"Just doesn't add up'"

• "I’m not sure I follow the arithmetic here."
• "It's all down to the numbers - something the article avoids and so is just pie-in-the-sky."
• "That clearly does not add up."
• "If you produce X in 30 hours you will produce > X in 40 - unless you are just sitting on your arse for the extra 10 hours."
• "If you work 40 hours your total output will be higher than if you work 30 hours - unless you are actually destroying output in those extra 10 hours."

The U.K. think tank Autonomy has published a report on working time, "The Shorter Working Week: A Radical And Pragmatic Proposal." Autonomy's co-director, Will Stronge, wrote an Op-Ed for the Guardian on Friday that outlines some of the proposal's main points. The Guardian piece received over 600 comments, around a quarter of which were opposed to the proposal. I am always fascinated with why people are hostile toward seemingly good things so I downloaded the comments and sorted and coded them. 

Twenty-eight percent of the negative comments included gratuitous disparaging remarks about the article and its author. "Riiiiight. ...whoever dreamed up this silly notion hasn't got a clue about the realities of life." "This drivel is always coming from some useless twit who sits on their backside…" "Yes, the article is nothing but pie-in-the-sky." "Really?  It's all a bit if a pipe dream isn't it?" "Comrades , rejoice!  Tractor production will still be up 130%." "Along with flying cars and pet unicorns for all, presumably." "Following the columnist's logic, why not a three day week? Or a two day week?" "better still just pay me full time but I don't want to turn up at all." 

Fifteen percent of the negative comments dwelt on what they perceived as the mathematical incongruity of the proposal. This compared with less than seven percent of the positive comments that mentioned arithmetic and around two percent of the neutral or digressive comments that did. 

Opponents of shorter working week were confident that the relationship between hours of work and units of output was "a simple sum in arithmetic" the result of which was patently obvious to them: "If you produce X in 30 hours you will produce > X in 40 - unless you are just sitting on your arse for the extra 10 hours." Some critics explicitly assumed that a 20% reduction in hours would have to be made up by a 25% increase in output to be economically feasible. Others conceded that a reduction in hours could result in an increase in hourly productivity but insisted that total output would inevitably be substantially less in the shorter week.

There are several subtleties to the mathematics of shorter hours that opponents systematically overlook. One is that the relationship between hours and output is dynamic and cumulative, not static and instantaneous ("fatigue and unrest"). Second is that the value of aggregate output isn't necessarily proportional to the quantity of output ("diminishing marginal utility"). Third is that the lost value of foregone leisure and additional stress and "wear and tear" to a worker has to be reckoned against the value of additional income ("opportunity cost"). Fourth, a shorter standard working week may shift proportions of income going to labor and to capital, respectively. And, finally, that shift in the distribution of income is likely to have an impact on final demand ("propensity to consume"). All of these subtleties are in addition to the more generally -- albeit, not universally -- acknowledged fact that physical output doesn't necessarily increase in proportion to hours of work even in the static case.

To make a long story short, critics of the shorter work week proposal commit the same errors that adherents to the wages-fund doctrine did in the 19th century and that led Nassau Senior to insist that the profits of enterprise were entirely due to the last hour of the working day. It is none other than the original, the actual, the one-and-only "lump-of-labor fallacy" committed obsessively and unabashedly by opponents of shorter working time!