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Commerce · V.02 · MMXXVI · daylight

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TEN CONCEPT BRIEFS · Chapter V.02 — Work as Metabolism

One page each. A reader who reads only these ten pages has the chapter.

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BRIEF 1 — The MET, and What a Shift Costs a Body

The idea. There is a standard unit for the intensity of any human activity, and it makes work comparable across every job in the economy.

One MET is resting metabolism: 3.5 millilitres of oxygen per kilogram of body mass per minute, which for arithmetic is one kilocalorie per kilogram per hour. A seventy-kilogram person at complete rest therefore burns 1 × 70 × 24 = 1,680 kilocalories a day. Every occupation in the Compendium of Physical Activities has a MET value, measured, and a shift's energy cost is simply MET × kilograms × hours.

Worked example. An eight-hour shift, for the same seventy-kilogram person.

The column that matters is the last one, because the first would be spent lying down. The net work energy of the site day is 9.0 times the office day — 2,520 / 280.

What to be careful of. MET values are population averages for untrained adults. A fit, practised worker performs the same task at a lower relative cost, and a heavier body burns more for the same motion. The ratios survive both corrections; the absolute numbers move.

You already know this because you have noticed that a day of physical work makes you hungry in a way that a day of meetings does not, and you have never needed a table to tell you which was which.

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BRIEF 2 — The Sustained Ceiling

The idea. There is an upper limit on how much energy a human being can spend per day week after week, and it is much lower than the limit for one day.

Caitlin Thurber and colleagues measured energy expenditure across events lasting from days to months — including athletes running across the United States — and found that sustained expenditure converges on about 2.5 times basal metabolic rate. The limit appears to be alimentary: it is the gut's capacity to absorb, not the muscle's capacity to work. Past that point the body funds the shortfall from itself.

Worked example. The labourer's whole day, at eight hours of 5.5-MET work, eight hours of sleep at 0.95 MET, and eight waking hours off the job at 1.6 MET:

  64.4 MET-hours x 70 kg          =  4,508 kcal/day
  divided by resting 1,680        =  2.68 x BMR
  the sustained ceiling           =  2.5 x BMR   =  4,200 kcal/day
  overshoot                       =    308 kcal/day   (7.3 % over)

Check it a second way, sharing no assumptions. Classical work physiology holds that an eight-hour day is sustainable at about a third of maximum oxygen uptake. For a worker with a VO₂max of 40.0 mL/kg/min, a third is 13.2, which is 3.77 MET. Site work at 5.5 MET is 1.46 times that. Two instruments, one verdict.

Why it matters. A full-time heavy manual job sits above the human sustained ceiling. That is not a moral observation; it is why those trades have always been organised around recovery, and why their workforces thin out with age.

You already know this because you have had one exceptional week you could not have had two of, and you knew that at the time.

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BRIEF 3 — The Cheap Brain

The idea. Cognitive work costs almost nothing metabolically, and exhausts people anyway.

The brain takes roughly 20 percent of resting energy — 0.20 × 1,680 = 336 kilocalories a day, or 14.0 kcal an hour. That is its baseline, and it runs whether you are proving a theorem or looking out of a window. Task-evoked increases above baseline are small; five percent is a generous upper bound.

Worked example.

  hard thinking adds   0.05 x 14.0   =  0.70 kcal/h
  a full 8-hour day of it            =  5.60 kcal
  as a share of the day's energy     =  0.33 %
  against the labourer's day         =  450 x less

Five and a half kilocalories. Less than a teaspoon of milk.

Why it matters, and it is the hinge of the whole chapter. The industrial apparatus for measuring, pricing and rationing work was built around energy expenditure, in the century when energy expenditure was the binding constraint. For most of the workforce it no longer is — and the measuring apparatus has not moved. Work is not a fuel problem. It is a recovery problem, and recovery is the quantity nobody has on a dashboard.

What this does not mean. It does not mean cognitive fatigue is imaginary. It means its currency is not calories, so a calorie-shaped management system cannot see it and will keep reporting that nothing is wrong.

You already know this because you have finished a day of difficult thinking unable to decide what to eat, and it would have been absurd to describe yourself as short of fuel.

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BRIEF 4 — Effort and Recovery

The idea. Effort produces a load that has to be discharged, and the discharging happens only in the absence of the load. If the next demand arrives before the discharge finishes, the residue carries forward.

This is the effort–recovery model of Meijman and Mulder, and its long-run form is Bruce McEwen's allostatic load: the cumulative wear of repeated adaptation. What makes it operationally difficult is not the physiology. It is that the person inside the deficit cannot report it.

