include correctly labeled diagrams, if useful or required, in explaining your answers. a correctly labeled diagram must have all axes and curves clearly labeled and must show directional changes. if the question prompts you to \calculate,\ you must show how you arrived at your final answer. the table below shows unemployment and labor force statistics for an economy. actual rate of unemployment 3% natural rate of unemployment 4% civilian, noninstitutional population age 16 and over 125 million number of people employed full time 92 million number of people employed part time 5 million number of people unemployed 3 million number of discouraged workers 2 million (a) calculate the size of the labor force. show your work. (b) calculate the labor force participation rate. show your work. (c) given the state of the economy described in the table, is actual real output less than, greater than, or equal to potential real output? explain. (d) calculate what the cyclical unemployment rate would be if the actual rate of unemployment increased to 5 percent. show your work. (e) suppose discouraged workers reenter the labor force and find employment. will the actual rate of unemployment increase, decrease, or stay the same?

Question

Accepted Answer

### Part (a)
# Explanation:
## Step1: Recall labor force formula
Labor force = Employed + Unemployed. Employed includes full - time and part - time.
Employed = Full - time employed + Part - time employed = $92 + 5=97$ million. Unemployed = 3 million.
## Step2: Calculate labor force
Labor force = $97+3 = 100$ million.
# Answer:
The size of the labor force is $\boldsymbol{100}$ million.

### Part (b)
# Explanation:
## Step1: Recall labor force participation rate formula
Labor force participation rate=$\frac{\text{Labor force}}{\text{Civilian, noninstitutional population age 16 and over}}\times100\%$
We know labor force = 100 million, civilian non - institutional population (age 16 and over)=125 million.
## Step2: Calculate the rate
Labor force participation rate=$\frac{100}{125}\times 100\%=0.8\times100\% = 80\%$
# Answer:
The labor force participation rate is $\boldsymbol{80\%}$.

### Part (c)
# Brief Explanations:
The natural rate of unemployment is the unemployment rate at potential real output (when the economy is at full - employment). The actual rate of unemployment ($3\%$) is less than the natural rate of unemployment ($4\%$). When actual unemployment is less than natural unemployment, the economy is producing at a level greater than potential real output (because firms are using more labor than the full - employment level, as more people are employed relative to the natural rate situation).
# Answer:
Actual real output is greater than potential real output. Because the actual rate of unemployment ($3\%$) is less than the natural rate of unemployment ($4\%$), indicating the economy is operating above full - employment, so actual real output exceeds potential real output.

### Part (d)
# Explanation:
## Step1: Recall cyclical unemployment formula
Cyclical unemployment rate = Actual unemployment rate - Natural unemployment rate.
First, when actual unemployment rate is $5\%$ and natural unemployment rate is $4\%$
## Step2: Calculate cyclical unemployment rate
Cyclical unemployment rate=$5\% - 4\%=1\%$
# Answer:
The cyclical unemployment rate would be $\boldsymbol{1\%}$.

### Part (e)
# Brief Explanations:
The formula for the unemployment rate is $\text{Unemployment rate}=\frac{\text{Unemployed}}{\text{Labor force}}\times 100\%$. When discouraged workers re - enter the labor force and find employment, the number of unemployed initially increases (as discouraged workers are not counted as unemployed before, but when they re - enter, if they don't find a job immediately, they are unemployed. However, in this case, they find employment). The labor force increases (because discouraged workers are now part of the labor force) and the number of employed also increases (since they find jobs). Let's assume initially: Unemployed ($U$) = 3, Labor force ($LF$) = 100. After discouraged workers (2 million) re - enter and find jobs: New employed ($E_{new}$)=$97 + 2=99$, New labor force ($LF_{new}$)=$100 + 2 = 102$, New unemployed ($U_{new}$)=$3$ (since the 2 discouraged workers found jobs). The new unemployment rate=$\frac{3}{102}\times100\%\approx2.94\%$, which is less than the initial $3\%$. So the actual rate of unemployment will decrease.
# Answer:
The actual rate of unemployment will decrease.

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QUESTION IMAGE

Question

Explanation:

Part (a)

Step1: Recall labor force formula

Step2: Calculate labor force

Step1: Recall labor force participation rate formula

Step2: Calculate the rate

Answer:

Part (b)