Let's dissect the problem and solve it step-by-step:
### Part a: Calculating the Unemployment Rate
The formula for the unemployment rate is given by:
[tex]\[ \text{Unemployment Rate} = \left( \frac{\text{Number of Unemployed People}}{\text{Labor Force}} \right) \times 100 \][/tex]
#### For Year 1:
- Population: 125 million (not used in the calculation)
- Labor Force: 67 million
- Unemployed: 4 million
Plug in the numbers:
[tex]\[ \text{Unemployment Rate for Year 1} = \left( \frac{4}{67} \right) \times 100 \approx 5.97\% \][/tex]
#### For Year 2:
- Population: 130 million (not used in the calculation)
- Labor Force: 69 million
- Unemployed: 4.3 million
Plug in the numbers:
[tex]\[ \text{Unemployment Rate for Year 2} = \left( \frac{4.3}{69} \right) \times 100 \approx 6.23\% \][/tex]
So, the unemployment rates are:
- Year 1: [tex]\( 5.97\% \)[/tex]
- Year 2: [tex]\( 6.23\% \)[/tex]
### Part b: Changes Between Year 1 and Year 2
#### i. Change in the Number of Unemployed Persons:
To find the increase in the number of unemployed persons:
[tex]\[ \text{Increase in Unemployed Persons} = 4.3 - 4 = 0.3 \text{ million} \][/tex]
Hence, the number of unemployed persons increased by:
[tex]\[ 0.3 \text{ million} \][/tex]
#### ii. Change in the Unemployment Rate:
To find the increase in the unemployment rate:
[tex]\[ \text{Increase in Unemployment Rate} = 6.23\% - 5.97\% = 0.26\% \][/tex]
Hence, the unemployment rate increased by:
[tex]\[ 0.26\% \][/tex]
Here is the detailed solution summarized:
1. Year 1 Unemployment Rate: [tex]\( 5.97\% \)[/tex]
2. Year 2 Unemployment Rate: [tex]\( 6.23\% \)[/tex]
3. Increase in Number of Unemployed Persons: [tex]\( 0.3 \)[/tex] million
4. Increase in the Unemployment Rate: [tex]\( 0.26\% \)[/tex]
