So, with all those prefaces out of the way, let’s learn some economics.

## 1. The two factors of the commodity: use-value and value (substance of value, magnitude of value)

Here’s that often-quoted line:

The wealth of societies in which the capitalist mode of production prevails appears as an ‘immense collection of commodities’

So first up, what’s a commodity?

First, it’s an ‘external object’ that satisfies arbitrary human needs. Every useful thing, says Marx, has many quantitative and qualitative properties implying many uses.

The usefulness of a thing makes it a use-value

I note that the phrases is ‘makes it a use-value’ not ‘gives it a use-value’. That is, ‘use-value’ doesn’t seem to be a property of an object, but rather the object itself is a use-value ‘or useful thing’. Honestly I find the use of the word ‘value’ here kind of confusing.

Nevertheless, we have established: objects that have a use together constitute use-values. Marx notes that it’s independent of the amount of labour used to make something. (I also notice there’s no intrinsic reason a service can’t also be a use-value?)

Marx emphasises a difference between the ‘material content’ and ‘social form’ of wealth:

Use-values are only realized [verwirklicht] in use or in consumption. They constitute the material content of wealth, whatever its social form may be. In the form of society to be considered here they are also the material bearers [Trager] of… exchange-value.

So ‘use-values’ are qualitative and essentially this word refers to how an object is actually used. Meanwhile ‘exchange-value’ is only a thing in ‘the form of society to be considered here’, capitalism.

Marx introduces exchange-value by pointing out that the quantitative relation, of how many of one thing you can exchange for another thing, looks pretty arbitrary at first glance and varies all over with time and place.

Exchange-values, Marx says, are transitive. That is, if A can be exchanged for B and C, then B and C must also be exchangeable. This, says Marx, implies there’s some underlying quantity that is equal between in each of the exchanged things.

In short, it is exchanged for other commodities in the most diverse proportions. Therefore the wheat has many exchange values instead of one. But x boot-polish, y silk or z gold, etc., each represent the exchange-value of one quarter of wheat. Therefore x boot-polish, y silk, z gold, etc., must, as exchange-values, be mutually replaceable or of identical magnitude. It follows from this that, firstly, the valid exchange-values of a particular commodity express something equal, and secondly, exchange-value cannot be anything other than the mode of expression, the ‘form of appearance’, of a content distinguishable from it.

Marx says that ‘exchange is transitive’ implies ‘there must be a common underlying quantity determining exchange values’. If you accept the former, you should accept the latter. (Later, I believe he will show how the common underlying quantity leads to exchange values that are transitive.)

Of course, this argument depends on the reader accepting that exchanging things is transitive. So I’m led to ask, what if they weren’t transitive? e.g., if you could exchange 1 quarter wheat for $$x$$ boot-polish and $$y$$ silk, but exchange $$x$$ boot-polish for $$y'$$ silk where $$y'\ne y$$. In that case, if you start with some wheat, and assuming ‘can be exchanged for’ is reflexive, and $$y'>y$$ you could obtain arbitrary amounts of wheat by trading 1 quarter wheat for $$x$$ boot-polish for $$y'$$ silk for $$\frac{y'}{y}$$ wheat. So if the system of exchange is to work at all, exchange has to be transitive?

After a discussion with edwad and a reminder about what David Harvey said, the answer is apparently that at this stage in the text, Marx isn’t trying to prove his assertions, so much as lay out the overall logic of his theory to be fleshed out later. I kind of wish he’d state that more clearly, something like ‘we will demonstrate that exchange is transitive later’.

Marx says that whatever this underlying thing is, it has to be totally abstracted from any ‘natural property’ of commodities.

But clearly, the exchange relation of commodities is characterized precisely by its abstraction from their use-values. Within the exchange relation, one use-value is worth just as much as another, provided only that it is present in the appropriate quantity.

To put it in vaguely mathematical language, because transitivity, symmetry and reflexivity apply, an equivalence relation applies. As far as this equivalence relation is concerned, use value is totally irrelevant.

Marx then declares that, having abstracted away all physical qualities, all that we have is that a commodity is ‘the product of labour’. But not just labour…

But even the product of labour has already been transformed in our hands. If we make abstraction from its use-value, we abstract also from the material constituents and forms which make it a use-value. All its sensuous characteristics are extinguished. Nor is it any longer the product of the labour of the joiner, the mason or the spinner, or of any other particular kind of productive labour. With the disappearance of the useful character of the products of labour, the useful character of the kinds of labour embodied in them also disappears; this in turn entails the disappearance of the different concrete forms of labour.

So it’s not any particular kind of labour represented by exchange-value, but ‘abstract’ labour. This leads to a third kind of value, ‘crystals’ of the ‘social substance’ of human labour, which Marx calls ‘commodity values’ (the translator notes Warenwerte as the German word). But he mostly just calls this unqualified ‘value’. Perhaps this is a translation issue, and the unqualified ‘value’ is somehow syntactically distinct in German.

Anyway, we have three kinds of value:

use-value
qualitative measure of what uses humans might put something to
exchange-value
quantitative measure of the amount of other commodities that one commodity might be exchanged for, in which the details of the commodity are irrelevant
value (commodity-value)
quantitative measure of the amount of abstract human labour embodied in an object.

I really wish Marx would not use value unqualified for one of the things and hyphenated types of value in the other two.

