The short-run trade-off between inflation and unemployment — buy lower joblessness with higher prices — and why the bargain vanishes in the long run. Once wage-setters expect the inflation, the curve stands straight up at the natural rate: no permanent trade-off, only a higher price level. These are models of an economy, not investment advice; forecasts are AMBER.
source A. W. Phillips, "The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957," Economica 25 (1958): 283–299 · doi:10.1111/j.1468-0335.1958.tb00003.x Rendered, not quoted.
The expectations-augmented curve:
π = πᵉ − h·(u − uₙ)
π actual inflation · πᵉ expected inflation · u unemployment · uₙ natural rate · h > 0 the slope.
Hold πᵉ fixed and the short-run curve slopes down: dπ/du = −h < 0. Lower unemployment is bought with higher inflation. At u = uₙ the surprise term is zero, so π = πᵉ.
Let expectations catch up — πᵉ → π — and the whole curve slides up until u = uₙ again. The long-run locus is a vertical line at uₙ: the trade-off is a disequilibrium mistake, not a lever.
Inflation versus unemployment — Phillips 1958 read the wage data; Friedman & Phelps (1968) added expectations. A downward short-run trade-off that goes vertical at the natural rate once πᵉ adjusts is the labour-market face of the-quantity-theory: MV=PQ makes money neutral in the long run, so extra money buys only extra inflation, never a permanently lower u.
Re-runs the live slope check every render. Downward & anchored at uₙ ⇒ green. If the TAMPER (window 6) inverts the slope, the witness turns red.
Expected inflation πᵉ, slope h, natural rate uₙ, and a scan over unemployment u.
Solid = short-run curve at current πᵉ. Faint = the same curve after expectations rise. Vertical dashed = the long-run curve at uₙ.
Proven at boot:
"There is always a stable menu — pick 3% unemployment and pay 6% inflation, forever." That reading of the 1960s curve is the wall. It assumes πᵉ is frozen. It is not: exploit the trade-off and expectations chase the inflation, the curve lifts, and you are back at uₙ with only higher prices. The 1970s stagflation — high u AND high π together — walked straight through this wall.
"The Phillips curve is a permanent, exploitable trade-off policymakers can sit anywhere on."
↳ Only short-run. Long-run curve is vertical at uₙ; raising πᵉ shifts it up, u returns to uₙ.
"A supply shock cannot raise inflation and unemployment at once."
↳ It can — AMBER: raise uₙ and add a cost-push intercept and both rise (stagflation), the naive trade-off breaks.
"Rational agents, perfect competition, ceteris paribus make this exact."
↳ AMBER idealizations. Economics is not physics; h, uₙ, and πᵉ are estimated and drift. Treat forecasts as AMBER.
The disclosed planted void: flip the slope positive (h → −h) so higher unemployment comes with higher inflation. The curve inverts; the WITNESS in window 7 catches it live.