The real meaning of Piero Sraffa’s standard commodity

Currently, we’re examining how a market-based economy partially solves the coordination problem. We last discussed price adjustment, and soon will turn to quantity adjustment. However, I must postpone the main thread of this blog for a few weeks due to other commitments. So, instead, I will discuss another technical aside, to complement the previous foray on why the labour theory of value is true.

Technical blog posts should be simple, make a single point quickly, and then stop. In contrast, this post deals with quite complex and esoteric issues in the theory of economic value, is not quick, and – for the curious – leads down a long, twisty but eventually rewarding rabbit hole. My sincere apologies …

For the busy, the quick summary is this: Piero Sraffa heroically reconstructed aspects of the classical approach to objective economic value, but didn’t quite go the whole distance. Many of his followers therefore reject the possibility of a labour theory of value. They shouldn’t.

That’s it. If you’re prepared to accept that, then feel free to move on. But for the brave or foolhardy, or those with skin-in-the-game, here goes …


Piero Sraffa was a Marxist economist who spent most of his academic life at Cambridge University. He kept his Marxism under his hat, no doubt due to the chilling effect of the Cold War. He published few works, but all are significant, once understood in their historical context. Sraffa is rightly credited for helping to resurrect the classical surplus approach to economic analysis, at least in academic circles, due to the publication of his enigmatic, terse and theoretically significant treatise, The Production of Commodities by Means of Commodities (PCMC). In this book Sraffa sticks a knife into neoclassical economic ideology. But here I want to concentrate on another aspect of Sraffa’s work – his construction of an invariable measure of objective value. Just like we measure length with a ruler, we need something analogous to measure economic value.

David Ricardo defined the problematic. He wished to identify an Archimedean standpoint, outside the marketplace, from which to measure the objective value of commodities. Although he knew of โ€œno other criterion of a thing being dear or cheap but by the sacrifices of labour made to obtain itโ€ his own arguments demonstrated that the profit component of equilibrium prices appears to be unrelated to labour cost. Although โ€œthe great cause of the variation of commodities is the greater or less quantity of labour that may be necessary to produce themโ€ there is another โ€œless powerful cause of their variationโ€, which Ricardo suggested was โ€œa just compensation for the time that profits were withheldโ€. In consequence, natural prices (the measurand) vary independently of real costs of production defined in terms of labour costs (the candidate measure of value). A measure that fails to vary with its measurand is not fit for purpose.

Ricardo grappled with this problem, and wrote a remarkable unfinished essay on the topic in the last weeks of his life, which finally concluded that โ€œit must then be confessed that there is no such thing in nature as a perfect measure of valueโ€. Ricardo retreated to proposing approximate, and therefore, imperfect measures of value, which minimise the discrepancies between the measure and measurand. But a ruler that, on theoretical grounds alone, fails to in variably measure length is not merely an imperfect empirical tool โ€“ it implies that oneโ€™s theory of length is flawed.

(As I may discuss another time, Ricardo’s problem of an invariable measure of value is the same problem Marx was trying to solve with his theory of the transformation in Volume 3 of Capital. Much of the pro and anti Marxist literature fails to explicitly link the two problems).

Sraffa’s incomplete reduction to dated quantities of labour

Anyhow, Sraffa was acutely aware of the problems of the classical labour theory (for example, he edited, with Maurice Dobb, The Works and Correspondence of David Ricardo). Sraffa demonstrated, in PCMC, that competitive prices necessarily vary independently of classical labour values by representing competitive prices as a โ€œreduction to dated quantities of labourโ€. This is a โ€œsum of a series of terms when we trace back the successive stages of the production of the commodityโ€ (this is vertical integration again). The costs of production at each ‘stage’ consist of the wages of labour and the interest on the money-capital advanced (to fund production) compounded over the ‘duration’ of the advance. Sraffa therefore reduces competitive prices to a sum of labour costs and interest income.

