The Medium Run & Labour Market

The Natural Rate of Unemployment

coreExam · highTA · PS3-Q3

The natural rate un is set where the wage-setting (WS) and price-setting (PS) relations are consistent: WS gives the real wage workers target (falling in u); PS gives the real wage firms will pay (fixed by markup m). Equilibrium: un ≈ (m+z)/α. It is positive, institution-dependent, and can be shifted by structural policy.

Derivation

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Wage and Price Setting

The natural rate emerges from two conflicting claims on the real wage:

Wage-setting (WS): Workers target a real wage that is higher when unemployment is low. When $u$ falls, bargaining power rises (easier to find another job, harder to replace a worker).

\frac{W}{P} = F(u, z) \quad \text{(decreasing in } u \text{)}

Price-setting (PS): Firms charge a markup $m$ over wage costs, implying a fixed real wage regardless of $u$ :

\frac{W}{P} = \frac{1}{1+m}

The Natural Rate

$u_n$ is the unemployment rate at which these two real-wage claims are consistent. No inflation surprises — wages grow at exactly the expected rate.

Setting WS = PS:

F(u_n, z) = \frac{1}{1+m} \implies u_n \approx \frac{m+z}{\alpha}

What Shifts It?

| Change | Effect on $u_n$ | Mechanism | |--------|----------------|-----------| | $\uparrow m$ (less competition) | $\uparrow$ | Firms pay lower real wages; more unemployment needed for WS to fall to PS level | | $\uparrow z$ (generous UI) | $\uparrow$ | Workers' outside option improves; WS shifts up; higher $u$ needed | | $\uparrow \alpha$ (wages more u-sensitive) | $\downarrow$ | WS steeper; WS and PS cross at lower $u$ |

Structural vs Demand Policy

Demand policy (monetary/fiscal) changes $u$ temporarily — the economy returns to $u_n$ in the medium run. Structural reform changes $u_n$ permanently — the whole equilibrium shifts.

Worked Example

α=2, m=0.1, z=0.1. Find un. Then employment-protection legislation raises z to 0.2. Find new un.

Baseline: un = (0.1 + 0.1)/2 = 0.2/2 = 0.10 = 10%.
After ↑z=0.2: un = (0.1 + 0.2)/2 = 0.3/2 = 0.15 = 15%.
ΔZ = +0.1 → Δun = 0.1/2 = +5 percentage points.

un rises from 10% to 15% when employment protection increases. Lower z reduces un.

Common Mistakes

—Saying the natural rate is 0% — it is a positive equilibrium determined by market institutions.
—Confusing actual u with natural un — in the short run u ≠ un; they equate only in the medium run.
—Treating un as fixed — it shifts when m or z change (e.g. labour market reforms).

Exam Cues

→un = (m+z)/α. Know the three determinants and the direction of each effect.
→Structural vs demand-side: demand policy changes u temporarily; structural reform changes un permanently.
→In the IS-LM-PC framework, the central bank targets u = un to prevent inflation from accelerating.