Numéraire The Wage · № I · viii — the standing pool
Plate viii.g′

The Standing
Pool

The monopsonist of the textbook is a single mill in a company town. A defendant can say, truthfully, that it is nothing of the kind — many rivals, free entry, every worker free to walk — and conclude the model cannot touch it. The conclusion is wrong, and the modern labour literature is built on why. Quitting takes time. A workforce is a standing pool, filled by recruitment and drained by separations, and a pool answers a wage cut only as fast as those flows allow. That sluggishness — not any scarcity of employers — is the whole of the firm's power. A restaurant whose cooks do not cross the street the instant a rival posts a better wage still pays them below their product — and the markdown runs deepest, by the evidence, exactly where pay is lowest and turnover highest, in the markets that look most competitive. Because the flows leave a trace in the firm's own records, it can be measured, bounded, and contested.

viii.g′ — monopsony without a monopsonist

Two knobs and a switch stand in for the whole of dynamic monopsony. The first sets how sharply a firm's people quit when the wage moves — the quit elasticity, the one quantity legible straight from payroll. The second sets how fast the pool turns over. The switch sets whether recruitment answers pay as sharply as quitting does. Move them, and three things appear at once: the firm's power, its price, and the time it takes to spend. None of it needs a single buyer — only that workers be slow.

the two flows · a pool filled and drained on log scales a constant elasticity is a straight ray — its slope is the elasticity ½× 1× 2× flow rate · indexed to today w₀ the posted wage → lower pay higher pay separations recruitment the pool the markdown · what the slowness is worth the steady wage the firm posts, as a share of the worker's product marginal product — the competitive wage 0 3 6 9 12 labour-supply elasticity ε 50% 75% 100% wage as share of product from separations · ε ≈ 4–10 the method this plate follows — and the same pool, now in time — the slowness · why no one can leave fast enough at t = 0 a rival opens paying 10% more; the firm holds its wage, and the pool drains toward a lower floor N₀ — the going-rate workforce 0 12 24 36 48 60 72 months since the firm fell behind the market → 0 25 50 75 100% workforce remaining · % of N₀
2.5
0.3 · barely move — captive decamp at once · 6
.04
1%/mo · long tenure a restaurant's churn · 12%/mo
Steady-state symmetry · η = ζ. In equilibrium your recruits are rivals' leavers, so recruitment answers pay as sharply as quits do — and the pool's elasticity is exactly twice the separation elasticity. on — ε = 2ζ
separation
elasticity ζ2.5
supply
elasticity ε5.0= 2ζ
wage as share
of product83%
the
markdown17%
grace —
half-life17months

Above — the steady state. Employment is a stock held where two flows balance: recruits arriving, workers separating. Plotted against the posted wage on log scales, a constant elasticity becomes a straight ray whose slope is the elasticity. Cut the wage and separations rise while recruitment falls — gently, because search and switching are costly — and the shallower the rays, the more captive the workforce; the firm's power is exactly that shallowness. The pool, employment itself, climbs twice as steeply, because it is fed by one flow and drained by the other, so its elasticity is their sum, η + ζ. A steady-state market forces a symmetry — your recruits are someone else's leavers, so recruitment is as wage-elastic as separation — which collapses the sum to ε = 2ζ. That number fixes the wage at ε/(ε+1) of marginal product; the markdown is the gap to the ceiling. The switch shows the load the word twice carries: let recruitment be stickier than quitting and the elasticity falls below 2ζ, the markdown deepens, and a figure read from quit records alone no longer suffices. The shaded band is the measured range — estimated from separations, the best studies put ε near four to ten, a quit elasticity of two to three, a markdown of a tenth to a fifth, with the deepest markdowns, by the evidence, in low-wage high-turnover work.

