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Equilibrium unemployment (NAIRU / WS-PS)
The one unemployment rate that does not make inflation accelerate — where the wage wanted meets the wage tolerated.
u* = (b + µ) / αProblem / motivation
Why does a central bank worry when unemployment becomes “too low”? Wouldn't 3% be pure good news?
Because it knows something counter-intuitive: even when the economy is running at full tilt, some unemployment remains — the time it takes to move from one post to another (frictional unemployment), or skills and locations that do not match the vacancies on offer (structural unemployment). That irreducible share forms a FLOOR: the natural unemployment of the course “Types of unemployment”. Its open question remained: why a floor, and why at THAT level? This course's answer: there is an EQUILIBRIUM rate of unemployment, the NAIRU (Non-Accelerating Inflation Rate of Unemployment). Above it, inflation slows; below it, inflation runs away.
The mechanism is a tug of war over how output is shared. Employees negotiate their REAL wage — not the amount in euros, but what it lets them buy (course “Inflation and purchasing power”). Firms, for their part, protect their MARGIN — the share of the selling price that does not go to wages. Each side pulls the blanket its way; the cake, meanwhile, does not grow any bigger.
What happens if employees demand more than the margin leaves? Nobody gives way: firms raise their prices to keep their share — but higher prices eat into what the wage can buy, so employees renegotiate, and prices set off again: that is the price-wage loop (course “The causes of inflation”). Only one level of unemployment calms this tug of war. This course builds it piece by piece, with two curves: WS (Wage Setting — what employees obtain) and PS (Price Setting — what margins tolerate).
Assumptions
In your view, which assumptions are needed for this model to hold? Jot down your ideas — no lead is wrong, this is your worksheet.
Your worksheet is still empty. Go for it: propose at least one idea.
0 idea(s) proposedFormalization
Let's put the tug of war into figures, on a simple base: for €100 of output, how much goes to employees? That number is the real wage, written w. On the employees' side — the WS curve — we start from the cake (100), add bargaining power (+ b points, assumption 1) and subtract the discipline of unemployment: each point of unemployment u shaves α points off the demand (assumption 2). Hence: w = 100 + b − α·u. Read it at u = 0: the demand would be 100 + b — more than the whole cake, before any margin at all. There is the heart of the model: without the discipline of unemployment, demands do not fit inside the 100. The higher unemployment climbs, the further the demand comes back down — the curve SLOPES DOWN.
On the firms' side — the PS curve — out of €100 of selling price, the margin µ is taken (assumption 3); what is left for wages is w = 100 − µ. A FIXED ceiling: it does not depend on unemployment. (In textbooks, the margin is often a RATE above cost — one then writes w = 100 ÷ (1 + markup rate). Our µ counts directly the share taken out of €100: same idea, simpler notation.)
Superimpose the two: a line that falls as u rises (WS), a fixed ceiling (PS). They cross at exactly ONE point. To the left of the crossing — low unemployment — the wanted wage exceeds the tolerated one: prices rise, inflation accelerates (assumption 4). To the right — high unemployment — it is the reverse: it slows. The crossing is the only rate at which the two demands coincide: equilibrium unemployment, written u* (“u star” — the floor already met in the courses “Types of unemployment” and “The expectations-augmented Phillips curve”).
Set the two wages equal: 100 + b − α·u* = 100 − µ. The 100s cancel, leaving α·u* = b + µ, so u* = (b + µ) ÷ α — the formula of the header. It reads like a sentence: equilibrium unemployment is the CONFLICT (employees' claims b plus firms' margin µ) divided by the DISCIPLINE (what one point of unemployment makes people give up: α). And it turns over — knowing u* and two ingredients means recovering the third (exercise 4 has you make that return journey). Click each term:
Solving / calculation
Let's set them equal, figures in hand — a toy with European features: b = 3, µ = 15, α = 2.5, three numbers in points of the base 100. Where does the tug of war settle? Work through it, check it wage in hand, then it is your turn.
