La Bourse / Volume V / Nº V.02 / Quiz, reflection, essays

A woman reading in an armchair in a room of plants, a tall window and hills beyond. — Plate V.02 · Quiz, reflection, essaysThe Third Hour.Every calorie spent has to be replaced, and the replacing is not an interruption of the labour. It is the other half of it.

ASSESSMENT · Chapter V.02 — Work as Metabolism

Three instruments: a ten-point quiz, eight reflection questions, five essay prompts. The quiz checks comprehension rather than recall. The reflections are private and first-person. The essays are arguable from more than one side.

THE QUIZ — ten points

Four on recall.

1. Define the MET and state what a seventy-kilogram person burns at complete rest in a day.

One MET is resting metabolism — 3.5 mL of oxygen per kilogram per minute, which for arithmetic is one kilocalorie per kilogram per hour. At rest: 1 × 70 × 24 = 1,680 kcal/day. One mark for the definition, one for the arithmetic. Credit the oxygen form and the kilocalorie form equally; they are the same unit wearing different clothes.

2. What is the sustained ceiling on human energy expenditure, in what units is it expressed, and what appears to set it?

About 2.5 times basal metabolic rate, over timescales of weeks to months — so for our reference body, 4,200 kcal/day. Thurber and colleagues find the limit is alimentary: the gut's capacity to absorb, not the muscle's capacity to work. Credit any answer that expresses it as a multiple of BMR rather than an absolute figure — that is the point of the unit.

3. Write the identity linking output per worker, output per hour and hours per worker, and say why it matters that it is an identity.

Y/N = (Y/H) × (H/N). It matters because it is arithmetic, not a theory: it cannot be argued with, only computed. Most public disagreement about working time is two people each holding one term of it.

4. State the shift-length risk figures and the one thing they are not.

Relative risk is roughly flat through eight hours, then 1.13 at hour nine, 1.27 at hour ten, 2.00 by hour twelve. They are not self-reported — they come from injury and error counts recorded whether or not anyone was running a study, which is why they are the sturdiest evidence in the chapter.

Four on application.

5. A colleague reports that a firm cut hours by a fifth and "productivity went up 25 percent." What have they told you, and what have they not?

They have told you output per hour rose by roughly the amount arithmetic requires for output per worker to be unchanged: 1/(1 − 0.20) − 1 = 25.0 percent. So the headline is consistent with total output being exactly flat. They have not told you what happened to output per worker, which is the term the firm is paid on. Full marks require naming the identity and noting that output per hour rises mechanically whenever hours are cut anywhere the elasticity is below one.

6. Your head of engineering says her team is not tired because "it's not physical work." Answer her with the chapter's arithmetic, and then say what the arithmetic does not prove.

A full eight-hour day of demanding cognition adds about 0.70 kcal/h, or 5.60 kcal over the day — 450 times less than the labourer's net 2,520 kcal, and 0.33 percent of the day's energy. So she is right that the energy cost is negligible. That is precisely why it is the wrong instrument: the constraint on cognitive work is recovery, not fuel, and a calorie-shaped management system is blind to it. The arithmetic does not prove cognitive fatigue is severe; it proves that energy expenditure cannot measure it.

7. A four-day-week pilot reports large improvements in self-reported wellbeing and staff who say they are not more tired. Why is that last claim the weakest sentence in the report?

Because Van Dongen and colleagues showed that people restricted to six hours in bed for fourteen nights degraded to the equivalent of two nights of total sleep loss while rating their own sleepiness as barely changed. People inside a chronic deficit cannot report it. Self-reported fatigue is the outcome we should be least confident in. Credit any answer proposing an objective substitute — errors observed by a third party, absence, injuries.

8. The Svartedalens trial is usually quoted as proof that a six-hour day works. Give the honest reading.

Sixty-eight nurses went from eight-hour to six-hour shifts — a 25 percent cut each. Coverage needed 68 / (6/8) = 90.7 staff; the city hired 17, which is 75 percent of that. Staff-hours fell from 68 x 8 = 544 to 85 x 6 = 510 per day, a 6.25 percent reduction, implying a 6.67 percent rise in output per hour. That is a real gain and a small one, bought with a quarter more headcount and about twelve million kronor. The trial was not extended. Full marks require both halves: the effect is genuine and it is nothing like the headline.

Two that require the arithmetic to be done.

9. A firm proposes cutting its standard week from 46 hours to 38. Using only the productivity-of-hours curve in the chapter, compute the predicted change in output per worker, and state the rise in output per hour that would be needed to offset it. Then say why this prediction should be treated with suspicion.

