Questions: A survey reveals that on a small island initially 40 people have jobs, 10 people are looking for jobs, and 30 people are neither working nor looking for work. Suppose that 10 of the 30 people who weren't looking for work now begin looking for work. There are now 20 people looking for work and 40 people working. What happens to the unemployment rate? A) It rises to 33.3%. B) It rises to 50.0%. C) It falls to 25.0%. D) Nothing happens to the unemployment rate, because these people weren't working before and they aren't working now.

The answer is A: It rises to 33.3%.

To understand why, let's break down the situation and calculate the unemployment rate step by step.

• Employed (E): 40 people
• Unemployed (U): 10 people (looking for jobs)
• Not in the labor force (N): 30 people (neither working nor looking for work)

The unemployment rate is calculated as: \[ \text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor Force}} \times 100 \]

The labor force consists of people who are either employed or unemployed: \[ \text{Labor Force (LF)} = E + U \] \[ \text{Initial Labor Force} = 40 + 10 = 50 \]

The initial unemployment rate is: \[ \text{Initial Unemployment Rate} = \frac{10}{50} \times 100 = 20\% \]

• Employed (E): 40 people (unchanged)
• Unemployed (U): 20 people (10 original + 10 new job seekers)
• Not in the labor force (N): 20 people (30 original - 10 new job seekers)

The new labor force is: \[ \text{New Labor Force} = E + U = 40 + 20 = 60 \]

The new unemployment rate is: \[ \text{New Unemployment Rate} = \frac{20}{60} \times 100 = 33.3\% \]

• A) It rises to 33.3%: Correct. As calculated, the new unemployment rate is 33.3%.
• B) It rises to 50.0%: Incorrect. This would imply that half of the labor force is unemployed, which is not the case.
• C) It falls to 25.0%: Incorrect. The unemployment rate actually increases, not decreases.
• D) Nothing happens to the unemployment rate, because these people weren't working before and they aren't working now: Incorrect. The unemployment rate changes because the labor force has increased with more people looking for work.

Thus, the correct answer is A: It rises to 33.3%.