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 expectations-augmented Phillips curve.
The expectations-augmented Phillips curve is generally written as
\[ \pi=\pi^e-\alpha(u-u_n) \]
where \(\pi\) is actual inflation rate, \(\pi^e\) is expected inflation rate, \(\alpha\) is responsiveness of inflation to unemployment gap, \(u\) is actual unemployment rate, and \(u_n\) is natural rate of unemployment.

Step 2: Identify the given values.
Given,
\[ \pi^e=5 \] \[ u_n=4 \] \[ \alpha=0.5 \] \[ u=5 \]

Step 3: Calculate the unemployment gap.
\[ u-u_n=5-4 \] \[ u-u_n=1 \]
This means actual unemployment is \(1\) percentage point above the natural rate of unemployment.

Step 4: Substitute the values in the Phillips curve equation.
\[ \pi=5-0.5(1) \]
\[ \pi=5-0.5 \]
\[ \pi=4.5 \]

Step 5: Interpret the result.
Since actual unemployment is greater than the natural rate of unemployment, inflation becomes lower than expected inflation.
Thus, actual inflation is below \(5\%\).

Step 6: Final conclusion.
Rounded off to one decimal place, the actual inflation rate is
\[ \boxed{4.5} \]