Below — the journey. A slope is a claim about where the pool would settle at each wage; it is silent on the trip, and the trip is the point. At month zero a rival opens paying ten percent more and the firm holds its wage. Workers leave faster than they are replaced, and the stock relaxes toward a new, lower floor along an exponential whose half-life is ln 2 ∕ s — set entirely by how fast the pool turns over. The dashed floor is where the workforce would sit at once if anyone could leave the moment a better wage appeared; everything above it is on the payroll only because leaving takes time. That shaded wedge is the firm's grace — the below-market labour it keeps while the pool drains — and its area, (N₀−N*)∕s, is the rent friction alone collects. Here is the reconciliation the upper panel needs: the firm can hold below market because no one can leave fast enough to punish it, and the permanent markdown is simply this transient lived in forever — the half-life is not a by-product of the markdown but its enforcement. Now the decisive move: drag the turnover knob from a long-tenure workforce to a restaurant's churn. The wedge narrows, the grace shortens — and the floor does not move. Speed is not size. A workforce can turn over in months and still be marked down a fifth, because the markdown is set by how sharply quits answer pay, never by how often they happen.

The company town was never the cause of the markdown.
The company town was only ever time — and time is everywhere.

Read the two halves together and the steady markdown stops being a fact separate from the slow drain; it is the drain, seen from far enough away. Which is why the single buyer of the textbook turns out to be one limiting case of something far more ordinary. Classical monopsony — one employer, no alternatives — and dynamic monopsony — a thousand employers, costly switching — write the same wage equation: a markdown of 1/(ε+1) against a finite supply elasticity. They are observationally equivalent at the level of pay; what differs is the story behind the slope, and the story can be left unsettled, because the wedge does not depend on it. The evidence reaches the same verdict from the data — the markdown is pervasive and, in the language of the movers studies, largely independent of the forces driving classical monopsony: present with one buyer or a hundred, requiring no company, no town, no mill, only that quitting is not instantaneous.

And none of it needs the boundary of "the market" to be drawn. The two parents of the firm's elasticity — how its recruitment and its retention answer the wage — sit in the firm's own personnel records: hires per posted wage, quits per posted wage. Under the symmetry the second alone recovers ε, and ε fixes the markdown; the competitive wage, the ceiling, is the one quantity never observed, and everything beneath it can be estimated from records a payroll department already keeps. That is what makes dynamic monopsony an empirical claim rather than an ideological one — and it is why the framework runs against the grain of how these cases are usually fought, where so much labour turns on defining a relevant market and counting the firms inside it.

For the defence

What the slowness gives you

Plaintiff-side economics increasingly reaches for monopsony — to argue an employer suppressed pay below competitive levels, that a no-poach or non-solicit term had real bite, that the "we paid the market rate" defence is hollow because the market rate was itself depressed. Two fronts press hardest on a restaurant practice. One is the wave of franchise no-poach litigation — the clauses that barred a worker at one franchisee from moving to another, revived against McDonald's by the Seventh Circuit and chased out of more than two hundred chains by Washington's attorney general — where the live questions are per se versus the rule of reason, ancillary restraint, and, again and again, the definition of the relevant labour market. The other is the ordinary wage-and-hour case, where "the prevailing market wage" is raised as a shield. The instinct to wave the theory away — we are hardly a company town — is the wrong one, because dynamic monopsony says the curiosity is the general case. Meet it on its own ground, where the same structure that makes the markdown real also makes it tractable.

i
Bound the exposure on the measured band. The markdown is 1/(ε+1), and firm-level supply elasticities estimated from separations cluster around four to ten (Bassier–Dube–Naidu; Sokolova–Sørensen) — a markdown of a tenth to a fifth, not a half, not nine-tenths. A claim of catastrophic suppression is, in disguise, a claim of an elasticity below anything the literature has found, and that is a falsifiable assertion an expert can be made to defend on cross. The band is a ceiling on damages before a single fact about the client is in evidence.
ii
Put the identity to the client's own records. ε = 2ζ means the whole question can be asked of payroll: how much do this firm's quits actually respond to its pay? If the answer is high — people do leave when a better wage appears — then ε is high and the implied markdown is small, provable from data the company already holds. The identity that lets a plaintiff measure power is the identity that lets a defendant bound it; which it does depends on the numbers, and only counsel who can read the model knows, before the expert is retained, which way they cut.
iii
Move the fight off market definition — and refuse the turnover smuggle. These cases stall where plaintiffs must define a relevant labour market and prove concentration within it; the movers evidence finds the markdown largely independent of concentration, which means the firm-level elasticity, not the market boundary, is the real terrain — stand there. And expect churn to be offered as proof of exploitation, or low churn as proof of competition: both are sleight of hand. The lower panel is the rebuttal in a picture — turnover is speed, the markdown is size, and they are independent. The separation rate settles nothing about the separation elasticity; do not let a churn statistic be entered as a markdown, and do not lean on one yourself, because by the evidence high-turnover low-wage work runs toward more markdown, not less.

