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 (in terms of unemployment and inflation) is given by:
$$\pi - \pi^e = -a(u - u_n)$$
Where:

• $\pi$ = actual inflation,
• $\pi^e$ = expected inflation,
• $a$ = Phillips Curve coefficient,
• $u$ = actual unemployment rate,
• $u_n$ = natural rate of unemployment.

Step2: Rearrange for actual unemployment

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

Step3: Plug in given values

Substitute $u_n=7$, $\pi=4$, $\pi^e=2$, $a=0.9$:
$$u = 7 - \frac{4 - 2}{0.9}$$
$$u = 7 - \frac{2}{0.9}$$
$$u = 7 - 2.\overline{22}$$

Step4: Calculate final value

$$u = 4.78$$

Answer:

4.78