What Hicks did with Chapman's theory in The Theory of Wages cannot be called a simplification either – at least not an acknowledged one. If he did assume somewhere that the given length of the working day was optimal (which he may well have done), Hicks didn't announce it. What Nyland mistook for such an acknowledgement, was only an appeal to disregard transition costs in entertaining the concept of a given length of a working day that was optimal for output. Hicks did not specify that he was assuming that the given day actually was that length. The difference is that the assumption Hicks actually made still allows for the circumstance where the given day is longer or shorter than optimal, whereas the alleged simplification would not. The statement cited by Nyland as evidence of a simplifying assumption was thus also in accord with Chapman's theory.
The closest Hicks (1932) came to specifying the alleged simplification is when he argued that, "[provided certain limitations were respected], it is perfectly possible to treat labour as a commodity consisting of discrete homogeneous units, for which there are well-defined curves of supply and demand" (p. 92). Such treatment may imply the assumption that the given day is optimal for output because it would be hard to conceive of Chapman's hours – during which productivity may vary with the effects of fatigue – as consistent with "discrete homogeneous units". Indeed, if such homogeneity implies that output per hour is constant, then treating labour as homogenous could go farther down the simplifying path than merely assuming that the given day was of optimal length. Hicks acknowledged, though, that treating labour as such was "a method with very considerable dangers, which can only be avoided if we think back our arguments into a more cumbrous but more realistic form as frequently as possible" (p. 93)
Abstract: Sidney Chapman's theory of the hours of labour, published in 1909 in The Economic Journal, was acknowledged as authoritative by the leading economists of the day. It provided important insights into the prospects for market rationality with respect to work time arrangements and hinted at a profound immanent critique of economists' excessive concern with external wealth. Chapman's theory was consigned to obscurity by mathematical analyses that reverted heedlessly to outdated and naïve assumptions about the connection between hours and output. The Sandwichman is serializing "Missing: the strange disappearance of S. J. Chapman's theory of the hours of labour" on EconoSpeak in celebration of the centenary of publication of Chapman's theory. (To download the entire article in a pdf file, click on the article title.)