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 is the fraction of unemployment spells lasts for one month? what fraction lasts for six months?
c. what is the average duration of completed spell of unemployment?
d. on any particular day, what fraction of the unemployed are suffering a long spell (six months) of unemployment?