Worked example — the decisive experiment. Hans Van Dongen and colleagues restricted people to six hours in bed for fourteen consecutive nights. Their cognitive performance degraded to the level produced by two nights of total sleep deprivation. Their self-rated sleepiness barely moved. The debt was 28 hours of sleep and none of them could feel it.

Why it matters. Every four-day-week trial that measures wellbeing by asking people how they feel is using an instrument that this experiment demonstrates is blind to chronic deficit. That does not make the trials worthless. It means self-reported wellbeing is the one outcome in the field we should be least confident in, which is the opposite of how it is usually reported.

What to do instead. Count things that are counted anyway: injuries, errors observed by a third party, absence, resignations, and objective output.

You already know this because you have had a holiday where the first three days were spent discovering how tired you had been, which is information you did not have on the Friday.

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BRIEF 5 — Chapman's Two Optima

The idea. The working day that maximises output today is longer than the working day that maximises output over a career. There are two optima, and the gap between them is the whole subject.

Sidney Chapman set this out in the Economic Journal in 1909. A day long enough to draw down a worker's capacity borrows from tomorrow's output at an interest rate that appears in no account. Chapman added the part that still governs policy: a competitive employer will not find the sustainable day alone, because it captures today's output in full and shares tomorrow's cost with every other employer that person will ever have.

Worked example. Two firms hire from the same labour market. Firm A works its people at the short-run optimum and books the extra output. The capacity it draws down is repaid — slowly, partially — by whoever employs those people next, and by the health system, and by the people themselves. Firm A's accounts show a gain. The loss is real and is simply somewhere else.

Why it matters. It explains the one durable empirical regularity in working time: hours limits that hold are almost always portable — a statute, a licence condition, a sector agreement — and hours limits adopted by single firms in competitive markets tend to erode. This is not a failure of will. It is the structure Chapman described.

You already know this because you have watched a good practice in one team quietly disappear once the team next door stopped doing it and looked faster for a while.

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BRIEF 6 — The Elasticity of Output to Hours

The idea. Output does not rise in proportion to hours. It rises in proportion up to a point, and then less than in proportion, and the point has been measured.

John Pencavel re-estimated the Health of Munition Workers Committee data from 1915–1918 — factory records where output was physically countable and the schedule changed while everything else held still. Below a threshold near 49 hours a week, output is proportional to hours. Above it, output rises at a decreasing rate, and output at seventy hours differs little from output at fifty-six.

The formal object. The elasticity ε is the percentage change in output for a one percent change in hours.

  below the threshold     e = 1      output tracks hours exactly
  above the threshold     e < 1      each hour adds less than the last
  at the top              e = 0      the next hour adds nothing

Worked example. A team at 56 hours a week, where the elasticity is somewhere near 0.35. Adding 10 percent more hours — five and a half hours each — adds roughly 3.5 percent more output. You have bought five and a half hours and received the equivalent of two.

What to be careful of. This was shell-turning in 1916. Whether the same elasticity governs software, nursing or teaching is an open question, and the honest position is that nobody has estimated an equivalent curve for modern work with anything like the same quality of data.

You already know this because you have had a week where you worked every evening and could not afterwards point to what the evenings produced.

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BRIEF 7 — The Identity That Ends Most Arguments

The idea. Output per worker is output per hour times hours per worker. It is not a theory. It is arithmetic, and it is exact.

        Y/N   =   (Y/H)  x  (H/N)

  in logs:   d ln(Y/N)  =  d ln(Y/H)  +  d ln(H/N)

Almost every public argument about working time is two people each holding one term of this identity and neither writing it down.

Worked example. A five-day week becomes a four-day week: hours per worker fall 20 percent. For output per worker to be unchanged, output per hour must rise by 1/(1 − 0.20) − 1 = 25.0 percent. So the headline "productivity rose" is compatible with output per worker falling by a fifth — because "productivity" almost always means output per hour, and output per hour rises mechanically whenever hours are cut anywhere the elasticity is below one.

The national version. OECD average annual hours actually worked per worker, 2023: Germany 1,343; France 1,500; the United States 1,799; Mexico 2,207. The United States works 1.34 times Germany's hours and Mexico 1.64 times them. For German output per worker to match the American, German output per hour must be 1.34 times it — which is roughly what it is. The two countries are not disagreeing about productivity. They are choosing different points on the identity.

Why it matters. Put both lines on the same page and require every proposal to say which one it moves, and a three-year argument ends in a meeting.

You already know this because you have met the phrase "we're more productive than ever" and quietly wondered per what.

