Sure, let's go step-by-step to solve this problem based on the given data:
1. Calculate the labor force
The labor force is the sum of employed and unemployed people.
- Employed people: 440 million
- Unemployed people: 54 million
[tex]\[
\text{Labor Force} = \text{Employed People} + \text{Unemployed People} = 440 + 54 = 494 \text{ million}
\][/tex]
2. Calculate the unemployment rate
The unemployment rate is calculated as the percentage of the labor force that is unemployed.
[tex]\[
\text{Unemployment Rate} = \left( \frac{\text{Unemployed People}}{\text{Labor Force}} \right) \times 100
\][/tex]
Substitute in the known values:
[tex]\[
\text{Unemployment Rate} = \left( \frac{54}{494} \right) \times 100 \approx 10.93\%
\][/tex]
3. Calculate the labor force participation rate
The labor force participation rate is calculated as the percentage of the adult population that is part of the labor force. The adult population is different from the overall population; we need to factor out those not in the labor force from the overall population.
- Overall population: 800 million
- People not in the labor force: 120 million
[tex]\[
\text{Adult Population} = \text{Overall Population} - \text{People Not in the Labor Force} = 800 - 120 = 680 \text{ million}
\][/tex]
Now, calculate the labor force participation rate:
[tex]\[
\text{Labor Force Participation Rate} = \left( \frac{\text{Labor Force}}{\text{Adult Population}} \right) \times 100
\][/tex]
Substitute in the known values:
[tex]\[
\text{Labor Force Participation Rate} = \left( \frac{494}{680} \right) \times 100 \approx 72.65\%
\][/tex]
To summarize:
1. Labor Force = 494 million
2. Unemployment Rate = 10.93%
3. Labor Force Participation Rate = 72.65%
