Question

In an expectations-augmented Phillips curve equation, expected inflation rate and natural rate of unemployment are \(5\%\) and \(4\%\), respectively. The responsiveness of inflation to unemployment gap is \(0.5\). If actual unemployment rate is \(5\%\), then the actual inflation rate (in %) is (rounded off to one decimal place).

Hint:

In the expectations-augmented Phillips curve, if actual unemployment is above the natural rate, actual inflation falls below expected inflation.

Answer 1

Correct Answer: 4.5

Step 1: Recall the augmented Phillips curve.
\[ \pi=\pi^e-\alpha(u-u_n) \]
where $\pi^e$ is expected inflation and $u_n$ is the natural unemployment rate.

Step 2: List the values.
Here $\pi^e=5$, $u_n=4$, $\alpha=0.5$ and $u=5$.

Step 3: Find the unemployment gap.
\[ u-u_n=5-4=1 \]

Step 4: Plug in.
\[ \pi=5-0.5(1)=4.5 \]

Step 5: Interpret.
Unemployment above the natural rate pulls inflation below the expected $5\%$, giving $4.5\%$.
\[ \boxed{4.5\%} \]