Chapter 10, Problem 2P

To determine

(a)

To compute:

The labor force participation and the unemployment rate.

Answer to Problem 2P

The labor force participation rate is $80\%$ and the unemployment rate is $12.5\%$.

Explanation of Solution

Given information:

Non-intuitional population is $200\text{million}$

Labor force is $160\text{million}$.

Therefore,labor Force participation rate is,

  $\begin{array}{c}\text{Labor}\text{Force}\text{Participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100\\ =\frac{160\text{million}}{200\text{million}}\times 100\\ =80\end{array}$

Now, unemployment rate can be calculated by first calculating the unemployed number of workers.

Given,

Non-intuitional population is $200\text{million}$,

labor force is $160\text{million}$,

And $140\text{million}$ people were employed.

As we know,labor force is the total employed and unemployed workers. That is,

$\text{Labor}\text{Force}=\text{Employed}+\text{Unemployed}$

Substitute the value to calculate unemployed workers,

$\begin{array}{c}\text{Labor}\text{Force}=\text{Employed}+\text{Unemployed}\\ \text{160}\text{million}=140\text{million}+\text{Unemployed}\\ \text{Unemployed}=1\text{60}\text{million}-140\text{million}\\ =20\text{million}\end{array}$

Substitute the values in the formula,

$\begin{array}{c}\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100\\ =\frac{20\text{million}}{160\text{million}}\times 100\\ =12.5\%\end{array}$

Therefore, the labor Force participation rate is $80\%$ and the unemployment rate is $12.5\%$.

Economics Concept Introduction

Labor force participation:

It refers to that percentage of current total population that is willing to work or is working; which means the labor force in total adult population.

$\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100$

Unemployment rate: It refers to the percentage of the people who are unemployed in the total labor force.

$\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100$

To determine

(b)

To compute:

The new labor force participation and the unemployment rate.

Answer to Problem 2P

The labor force participation is $90\%$ and unemployment rate is $16.6\%.$

Explanation of Solution

Given

New jobs $10\text{million}$, That means increase of employed worker from $140\text{to}150\text{million}$.

Also addition of $20\text{million}$ in labor force, So new labor force would be $180\text{million}$

The new employed workers number would be:-

$\begin{array}{c}\text{Labor}\text{Force}=\text{Employed}+\text{Unemployed}\\ \text{180}=150+\text{Unemployed}\\ \text{Unemployed}=180-150\\ \text{Unemployed}=30\text{million}\end{array}$

Now substitute the values in the formula to obtain labor force participation:-

$\begin{array}{c}\text{Labor}\text{Force}\text{Participation}=\frac{\text{labor}\text{force}}{\text{Total}\text{Adult}\text{population}}\times 100\\ =\frac{180}{200}\times 100\\ =90\%\end{array}$

Now, substitute the value to obtain unemployment rate

$\begin{array}{c}\text{Unemployment}\text{rate}=\frac{\text{unemployed}}{\text{labor}\text{force}}\times 100\\ =\frac{30}{180}\times 100\\ =16.6\%\end{array}$

Thus, the Labor Force participation is $90\%$ and unemployment rate is $16.6\%.$

Economics Concept Introduction

Labor force participation:

It refers to that percentage of current total population that is willing to work or is working; which means the labor force in total adult population.

$\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100$

Unemployment rate: It refers to the percentage of the people who are unemployed in the total labor force.

$\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100$

To determine

(c)

To compute:

The new labor force participation and the unemployment rate.

Answer to Problem 2P

The labor force participation is $75\%$ and unemployment rate is $6.7\%$

Explanation of Solution

Non-intuitional population is $200\text{million}$,

labor force is $160\text{million}$, and

$140\text{million}$ People were employed.

If $10\text{million}$ people stop looking for job: The new labor force would be $160\text{million}-10\text{million}=150\text{million}$.

Calculate the labor force participation rate:

$\begin{array}{c}\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100\\ =\frac{150\text{million}}{200\text{million}}\times 100\\ =75\%\end{array}$

Now, to calculate unemployment rate, first calculate total number of unemployed:

$\begin{array}{c}\text{Labor}\text{force}=\text{Employed}+\text{Unemployed}\\ \text{150}\text{million}=140\text{million}+\text{Unemployed}\\ \text{Unemployed}=150\text{million}-140\text{million}\\ =10\text{million}\end{array}$

Substitute the values to find the unemployment rate,

$\begin{array}{c}\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100\\ =\frac{10\text{million}}{150\text{million}}\times 100\\ =6.67\%\end{array}$

Economics Concept Introduction

Labor force participation:

It refers to that percentage of current total population that is willing to work or is working; which means the labor force in total adult population.

$\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100$

Unemployment rate: It refers to the percentage of the people who are unemployed in the total labor force.

$\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100$

To determine

(d)

To compute:

The new labor force participation and the unemployment rate.

Answer to Problem 2P

The labor force participation is $75\%$ and the unemployment rate is $6.67\%$

Explanation of Solution

Non-intuitional population is $200\text{million}$,

labor force is $160\text{million}$, and

$140\text{million}$ people were employed.

If $10\text{million}$ people retire,the new labor force would be $160\text{million}-10\text{million}=150\text{million}$

Calculation of the labor force participation rate:

  $\begin{array}{c}\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100\\ =\frac{150\text{million}}{200\text{million}}\times 100\\ =75\%\end{array}$

Now, to calculate unemployment rate, first calculate total number of unemployed:

$\begin{array}{c}\text{Labor}\text{Force}=\text{Employed}+\text{Unemployed}\\ \text{150}\text{million}=140\text{million}+\text{Unemployed}\\ \text{Unemployed}=150\text{million}-140\text{million}\\ =10\text{million}\end{array}$

Substitute the valuesto find the unemployment rate,

$\begin{array}{c}\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100\\ =\frac{10\text{million}}{150\text{million}}\times 100\\ =6.67\%\end{array}$

Economics Concept Introduction

Labor force participation:

It refers to that percentage of current total population that is willing to work or is working; which means the labor force in total adult population.

$\text{Labor}\text{force}\text{participation}=\frac{\text{Labor}\text{force}}{\text{Total}\text{adult}\text{population}}\times 100$

Unemployment rate: It refers to the percentage of the people who are unemployed in the total labor force.

$\text{Unemployment}\text{rate}=\frac{\text{Unemployed}}{\text{Labor}\text{force}}\times 100$