In any case, Marx briefly says that the analysis of value will lead us back to exchange-value, but for now mostly talks about exactly what sort of abstract labour he means. He does not mean the amount of labour taken by an individual worker, but rather the whole ‘homogeneous mass of human labour-power’, in which the individual ‘units of labour-power’ are interchangeable. (The distinction between ‘labour’ and ‘labour-power’ will become important later I believe.)

Here is a definition:

Socially necessary labour-time is the labour-time required to produce any use-value under the conditions of production normal for a given society and with the average degree of skill and intensity of labour prevalent in that society.

To clarify this, Marx gives an example of a new technology (the power loom) drastically reducing the socially necessary labour time to produce a use-value, and therefore reducing the value produced by an hour’s work by a worker using the old method (hand-looms). There’s a list of things that might affect the labour-time required for production:

it is determined amongst other things by the workers’ average degree of skill, the level of development of science and its technological application, the social organization of the process of production, the extent and effectiveness of the means of production, and the conditions found in the natural environment.

He discusses a few examples, concluding:

The value of a commodity, therefore, varies directly as the quantity, and inversely as the productivity, of the labour which finds its realization within the commodity.

This all makes sense with the definition given of socially necessary labour-time, but so far it’s just definitions. That is, if we define ‘value’ as socially necessary labour-time, it might be a well-defined quantity, but it’s not necessarily a useful quantity or leading to any empirical predictions.

Marx also notes that use-values, and even labour, does not necessarily correspond to values.

A thing can be a use-value without being a value. This is the case whenever its utility to man is not mediated through labour. Air, virgin soil, natural meadows, unplanted forests, etc. fall into this category. A thing can be useful, and a product of human labour, without being a commodity. He who satisfies his own need with the product of his own labour admittedly creates use-values, but not commodities. In order to produce the latter, he must not only produce use-values, but use-values for others, social use-values.

And not just produced for others, but produced to exchange to others, not under feudalism. Having some use is also necessary, or else the labour ‘does not count as labour’. This seems awkwardly ad-hoc, to say that use-value does not enter the question of value unless it’s nonexistent? Though with a sufficiently broad definition of ‘use’, you could probably say that if people want it even for something totally pointless, it has a use.

## The Dual Character of the Labour Embodied in Commodities

Initially the commodity appeared to us as an object with a dual character, possessing both use-value and exchange-value. Later on it was seen that labour, too, has a dual character: in so far as it finds its expression in value, it no longer possesses the same characteristics as when it is the creator of use-values.

This, apparently, is ‘crucial to an understanding of political economy’.

Guess what? It’s time for the infamous ‘coat and 10 yards of linen’ example.

Let us take two commodities, such as a coat and 10 yards of linen, and let the value of the first be twice the value of the second, so that, if 10 yards of linen = W, the coat = 2W.

I don’t like the way Marx uses mathematical notation so loosely but whatever. I thought we’d said that objects are use-values, not values, so it would seem to make more sense to write something like

\begin{align}val(\text{10 yards of linen})&=W\\ val(\text{1 coat})&=2W\end{align}

This should make it clearer that what we’re equating is not the objects themselves, but the values.

Anyway, it doesn’t really matter.

Another definition:

The coat is a use-value that satisfies a particular need. A specific kind of productive activity is required to bring it into existence. This activity is determined by its aim, mode of operation, object, means and result. We use the abbreviated expression ‘useful labour’ for labour whose utility is represented by the use-value of its product, or by the fact that its product is a use-value. In this connection we consider only its useful effect.

Marx declares that the coat and linen can only ‘confront each other as commodities’ because the kinds of labour used to produce them are different. The variedness of stuff ‘reflects’ labour that’s just as varied, which Marx terms the social division of labour, noting that it’s necessary for commodity production (but the converse is not true, and you can have division of labour without commodities).

To illustrate this, Marx cites the ‘primitive Indian community’; it’s not clear (and the translator does not comment) whether Marx means India the country, or the pejorative term for Indigenous people. I’d be skeptical that no Indigenous people had any kind of commodity production, even if not on the same scale as imperial capitalism. Marx’s second example, of workers within a factory dividing labour but not to trade with each other, is a much better and more relevant one.

To sum up, then: the use-value of every commodity contains useful labour, i.e. productive activity of a definite kind, carried on with a definite aim. Use-values cannot confront each other as commodities unless the useful labour contained in them is qualitatively different in each case.

The result is that a society of independent, private commodity producers ‘develops into a complex system, a social division of labour.’

Useful labour, Marx announces, is

a condition of human existence which is independent of all forms of society; it is an eternal natural necessity which mediates the metabolism between man and nature, and therefore human life itself.

But with the social division of labour, it’s possible for someone to become a tailor.

Marx then addresses the ‘externalities’ so often brushed aside by other kinds of economics:

If we subtract the total amount of useful labour of different kinds which is contained in the coat, the linen, etc., a material substratum is always left. This substratum is furnished by nature without human intervention. When man engages in production, he can only proceed as nature does herself, i.e. he can only change the form of the materials.13 Furthermore, even in this work of modification he is constantly helped by natural forces. Labour is therefore not the only source of material wealth, i.e. of the use-values it produces. As William Petty says, labour is the father of material wealth, the earth is its mother.

I’m going to be interested to see how much Marx, who’s famously incisive in his analysis of labour, takes into account the environment.