The Phillips curve looks like a gift: pick less unemployment, accept a little more inflation, choose your spot on the trade-off. For years it seemed to hold — then it broke, as inflation and unemployment climbed together and the menu stopped predicting anything. This page rebuilds it with expectations doing the work, and shows why the long-run menu has just one item. It is the topic that most often sends intermediate students looking for a macroeconomics tutor in New York — the fix is conceptual, not a formula.
1 · From a fixed trade-off to a shifting curve
The original curve plotted inflation against unemployment and found them inversely related — low unemployment with high inflation, and the reverse. Read literally, it offered a menu: run the economy hot, tolerate faster price rises, buy a lower jobless rate. The trouble is the word permanent: it treated the trade-off as fixed, forever. It is not — the fix is expectations.
The modern short-run Phillips curve is written
π = πᵉ − a(u − u*)
Here π is actual inflation and πᵉ is expected inflation — what workers and firms build into wages and prices. u is unemployment, u* the natural rate, and a > 0 sets how strongly slack moves inflation. Push u below u* and inflation overshoots; push it above and inflation undershoots.
Here is the fact the diagram turns on. Each πᵉ draws its own short-run curve, and every one passes through the natural rate at its own expected inflation — set u = u* and π = πᵉ. Under adaptive expectations, people expect this year what they saw last year, so πᵉ equals last period’s π. Fool them once and they adjust — shifting the curve up.
2 · The natural rate and the vertical long-run curve
The natural rate of unemployment, u*, is the rate consistent with stable, correctly-anticipated inflation. It reflects the structure of the labour market — job search, skills, institutions — not the current inflation rate. Frictional and structural unemployment live here; cyclical unemployment does not.
Now the key step. In the long run expectations cannot stay wrong: people expect the inflation they get, so πᵉ = π. That forces the a(u − u*) term to zero, so u = u*.
So the long-run Phillips curve is vertical at u*. Whatever the inflation rate, the economy sits at u* — no permanent trade-off. This is the natural-rate hypothesis of Friedman and Phelps; a central bank can move unemployment only in the short run.
3 · Disinflation and the sacrifice ratio
Run the mechanism backwards. To cut inflation, push unemployment above u*: then π − πᵉ = −a(u − u*) is negative, inflation undershoots expectations, and the curve shifts down. Inflation ratchets lower.
It works, but is costly. The sacrifice ratio is the bill: the excess unemployment — points of u above u*, summed over the years — needed to lower inflation by one point. Faster disinflation means a deeper recession; credibility cuts it by moving πᵉ down first.
Worked example — holding unemployment below the natural rate
Take a = 2, u* = 5, and adaptive expectations (each year, expect last year’s inflation). Start calm, with πᵉ = 2.
Step 1 — The curve. π = πᵉ − 2(u − 5). At u = 5 the slack term is zero, so π = πᵉ.
Step 2 — Base case. With πᵉ = 2 and u = 5, π = 2 − 2(5 − 5) = 2. Point A = (5, 2); expectations are fulfilled.
Step 3 — A rest point. Inflation matches expectations, so A repeats — a rest point on both the short-run and long-run curves.
Step 4 — Perturbation. The government stimulates demand to push u to 3. Expectations still lag at πᵉ = 2, so the economy slides along the original curve: π = 2 − 2(3 − 5) = 6 (B = (3, 6)) — the trade-off exploited.
Step 5 — Expectations catch up. Each year expectations rise to last year’s inflation, shifting the curve up. With πᵉ = 6, holding u = 3 gives π = 6 − 2(3 − 5) = 10 (C = (3, 10)); next year πᵉ = 10 gives π = 14 (D = (3, 14)). Inflation accelerates — 6, 10, 14 — four points a year, without limit.
Step 6 — The way out. Holding u = 3 needs inflation rising without limit — the accelerationist result. Let u return to 5 instead: at the natural rate π = πᵉ = 10 (E = (5, 10)), back on the long-run curve.
