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?
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.)
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%.
How did you get
- Employed: 147.3 million
- Unemployed: 7.0 million
- Not in labor force: 92.8 million
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.
To find the new values of the labor force and unemployment rate, we need to adjust the initial distribution of the population based on the changes mentioned.
Step 1: Calculate the new number of employed individuals:
Initial number of employed individuals: X
Change in employed individuals: +9.2 million
New number of employed individuals: X + 9.2 million
Step 2: Calculate the new number of unemployed individuals:
Initial number of unemployed individuals: Y
Change in unemployed individuals: +7.1 million
New number of unemployed individuals: Y + 7.1 million
Step 3: Calculate the new labor force:
New labor force = New number of employed individuals + New number of unemployed individuals
Step 4: Calculate the new unemployment rate:
New unemployment rate = (New number of unemployed individuals / New labor force) * 100
Now, let's calculate the values.
Given that:
Initial number of employed individuals (X) = X
Initial number of unemployed individuals (Y) = Y
Part 1:
New number of employed individuals = X + 9.2 million
New number of unemployed individuals = Y + 7.1 million
New labor force = New number of employed individuals + New number of unemployed individuals
New labor force = (X + 9.2 million) + (Y + 7.1 million)
New unemployment rate = (New number of unemployed individuals / New labor force) * 100
New unemployment rate = ((Y + 7.1 million) / ((X + 9.2 million) + (Y + 7.1 million))) * 100
Part 2:
If the total adult population remains unchanged, then:
Total adult population = Initial labor force + Number not in the labor force
Total adult population = Initial number of employed individuals + Initial number of unemployed individuals + Number not in the labor force
Total adult population = X + Y + Number not in the labor force
New value of the labor force = New number of employed individuals + New number of unemployed individuals
New value of the labor force = (X + 9.2 million) + (Y + 7.1 million)
New value of the unemployment rate = (New number of unemployed individuals / New value of the labor force) * 100
New value of the unemployment rate = ((Y + 7.1 million) / ((X + 9.2 million) + (Y + 7.1 million))) * 100
To find the new values of the labor force and the unemployment rate, we first need to understand the initial distribution of the population.
Let's denote the initial values as follows:
- Employed: E
- Unemployed: U
- Not in the labor force: NLF
From the information given, we know that the initial distribution can be represented visually as follows:
+---------------------+
| E U NLF |
+---------------------+
Now, if the number of people employed were to expand by 9.2 million, we need to add 9.2 million to the initial value of employed people:
New value of employed (E'): E + 9.2 million
Similarly, if the number of people unemployed were to rise by 7.1 million, we need to add 7.1 million to the initial value of unemployed people:
New value of unemployed (U'): U + 7.1 million
Now, let's find the new values of the labor force and the unemployment rate.
The labor force consists of employed and unemployed individuals, so the new labor force (LF') is given by the sum of the new values of employed and unemployed:
LF' = E' + U'
To find the new unemployment rate, we need to calculate the percentage of unemployed people out of the labor force:
Unemployment rate = (U' / LF') * 100
Now, let's calculate the new values.
Part 1:
New labor force (LF') = Initial LF (E + U) + 9.2 million + 7.1 million
New unemployment rate = (U' / LF') * 100
Part 2:
If the total adult population did not change, it means that the number of people not in the labor force (NLF) remains the same. Therefore, the new labor force (LF') in this case would be equal to the sum of the new values of employed and unemployed:
LF' = E' + U'
= E + 9.2 million + U + 7.1 million
To find the new unemployment rate:
Unemployment rate = (U' / LF') * 100
Now, you can substitute the given values for E, U, and NLF into the equations and calculate the new values of the labor force and unemployment rate.