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BRIEF 8 — The Flat Top, and the Interval Nobody Quotes

The idea. The hours at which total output peaks can be computed, and the honest uncertainty around that peak is about two working days wide.

Fit a quadratic in logs so the elasticity is ε(H) = b + 2c·ln H, and pin it at two points: elasticity 1.00 at 49 hours, elasticity 0.35 at 56 hours.

  2c  =  (0.35 - 1.00) / (ln 56 - ln 49)  =  -0.65 / 0.13353  =  -4.8678
  H*  =  49 x exp(-1 / -4.8678)  =  49 x 1.22806  =  60.2 h/week

Total output peaks near 60.2 hours a week. Output per hour peaks at or below 49. The gap is 11.2 hours a week, and it is where the whole argument lives.

Now the interval. Move the anchors across plausible ranges — threshold anywhere from 46 to 52 hours, elasticity at 56 hours anywhere from 0.15 to 0.55 — and the peak runs from 56.7 to 71.2 hours a week: a width of 14.5 hours.

The important part about that interval. It is calibration uncertainty, not sampling error. The published standard errors are respectably narrow — around the elasticity, which is what the data identify. The peak is not what the data identify, because near the top the curve is almost flat and a flat curve has a barely located maximum.

Why it matters. Anyone quoting a precise optimal working week is reporting their functional form and calling it evidence.

You already know this because you have stood on a broad hilltop in fog and been unable to say, within fifty paces, where the top was — while being entirely certain which way was down.

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BRIEF 9 — Fatigue Risk Is Not Linear in Hours

The idea. Risk does not rise smoothly with shift length. It is roughly flat through eight hours and then climbs steeply.

The numbers.

Worked example. Extending an eight-hour shift to twelve adds 50 percent more hours and about 100 percent more risk in those hours. If the extension is meant to buy output, note that it is being bought in the part of the curve where the elasticity is falling and the risk is doubling at once.

The clean end of the evidence. Interns on traditional schedules made 35.9 percent more serious medical errors and 5.6 times more serious diagnostic errors than on a schedule with the extended shifts removed — counted by observers, not self-report. The odds of crashing on the drive home after an extended shift were 2.26 times those after a normal one.

And the long end. Across 603,838 people, a week of 55 hours or more carried 1.13 times the coronary heart disease risk and 1.33 times the stroke risk of a 35-to-40-hour week. The WHO and ILO attribute 745,000 deaths in 2016 to that exposure.

You already know this because you have watched somebody make a simple mistake at the end of a very long day and have not, for a moment, thought it was about their ability.

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BRIEF 10 — What Would Actually Settle It

The idea. The four-day-week question is unsettled, and it is unsettled for reasons of design rather than reasons of ideology. The design that would settle it can be specified, and its size can be computed.

What the existing trials are. The 2022 UK pilot: 61 organisations, about 2,900 employees, six months, self-selected, unblinded, revenue self-reported, no control arm. Iceland: 2,500 workers, about 1 percent of the workforce, and a 10.0 to 12.5 percent hours cut — not a four-day week. Microsoft Japan: one August, 2,300 staff, +39.9 percent sales per employee against the previous August, no control, confounded with a meeting-length policy.

The one with a control. Svartedalens, Gothenburg: 68 nurses from eight-hour to six-hour shifts. Holding coverage needs 68 / (6/8) = 90.7 staff; they hired 17, which is 75 percent of that. Staff-hours went from 68 x 8 = 544 to 85 x 6 = 510 per day — a 6.25 percent reduction, so output per hour rose 6.67 percent. Real, modest, expensive, not extended.

The trial that would settle it. Randomised at site level within firms; a control arm; output per worker from administrative data as the pre-specified primary outcome; twelve months plus a twelve-month follow-on to catch novelty decay and reversion; work intensity measured alongside output; and a pre-registered failure condition.

The size. To detect a 5 percent difference in output per worker with a within-site standard deviation of 0.15, at 5 percent significance and 80 percent power:

  n per arm  =  2 x (1.960 + 0.842)^2 x 0.15^2 / 0.05^2  =  141.3
  sites per arm 142   ->   total sites 284

284 sites. The UK pilot ran 61 organisations and no control arm — the trial that would settle this is 4.7 times larger than the largest one yet run, and differently shaped.

You already know this because you have seen a pilot succeed, been unable to say whether it would have succeeded anyway, and known that the missing thing was the group that did not do it.

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All figures in these briefs are computed in lib/verify/V_02.py and sourced in the chapter's Works Cited.