Sraffa’s reduction equation makes it particularly clear that competitive prices can change due to an alteration in the wage or interest-rate, even though the labour supplied to produce commodities remains constant. Sraffa therefore rejects the idea that real costs, such as labour time, can function as a measure of objective value. In consequence post-Sraffian scholarship is near unanimous in rejecting this aspect of classical theory, especially Marx’s assertions of a necessary link between prices and labour time.

In the paper and talk, attached at the close of this post, I demonstrate that Sraffa’s reduction equation is incomplete in the specific sense that some actual labour supplied during the โ€œsuccessive stages of the production of the commodityโ€ is missing. The key issue is that classical labour values, which Sraffa employs, do not include the labour supplied to produce capitalists’ real income as a cost of production. In a very literal sense, classical labour values are counterfactual, not actual, measures of the labour supplied to produce commodities in the institutional circumstances of a capitalist economy.

In contrast, we can construct the complete โ€œreduction to dated quantities of labourโ€ equation that includes this labour. Competitive prices, in this alternative but quantitatively equivalent representation, completely reduce to a sum of wage costs only. The complete reduction equation makes it particularly clear that competitive prices are always proportional to actual labour costs, regardless of the distribution of income. Sraffa’s rejection of the possibility of a labour theory of value is therefore based on an incomplete โ€œreduction to dated quantities of labourโ€.

Sraffa’s incomplete reduction to a variable quantity of labour

Nonetheless, Sraffa constructs a subtle and refined objective theory of value, which reconstructs some aspects of the classical theory. In particular Sraffa proposes a partial solution to Ricardo’s problem of an invariable measure of value.

Sraffa observes that competitive prices are relative, rather than absolute, since they are under-determined up to an arbitrary choice of numeraire. For example, assume that the natural prices of a two-commodity economy are p1=1 and p2=4, if we choose the numeraire p1=1; or p1=1/4 and p2=1, if we choose the numeraire p2=1 (stop and think about this for a bit, it’s pretty simple but subtle). In both cases the relative cost structure is identical. The choice of numeraire then fixes an absolute, although arbitrary, scale.

Sraffa notes the following problem: consider a change in the distribution of income (i.e. a change in the wage or profit-rate) that alters the structure of natural prices. For example, assume that prices change to p1=1 and p2=2, given our choice of numeraire p1=1. Can we therefore assert that p2 halved due to the change in the distribution of income?

No, because the change in the distribution of income alters the entire structure of competitive prices, including the relative price of the numeraire commodity. For example, if we instead had chosen the numeraire p2=1 then we might be tempted to assert that p2 remained constant while p1 doubled.

Sraffa states โ€œit is impossible to tell of any particular price-fluctuation whether it arises from the peculiarities of the commodity which is being measured or from those of the measuring standardโ€. Sraffa’s problem is precisely Ricardo’s problem of finding an invariable measure of value, except restricted to the special case of changes in the distribution of income.

It is not sufficiently appreciated that Sraffa’s problem only arises because the classical labour theory fails to explain the structure of competitive prices. If that theory succeeded then competitive prices would reduce to labour values, and therefore labour values would function as price-independent, absolute measure of value.

However, the failure of the classical theory does not prompt Sraffa to adopt Bailey‘s nihilist position that competitive prices are merely exchange ratios (i.e., relative quantities) that do not denote, refer to, or measure some non-price substance. Instead, Sraffa, via a remarkable and often misunderstood argument, constructs an invariable measure that partially solves Ricardo’s problem.

The invariable measure is Sraffa’s celebrated โ€œstandard commodityโ€, which is a special collection of commodities with the peculiar property that its price is independent of the fluctuations in prices that accompany a change in the distribution of income. In the attached paper I explain, in precise and formal terms, how Sraffa’s standard commodity functions as an Archimedean standpoint, outside the system of relative prices, from which to measure  the objective value of commodities. Once we adopt the standard commodity as numeraire then we can be sure that any price fluctuations do not arise โ€œfrom the peculiarities … of the measuring standardโ€.