And the wage-and-hour front itself. Monopsony does not stay in the antitrust lane. In a misclassification fight — the daily work of a restaurant practice — plaintiffs are learning to run the model backward: the very illiquidity that produces the markdown is offered as evidence of economic dependence, and economic dependence sits at the heart of the employee-versus-contractor test, under California's Borello factors and the federal economic-realities standard alike — a worker who cannot readily leave is, on the argument, not in business for herself. The same picture answers it: dependence is the separation elasticity, not the separation rate, and a workforce that leaves readily when paid more can hardly be called captive, whatever its churn. And where "we paid the prevailing market wage" is raised to defeat a wage claim, the model is the reason the phrase cannot close the inquiry — the prevailing wage in a frictional market already carries the markdown, so the benchmark the defence invokes is, on the plaintiff's theory, the very quantity in dispute. Better to know that before a case is built on it.

The throughline is the firm's own: a defence that understands wage formation at this depth argues from the architecture of the labour market — the flows, the friction, the identity binding them — rather than from a form book. The same equation is a sword for the plaintiff and a shield for the defendant, and the difference between them is the data. That is ground a treatise cannot reach by memorising rules. It is reached only by understanding the thing the rules are about.

the arithmetic of the source

ε = η + ζ
The firm's labour-supply elasticity is the sum of how its recruitment and how its retention answer the wage. A stock fed by one flow and drained by another moves with both — an accounting identity, true before any economics is added.
ε = 2ζ
In a steady-state market your recruits are rivals' leavers, so recruitment is as wage-elastic as separation (η = ζ) and the elasticity is twice the wage-elasticity of quits. The market boundary need never be drawn; the number lives in the quit records — provided the symmetry holds, which is the one assumption to name and to defend.
¹⁄₍₂ζ₊₁₎
The markdown. Finite friction, finite ζ, a positive wedge — it survives free entry and a thousand competitors. A quit elasticity of two to three, the central estimate, leaves workers paid 80–85% of their product. Fewness was never required — only friction.
one ≡ many + friction
Classical monopsony and dynamic monopsony write the same equation — a markdown of 1/(ε+1) against a finite elasticity. They are observationally equivalent at the level of pay; the microfoundation is contested, the wedge is not. The evidence finds it largely independent of the forces driving the classical case.
size ≠ speed
The markdown is set by how sharply quits answer pay — the elasticity ζ. The pace of adjustment is set by how fast the pool turns over — the rate s, with half-life ln 2 ∕ s. A workforce can churn quickly and still be marked down deeply. Never read a rate as a markdown.

What the picture assumes

Every line in the instrument rests on a premise, and naming them is not modesty — each is a place the other side's expert can be met, and a place one's own can be checked before he is retained.

linearity
Constant elasticity. The rays are straight because the elasticity is held constant across the wage range. Real responses bend, and the clean markdown 1/(ε+1) holds exactly only in the neighbourhood where it is measured.
symmetry
η = ζ in equilibrium. The identity ε = 2ζ depends on a firm's recruits being rivals' leavers in a steady state. A firm that is growing or shrinking, or a market in slack, breaks the symmetry — and then the quit record alone misstates ε, in a direction one can name.
flat hazard
A constant separation rate. The exponential drain assumes a level monthly hazard. If quitting accelerates as the firm falls further behind the market, the half-life is shorter and the grace smaller than the curve shows.
one cause
The whole gap is monopsony. The plate reads the entire distance to marginal product as the wedge. Compensating differentials, mismeasured product, and rents shared for other reasons inhabit that same gap; they must be argued out, not assumed away.

Each line is a question on cross-examination — which is the use of stating them. The advocate who has named the assumptions beneath his own figure is the one prepared to test the assumptions beneath the other side's.