7. 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?