# Output Optimum and the Roller Coaster of Immiseration

Following up on my post from two weeks ago, Immiseration Revisited, I built a spreadsheet replica of the marvelous Chapman diagram. In addition to lines on the page, the replica provides me with tables of numbers that I can add, subtract, multiply and divide in accordance with the conceptual logic of the diagram.

The chart below shows the results of some of these calculations. The red curve graphs cumulative gross “output” and green curve subtracts the value of foregone leisure and the pain cost of fatigue and wear and tear from output to calculate net “income” (green). The length of each vertical line measures the values of output and income, respectively for a work week of the length indicated by the scale on the x-axis.

 “Big Dipper”: the Roller Coaster of Immiseration

I have set the hypothetical “output optimum” work week at 48 hours in deference to the diagram’s 1909 vintage. Assuming such an optimum and taking the conceptual diagram’s proportions literally, the ideal length of a work week for a laborer would be 36 hours. That is the point at which the value of foregone leisure and the pain cost of additional work begin to outweigh the additional earnings from the longer week. A workweek of 40 hours marks the threshold beyond which the value of foregone leisure alone exceeds the additional wage earnings.

If the optimal output workweek was 40 hours, the corresponding ideal length of workweek for the worker would be 30 hours, again assuming the reasonableness of the diagram’s proportions. There is, of course, only impressionistic evidence for the general shape of the curves and not for the accuracy of the proportions depicted. Nevertheless, the derived calculations indicate a steep acceleration of the discrepancy between output and worker welfare beginning well in advance of the output optimum.

Calculations based on the diagram suggest that by working 34 percent more hours per week, the employee can look forward to “enjoying” 29 percent LESS net benefit. If the actual cost to workers of working longer is even half or a third of those estimates, this still would represent a significant deviation not only from what Lionel Robbins dismissed as “the naïve assumption that the connection between hours and output is one of direct variation” but also from the equally indefensible premise of a consistently proportional relationship between work effort and reward.

(Most) Economists Balk

In a recent article, “Whose preferences are revealed in hours of work,” John Pencavel noted the “radical change in economist’s thinking about working hours” following the 1957 publication of H. Gregg Lewis’s article, “Hours of Work and Hours of Leisure,” Earlier textbooks attributed reductions in hours to pressure from trade unions, either directly through collective bargaining or by legislation promoted by organized labor. The earlier textbooks also addressed the effect that hours of work have on productivity, with reductions in hours usually leading to increases in hourly output and sometimes even to “no decline in total daily output.”

In later textbooks, the orthodoxy followed Lewis’s explanation that workers choose their own hours, based on their preferences for income or leisure. The connection between output and shorter hours vanished, as did the role of trade unions in achieving reductions of working time. But, Pencavel wondered, “If ’employers are completely indifferent with respect to the hours of work schedules of their employees,’ [as Lewis had posited] why did employers oppose so resolutely workers’ calls for shorter hours?”

In a footnote, Pencavel also mentioned that in Lewis’s 1957 model, employers face no obstacle “to replacing shorter hours per worker with more workers.” This is an interesting point because many economists’ arguments against the employment potential of shorter working time rest on claims that workers and hours are not suitable substitutes. That conclusion is reached by smuggling back in the output/hours relationship concealed in a Cobb-Douglas production function with the Robbins/Hicks “simplifying assumption” that the current hours of work are optimal for output, so that any reduction of hours would result in a reduction of output. It is difficult to imagine how both of these things can be true at the same time.

Although the earlier textbooks and economists acknowledged the connection between hours of work and output, most were silent on the discrepancy — or at least the magnitude of the discrepancy — between an output optimum and worker welfare. Cecil Pigou, Philip Sargant Florence, Lionel Robbins, John Hicks and Edward Denison treated the output optimum as the economic ideal. Richard Lester and Lloyd Reynolds, authors of “institutionalist” labor economics textbooks, showed more sympathy to trade union arguments but did not emphasize the discrepancy between the output optimum and worker welfare.

Sydney Chapman clearly distinguished analytically between worker welfare and the output optimum but his presentation was obscured by digressions that dwelt on shift-work as a palliative and on the philosophical necessity of paying more attention to the non-tangible aspects of culture. Clyde Dankert clearly distinguished between the output optimum and worker welfare but had the rather eccentric view that although “maximization of worker satisfactions” rather than output should be the social objective, shorter hours would have to be postponed “in view of the current cold war situation.” Only Maurice Dobb clearly and concisely stated what was at stake (although he left out the increasing value of leisure):

…trade unionists in the nineteenth century were severely castigated by economists for adhering, it was alleged, to a vicious ‘Work Fund’ fallacy, which held that there was a limited amount of work to go round and that workers could benefit themselves by restricting the amount of work they did. But the argument as it stands is incorrect. It is not aggregate earnings which are the measure of the benefit obtained by the worker, but his earnings in relation to the work he does — to his output of physical energy or his bodily wear and tear. Just as an employer is interested in his receipts compared with his outgoings, so the worker is presumably interested in what he gets compared with what he gives. A man who works longer hours or is put on piece-rates, and increases the intensity of his work as a result, may earn more money in the course of the week; but he is also suffering more fatigue, and probably requires to spend more on food and recreation and perhaps on doctor’s bills.

To compare “what s/he gets” with “what s/he gives” requires above all some way of estimating the value of what is given relative to what is being received. One may even suggest that constructing those estimates was the job economists should have been doing instead of castigating trade unionists and other advocates of shorter hours for adhering to a vicious “lump-of-labor” fallacy. Heck of a job, economists!