Why do the short‑run and long‑run Phillips curves imply different inflation–unemployment tradeoffs

What Are the Short‑Run and Long‑Run Phillips Curves?

The short‑run Phillips Curve (SRPC) is downward sloping: lower unemployment is associated with higher inflation, holding expectations fixed. The long‑run Phillips Curve (LRPC) is vertical at the natural rate of unemployment: in the long run, inflation does not affect unemployment.

Why the Short‑Run and Long‑Run Phillips Curves Differ

1. Expectations are fixed in the short run

In the short run, workers and firms have given inflation expectations. Unexpected inflation can temporarily reduce real wages and stimulate hiring, creating a negative relationship between inflation and unemployment.

2. Expectations adjust in the long run

Over time, agents update their expectations to match actual inflation. Once expectations catch up, the temporary trade‑off disappears.

3. The natural rate of unemployment anchors the long run

In the long run, unemployment returns to its natural rate, determined by structural factors (frictions, matching, institutions), not by inflation.

4. Policy can move along the SRPC, but not the LRPC

Expansionary policy can move the economy along the short‑run curve, but it cannot permanently lower unemployment below the natural rate without ever‑rising inflation.

How Expectations Shift the Short‑Run Phillips Curve

Step 1: Start with expected inflation

Suppose expected inflation is \(\pi^e\). The short‑run Phillips Curve is drawn for that expectation.

Step 2: Actual inflation exceeds expectations

If actual inflation \(\pi\) > \(\pi^e\), real wages fall, firms hire more, and unemployment temporarily drops below the natural rate.

Step 3: Expectations adjust upward

Over time, workers and firms revise \(\pi^e\) upward to match actual inflation.

Step 4: The SRPC shifts upward

A higher \(\pi^e\) shifts the entire short‑run Phillips Curve upward, so the same unemployment rate now corresponds to higher inflation.

Step 5: The economy returns to the LRPC

Unemployment returns to the natural rate, but at a higher inflation level. This is why the long‑run curve is vertical.

Numerical Illustration

Consider a simple expectations‑augmented Phillips Curve:

\[ \pi = \pi^e – \alpha (u – u_n) \]

• \(\pi\): actual inflation
• \(\pi^e\): expected inflation
• \(u\): unemployment rate
• \(u_n\): natural rate of unemployment
• \(\alpha > 0\): sensitivity parameter

For a given \(\pi^e\), this equation defines a downward‑sloping SRPC in \((u, \pi)\) space. In the long run, \(\pi = \pi^e\) and \(u = u_n\), so the relationship collapses to a vertical line at \(u_n\).