Question

Picture an economy with 100,000 workers in its labor force. The unemployment rate is simply the number of unemployed workers divided by the number of workers in the labor force. At the beginning of January, the unemployment rate is 4.76%, so 4,760 people in the labor force are unemployed.

Suppose that in January, 10% of the workers who were unemployed at the beginning of the month start new jobs. This means that ________ people leave the unemployment category in January.

Suppose that in January the job separation rate equals 1%. That is, 1% of the people who were employed at the beginning of the month are laid off or quit. This means _______ people are added to the unemployment category that month. (Hint: Round your answer to the nearest whole number.)

Assume the size of the labor force does not change from January to February. Considering that the job separation rate is 1% during January, and 10% of unemployed workers find new jobs, the unemployment rate at the beginning of February will be approximately ___________ .(Hint: Round your answer to the nearest hundredth.)

Generalizing from your calculations for January, if in February, the job separation rate is 1%, and 10% of unemployed workers get jobs, the unemployment rate at the end of February will be__________ .

Suppose that at the beginning of August, the unemployment rate is 4.76%, however, this month just 0.1% of the employed workers become unemployed.

Suppose that in August, 10% of the workers who were unemployed at the beginning of the month find new jobs. The unemployment rate be at the beginning of September will be __________ . (Hint: Round your answer to two decimal places.)

Now suppose that in September, the job separation rate returns to normal: 1% of the workers who were employed at the beginning of the month become unemployed. As always, 10% of the workers who are unemployed find jobs during the month.

In the last question, you calculated a lower unemployment rate for the beginning of September. Use the numbers of employed workers and unemployed workers implied by this unemployment rate to calculate how many employed workers become unemployed during September and how many unemployed workers find jobs during September.

The unemployment rate at the end of September is ____________ .

Answer 1

Given,

Labor force = 100,000

At the beginning of January, Unemployed = 4,760

Employed = Labor force - Unemployed = 100,000 - 4,760 = 95,240

1. 10% of the unemployed start new jobs. Number of workers who leave the unemployed category = 0.10 x 4760 = 476 (Blank 1)

Job separation rate in January = 1%

Number of workers who are added to the unemployed category = 0.01 x 95,240 = 952 (Blank 2)

Number of unemployed at the beginning February = 4760 - 476 + 952 = 5,236

Unemployment rate at the beginning of February = Unemployed/Labor force x 100 = 5236/100000 x 100 = 5.24% (Blank 3)

Number of unemployed at the end of February = 5236 - 0.10 x 5236 + 0.01 x (100000-5236) = 5236 - 524 + 948 = 5660

Unemployment rate at the end of February = 5660/100000 x 100 = 5.66% ( Blank 4)

Given,

At the start of August: The unemployment rate = 4.76%

Unemployed = Unemployment rate x Labor force/100 = 4.76 x 100,000/100 = 4760

Number of workers who levae unemployment category = 0.10 x 4760 = 476

Number of workers who are added to unemployed category = 0.001 x (100000 - 4760) = 0.001 x 95240 = 95

Unemployed at the end of August = 4760 - 476 + 95 = 4379

Unemployment rate at the beginning of September = 4379/100000 x 100 = 4.38% (Blank 5)

In September,

Number of people who leave the unemployed category = 0.10 x 4379 = 438

Number of people who join the unemployed category = 0.01 x (100000-4379) = 956

Unemployed at the end of September = 4379 - 438 + 956 = 5773

Unemployment rate at the end of September = 5773/100000 x 100 = 5.77%(Blank 6)