Final answer:
To find the new unemployment rate after the labor force changes, we calculate the total labor force and the number of unemployed individuals. In this case, 100 people joined the labor force and 50 found jobs, so the new unemployment rate is approximately 19.23%.
Step-by-step explanation:
To calculate the unemployment rate on the island after 100 of the 200 people who weren't looking for work begin to do so and half of them find a job, we need to understand how to compute unemployment rates. Initially, there were 1,000 employed people, 200 unemployed people, and 200 who were not part of the labor force. The labor force consists of both employed and unemployed people who are looking for work. The unemployment rate is the number of unemployed persons divided by the labor force, expressed as a percentage.
When 100 people start looking for work:
Labor force = Originally employed (1,000) + Originally unemployed (200) + New job seekers (100) = 1,300 people
50 of these new entrants find a job, so employed count goes up to 1,050.
Unemployed count = Those originally unemployed (200) + New entrants who didn't find jobs (50) = 250 people
Therefore, the new unemployment rate is:
(Unemployed count / Labor force) * 100
=(250 / 1,300) * 100
≈ 19.23%