Question

question 93
2 pts
the natural rate of unemployment is 7 percent, expected inflation is 2 percent, actual inflation is 4 percent, and the phillips curve equation a is 0.9. what is the actual unemployment rate? (answer in terms of percentage points to 2 decimal places. e.g. if your answer is 0.0823 then answer 8.23)

Explanation:

Step1: Recall Phillips Curve formula

The short-run Phillips Curve (expectations-augmented) is:
$$\pi - \pi^e = -\alpha(u - u_n)$$
Where:
$\pi$ = actual inflation, $\pi^e$ = expected inflation, $\alpha$ = curve parameter, $u$ = actual unemployment, $u_n$ = natural unemployment rate.

Step2: Rearrange for actual unemployment

Rearrange to solve for $u$:
$$u = u_n - \frac{\pi - \pi^e}{\alpha}$$

Step3: Plug in given values

Substitute $u_n=7$, $\pi=4$, $\pi^e=2$, $\alpha=0.9$:
$$u = 7 - \frac{4 - 2}{0.9} = 7 - \frac{2}{0.9}$$

Step4: Calculate the result

Compute the fraction and final value:
$$\frac{2}{0.9} \approx 2.2222$$
$$u = 7 - 2.2222 = 4.7778 \approx 4.78$$

Answer:

4.78