these fluctuations. So, for example, in a section titled “The Quantitative determination of Relative value”, Marx writes:

Every commodity, whose value it is intended to express, is a useful object of given quantity, as 15 bushels of corn, or 100 lbs of coffee. And a given quantity of any commodity contains a definite quantity of human labour. The value form must therefore not only express value generally, but also value in definite quantity. Therefore, in the value relation of commodity A to commodity B, of the linen to the coat, not only is the latter, as value in general, made the equal in quality of the linen, but a definite quantity of coat (1 coat) is made the equivalent of a definite quantity (20 yards) of linen.

The equation, 20 yards of linen = 1 coat, or 20 yards of linen are worth one coat, implies that the same quantity of value substance (congealed labour) is embodied in both; that the two commodities have each cost the same amount of labour of the same quantity of labour time. But the labour time necessary for the production of 20 yards of linen or 1 coat varies with every change in the productiveness of weaving or tailoring. We have now to consider the influence of such changes on the quantitative aspect of the relative expression of value.

I. Let the value of the linen vary, that of the coat remaining constant. If, say in consequence of the exhaustion of flax-growing soil, the labour time necessary for the production of the linen be doubled, the value of the linen will also be doubled. Instead of the equation, 20 yards of linen = 1 coat, we should have 20 yards of linen = 2 coats, since 1 coat would now contain only half the labour time embodied in 20 yards of linen. If, on the other hand, in consequence, say, of improved looms, this labour time be reduced by one-half, the value of the linen would fall by one-half. Consequently, we should have 20 yards of linen = ½ coat. The relative value of commodity A, i.e., its value expressed in commodity B, rises and falls directly as the value of A, the value of B being supposed constant.

II. Let the value of the linen remain constant, while the value of the coat varies. If, under these circumstances, in consequence, for instance, of a poor crop of wool, the labour time necessary for the production of a coat becomes doubled, we have instead of 20 yards of linen = 1 coat, 20 yards of linen = ½ coat. If, on the other hand, the value of the coat sinks by one-half, then 20 yards of linen = 2 coats. Hence, if the value of commodity A remain constant, its relative value expressed in commodity B rises and falls inversely as the value of B.

If we compare the different cases in I and II, we see that the same change of magnitude in relative value may arise from totally opposite causes. Thus, the equation, 20 yards of linen = 1 coat, becomes 20 yards of linen = 2 coats, either, because the value of the linen has doubled, or because the value of the coat has fallen by one-half; and it becomes 20 yards of linen = ½ coat, either, because the value of the linen has fallen by one-half, or because the value of the coat has doubled.

III. Let the quantities of labour time respectively necessary for the production of the linen and the coat vary simultaneously in the same direction and in the same proportion. In this case 20 yards of linen continue equal to 1 coat, however much their values may have altered. Their change of value is seen as soon as they are compared with a third commodity, whose value has remained constant. If the values of all commodities rose or fell simultaneously, and in the same proportion, their relative values would remain unaltered. Their real change of value would appear from the diminished or increased quantity of commodities produced in a given time.

IV. The labour time respectively necessary for the production of the linen and the coat, and therefore the value of these commodities may simultaneously vary in the same direction, but at unequal rates or in opposite directions, or in other ways. The effect of all these possible different variations, on the relative value of a commodity, may be deduced from the results of I, II, and III.

Thus real changes in the magnitude of value are neither unequivocally nor exhaustively reflected in their relative expression, that is, in the equation expressing the magnitude of relative value. The relative value of a commodity may vary, although its value remains constant. Its relative value may remain constant, although its value varies; and finally, simultaneous variations in the magnitude of value and in that of its relative expression by no means necessarily correspond in amount. (emphasis mine)

In other words, we have direct empirical access only to the shifts in the relative proportions in which goods are exchanged. There is no way to get back “behind” these empirically perceptible shifts, to perceive what value is “in itself” – value is operating in the text here as an an sich. Lukács takes Marx to be arguing that this is how the matter appears from the standpoint of bourgeois political economy. Lukács therefore supposes that, from a different standpoint – the standpoint of the proletariat – there is a means to make transparent and explicit, an underlying reality that remains opaque and mysterious from other standpoints.

