In an economy of 100 people in the labor force, if 10 people are unemployed for 4 weeks during the year, and 30 people are unemployed for 8 weeks during the year, and the rest are employed continuously throughout the year, then the average duration of unemployment in this economy is:

7 weeks

Explanation:

in total there are 40 unemployed people in the economy, and the average duration of unemployment will be:

[ (10 unemployed x 4 weeks) + (30 unemployed x 8 weeks) ] / 40 unemployed = (40 + 240) / 40 = 280 / 40 = 7

*I used an adjusted expected value formula = ∑ (unemployed x unemployment length) / total unemployed