To determine how the unemployment rate changes when actual output falls to 5 percentage points below potential output, we can use a principle known as Okun's Law. According to Okun's Law, a 1% increase in the unemployment rate is associated with a 2% decrease in output.
Let's walk through the steps to find the new unemployment rate:
1. Potential Output and Actual Output:
- We start with the potential output being 100% (our base value for potential output).
- Since the actual output is 5 percentage points below this potential output, the actual output is [tex]\(100\% - 5\% = 95\%\)[/tex].
2. Output Gap:
- The difference between potential output and actual output is known as the output gap.
- Here, the output gap is [tex]\(100\% - 95\% = 5\%\)[/tex].
3. Unemployment Rate Change:
- According to Okun's Law, a 2% decrease in output is typically associated with a 1% increase in the unemployment rate.
- Given the output gap is 5%, we can calculate the expected change in the unemployment rate:
[tex]\[
\text{Unemployment Change} = \frac{\text{Output Gap}}{2} = \frac{5\%}{2} = 2.5\%
\][/tex]
4. Equilibrium Unemployment Rate:
- The equilibrium unemployment rate is given as 5%.
- To find the new unemployment rate, we add the calculated change in the unemployment rate to the equilibrium unemployment rate:
[tex]\[
\text{New Unemployment Rate} = \text{Equilibrium Unemployment Rate} + \text{Unemployment Change} = 5\% + 2.5\% = 7.5\%
\][/tex]
Therefore, the unemployment rate is expected to increase by 2.5 percentage points, resulting in a new unemployment rate of 7.5%.
