Question

Okun’s law says that a 1% increase in unemployment for one year is associated with a 2% decrease in GDP growth. Suppose an economy has the following expectations augmented Phillips curve: \[ \pi = \pi^e - \beta (U - U^N), \quad \beta>0 \] where \( \pi \) and \( \pi^e \) are the inflation and expected inflation rates, respectively. \( U \) and \( U^N \) are the unemployment and natural rate of unemployment, respectively. \( \beta \) measures sensitivity of inflation to unemployment gap. When \( \beta = 2 \), by what percentage does output fall short of full-employment given that the inflation rate, expected inflation rate, and natural rate of unemployment are 8%, 10%, and 6%, respectively?

• A. 2
• B. 4
• C. 6
• D. 8

Hint:

Okun's law relates changes in unemployment to changes in GDP growth. The output gap can be calculated based on the unemployment rate relative to the natural rate of unemployment.

Answer 1

The Correct Option is A

Step 1: Understand the Phillips curve equation.
The equation is given by: \[ \pi = \pi^e - \beta (U - U^N) \] Where:
- \( \pi \) = inflation rate
- \( \pi^e \) = expected inflation rate
- \( U \) = unemployment rate
\ - \( U^N \) = natural rate of unemployment
- \( \beta \) = sensitivity of inflation to the unemployment gap
Step 2: Apply the given values.
We are given: - \( \pi = 8% \),
- \( \pi^e = 10% \),
- \( U^N = 6% \),
- \( \beta = 2 \).
Substitute these values into the Phillips curve equation: \[ 8 = 10 - 2 (U - 6) \] Solving for \( U \): \[ 8 = 10 - 2U + 12 \] \[ -14 = -2U \] \[ U = 7 \] Step 3: Determine the output gap.
The natural unemployment rate is 6%, and the actual unemployment rate is 7%. Hence, the economy is operating with an unemployment gap of 1%. Okun’s law tells us that for every 1% increase in unemployment, GDP falls by 2%. Therefore, the output falls short of full-employment by 2%. Step 4: Conclusion.
Thus, the correct answer is (A) 2%.