The canonical labour-supply model, based on the analysis of income-leisure choice, differs from both Walras and Hicks in establishing the constraint of 24 hours as the sum of the hours of leisure and of labour. In very general terms, the formula for such a calculation was stated by David I. Green (1893). Green argued that "the laborer stops work at a certain hour, not simply because he is tired, but because he wants some opportunity for pleasure and recreation" (p. 222) and further, that "the economic opportunities which a man sacrifices by pursuing a certain course of action are more capable of objective measurement. These sacrifices of opportunity are what constitutes the principal part of the costs of production which determine normal exchange values" (p. 223).
Although Green made explicit a trade-off of limited hours between labour and leisure, he didn't take the obvious next step of dividing the day into 24 hours to be apportioned between the two activities, nor did he specify an hourly wage. Enrico Barone (1908/1935) did, however:
It is convenient to suppose – it is a simple book-keeping artifice, so to speak – that each individual sells the services of all his capital and re-purchases afterwards the part he consumes directly. For example, A, for eight hours of work of a particular kind which he supplies, receives a certain remuneration at an hourly rate. It is a matter of indifference whether we enter A's receipts as the proceeds of eight hours' labour, or as the proceeds of twenty-four hours' labour less expenditure of sixteen hours consumed by leisure. (pp. 248-249).
Barone's "simple book-keeping artifice" constituted a second, not entirely congruent, version of opportunity-cost doctrine. The first version, as articulated by Green, was vague enough about time to defeat the pain-cost argument as an explanation of prices. Barone's version was precise enough about the division of the 24 hours in a day to be incorporated into mathematical formulae. Such precision came only at the (unexamined) cost of resurrecting what Robbins called the 'naïve' assumption that "the connection between hours and output is one of direct variation."
Abram Bergson (1939) adopted Barone's framework as a basis for his "Reformulation of certain aspects of welfare economics." Although it may have seemed a matter of indifference to Barone whether to count the receipts of labour as eight hours or as twenty-four hours minus sixteen hours of leisure, the book-keeping artifice was essential to the flourishing of the indifference-curve analysis, unhampered by the essentially unquantifiable spectres of worker fatigue, unrest or even intrinsic enjoyment of work. The founding myth of the new orthodox approach thus passed unannounced into the canon. Chapman's theory was rendered expendable not by an explicit simplification but by the quiet revival of a naïve and anachronistic assumption about the connection between hours and output.
Chapman theory appears to have covered both the opportunity-cost and pain-cost bases. In a technical footnote, he drew two dotted-line curves to describe the effects of the length of the working day on the worker (see appendix). The first curve, labelled I, clearly indicates an opportunity-cost analysis of the value "of the leisure destroyed by the addition of [an] increment of time" (p. 364). The second curve, labelled L, retains the notion of absolute satisfaction or dissatisfaction involved in working. There doesn't seem to be a suggestion that this curve L directly determines the cost or value of labour, only that it affects the welfare of the worker. To paraphrase Chapman, what curve L addressed was not "the quantity of external wealth produced" but rather the "balance between internal and external wealth" (p. 373).
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.)