Question

Consider an economy with 500 people in the labor force. At the beginning of every month, 5 people lose their jobs and remain unemployed for exactly one month; one month later, they find new jobs and become employed. In addition, on January 1 of each year, 20 people lose their jobs and remain unemployed for six months before finding new jobs. Finally, on July 1 of each year, 20 people lose their jobs and remain unemployed for six months before finding new jobs.
a. What is the unemployment rate in this economy in a typical month?
b. What fraction of unemployment spells lasts for one month? What fraction lasts for six months?
c. What is the average duration of a completed spell of unemployment?
d. On any particular date, what fraction of the unemployed are suffering a long spell (six months) of unemployment?

Answer 1

Answer:

a. What is the unemployment rate in this economy in a typical month?

• 5%

b. What fraction of unemployment spells lasts for one month? What fraction lasts for six months?

• 1% lasts 1 month, 4% lasts 6 months

c. What is the average duration of a completed spell of unemployment?

• 5 months

d. On any particular date, what fraction of the unemployed are suffering a long spell (six months) of unemployment?

• 80%

Explanation:

given:

total labor force = 500 people

every month 5 people are frictionally unemployed

at January 1, 20 people lose their jobs and find new jobs by the end of June

at July 1, 20 people lose their jobs and find new jobs by the end of December

total unemployed on a typical month = 5 + 20 = 25 ⇒ 5%

unemployed for 1 month = 5 ⇒ 1%

unemployed for 6 months = 20 ⇒ 4%

average duration of unemployment = [(20 x 6) + (5 x 1)] / 25 = 5 months

on any day, 20/25 = 80% of the unemployed are suffering a long spell unemployment

Answer 2

Answer:

a) 5%

b) 0.60 0.40

c) 3months

d) 80%

Explanation:

The solution is attached in the picture below