Here's a shorter summary of the Chapman model, originally published in "The 'lump-of-labor' case against work-sharing: populist fallacy or marginalist throwback." from Working Time: International trends, theory and policy perspectives and reposted on MaxSpeak in 2006.
Chapman revisited the issue of the hours of labor in his presidential address -- delivered in Winnipeg, Manitoba -- to the British Association for the Advancement of Science, Section on Economic Science and Statistics (1909). That analysis came to be considered the "classical statement of the theory of 'hours' in a free market" (Hicks 1932: 102n.; Nyland 1989). Arthur Pigou restated Chapman's argument in Economics of Welfare (Pigou 1952; 462-469). Alfred Marshall referred to Chapman's analysis as authoritative, as did Lionel Robbins (Marshall 1961: 695; Robbins 1929: 25). Concluding his footnote reference to Chapman and Pigou, Hicks declared, "There is very little that needs to be added to the conclusions of these authorities." Very little, perhaps, other than the strange occurrence that although Chapman's argument has never been challenged, economists today are oblivious to its major conclusions. Most are unaware not only of the theory's authoritative status but even of its existence.
Unlike [John] Rae, Chapman saw no particular danger in workers' views -- "fallacious or otherwise" -- about the mechanics of distribution (Chapman: 365). On the contrary, Chapman suggested that such attitudes probably had protected workers "against the injurious consequences of short-sightedness."
Chapman began his discussion of the hours of labor by reviewing the mass of evidence that reductions in the hours of work had not led to proportionate declines in output. Chapman attributed the phenomenon to the fact that as production methods become more intensive, workers require more leisure time to fully recover from the fatigue of work. He emphasized that in modern industry fatigue was increasingly psychological, resulting from the demands of modern industry for specialization and mental concentration as well as from the workers' attitude toward leisure rather than from the strictly physiological demands of the work. When the hours of labour were reduced, the better-rested workers were often able to produce as much or more in the shorter hours than they had previously in longer hours.
The total value of the output from standard working days of different lengths would thus initially increase as the day became longer but eventually the total output -- not only the output per hour -- would decline as the standard day became too long to allow the worker to recover sufficiently from fatigue. Beyond a certain point, each additional hour of work would continue to add a quantum of output to the current day's total output but only at the expense of reducing the next day's hourly pace. What that point was, Chapman maintained, depended on the intensity of the specific production methods and thus would vary in response to changes in those methods.
Having established the idea of an optimal length of standard working day that would maximize output, Chapman next turned to the questions of whether such an optimal length would likely be established by the workings of a free market and whether the optimal length of day for output coincided with the optimal length from the perspective of the workers' welfare. His conclusions in both cases were negative.
From the perspective of the employer, Chapman argued, the optimal length of day for output could only be achieved if all employers acted in enlightened accord. This is because the maintenance of the long-term optimum would always require some short-term restraint. A single employer could never be entirely certain of reaping the benefit of that restraint. Another firm could always potentially offer a small wage premium and hire away the first firm's well-rested workers. For employers, the optimal output work-time would thus be a form of investment without equity:
The reforming employer would run the risk of paying the whole cost of the labour value created by shorter hours and getting little in return; other employers might secure and exhaust the new labour value and no permanent good would be effected (1909: 361).From the perspective of the worker, the optimal length of day could, for all practical purposes, be considered to be shorter than the optimal length of the day for output. Chapman considered three elements in assessing the optimal day for the worker:
- the wage, which Chapman assumed for the purpose of analysis to exactly equal the worker's marginal productivity;
- the marginal value of leisure, which Chapman assumed to vary in response to changes in the level of wages; and
- the disutility of work, which Chapman assumed to also be a function of the length of the working day -- during some intermediate period of the working day, Chapman assumed that work could often be experienced as pleasurable.
In the two decades following Chapman's address, his demonstration of market failure in the determination of working time led to systematic empirical study of the relationship between fatigue and work intensity. According to Nyland (1989), however, attention to the question of work intensity faded during the 1930s and after, largely because "the fact that worktime had both a temporal and intensive character made it difficult to utilise marginal productivity theory to determine the return on various factors of production" (1989: 33). As a simplifying abstraction, economists assumed that the given working day was of optimal length. Eventually, the hypothetical -- and antithetical -- status of that assumption came to be overlooked. Economists negligently reverted to a pre-Chapman faith that unencumbered market forces would spontaneously lead to the establishment of an optimal length of work time.