expectations-augmented Phillips curve (short- and long-run Phillips curve)

Short‑Run Phillips Curve

The Phillips curve shows a trade‑off between inflation ($\pi$) and unemployment ($u$). In the short run, expectations of future inflation are not fully adjusted, so the curve is downward sloping.

Equation (short‑run): $$ \pi = \pi^e - \beta (u - u^n) $$
where:

• $\pi^e$ = expected inflation
• $u^n$ = natural rate of unemployment
• $\beta > 0$ = slope parameter

Analogy: Think of a seesaw. If the left side (inflation) goes up, the right side (unemployment) goes down, but only until the seesaw reaches a new balance point.

Long‑Run Phillips Curve

In the long run, people fully anticipate inflation, so the trade‑off disappears. The curve becomes vertical at the natural rate of unemployment.

Equation (long‑run): $$ \pi = \pi^e $$
This means unemployment will always be $u^n$, regardless of inflation.

Example: If the government tries to keep unemployment below $u^n$ by pushing inflation higher, workers will eventually notice the higher prices and adjust their wage demands, bringing unemployment back to $u^n$.

Exam Tips 🎯

1. Draw both curves clearly; label axes and key points.
2. Explain why the short‑run curve is downward sloping and the long‑run is vertical.
3. Use the expectations‑augmented equation to show how a shift in expectations moves the curve.
4. Remember the natural rate of unemployment ($u^n$) is the long‑run equilibrium.
5. Include a brief discussion on the policy trade‑offs (e.g., inflation targeting vs. unemployment).