The figure to the right shows the initial distribution of the population aged 16 and older into three​ groups: people who are​ employed, those who are​ unemployed, and those not in the labor force. If the number of people employed were to expand by 9.2​ million, and the number of people unemployed were to rise by 7.1​ million, what would be the new values of the labor force and of the unemployment​ rate?

Question

Part 2
If the number of people employed were to expand by 9.2​ million, and the number of people unemployed were to rise by 7.1​ million, but the total adult population did not​ change, the new value of the labor force would be enter your response here

million people and the new value of the unemployment rate would be enter your response here

percent. ​(Enter your responses rounded to one decimal​ place.)

Answer 1

We can start by analyzing the initial distribution of the population:

- Employed: 147.3 million
- Unemployed: 7.0 million
- Not in labor force: 92.8 million

The labor force is the sum of employed and unemployed individuals:

Labor force = Employed + Unemployed = 147.3 + 7.0 = 154.3 million

The unemployment rate is the percentage of the labor force that is unemployed:

Unemployment rate = (Unemployed / Labor force) x 100
Unemployment rate = (7.0 / 154.3) x 100 = 4.5%

Now, if the number of employed individuals were to increase by 9.2 million, and the number of unemployed individuals were to increase by 7.1 million, we can calculate the new values as follows:

- Employed: 147.3 + 9.2 = 156.5 million
- Unemployed: 7.0 + 7.1 = 14.1 million

The labor force would be the sum of the new employed and unemployed values:

Labor force = Employed + Unemployed = 156.5 + 14.1 = 170.6 million

The new unemployment rate would be:

Unemployment rate = (Unemployed / Labor force) x 100
Unemployment rate = (14.1 / 170.6) x 100 = 8.3%

For part 2, if the total adult population does not change, the size of the not in labor force group would remain the same. Therefore, the new labor force would still be 170.6 million.

The new unemployment rate would also remain the same, because the increase in the number of unemployed individuals is proportional to the increase in the labor force. Therefore:

Unemployment rate = (Unemployed / Labor force) x 100
Unemployment rate = (14.1 / 170.6) x 100 = 8.3%

Therefore, the new value of the labor force would be 170.6 million people and the new value of the unemployment rate would be 8.3%.

Answer 2

How did you get

- Employed: 147.3 million
- Unemployed: 7.0 million
- Not in labor force: 92.8 million

Answer 3

The given information in the problem provides the initial distribution of the adult population aged 16 and older into three groups: employed, unemployed, and not in the labor force.

The figure to the right (which we cannot see as we are having a text conversation) shows this distribution, so we can read the values off the figure:

- Employed: 147.3 million
- Unemployed: 7.0 million
- Not in labor force: 92.8 million

These values represent the number of individuals in each group in the initial distribution of the population.