Lecture 15: The Phillips CurveFrom AS to the Phillips Curve* The price level vs The inflation rateP(t) = P (t) (1+ µ) F(u(t), z)eNote that: P(t)/P(t-1) = 1 + (P(t)-P(t-1))/P(t-1)P(t)/P(t-1) = 1 + (P(t)-P(t-1))/P(t-1)Let π(t) = (P(t)-P(t-1))/P(t-1)ee•Then(1+π(t)) = (1+π(t)) (1+ µ) F(u(t), z)butln(1+x) ≈ x if x is “small”Let also assume that ln(F(u(t), z)) = z – αu(t)eThe Phillips Curve* The price level vs The inflation rateP(t) = P (t) (1+ µ) F(u(t), z)e≈>π(t) = π (t) + (µ+z) - α u(t)e* original Phillips curve; Figures: 8-1/8-2/8-3/8-4/8-5The Phillips Curve and The Natural Rate of Unemploymentπ (t) = π (t) => u = (µ+z)απ(t) = π (t) - α (u(t) - u
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