After this breakthrough Sraffa then delivers something like a punchline to an elaborate theoretical joke. Sraffa reduces his standard commodity to the (variable) quantity of labour that can be purchased by it. (The quantity is variable because the price of the standard commodity, although independent of prices, nonetheless varies with the distribution of income). Sraffa explains how we can adopt this variable quantity of labour as the numeraire without needing to specify the composition of the standard commodity! The standard commodity, therefore, is โ€œa purely auxiliary constructionโ€, a mere step in an argument towards the conclusion that a scalar quantity of labour, rather than a heterogeneous collection of commodities, is an invariable measure of value.

Sraffa’s argument reconstructs, in attenuated form, aspects of the classical theory of value, specifically the attempt to measure a given physical surplus in terms of labour costs and relate how that quantity of labour breaks down into wage and profit income. However, as Sraffa notes, this invariable measure is not a real cost of production but โ€œequivalent to something very close to the standard suggested by Adam Smith, namely ‘labour commanded’โ€.

A general labour theory of value, which admits both classical and super-integrated labour values, provides an entirely different perspective of Sraffa’s problematic, and clarifies the meaning of Sraffa’s argument.

In the paper, I prove that Sraffa’s โ€œvariable quantity of labourโ€ is the super-integrated labour value of the standard commodity. Sraffa’s invariable measure of value is therefore a proxy or indirect reference to the actual (non-classical) labour costs supplied to produce commodities. In consequence, Sraffa’s invariable standard is not merely a ‘labour commanded’ but also a ‘labour-embodied’ measure of value that denotes a real cost of production. Sraffa implicitly refers to super-integrated labour value, which is the external standard of price missing from the classical theory.

Sraffa’s remarks that some properties of his argument are โ€œcuriousโ€, especially โ€œthat we should be enabled to use a standard without knowing what it consists ofโ€. The mystery lessens once we realise that Sraffa’s argument is highly indirect: the standard commodity is a bridge from the premise that labour values cannot measure competitive prices to the conclusion that a โ€œquantity of labourโ€ is nonetheless an invariable measure. The bridge can be thrown away, as Sraffa’s analysis demonstrates, because the premise is mistaken. Sraffa’s argument is a rather large hint that an invariable measure of value exists, which is not a composite, but rather a single substance.

Sraffa’s remarkable construction of the standard commodity therefore partially identifies the actual labour costs that natural prices denote. In consequence, Sraffa’s original problem of choosing an invariable numeraire disappears since we immediately possess a real cost standard outside the market and its system of relative prices.

In conclusion, Sraffa’s masterful reconstruction of classical economics remains incomplete since it fails to reconstruct a measurement relation between competitive prices and real costs of production. His theoretical tools gave us a knife, but less so a ruler. We need the perspective of a more general theory to continue Sraffa’s research programme and lay the foundations for the complete reconstruction.

A paper on the real meaning of Sraffa’s standard commodity

An accompanying talk on the real meaning of Sraffa’s standard commodity:


1 Comment

  1. Interesting. I would just like to make a comment relating to the “invariable measure” of value, because I think Sraffa, from what I got from your article here at least, re-invents in essence the wheel. What is interesting is how similar this problematic is to problems that pertain to physics and the way theories are formulated to describe the object of interest. For example, it is known that certain objects that are meant to have “objective” essence (since they correspond to physical processes) should be independent of the frame of reference we use. That, however, does not mean that we get the same “numbers” when we measure these objects under different frames of reference but that, whatever the numerical representation is under a certain frame of reference (coordinate system), the object still remains invariant. A typical example is the tensor, which arises naturally in the description of many phenomena. A stress tensor is represented by a 2D matrix. Its entries will differ for different depending on the coordinate system used, but the results you get (failure at a point on a body for example) are (and should be) always the same. A typical test we use to see if a tensor in particular is “objective” is how it transforms under a rotation of the coordinate system. I think similar ideas can apply or at least inspire the treatment of the value theory. That the numenaire can be arbitrary also reminds of the total potential energy calculations, where you set the level that you measure the potential energy from arbitrarily but the minimization principle always holds. These all point to objective processes.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s