Both 46 and 38 lie below the 49-hour threshold, in the region where the estimated elasticity is one. So output tracks hours exactly: 38/46 − 1 = −17.4 percent in output per worker. To hold output per worker flat, output per hour must rise 46/38 − 1 = 21.1 percent.
Treat it with suspicion because the curve was estimated on shell-turning in 1916, and nobody has estimated an equivalent for modern work with comparable data. Full marks require the two computations and the caveat. A strong answer also notes that this is the chapter's honest negative: below the threshold, the only well-identified curve we have says shorter hours cost output proportionally.

10. A ninety-kilogram labourer works the same day as the chapter's reference worker — eight hours at 5.5 MET, eight asleep at 0.95, eight at 1.6. Compute the net work energy of the shift and the day's physical activity level. What do you notice?

Net work energy: (5.5 − 1) × 90 × 8 = 3,240 kcal — larger than the seventy-kilogram figure of 2,520, in proportion to mass.
Physical activity level: 64.4 MET-h × 90 / (90 × 24) = 2.68 × BMR — exactly the same as for the seventy-kilogram worker. The mass cancels. The absolute energy cost scales with body size; the position relative to the 2.5 ceiling does not. That is why the ceiling is expressed as a multiple of BMR, and it is the whole point of the question.

REFLECTION — eight questions, for one person and a pen

These are not for a room. Write the answers by hand if you can; the slowness is the point.

Think of a stretch of weeks when you were properly rested. What was different about your judgement then — not your output, your judgement?

What is your own recovery mechanism, named precisely? Not "I relax" — what specifically discharges load for you, how long does it take, and when did you last give it that long?

Where in your working life are you currently paid on output per hour, and where on output per worker? Which one do you behave as though you are paid on?

Recall a decision you made at the end of a very long day. Would you make it again? What does your answer tell you about how you should schedule decisions rather than how you should schedule hours?

What is the hour of your week that produces the least, and what would have to be true for you to simply stop having it?

If someone measured your intensity of work rather than your hours of work, what would they find that your calendar does not show?

Where have you claimed a result — to yourself or to someone else — on evidence you would not accept from a stranger? Write down what a control group for that claim would have looked like.

What would you be willing to have measured about your own working time, and what would you not? The second list is the more interesting one. Why?

ESSAY PROMPTS — five

Each is arguable from more than one side. Each requires at least one source the chapter cites and at least one it does not.

1. The transferability of the munitions curve. Pencavel's estimates come from repetitive manual work in 1915–1918 under wartime conditions. Argue either that the functional form is a general feature of human working capacity and therefore transfers to modern cognitive labour, or that it is a fact about lathe operation and transfers to nothing. Use Pencavel (2015) and Chapman (1909), and at least one empirical study of hours and output in a modern setting that the chapter does not cite.

2. What the four-day-week trials actually establish. The chapter argues that the productivity result is much weaker than its reporting: self-selected firms, self-reported revenue, no control arms, short horizons. Take a position on what the existing body of trials does establish, and defend it. You may argue that continuation rates are themselves informative evidence — 56 of 61 firms continuing is a revealed preference, not a survey — or that they are contaminated by exactly the selection that makes the output data weak. Use the Autonomy/Boston College report and the Gothenburg evaluation, and one source on selection bias or publication bias in field trials that the chapter does not cite.

3. Is self-reported wellbeing a legitimate primary outcome? Van Dongen's work implies that people inside a chronic deficit cannot report it, which undercuts the main outcome measure used in most working-time pilots. Argue either that objective outcomes must replace self-report as the primary endpoint, or that wellbeing is intrinsically subjective and an objective-only regime would measure the wrong thing well. Engage Van Dongen et al. (2003) and at least one source on subjective wellbeing measurement that the chapter does not cite.

4. Chapman's externality, and who should fix it. Chapman argued in 1909 that competitive firms cannot find the sustainable working day because they capture the output and share the cost. Argue either that this is a classic externality requiring a portable limit — statute, licence condition, sector agreement — or that firms internalise more of the cost than Chapman allowed, through turnover, injury and reputation, and that a mandated limit would therefore destroy more value than it saves. Use Chapman (1909) and Ostrom (1990) on institutional design, and one empirical evaluation of a statutory hours reduction — the French 35-hour week is the obvious candidate — that the chapter does not cite in the body.

5. Intensification: the result that looks identical to success. Hours fall, output holds, and output per hour rises. This is the reported result of a successful working-time reduction and also the signature of pure work intensification with the breaks removed. Argue which interpretation the existing evidence better supports, and specify the measurement that would tell them apart. Use the chapter's Svartedalens arithmetic and Dembe et al. (2005), and one source on work intensity or effort measurement that the chapter does not cite.