Subsystems are implicitly defined by an economy’s technology and help us to partially solve the coordination problem. Subsystems are also essential for a complete understanding of Marx’s theory of value. In this post, I want to take a first step towards that goal by examining the relationship between subsystems and Marx’s concept of the “value” of reproducible commodities.
It’s a fact that aeroplanes are significantly more expensive than pens. Why? Clearly, far more of society’s material resources (metals, plastics, electronics, fabrics etc.) are used-up to manufacture a plane compared to a pen. An aeroplane is objectively more “difficult to produce” than a pen. Perhaps this objective difficulty of production explains why some things cost more money than others?
Before we can pursue this thought (which we will, eventually) we first need to clarify what we mean by objective difficulty of production.
Producing an aeroplane consumes more of society’s resources than a pen. Can we quantify this?
We immediately face a problem: we cannot, in all good conscience, add up quantities of disparate things. It’s not helpful to state that an aeroplane ‘costs’, say, 50 tons of aluminium, 1 ton of plastic, 0.1 tons of fabric, 50 million labour hours etc. We need a method to reduce amounts of qualitatively different real resources to a single measure.
It turns out that subsystems already provide such a method.
Let’s return to our simple economy (with only 3 different commodities) and recall how we vertically integrated corn production:
As we continue the process we find that all the input coefficients vanish in the infinite limit. We then sum all the input paths to give us the final corn subsystem:
What do the final quantities in the subsystem — 1.25 corn, 5 iron and 3.875 labour hours — really represent?
Look again at Figure 1, and notice that when we vertically integrate backwards we treat the inputs to corn production (that is the seed corn, iron and labour) in an asymmetrical manner. We always reduce the corn and iron inputs to their inputs, and do so ad infinitum. But with labour inputs we stop, and don’t reduce any further. (We could reduce further, since labour has inputs, namely the real wage, which in our example is corn and sugar).
So the labour inputs, during vertical integration, are treated differently — they are always a terminus. But for every other input we keep on reducing.
As a reminder, here’s the process after a few more steps. Notice that, in every layer, we see some terminal nodes, and those terminal nodes are always labour inputs:
In consequence, we can view vertical integration as an operation that reduces 1 unit of a commodity (e.g., corn) to the qualitatively different commodities directly used-up to produce it. We then replace all the direct inputs, except labour, by further reducing those inputs to their direct inputs (e.g., the seed corn and iron). And we keep going, replacing more and more indirect commodity inputs, until, in the limit, there are no more inputs remaining. But we never replace the used-up labour.
Hence the quantity of 3.875 labour hours, in the final subsystem of Figure 2, measures the total labour time used-up to replace all the other used-up inputs. Note the asymmetry: labour is a resource that’s used-up, whereas all other commodity inputs are resources that are not used-up, but replaced.
So (hypothetically) if we produce according to the activity levels of the subsystem in Figure 2, as we did when we first introduced vertical integration, we find that our corn stock increases by 1 (since we’re producing 1 unit of corn as output), and our stock of iron remains constant (since the subsystem replaces iron) but our stock of labour reduces by 3.875 hours (since the subsystem uses-up, and does not replace, labour inputs).
The meaning of the 3.875 labour hours in the corn subsystem should now be clear: they measure the total labour resources used-up to produce 1 unit of corn and perfectly replace every other used-up resource. So if we produce according to the subsystem then only one resource is actually used-up, and that’s labour. Hence, in these precise circumstances, the real cost of producing corn is measured in terms of labour alone.
Subsystems therefore solve the problem we originally stated: they reduce qualitatively different resources to a single resource. So we can measure the objective “difficulty of producing” corn, or iron, or sugar — or planes or pens — in terms of labour time. And we can also say, as an operational definition, that an aeroplane is objectively more difficult to produce than a pen because it takes more vertically integrated labour time to produce.
But there’s one last twist in this particular tale.
What is this vertically integrated labour time anyway? Whose labour is it? And when is the work actually performed?
One tempting — but wrong — answer is that the operation of vertical integration corresponds to production further and further back in historical time. Each step of the reduction is labour that occurred before — antecedent labour — and, as we reach the infinite limit, we find labour bootstrapping itself from nothing to make all the variety of commodities we see around us today.
Of course, this picture is nonsensical. (Although you might be surprised to know that some economists, both for and against Marx’s theory of value, promulgate it).
Instead, as we saw in self-replacing subsystems, the “vertically integrated labour time” of the corn subsystem is the total labour hours that are simultaneously applied, by workers in different sectors of production, in order to produce 1 unit of corn as output (and replace all the used-up input stocks). The 3.875 hours includes farm labour (sowing and reaping corn) and factory work (smelting and rolling iron). And, more generally, the vertically integrated labour time used-up to produce an aeroplane includes a bewildering array of concrete activities all coexisting together, producing many different kinds of commodities, and in many different sectors of the economy.
Marx defined the “value of a commodity” (in contrast to its price or its usefulness) as “the labour time socially necessary for its production” (Capital, Vol 1).
The word “value” is overloaded. So, to avoid confusion, we’ll use the more specific term “labour value” for Marx’s “value”. And we’re going to deliberately ignore the modifier “socially necessary” (for now).
