The city of Hope has a labour force of 1000.Twenty people lose their jobs each month and remain unemployed for exactly one month before finding jobs.On January 1,May 1,and September 1 of each year,50 people lose their jobs for a period of four months before finding new jobs.What is the average duration of an unemployment spell?
A)2.15 months
B)2.85 months
C)3.14 months
D)3.43 months

Question

Quizplus · Accepted Answer

The average duration of an unemployment spell is the total number of months of unemployment divided by the total number of unemployment spells. In this case, there are 1000 people in the labor force, and 20 people lose their jobs each month. This means that there are 20 * 12 = 240 unemployment spells per year. In addition, there are 50 people who lose their jobs on January 1, May 1, and September 1 of each year, and these people remain unemployed for four months. This means that there are 50 * 3 = 150 unemployment spells per year that last for four months. Therefore, the total number of unemployment spells per year is 240 + 150 = 390. The total number of months of unemployment per year is 20 * 12 + 50 * 3 * 4 = 1200. Therefore, the average duration of an unemployment spell is 1200 / 390 = 3.077 months.

The City of Hope Has a Labour Force of 1000