7. Consider an economy with 500 people in the labour force. At the beginning of every month, five 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 unem- ployed 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 an unemployment spell?

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