- We set WS = PS: the wanted wage equals the tolerated wage
100 + b − α·u = 100 − µ - The 100s cancel — leaving the conflict against the discipline
α·u = b + µ = 3 + 15 = 18 - We solve
u* = (b + µ)/α = 18/2.5u* = 7.2% - Cross-check through the wages: the two curves say the same thing
WS: 100 + 3 − 2.5 × 7.2 = 85 | PS: 100 − 15 = 85w = 85 ✓ - Reading it for inflation: what if unemployment fell to 5%?
wanted: 100 + 3 − 2.5 × 5 = 90.5 > tolerated: 85+5.5 → accelerating inflation
The toy's NAIRU is 7.2%. At 5% unemployment, employees want 90.5 when margins tolerate only 85: those 5.5 points of gap do not vanish — they turn into price increases, year after year. For a LOWER equilibrium rate, the formula shows the only levers: the numerator (b, µ) or the denominator (α) — not a demand stimulus, which shifts neither curve (Interpretation step).
u* = (b + µ) / αSet the conflict (b, µ), the discipline (α) and observed unemployment (u): the two wages, the NAIRU and the inflation regime follow. Bring u onto u* to find the equilibrium.
Economic interpretation
An EXPLAINED floor means levers identified. The WS-PS model — formalised by the economists Richard Layard, Stephen Nickell and Richard Jackman in a 1991 book — says precisely what to act on, and what not to count on.
The NAIRU is the unemployment rate that makes employees' claims (b) and firms' margin (µ) compatible. Lowering it durably means reducing the CONFLICT: benefit or minimum-wage rules on the b side; more competition in protected markets on the µ side; and everything that improves MATCHING — training, mobility, the structural remedies of the course “Types of unemployment” — eases wage pressure at a given unemployment rate: a lower effective b. Every lever has its social cost — lowering b means trimming protections: the model identifies the levers, it does not say which are desirable. A demand stimulus, for its part, shifts NEITHER curve: it merely slides u below u* — and inflation pays the difference.
As long as u > u*, cyclical unemployment remains to be absorbed: stimulus is possible — cutting the policy rate (course “The policy rate and transmission”) — without waking prices. Past u*, every tenth of a point is paid for in accelerating inflation: hence the braking when unemployment becomes “too low”, the opening question. This u* is exactly the one of the Phillips curve: this course explains where it COMES FROM (the WS-PS tug of war), the course “The expectations-augmented Phillips curve” puts a number on what it COSTS to depart from it — how much inflation per point of unemployment gained below u*, and why the bill grows year after year.
The course “Types of unemployment” defined natural unemployment by its COMPOSITION: frictional + structural. WS-PS recovers the same floor through its MECHANISM: the institutions and frictions that feed b, µ and α. Two readings of the same u* — and the same residual: cyclical = u − u*, the one Okun's law links to growth.
In early 2026, observed unemployment stands at 8.1% (course “Measuring unemployment”). The Banque de France estimates French STRUCTURAL unemployment at about 7.8% in 2025 (“structural” in the institutes' BROAD sense: the whole floor, frictions included — our u*) — down by about 1.3 point since 2015, which notably reflects labour market reforms: b, in the model's broad sense, in action. The model's reading: most of the 8.1% is equilibrium unemployment, and the cyclical residual is thin — which is why “more growth” has never been enough to bring it very low (the diagnosis of the course “Types of unemployment”).
Limits / critiques
Exercises
With b = 2, µ = 18 and α = 4, compute equilibrium unemployment u* (in %).
True or false: a reform that reduces firms' margin (µ) lowers the NAIRU.
b = 3, µ = 15, α = 2.5, and unemployment falls to u = 4%. What real wage do employees negotiate (WS, per €100 of output)?
Which of these measures lowers the NAIRU u*, according to the WS-PS model?
Observed unemployment is 6% while the NAIRU is estimated at 8%. What does the WS-PS model predict for inflation?
A country shows u* = 8% with µ = 15 and α = 2.5. What is bargaining power b (in points)?
Early 2026: observed unemployment 8.1%; structural unemployment estimated by the Banque de France at about 7.8%. What cyclical unemployment do you read as a residual (in points)?
True or false: after a long recession, the NAIRU itself may have risen.