I take Marx’s point to be otherwise. On the one hand, I hear Marx’s argument as an account of how a concept like an an sich might emerge historically at a given moment, due to social actors’ experience with a very mundane dimension of their social existence that provides everyday practical exposure to navigating something like a phenomena/noumena divide. On the other hand, I hear Marx’s argument to be that value is an immanent order – something that has no separate existence apart from the flux in which it manifests itself – something that does not lie behind empirical phenomena or otherwise exist separately from empirical phenomena, such that it might explain those phenomena. Instead, value is a pattern of empirical phenomena – a “determination” (not a cause, but a specification) of the qualitative characteristics of their movements.

Long-term and contradictory historical trends to displace labour in certain forms by increasing productivity, while reconstituting labour in new forms by constituting new industries and new needs: these tendencies amount to a collective enactment or performance of human labour as a sort of social pivot around which other aspects of “material” life revolve. This social centrality of human labour – revealed over time as productivity increases do not lead to commensurate reductions in human labour expenditure – suggests that there is a unique and distinctive non-economic sense in which capitalist society values labour, quite apart from the role human labour might play as a motive force in material reproduction. Material reproduction, for Marx, might plausibly be facilitated by nature – or machinery. Capitalism, however, relies on human labour – even as it also continues to accumulate historically unprecedented technological, organisational, and scientific capacities that render the contribution of human labour as a motive force for material production, increasingly negligible. Marx suggests that the political economists both stumble across the traces of these trends, and then make the plausible – but inappropriate – move of substantialising what they find – treating the consequences of historical trends – treating value – as something whose existence becomes manifest in the movement of phenomenal forms, and therefore missing how value is not a justification or explanation or cause of the movements that take place, but rather itself a product or implicit order acted out in and through those movements themselves, and inseparable from them…

I’m expressing this in a very imprecise way – just scattering notes here for myself…

### 5 responses to “The Quantitative Indeterminacy of Value”

1. sachin garg May 5, 2008 at 5:28 pm

what is the quantitative techniques ?

2. N Pepperell May 5, 2008 at 7:27 pm

Yes, this is the question, isn’t it? 🙂

3. Mike Beggs May 6, 2008 at 11:45 am

I’m not sure Marx is criticising earlier political economists for substantialising or quantifying value. Generally his criticism is that they are inconsistent or incorrect in how they see value or price as being determined.

It’s just not true that Smith or Ricardo had historically-naive views of value, or saw it as a substance rather than a relation. Smith was acutely conscious of socio-historical change and how it affects production and exchange. The ‘Digression on Silver’ in Book One of the WoN, to take a single example, shows this pretty clearly.

Ricardo, meanwhile, was much less concerned with history but very interested in value as a relation that could _not_ be represented as inhering in a commodity. His puzzlings over this obsessed him towards the end of his life – famously he tried to conceive of a ‘standard commodity’ that could measure the value of other commodities without its own value changing with distribution between wages and profit, and realised that this was a can of worms.

Marx’s criticisms of political economists always take the form of trying to extract what is useful from what is confused. He wants to positively develop political economy as a science, including its quantitative dimensions, not to bury it.

So summing up his criticism of Smith in ‘Theories of Surplus Value’ he portrays him as oscillating between surface empiricism and exploring “more or less correctly” the “inner connection, the physiology… of the bourgeois system”. I basically agree with your take, that for Marx the ‘inner connection’ is immanent in the ‘surface flux’ (or at least that this is what he should have been saying), but it’s easy to see why people read him differently:

