A survey reveals that, on a small island, initially 1,000 people have jobs, 200 people are unemployed but are looking for jobs, and 200 people are neither working nor looking for work. Suppose that 100 of the 200 people who weren't looking for work now begin looking for work and that half of the new entrants find a job. The unemployment rate:
A) rises to 19.2%.
B) rises to 21.4%.
C) rises to 28.6%.
D) Nothing happens to the unemployment rate.

Question

Quizplus · Accepted Answer

The unemployment rate is calculated as the number of unemployed individuals divided by the labor force (employed + unemployed looking for work). Initially, the unemployment rate is 200 / (1000 + 200) = 16.7%. After 100 people start looking for work and 50 find jobs, the number of unemployed becomes 150, and the labor force becomes 1250. The new unemployment rate is 150 / 1250 = 12%. However, the correct calculation for the new unemployment rate should consider the updated numbers: initially, there are 200 unemployed and 1000 employed, making the labor force 1200. When 100 more start looking and 50 find jobs, the unemployed becomes 250 (150 who were already unemployed plus 100 new seekers minus 50 who found jobs), and the labor force becomes 1350 (1000 + 250 + 100). The new unemployment rate is 250 / 1350 = 18.5%, not 12%. The initial explanation mistakenly calculated the new unemployment rate. The correct choice should reflect the increase in the unemployment rate due to the addition of job seekers, which is closest to option A, acknowledging an error in the initial calculation.

A Survey Reveals That, on a Small Island, Initially 1,000