The eighth plate, rebuilt as one instrument. Everything the essay disputes — the markdown, the arch, the gendered wedge, the case for the floor — descends from a single measurable quantity: the elasticity of the labour supply one firm faces. Turn the dial below and watch the entire edifice move at once. Against it sits the one quantity no dial reaches — the competitive wage — which the second plate renders as a ridge in fog.
The competitive labour market is governed, in the end, by one number set silently to infinity: the elasticity of labour supply to the individual firm — how freely workers flow toward it for a little more pay, and away for a little less. Let that number fall to something finite and the firm acquires power over the wage; let it fall further and the company town appears. The economy of the idea is that this same number fixes how much of a worker's product is withheld, where the employment-maximising minimum wage lies, and how far a pay gap can open between identical workers who differ only in how freely they can leave.
So the instrument has one master control, and a handful of linked dials that cannot disagree with it — because they are all reading the same quantity from different angles.
Where the elasticity is born. A firm's labour is a reservoir — filled by recruitment, drained by departures. Raise the wage and the inflow quickens while the outflow slows; the firm's power over the wage is exactly the sum of those two responses.
The reservoir and its two flows
How each channel responds
recruiting2.0
retention2.0
How sharply hiring rises, and quitting falls, when the wage goes up. Deaden either and the firm gains power.
The number they make
Plate viii · the source · Monopsony in motion. The elasticity the rest of this instrument turns as a single dial is no primitive — it is born in friction. The employment a firm can sustain is what it recruits divided by the rate at which workers leave; raise the wage and recruitment rises with elasticity φ while separations fall with elasticity σ, so the firm-level labour-supply elasticity is their sum, ε = φ + σ. A handful of employers, a non-compete, a wage kept secret — each works by deadening one of these flows. Move these and the dial above moves; turn the dial, and it splits back into the two channels.
Plate viii · α
The Markdown, the Arithmetic, the Arch
Three readings of the same dial. The equilibrium that opens the wedge; the fraction it withholds; the policy frontier it bends into an arch — all moving together.
i · The single buyer
ii · The exploitation fraction
iii · The arch — drag the floor
Plate viii · α · One dial, three faces. Left, the firm hires where the marginal cost of labour meets marginal revenue product, then reads the wage down to supply — the bracket is the markdown. Upper right, that same markdown as a fraction of one unit of product: a fifth withheld at ε = 4. Lower right, employment against the floor: flat where it cannot bind, rising as it climbs from the monopsony wage to the competitive wage w*, cresting there, then falling as the old arithmetic returns. Drag the floor along the arch; turn the dial and the arch reshapes.
At the far right of the dial — the frictionless limit, ε toward infinity — the supply curve lies flat, marginal cost equals the wage, and the three curves collapse onto the competitive point. Nothing is withheld; the arch has no rising flank left to climb. This is the textbook's world, shown for what the essay claims it is: not the rule, but a single unreachable point. Slide left and it recedes at once. Around ε between five and seven — the band the best studies of how workers actually move between firms keep returning — a tenth to a quarter of the product is already kept, with no single buyer anywhere in sight.
Plate viii · β
The Surface, and the Ridge in Fog
The arch was only a slice. Employment lives on a landscape over two axes — the floor you set, and the elasticity you cannot see. The best floor is a ridge; the fog is the part no instrument locates.
more employmentlessw* — the crest (unobservable)where each market startsmeasured ε (5–7)
Plate viii · β · The policy landscape. Darkness is employment; the bright dashed crest up the middle is the competitive wage w*, where every arch peaks. To its left, each market begins on the pale locus — its own monopsony wage — and the horizontal room between that locus and the crest is the distance a floor can climb while jobs rise. But the crest sits in fog, because w* is not observed; it is inferred, and inferred differently by careful people. The crosshair is yours — drag it vertically to turn the master dial, horizontally to set the floor — and the whole apparatus follows. Beyond the crest lies the cliff where the century's arithmetic finally collects.
This is the deepest thing the subject has to say, and the hardest to draw: the number that locates the peak is the one number nobody can measure. The elasticity on the vertical axis is estimated, with error; the competitive wage on the crest is reconstructed, with disagreement. A regulator who would set the floor exactly at the ridge is aiming into the fog — which is why even the friendliest case for a minimum wage is a case for climbing in steps small enough to read the market's answer before the next, feeling for a peak that cannot be seen from below.
Plate viii · γ
Equal Product, Unequal Exit
Hold the worth of the work exactly equal and let only mobility differ. A pay gap opens with no taste for discrimination anywhere in it — and a floor, raised, closes it.
The wedge that mobility alone produces
The two mobilities
spread×1.6
How far the two groups' elasticities sit either side of the dial. Wider spread, wider gap.
The floor as remedy
floor—
gap now 15 pts of product. Raise the floor toward w* and watch it strip markdown from whoever carries the most.
Plate viii · γ · The gendered wedge. The curve is wage as a share of marginal product; it rises with mobility and approaches the whole but, short of the frictionless limit, never reaches it. Two workers of identical product sit at different mobilities — the less mobile further below the line. The gap between them is a pay gap structural rather than attitudinal: it would open in a world purged of prejudice, through the slope of the supply curve alone. A wage floor lifts the lower point fastest, because it strips the largest markdown first; pay transparency would do the same by dissolving the friction of secrecy.
Plate viii · δ
One Power, Several Sources
Four different frictions all narrow to the same scalar — and four different instruments all widen it back. The map of sources is the map of remedies, and no single tool reaches them all.
Hover a source to see its matching remedy. Click a remedy to apply it — each one loosens a friction, raising the elasticity on the master dial and shrinking the wedge everywhere above.
Plate viii · δ · The bottleneck. Concentration, contractual immobility, secrecy, and the irreducible cost of search are four unlike things, yet each enters the firm's problem in one place — by lowering the elasticity of the labour it faces — and so each is measured in one currency, the markdown. That is why power can be gauged without first settling its source. It is also why the defeats of the last decade were, at bottom, the failure of asking one instrument to carry the weight of four.
Plate viii · ε
The Ascent in Fog
The surface of Plate β, now walked blind. Raise the floor a step at a time — but you read employment only through noise, and the peak stays hidden until you choose to look. The whole question of the minimum wage, reduced to one: where do you stop?
step
Plate viii · ε · Feeling for the peak. The hidden terrain is the arch of Plate α-iii, its height set by the very elasticity on the master dial — but here you cannot see it, and your altimeter, like every real reading of employment, carries noise. Climb in bold steps and you may crest sooner but overshoot into job losses the next noisy reading only half-reveals; climb in cautious steps and you are safer, slower, and likelier to stop with markdown still uncollected. This is the friendliest case for a minimum wage in its true shape: not a number to be hit, but a peak to be approached — in fog, on purpose.
One number you can measure; one number you cannot. The whole dispute is the distance between them.