“Smith himself moves with great naïveté in a perpetual contradiction. On the one hand he traces the intrinsic connection existing between economic categories or the obscure structure of the bourgeois economic system. On the other, he simultaneously sets forth the connection as it appears in the phenomena of competition and thus as it presents itself to the unscientific observer just as to him who is actually involved and interested in the process of bourgeois production. One of these conceptions fathoms the inner connection, the physiology, so to speak, of the bourgeois system, whereas the other takes the external phenomena of life, as they seem and appear and merely describes, catalogues, recounts and arranges them under formal definitions. With Smith both these methods of approach not only merrily run alongside one another, but also intermingle and constantly contradict one another. With him this is justifiable (with the exception of a few special investigations, [such as] that into money) since his task was indeed a twofold one. On the one hand he attempted to penetrate the inner physiology of bourgeois society but on the other, he partly tried to describe its externally apparent forms of life for the first time, to show its relations as they appear outwardly and partly he had even to find a nomenclature and corresponding mental concepts for these phenomena, i.e., to reproduce them for the first time in the language and [in the] thought process. The one task interests him as much as the other and since both proceed independently of one another, this results in completely contradictory ways of presentation: the one expresses the intrinsic connections more or less correctly, the other, with the same justification—and without any connection to the first method of approach—expresses the apparent connections without any internal relation.” [TSV ch. 10]

On the other hand, Marx is even more favourable towards Ricardo, and because he saw him as basically right on the question of how to quantify value – and that he was consistent about it:

“But at last Ricardo steps in and calls to science: Halt! The basis, the starting-point for the physiology of the bourgeois system—for the understanding of its internal organic coherence and life process—is the determination of value by labour-time. Ricardo starts with this and forces science to get out of the rut, to render an account of the extent to which the other categories—the relations of production and commerce—evolved and described by it, correspond to or contradict this basis, this starting-point; to elucidate how far a science which in fact only reflects and reproduces the manifest forms of the process, and therefore also how far these manifestations themselves, correspond to the basis on which the inner coherence, the actual physiology of bourgeois society rests or the basis which forms its starting-point; and in general, to examine how matters stand with the contradiction between the apparent and the actual movement of the system. This then is Ricardo’s great historical significance for science.” [TSV ch. 10]

4. N Pepperell May 6, 2008 at 1:59 pm

Hi Mike – My target here wasn’t classical political economy, but rather a number of Marxist approaches to what Marx is trying to grasp with the concept of value. Marx’s critique of political economy acknowledges that political economy is a historicist form of thought – I’ve always claimed this. Marx then criticises the partial character – the incomplete character – of the form of historicism involved, but he doesn’t treat political economy (other than the most vulgar examples) as naively naturalising value. Similarly, his comments about the “relationality” of value are derived fairly directly from classical political economy: you’re right, and I’m not trying at all to contest this. I think Marx is making an argument that political economy doesn’t sufficiently grasp how this particular kind of relationality is constituted in practice – how it becomes a result.

My target here, though, wasn’t these sorts of things – apologies if this was unclear: it wasn’t what I had in mind, so I didn’t guard against this reading of the post. I see the opening chapter of Capital as laying the foundation for analysing certain forms of everyday consciousness and certain characteristic moves in philosophy, that revolve around notions of an “in itself”. My target here is Lukacs’ specific explanations of Marx’s argument about the “in itself” – that’s what I’m contesting. I’ve always read Marx as taking up from the political economists and then attempting to understand the social conditions for the plausibility – the social validity – of their positions. Marx can be very dismissive toward vulgar economy, but is (critically) respectful of Smith and Ricardo.

Sorry for the confusion (and also, on your other point that it’s somewhat easy to read Marx in the way I’m criticising here: I agree with this too – I’m obviously pushing for a different sort of reading, but I’m not unsympathetic to alternative readings: I think Marx opened himself in many ways to them…).

5. N Pepperell May 6, 2008 at 3:00 pm

P.S. Sorry for posting so abruptly – my schedule is beyond insane today, and so I don’t have time to be very nuanced 🙂 – but it occurred to me after I posted that I’m basically making a point somewhat similar to Elson here, about the sort of category “value” is, is this makes any more sense than what I wrote above. In any event, the post was probably too abbreviated to make much sense – I’m still processing scattered thoughts on Lukacs, but I didn’t have time when I wrote this post (or now) to explain how what I’ve written relates back to what’s worrying me about Lukacs, so the “motivation” for my post is probably profoundly unclear. Apologies for this…

Take care…