## Friday, October 26, 2012

### The standard commodity and the labor theory of value

In a previous post I promised to deal with Sraffa's standard commodity (chapter IV of his Production of Commodities by Means of Commodities, PCMC). So here is a brief and simple explanation of this somewhat arcane topic. The standard commodity is basically a more developed version of Ricardo's corn model.

Ricardo, remember, wanted to explain the rate of profit, to show that tariffs on corn (not corn, grain imports really) would reduce the rate of profit, and as a result would be detrimental for capital accumulation (which was based on profits for him). To determine the rate of profit he needed to obtain the prices at which commodities were bought and sold. Yet, to get the prices he needed the uniform rate of profit earned on the production of those commodities.

His solution in the Corn Essay of 1815 was brilliantly simple. Assume that the economy produces corn by means of corn seeds and labor. So the total output consisted of corn, the wages paid to workers were also in corn, and of course the means of production advanced to produce corn were corn seeds. So the profit rate could be measured as the surplus left over after wages were paid over the amount of corn advanced for production. A physical ratio that was independent of prices [Note that tariffs would increase the rents of landowners and reduce the profits left over for accumulation].

Malthus, Ricardo’s nagging friend, suggested that this would not be true in a world in which there are more goods than corn. This is, in fact, correct. Once you have that the means of production and the surplus are not a single commodity you need a numeraire to sort out the problem, which brings about the problem of determining profits (distribution) independently from relative prices (value).

Ricardo’s solution in his Principles was the Labor Theory of Value, meaning to assume that relative prices were proportional to the amounts of labor directly and indirectly used in production. Lets say we have two commodities i and j, produced with a homogenous type of labor that is paid w and a normal rate of profit is obtained.

We have:

pi = wli(1+r)
pj = wlj(1+r)

where l is the amount of labor used in production. Hence, the relative prices are proportional to labor ratios, since:

pi/pj = [wli(1+r)]/[wlj(1+r)] = li/lj

But Ricardo knew that his solution had a fatal flaw (and so did Marx, by the way). The problem is that once you introduce produced means of production it is not possible anymore to assume that relative prices would be exactly proportional to the amounts of labor directly and indirectly used in production. If for simplicity we assume that it takes time to produce the means of production, then we can re-write the price equations as:

pi = wli(1+r)ti
pj = wlj(1+r)tj

where the superscript ti and tj stand for the time it takes to produce the means of production in sector i and j. Clearly relative prices would be proportional to labor incorporated if r=0 or ti=tj [that is, in Marx’s terms, no means of production or same organic composition of capital].

In any other situation you would have that prices depend on the proportion of labor to means of production, but also retroactively on the proportions of labor to means of production with which the means of production have been produced, or in the example above the time it took for the means of production to be produced [see paragraph 20 in PCMC, pp. 16-17 in the linked edition].

In general, you would have that some commodities would have a higher proportion of labor to means of production and some would have a lower proportion of the same ratio. Or, in terms of the example, some commodities would be above and some below the average time that would make prices proportional to labor. So in general there are surplus and deficit industries, with higher and lower proportions of labor to means of production in their production [see paragraph 17, pp.14-15].

Sraffa’s standard commodity is based on the possibility of building a composite commodity that would be produced in such a way that it would have the same proportion of labor to means of production than the means of production used in its production, and would be in the exact threshold between surplus and deficit industries [the proof that all prices systems have such a standard commodity is provided in a simple thought experiment in paragraph 37, pp. 30-31].

Note that the proportion of labor to means of production in the production of the surplus product, and in the production of the means of production could be measured in terms of the standard commodity, and, hence, as in Ricardo’s corn model, as a physical ratio independently from relative prices. Like the Ricardian (and Marxist) theory, the standard commodity implies that the rate of profit is determined by the material conditions of production and the need of reproducing the system, including the labor force. The amount of the surplus, or what is kept by workers, is independent of the determination of relative prices.

Not only is distribution determined by conflict, and the remuneration of capital is NOT dependent on the services rendered by ‘capital’ (the means of production) in the productive process, but also exploitation is possible and likely, since it is a common way of extracting surplus from society. Further, the standard commodity is perfectly compatible with a notion of a labor theory of value. Note that the standard commodity may command a certain amount of labor and as a result prices could be determined as ratios of labor commanded in a Smithian way [see paragraph 2, Appendix D, pp. 112].

1. An excellent and useful comment -- and a timely one too! In this day and age, with 'Big Data' and Web Analytics, we are learning again the lessons of Sraffa and Ricardo (and maybe Marx) -- it seems that every generation is doomed to rethink these issues, and master for themselves, by the sweat of their brow, the meaning and understanding that previous generations attained.

Paid search advertising requires search time (of products) in order to produce conversion value in firms (realised profit) that leads them to advertise further, resulting in more attention during the next cycle of search-click-buy. That is, the process is circular and self-replicating.

This is, in fact, the core meaning of the PageRank model (itself mathematically identical to Leonief's Input-Output model, if your background is in Economics and not 'Big Data').

Sraffa's 'standard commodity' is, I suppose, just the dominant eigenvector of the Google matrix. That is, the vector containing the page ranks of the nodes in the production graph. Some pages are Sraffa's luxuries, and result in an exit from the system (absorbing Markovian states, for those who dabble in such things).

1. I know someone told me recently. The production of information by means of information!

2. Thanks for the link to Ricardo's essay. The man was a genius, but his lack of finesse in writing is remarkable. He apparently didn't think it was necessary to state in Principles that he was assuming the only commodity to be corn -- let alone explain *why* he was assuming this. (Some other imprecisions of expression have been frequently noted).

1. That's pretty much the sense that his contemporaries seemed to have about Ricardo. In a parliamentary debate on 30 May 1820 on petitions upon the subject of 'agricultural distress' Ricardo had been accused of having 'argued as if he had dropped from another planet' (Ricardo, Works, Vol. V, p. 56).

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