However, under capitalist machine production, the potential arises for productivity to rise sharply in one sphere relative to another, so that these disproportions may arise. For example, suppose the producers of linen produce 1,000 metres per year, and these exchange for 1,000 kg of corn, so that the needs of both producers and consumers are met. Then there is a sharp rise in productivity in textile production, so that 2,000 metres are produced in a year. The linen producers will still want their 1,000 kg of corn to consume, but its quite possible that the corn producers will not want 2000 metres of linen, even though the value of this linen is still equal to the value of the corn, i.e. both are equal to 1 years labour-time.
In that case, half of the labour-time spent on producing linen was not socially necessary labour. A disproportion has arisen due to different levels of productivity growth in the two spheres. A crisis of overproduction, therefore, arises in linen production. As Marx points out, such potential disproportions exist with all commodity exchange, but it is only because capitalism produces on such a mammoth scale, and because productivity is being continually revolutionised, but at different speeds, in different industries, that such disproportions and crises of overproduction becomes inevitable.
“If the necessary labour-time is given, and therefore also that a certain quantity of linen can be produced in one day, the question arises how many such days are to be used in the production of linen? The labour-time used on the total of particular products, in a year for example, is equal to a definite quantity of this use-value—for example, 1 yard of linen (say equivalent to 1 day’s labour)—multiplied by the number of days’ labour used in all. The total quantity of labour-time used in a particular branch of production may be under or over the correct proportion to the total available social labour, although each aliquot part of the product contains only the labour-time necessary for its production, or although each aliquot part of the labour-time used was necessary to make the corresponding aliquot part of the total product.” (p 231-2)
In other words, as explained above, it may be the case that any particular commodity unit is produced using only the necessary labour, and yet the total quantity of such commodities may be overproduced. I might produce a metre of linen by the most efficient means possible, but, if I produce 1,000 such metres, when there is only a demand for 800 metres, I have still overproduced 200 metres of linen, 20% of labour-time expended was not socially necessary.
“From this standpoint, the necessary labour-time acquires another meaning. The question is, in what quantities the necessary labour-time itself is distributed among the various spheres of production. Competition constantly regulates this distribution, just as it equally constantly disorganises it. If too large a quantity of social labour-time is used in one branch, the equivalent can be paid only, as if the correct quantity had been used.” (p 232)
Consequently, the value of this product is not equal to the total labour-time expended on its production, but only that which was necessary for the production of the output demanded. On that basis, the value of each commodity unit is proportionally devalued.
If 1,000 hours of labour are used in the production of 1,000 metres of linen, but a demand for only 800 metres exists, 20% of the labour expended was not necessary. The value of the 1000 metres is then only 800 hours, not 1000 hours, and the value of one metre of linen falls to 0.8 hours.
This is not the same as a fall in the value of linen due to the rise in productivity. For example, previously, in 1000 hours only 500 metres of linen may have been produced, making the value of each metre equal to 2 hours. The rise in productivity simply reduces the value per metre to 1 hour. The fall in the value to 0.8 hours is due to the fact that 200 metres are thereby overproduced relative to the demand, and that 200 hours of labour that were expended, were not socially necessary.
In other words, the changed conditions of productivity, in this branch of production, relative to other branches, has caused a disproportion, which results in an overproduction.
“Assuming that the commodity has use-value, the fall of its price below its value therefore shows that, although each part of the product has cost only the socially necessary labour-time
, a superfluous—more than necessary —total quantity of social labour has been employed in this one branch.” (p 232)
This is different from the fall in the market value of the commodity due to a reduction in the labour-time required on average for its production. For example, if producer A produces 100 metres of linen, in line with the average required for its production of say 10 hours, then, if a rise in productivity causes the average to drop to 8 hours, whilst A still requires 10 hours, then the value of A's production will be 8 hours, as defined by the social average, and not 10 hours, which is the labour-time they continue to embody in their individual production.