You are given the following information for a country: Participation rate = 75%, Unemployment rate = 10%, Employment rate = 67.5%, and Number of employed = 27 million. Based on thi... You are given the following information for a country: Participation rate = 75%, Unemployment rate = 10%, Employment rate = 67.5%, and Number of employed = 27 million. Based on this information, which of the following is correct? The working age population is 30 million. The number of unemployed is 3 million. The size of the labor force is 40 million. The unemployment rate is 12%.
Understand the Problem
The question provides economic data for a country, including the participation rate, unemployment rate, employment rate, and the number of employed individuals. The goal is to determine which of the given statements about the country's workforce is accurate based on this information. We'll need to use the provided data to calculate the working age population, the number of unemployed individuals, the size of the labor force, and the unemployment rate to verify each statement.
Answer
The number of unemployed is 3 million.
Answer for screen readers
The number of unemployed is 3 million.
Steps to Solve
- Calculate the Working Age Population The Employment Rate is the percentage of the Working Age Population that is employed. We can use the Employment Rate and the number of Employed people to calculate the Working Age Population.
$$ \text{Employment Rate} = \frac{\text{Number of Employed}}{\text{Working Age Population}} $$
Rearrange the formula to solve for the Working Age Population.
$$ \text{Working Age Population} = \frac{\text{Number of Employed}}{\text{Employment Rate}} $$
Substitute the known values. Number of Employed = 27 million and Employment Rate = 67.5% = 0.675
$$ \text{Working Age Population} = \frac{27 \text{ million}}{0.675} = 40 \text{ million} $$
Therefore, the Working Age Population is 40 million.
- Calculate the Labor Force. The Participation Rate represents the percentage of the Working Age Population that is in the Labor Force.
$$ \text{Participation Rate} = \frac{\text{Labor Force}}{\text{Working Age Population}} $$
Rearrange to solve for the Labor Force.
$$ \text{Labor Force} = \text{Participation Rate} \times \text{Working Age Population} $$
Substitute the known values. Participation Rate = 75% = 0.75 and Working Age Population = 40 million.
$$ \text{Labor Force} = 0.75 \times 40 \text{ million} = 30 \text{ million} $$
Therefore, the Labor Force is 30 million.
- Calculate the number of Unemployed individuals. The Labor Force is the sum of the number of Employed and the number of Unemployed individuals.
$$ \text{Labor Force} = \text{Number of Employed} + \text{Number of Unemployed} $$
Rearrange to solve for the Number of Unemployed.
$$ \text{Number of Unemployed} = \text{Labor Force} - \text{Number of Employed} $$
Substitute the known values. Labor Force = 30 million and Number of Employed = 27 million.
$$ \text{Number of Unemployed} = 30 \text{ million} - 27 \text{ million} = 3 \text{ million} $$
Therefore, the number of Unemployed individuals is 3 million.
- Calculate the Unemployment Rate
$$ \text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor Force}} $$
Substitute the known values. Number of Unemployed = 3 million and Labour Force = 30 million.
$$ \text{Unemployment Rate} = \frac{3 \text{ million}}{30 \text{ million}} = 0.1 = 10% $$
Therefore, the Unemployment Rate is 10%, as given in the question.
- Determine which statement is correct
- The working age population is 30 million. (Incorrect, we calculated 40 million)
- The number of unemployed is 3 million. (Correct, we calculated 3 million)
- The size of the labor force is 40 million. (Incorrect, we calculated 30 million)
- The unemployment rate is 12%. (Incorrect, given as 10% and we calculated 10%)
The number of unemployed is 3 million.
More Information
The labor force participation rate is an important economic indicator that measures the proportion of the working-age population that is actively participating in the labor market, either by being employed or actively seeking employment.
Tips
A common mistake is to confuse the participation rate with the employment rate or the unemployment rate. Each of these rates provides unique information about the labor market and is calculated differently.
Another mistake is to incorrectly rearrange the formulas. Always double-check your algebra to ensure you're solving for the correct variable.
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