the second hundred · metaphor 197
Why does the human work — the nurse's hour, the teacher's attention, the quartet playing live — keep getting more expensive, decade after decade, exactly while everything a machine can touch keeps getting cheaper?
A phone that would have cost a fortune in 1990 is now nearly free; a television, a calculator, a photograph — the things we make faster each year fall in price until they barely register. And yet a year of college, an hour with a good doctor, a seat at the symphony climbs and climbs. It's tempting to blame greed, or bloat, or bad management. But the strangest possibility is that nothing has gone wrong at all — that the rising price is the shadow cast by everything else getting cheap.
Here is the trap. Some work can be sped up: a factory doubles what a worker makes in an hour, then doubles it again. Some work is the time — a Beethoven quartet still takes four players the same twenty-odd minutes it took in 1826, and a lesson still takes the lesson's length. But everyone competes in the same labour market. When the productive jobs get more valuable, they bid up wages everywhere — and the teacher, no faster than before, must now be paid the higher wage too. The unspeedable work grows dear not because it worsened, but because it cannot join the race.
The engine
Price, at bottom, is labour: how much worker-time a thing takes, times what that time is paid. Split the economy in two. In the progressive sector, output per hour rises year after year — the same hour makes more widgets. In the stagnant sector, an hour makes what it always did: one lesson, one consultation, one performance.
Now the crucial link: wages don't stay in their lane. A teacher who could earn more on a factory floor must be paid enough to keep her teaching, so pay rises across the whole economy roughly with the leading sector. In the productive sector that raise is absorbed by rising output — the widget's price barely moves. In the stagnant sector there is no extra output to absorb it, so the higher wage lands directly on the price. The care-hour costs more because the factory got faster. Speed somewhere else made the unspeedable thing dear.
And it compounds. Because the productive sector's price keeps falling relative to the stagnant one, a household buying both spends an ever-larger share on the human work — even if it buys no more of it. That's why, over a lifetime, health, education and care quietly swell to fill the budget. Not because we chose them; because everything else got out of the way.
What to try
Press play and let the decades run. The blue line — a manufactured good — sits pinned at 1.00, our yardstick. The coral line — an hour of care — drifts upward, and the amber wage rises with it: your hour of labour buys ever more widgets, yet ever fewer care-hours per pound of your rising pay. Nothing broke. The gap is the disease.
Now push factory productivity growth up. The coral care-line climbs steeper — faster progress elsewhere makes the human hour dearer, faster. Then lift care productivity growth toward the factory's rate and watch the climb flatten: the disease is precisely the gap between the two speeds, and it vanishes only when the stagnant sector stops being stagnant. Set them equal and care holds flat against widgets — cured. The budget-share bar underneath tells the felt story: the share you spend on unspeedable work creeps rightward the whole time.
The mapping
Baumol found the pattern in the concert hall and it turned out to be everywhere the work is the human presence. Health care: a nurse tends a patient at roughly the human pace she always did, so as the economy's wages rise her hour costs more — and health's share of national spending climbs for a century. Education: a seminar is still a room of people thinking together; class sizes and salaries set its cost, and it outpaces inflation decade on decade. The performing arts: the quartet cannot play faster to save money, so live music leans forever on subsidy and patronage. Care of the old, the craft of repair, the hand-made: all catch the same cold.
The reframing is the gift. When the cost of teaching or nursing or eldercare rises faster than gadgets, the reflex is to hunt for waste and demand efficiency. Sometimes there's waste. But often the rising price is a receipt for progress everywhere else — the unavoidable cost of keeping humans doing the things only humans can do, in a world that keeps making the rest for almost nothing. Fighting the disease by speeding the unspeedable usually just means doing it worse: forty students instead of twelve, seven minutes with the doctor instead of thirty.
Read as life lessons
A rising relative price can mean the thing failed to speed up, not that it decayed. The nurse's hour costs more because it's still an hour of a person — which was always the point.
Everyone draws from one labour pool, so a raise won in one sector spreads to all. Progress in what can be sped up bids up the price of what can't.
As gadgets fall toward free, the human services swell to fill the space — health, teaching, care claim an ever-larger share, whether or not we buy any more of them.
The mapping, exactly
| Mathematics | Life |
|---|---|
| progressive productivity A_P | Work a machine can speed up — chips, screens, freight — making more per hour every year. |
| stagnant productivity A_S | Work that is the human time itself — a lesson, a consultation, a live performance — no faster than before. |
| economy-wide wage w ∝ A_P | Pay rising with the leading sector, because everyone competes in one labour market. |
| unit price = w / A | What a thing costs: the wage it takes divided by how much that time produces. |
| relative price A_P / A_S | The cost disease itself — the human hour priced against the goods that keep getting cheaper. |
| the budget share rising | Health, education and care quietly claiming more of every paycheck as everything else falls away. |
The honest model
Two sectors compound quietly. Factory output per hour is A_P(t)=(1+g)ᵗ; care output per hour is A_S(t)=(1+gₛ)ᵗ. The one wage tracks the leading sector, w(t)=(1+g)ᵗ. A thing's price is its unit labour cost, wage over productivity: the manufactured good costs w/A_P = 1 (our yardstick, flat by construction), and a care-hour costs w/A_S = ((1+g)/(1+gₛ))ᵗ — the whole disease in one ratio, climbing whenever g > gₛ.
The wage line plots w/A_P·A_P = A_P(t) — what an hour of pay buys in widgets, rising with progress. The budget share assumes a household buys fixed physical amounts of each (inelastic demand for care): share on care = p_S·q_S / (p_S·q_S + p_P·q_P), which drifts toward 1 as the care price grows. Every chip, line and bar is evaluated from those closed forms at the current year — scrub the slider and each recomputes exactly. Set gₛ = g and the ratio collapses to 1: the model says, correctly, that the cure is closing the productivity gap.
Where the metaphor tears
The model freezes the stagnant sector's productivity, but real teaching and medicine do change — vaccines, imaging, better pedagogy raise what an hour achieves even if it still takes an hour. Quality can climb while the clock stays fixed, and a pure cost-disease story, blind to quality, will read genuine progress as mere inflation. Some of the rising price buys more, not just dearer.
“It's just Baumol” is a comfortable shield for real waste — administrative bloat, rent-seeking, monopoly pricing, and costs that have nothing to do with anyone's unspeedable hour. The theory explains a floor under which these prices should rise; it does not certify that every rise above that floor is innocent. Diagnosing the disease is not a licence to stop looking for the ordinary diseases too.
Wages don't actually rise in perfect lockstep; teachers and nurses have fallen behind the productive sector for stretches, held up by unions, immigration, or public budgets rather than a tidy market. The clean ratio assumes a frictionless labour pool the real world only approximates — which is why the disease shows up as a long-run tendency, not a law that binds every year and every occupation.