The Medium Run & Labour Market

Wage and Price Setting

coreExam · high

The WS–PS framework models the two sides of the labour market. Workers set nominal wages based on expected prices and the tightness of the labour market (WS: W = Pe·F(u,z)). Firms set prices as a markup over wages (PS: P = (1+m)W → W/P = 1/(1+m)). The natural rate un is where the two claims on the real wage are consistent.

Derivation

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The Two Claims on the Real Wage

Wage setting (workers): target a real wage that is higher when unemployment is low (bargaining power) and higher when $z$ is generous (outside options).

W = P^e \cdot F(u, z) \iff \frac{W}{P^e} = F(u, z)

Price setting (firms): charge a constant markup $m$ over wage costs.

P = (1 + m) W \iff \frac{W}{P} = \frac{1}{1+m}

Diagrammatic Representation

In $(u, W/P)$ space:

WS is downward-sloping — lower $u$ → higher target real wage.
PS is horizontal at $1/(1+m)$ — independent of $u$ .

They cross at the natural rate $u_n$ . At lower unemployment, workers' target exceeds what firms pay → wage pressure → inflation. At higher unemployment, workers accept less → disinflation.

Structural Determinants of $u_n$

| Change | Curve | Direction | Effect on $u_n$ | |--------|-------|-----------|-----------------| | $\uparrow m$ (less product competition) | PS | Shifts down | $\uparrow$ | | $\uparrow z$ (more generous UI, stronger EPL) | WS | Shifts up | $\uparrow$ | | $\uparrow \alpha$ (WS more sensitive) | WS | Steeper | $\downarrow$ |

Linear Approximation

With $F(u, z) = 1 - \alpha u + z$ and $1/(1+m) \approx 1 - m$ :

u_n \approx \frac{m + z}{\alpha}

This is the workhorse formula used in problem sets.

Short Run vs Medium Run

Short run: $u \neq u_n$ ; wage-price dynamics push inflation up or down via the Phillips curve.
Medium run: expectations adjust → $u \to u_n$ → inflation stabilises.
Structural reform: $u_n$ itself moves (e.g., labour-market liberalisation).

Worked Example

α = 2, m = 0.1, z = 0.1 (baseline). Find un. Then a structural reform lowers z to 0.04. Find new un.

Baseline: un = (m+z)/α = (0.1 + 0.1)/2 = 0.10 = 10%.
After reform: un = (0.1 + 0.04)/2 = 0.07 = 7%.
Lower z → WS shifts down → WS and PS intersect at lower u.

un falls from 10% to 7%. Structural reform (lower UI generosity) reduces the natural rate by 3 pp.

Common Mistakes

—Saying WS-PS determines actual u — it determines the natural rate un, not short-run u.
—Confusing m (product-market markup) with z (labour-market catchall) — they shift different curves.
—Forgetting that PS is horizontal — it is fixed by m alone, independent of u.
—Assuming WS shifts imply demand-side policy — they are structural (change un).

Exam Cues

→Two-curve diagram: WS downward, PS horizontal. They cross at un.
→↑m: PS shifts down → un rises. ↑z: WS shifts up → un rises. ↑α: WS steeper → un falls.
→Distinction: WS is workers' target real wage; PS is the real wage firms actually pay.
→Bargaining story: low u → strong workers → higher W → higher P → wage-price spiral if expectations adapt.