Inflation and the Phillips curve · A tool for lessons 8 to 12
The Natural-Rate Workbench
Four wage-setting rules, one engine. Pick a rule, set the mark-up and the productivity, and the page computes the natural rate with its working, the Phillips relation the rule implies, what moves the natural rate, and where inflation goes when unemployment is held away from it. Two identities are checked live against the numbers it has just found. The buttons load the set-ups of the Delhi School entrance questions.
Pick the wage-setting rule, then move the mark-up, productivity and the workers’ claim. Price-setting (red) is the real wage firms allow, wage-setting (blue) is the real wage workers claim at each unemployment rate, and they meet at the natural rate (gold). The second plot holds unemployment at a target you choose, measured from the natural rate, and follows inflation for ten years.
W/P = A(1 + z − u). The claim scales with productivity, as does the real wage firms allow, so productivity cancels.
Wage-settingPrice-settingNatural rate
Inflation2% anchor
The natural rate
20%. uₙ = z + m/(1 + m) = 0 + 0.25/1.25 = 20%. The real wage there is 0.8.
Holding unemployment at 18%
That is 2 points below the natural rate. After ten years inflation is 30.57%. With θ = 1 it climbs every year and does not settle.
The Phillips relation this rule implies
1 + π = (1 + πᵉ) × (1 + m)(1 + z − u) = (1 + πᵉ) × 1.25 × (1 − u). Near the natural rate, π ≈ πᵉ − β(u − uₙ) with β = 1.25 (inflation lost per point of unemployment above uₙ).
What moves the natural rate
| Change | New uₙ | Natural rate |
|---|---|---|
| Productivity A up 10% | 20% | no change |
| Mark-up m up 5 points | 23.1% | rises by 3.08 points |
| Workers' claim z up 0.05 | 25% | rises by 5 points |
Checks, recomputed live
At uₙ with πᵉ = 2%, π = 2% ✓. At uₙ with πᵉ = 10%, π = 10% ✓. The wage-setting factor at uₙ is 1, so uₙ does not depend on expected inflation.
Things to try
- Productivity, three ways. Load 2019 Q24 and raise A: the natural rate does not move. Load 2012 Q51 to Q56 and raise A: it rises. Load 2020 Q08 and raise A: it falls. Only how A enters the wage claim differs.
- The mark-up. In all four rules a larger mark-up raises the natural rate. Try it on each and read the table under the plots.
- Accelerating inflation. Hold unemployment two points below the natural rate with θ = 1 and read the ten-year inflation. Move θ down to 0.5 and inflation settles instead of climbing.
- No natural rate. Choose the exponent rule, set the mark-up to 0 and raise A above 1. Price-setting then allows a real wage that workers’ claim never reaches at any unemployment rate, so the curves do not meet between 0% and 100% and the page says so instead of drawing a number.
The tool runs on the same engine as the lessons, and every number in them was checked against it. The lessons start at Lesson 8; the Delhi School questions are worked in Lesson 12.
Read next
All resources →MacroeconomicsThe natural rate of unemployment: wage-setting, price-setting, efficiency wages and hysteresisPrice-setting and the mark-up, wage-setting and bargaining, why they meet at one unemployment rate, what moves it, the three ways productivity can enter, efficiency wages, insiders and outsiders, hysteresis, and the step to the Phillips curve. With the Natural-Rate Workbench.MacroeconomicsInflation and the Phillips curve: the Delhi School problems on wage-setting, the natural rate and the NAIRUThe Delhi School entrance's seventeen wage-setting, price-setting and Phillips curve questions, worked by technique, with the Natural-Rate Workbench preloaded with each set-up.MacroeconomicsInflation, unemployment and the Phillips curve: a module from price indices to the natural rateA module in twelve lessons: measuring inflation and unemployment, the causes and costs of inflation, the original and expectations-augmented Phillips curves, Okun's law, wage-setting and price-setting, supply shocks, disinflation, the curve in real data, and a lesson of Delhi School problems. With labs, worked questions and graded past papers.