Marx, following the Ricardian socialist Thomas Hodgskin, illustrated the idea of labour time in terms of coexisting labour. This concept is so important it’s worth quoting Marx’s remarks at length (this excerpt is from Capital Vol 4, Theories of Surplus Value):
Cotton, for example, advances from one phase of production to another. It is produced first of all as raw material, then it is subjected to a number of operations until it is fit to be exported or, if it is further worked up in the same country, it is handed over to a spinner. It then goes on from the spinner to the weaver and from the weaver to the bleacher, dyer, finisher, and thence to various workshops where it is worked up for definite uses, i.e., articles of clothing, bed-linen, etc. Finally it leaves the last producer for the consumer and enters into individual consumption if it does not enter into industrial consumption as means (not material) of labour. But whether it is to be consumed industrially or individually, it has acquired its final form as use-value. What emerges from one sphere of production as a product enters another as a condition of production, and in this way, goes through many successive phases until it receives its last finish as use-value. Here previous labour appears continually as the condition for existing labour.
Simultaneously, however, while the product is advancing in this way from one phase to another, while it is undergoing this real metamorphosis, production is being carried on at every stage. While the weaver spins the yarn, the spinner is simultaneously spinning cotton, and fresh quantities of raw cotton are in the process of production.
[Raw] cotton, yarn, fabric, are not only produced one after the other and from one another, but they are produced and reproduced simultaneously, alongside one another. What appears as the effect of antecedent labour, if one considers the production process of the individual commodity, presents itself at the same time as the effect of coexisting labour, if one considers the reproduction process of the commodity, that is, if one considers this production process in its continuous motion and in the entirety of its conditions, and not merely an isolated action or a limited part of it. There exists not only a cycle comprising various phases, but all the phases of the commodity are simultaneously produced in the various spheres and branches of production.
Marx paints a vivid picture of the production of cotton as a living process occurring across an economy all the time and in parallel. From this bird’s eye view corn is produced by an definite amount of coexisting labour working together at the same time.
This is a good place to stop. I’ll conclude with an assertion: Marx’s concept of labour value is identical to the total coexisting labour supplied to produce 1 unit of a commodity and replace all the used-up inputs.
There are immediate consequences of this assertion, which we’ll merely note in passing for now. First, labour value is a property of a social practice at a point in time, specifically the productive techniques (and therefore labour value has a “social reality” and is definitely not a substance literally ’embodied’ within a commodity). Second, vertical integration adds up huge numbers of different labouring activities (sowing, reaping, smelting, rolling, planning, directing, lifting, moving etc.) across many different sectors of production. So it immediately abstracts human labour from its many concrete manifestations. Third, since subsystems help solve the coordination problem we expect Marx’s labour values to be somehow connected to the equilibrium, or balanced, conditions in an economy.
The next time you hold a commodity in your hand — a computer mouse, a biscuit, a mug or your smartphone — take a moment to imagine its technology graph “out there” in the social world, and consider all the coexisting labour, in all the different branches of production, that worked together to bring it into your reach. What an extraordinary feat of human ingenuity and organisation! A large and diverse set of difficulties had to be overcome to manufacture these wonderful articles. These difficulties are an objective property of our economic practices that we can, in principle, measure — in terms of hours of labour time.
(I thought this post would be short and relatively self-contained, but — as is always the case with foundational concepts that come with a lot of history and baggage — its difficult to focus on the substantive (and hopefully new and clarifying) content without straying too far ahead and without acknowledging the wider debates. Well, this will have to do to begin with. There’s a great deal more to say … but we mustn’t tarry too long here. All I wanted to establish, for now, was (i) the idea of an objective value of a commodity and (ii) its precise meaning in terms of the coexisting labour supplied to an associated subsystem).
(Note that any system of measurement defines a standard unit (e.g., the metre). We never ask, “How many metres are in one metre?” since the measure of the standard unit is by definition a unit of the standard. In a labour theory of value the question, “What is the labour-value of one unit of direct labour?” is similarly ill-formed: the real cost of 1 hour of labour, measured by labour time, is 1 hour. No further reduction is possible or required. The self-identity of the measuring standard is a conceptual necessity in any system of measurement. So whether workers consume one bushel or a thousand bushels of corn to supply a unit of direct labour makes no difference to the labour value of that unit of direct labour: an hour of labour-time is an hour of labour-time. In consequence, the operation of vertical integration we have discussed above always terminates at labour inputs and does not further reduce labour inputs to the real wage.)
(There are alternative ways to define vertical integration. For example, we could decide to reduce labour to its inputs (the real wage) and instead nominate another commodity — say corn — as the resource that’s not replaced, but used-up. This alternative method of vertical integration measures difficulty of production in terms of any commodity. E.g., we can calculate the corn value of iron, the corn value of labour time etc. There is one restriction however: a truly useful objective standard needs to, ultimately, be an input in the production of every commodity. So some commodities — say smartphones — wouldn’t fit the bill. But many do (e.g., basic foodstuffs, oil, energy etc.) Why choose labour then? The full answer has to wait, but for now we can somewhat enigmatically state that it’s not up to us — as theorists — to choose. Our social practices in fact “choose” labour, whether we are aware of it or not. This insight is one of the ways Marx’s theory of value differs, and advances beyond, the classical real costs theories of production, which we find in thinkers such as Smith, Ricardo and Mill.)