In chapter four of TSV, Marx discusses two (or possibly three?) aspects of socially necessary labour time: the devaluation of labour and commodities produced under less efficient methods, and the fall in value of commodities when more have been produced than there is demand for. Note that pursuit of greater efficiency through economies of scale (see underlining) risks overproduction, which compounds the impact on the less efficient producers.
There is a teaser at the end of the last paragraph that could count as a third aspect of socially necessary labour time. If the production cost of linen remains the same while the production cost of other commodities rises, the relative value of linen to those other commodities would fall. I have a hard time deciding whether that is a distinctive case or simply another path to (relative) overproduction.
The shifting of labour and capital which increased productivity in a particular branch of industry brings about by means of machinery, etc., is always only prospective. That is to say, the increase, the new number of labourers entering industry, is distributed in a different way; perhaps the children of those who have been thrown out, but not these themselves. They themselves vegetate for a long time in their old trade, which they carry on under the most unfavourable conditions, inasmuch as their necessary labour-time is greater than the socially necessary labour-time; they become paupers, or find employment in branches of industry where a lower grade of labour is employed.
It may be noted in passing: that no more necessary labour-time is employed on a product than is required by society—that is to say, no more time than on the average is required for the production of this commodity—is the result of capitalist production, which even continuously reduces the minimum of necessary labour-time. But in order to do so, it must constantly produce on a rising scale.... 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.... 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.
The sinking of the relative value of the commodity as a result of altered conditions of production is something entirely different; this piece of linen on the market has cost 2s., equal for example to 1 day’s labour. But it can be reproduced every day for 1s. Since the value is determined by the socially necessary labour-time, not by the labour-time used by the individual producer, the day that the producer has used for the production of the one yard is now only equal to half the socially determined day. The fall of the price of his yard from 2s. to 1s.—that is, of its price below the value it has cost him—shows merely a change in the conditions of production, that is, a change in the necessary labour-time itself. On the other hand, if the production costs of the linen remain the same while those of all other articles rise—with the exception of gold, the material of money; or even [if the rise applies to] certain articles such as wheat, copper, etc., in a word, to articles which do not enter into the component parts of the linen—then one yard of linen would be equal to 2s. as before. Its price would not fall, but its relative value expressed in wheat, copper, etc., would have fallen.
The term "labour-time necessary" appears twice in chapter four. By context, it would appear to be a synonym for socially necessary labour time or labour time [socially] necessary. Labour-time necessary also appears in chapter 1, "The Commodity" of A Contribution to the Critique of Political Economy where "socially necessary labour time" does not occur. Marx also made an important distinction there about what he meant by "social" in reference to exchange value:
...it is assumed that the labour-time contained in a commodity is the labour-time necessary for its production, namely the labour-time required, under the generally prevailing conditions of production, to produce another unit of the same commodity.
From the analysis of exchange-value it follows that the conditions of labour which creates exchange-value are social categories of labour or categories of social labour, social however not in the general sense but in the particular sense, denoting a specific type of society.
In volume 1 of Capital, Marx used the shorter phrase "labour-time necessary" fifteen times, with seven of those referring to the labour-time necessary for the reproduction of labour power.
Index to all posts on socially necessary labour time.
I will take the opportunity to plug my publication, "The Ambivalence of Disposable Time" in each of these episodes. I am linking to the published journal article. If anyone needs free access to the author's preprint, let me know in comments and I will leave a link there.