Step 7 — Interpret. Unemployment is back at 5, but inflation is stuck at 10, not the 2 it began at — the dip bought only permanently higher inflation. A and E sit one above the other at u*: the economy rests at any inflation rate, but only at the natural rate.
Can you tell a movement along a Phillips curve from a shift of the whole curve? That one distinction — short run versus long run, expected inflation held fixed versus changing — is where most exam marks on this topic are won or lost. A one-on-one macroeconomics tutor traces the shifting curve with you until the sequencing is automatic. Book a trial session.
Practice
Q1. On the curve π = πᵉ − 2(u − 5) with πᵉ = 4, find π (a) at u = 5 and (b) at u = 2.
Q2. A central bank holds unemployment three points above the natural rate for four years, and inflation falls from 11% to 3%. Find (a) the excess-unemployment cost in point-years and (b) the sacrifice ratio (point-years per point of disinflation).
Q3. Expectations are adaptive and u* = 5. The central bank holds unemployment at 5 permanently; last year’s inflation was 7%. Find inflation this year and the long-run resting point.
Answers. Q1: (a) π = 4 (slack term zero); (b) π = 4 − 2(2 − 5) = 10. Q2: (a) 3 × 4 = 12 point-years; (b) inflation fell 8 points, so 12 ÷ 8 = 1.5 point-years per point. Q3: at u*, π = πᵉ = 7%; expectations stay 7, so the economy settles at (5, 7) — any inflation rate is a long-run equilibrium at u* = 5, since the curve is vertical.
Key takeaways
- The short-run curve is a trade-off; the long-run curve is not. π = πᵉ − a(u − u*) slopes down only for a given πᵉ, and every such curve is anchored at the natural rate (set u = u* and π = πᵉ).
- Exploiting the trade-off shifts the curve up as adaptive expectations chase realised inflation.
- Holding u below u* needs ever-rising inflation — the accelerationist result. Unemployment returns to u* with permanently higher inflation, no lasting gain.
- Disinflation is costly, measured by the sacrifice ratio: excess unemployment per point of inflation cut. Credibility lowers it.
Why New York students choose our macroeconomics tutoring
- Built for the intermediate core: sessions use the expectations-augmented framework your course teaches — the shifting short-run curve, the vertical long-run curve, the natural-rate hypothesis — in your notation.
- The distinctions that carry marks, drilled: movement along a curve versus a shift, short run versus long run, adaptive versus rational expectations — clean under exam pressure.
- Online and one-on-one: a PhD tutor works from your problem sets and past papers over a shared screen, on the questions your paper will ask.
FAQ
Q: Why did the Phillips curve break down?
A: It assumed a fixed trade-off and ignored expectations. Once people expected ongoing inflation, they built it into wages and the curve shifted up — so inflation and unemployment could rise together, which a fixed curve cannot explain.
Q: Shift of the curve, or movement along it?
A: Moving along one curve changes unemployment with expected inflation held fixed — the short-run trade-off. A shift comes when expected inflation itself changes, redrawing the curve higher.
Q: Why is the long-run Phillips curve vertical?
A: In the long run expectations are correct, so π = πᵉ. That forces the slack term to zero, so u = u* at any inflation rate — a vertical line at u*.
Q: What is the natural rate of unemployment?
A: The rate consistent with stable, correctly-anticipated inflation. It reflects frictional and structural forces — job search, skills, institutions — not current inflation.
Q: What does the sacrifice ratio measure?
A: The cost of disinflation: the excess unemployment, in point-years, needed to cut inflation by one point. Credibility lowers it.
Book a macroeconomics tutor in New York
The Phillips curve rewards students who keep the short run and long run apart, and can trace the shifting curve, not just name it. One-on-one online sessions build both, on your course’s own past papers. Tell us your module and exam date, and we will match you with the right tutor this week.
