Suppose the adult population is 200 million, the labor force is 160 million, and the number of employed persons is 140 million.
What is the unemployment rate?
What is the labor force participation rate?
Suppose half of the unemployed persons in exercise (1.) become discouraged workers. That is, they stop looking for work and drop out of the labor force.
What is the new unemployment rate?
What is the new labor force participation rate?
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To find the answers to these questions, we'll need to understand and calculate some key concepts related to employment and unemployment. Here's how:
1. Unemployment Rate:
The unemployment rate is the percentage of the labor force that is unemployed. It can be calculated using the following formula:
Unemployment Rate = (Number of Unemployed / Labor Force) * 100
Given the information:
- Adult population: 200 million
- Labor force: 160 million
- Employed persons: 140 million
First, let's find the number of unemployed persons:
Number of Unemployed = Labor Force - Number of Employed = 160 million - 140 million = 20 million
Now, we can calculate the unemployment rate:
Unemployment Rate = (20 million / 160 million) * 100 = 12.5%
Therefore, the initial unemployment rate is 12.5%.
2. Labor Force Participation Rate:
The labor force participation rate is the percentage of the adult population that is in the labor force. It can be calculated using the following formula:
Labor Force Participation Rate = (Labor Force / Adult Population) * 100
Given the information:
- Adult population: 200 million
- Labor force: 160 million
We can calculate the labor force participation rate:
Labor Force Participation Rate = (160 million / 200 million) * 100 = 80%
Therefore, the initial labor force participation rate is 80%.
3. New Unemployment Rate (after discouraged workers):
If half of the unemployed persons become discouraged workers and drop out of the labor force, we need to adjust the number of unemployed and the labor force.
Since half of the previously unemployed have dropped out, the new number of unemployed persons is half of the initial value:
New Number of Unemployed = Number of Unemployed / 2 = 20 million / 2 = 10 million
To find the new unemployment rate, we adjust the formula:
New Unemployment Rate = (New Number of Unemployed / New Labor Force) * 100
Since the discouraged workers have dropped out of the labor force, the new labor force would be the initial labor force minus the number of discouraged workers:
New Labor Force = Labor Force - (Number of Unemployed / 2) = 160 million - 10 million = 150 million
Now, we can calculate the new unemployment rate:
New Unemployment Rate = (10 million / 150 million) * 100 ≈ 6.67%
Therefore, the new unemployment rate is approximately 6.67%.
4. New Labor Force Participation Rate (after discouraged workers):
The new labor force participation rate will be adjusted due to the decrease in the labor force caused by discouraged workers dropping out.
To calculate the new labor force participation rate, we use the formula:
New Labor Force Participation Rate = (New Labor Force / Adult Population) * 100
Using the values we previously determined:
New Labor Force Participation Rate = (150 million / 200 million) * 100 = 75%
Therefore, the new labor force participation rate is 75%.