In May 1900, an article appeared in The Engineering Magazine, "Labour Questions in England and America," that well describes what, from the employers' perspective, is at stake in the "lump of labor" game. As far as I can determine, the article by Charles Buxton Going contains the first published American reference to the the "lump of labour" fallacy (curiously, this American-born and educated editor of an American magazine used the British spelling of labour).
The key to understanding the matter lies in Going's distinction between "the seeming and the real issues". According to Going, and to J. Stephen Jeans whom Going quotes extensively, the unions' demands for a reduction in the hours of labour were NOT the "real issue." In fact, Going conceded, "there is little question that the hours of working might be materially reduced without loss of wage earnings to the workman nor increase of cost of product to the employer... the theorem that a man's labour-production is directly proportional to his hours of working, is almost as fallacious as the trade-union proposition, that the amount of wage winning work in the world is a definite quantity, and will be exhausted sooner by more diligent working." The REAL issue, according to both Going and Jeans was the determination of labor unions to "tyrannize" over the employers and dictate working arrangements. The claim of a lump of labor fallacy did not pertain to the putative issue of the reduction of working time but to alleged union regulations aimed at restricting output. Above all, the employers' argument was about resistance by the unions to the introduction of piece-work rates in place of hourly wages. Over time, the employers' and management engineers' infatuation with piece-work as an industrial productivity panacea faded. Labor unions increasingly embraced higher output as a path to higher wages. And, so, the lump of labor objection drifted, imperceptibly, from the "real" issue of restrictions on output to the "seeming" issue of shorter work time. Meanwhile, economists have enshrined in their economic modeling the "almost as fallacious" theorem that output is proportional to hours in the form of a "simplifying assumption" (Hicks) that the given hours of work arrangements are optimal. That is to say a *real* fallacy has been incorporated into the heart of mathematical modeling at the same time a *seeming* and utterly spurious fallacy has been projected onto demands for shorter working time. -- Sandwichman
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