Assume that a society has two types of workers that lose jobs in a given year. Society A has 2 million workers losing their jobs; each person takes a year to find a new job. Society B has 24 million workers losing their jobs; each worker takes a month to find a new job.

i. How many 'spells' of unemployment occur each year in the economy? What percentage of the spells is only one month long?

ii. If you take all the unemployed workers each year and multiply each by the length of the unemployment 'spell', how many 'worker months' of unemployment would there be in the economy each year? Of all the 'worker months' of unemployment, how many are accounted for by the workers unemployed one year at a time?

iii. The residents of a certain dormitory have collected the following data: people who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 5 percent enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved?

iiii. If the economy were at a steady-state unemployment rate with a separation rate of 0.04 per month and a job-finding rate of 0.16 per month, and the labor force was 200 million, how many individuals would lose their jobs each month?