Question

The rate of job separations in the economy is 0.013 (1.3 percent) and the rate of job finding is 0.25 (25 percent).

a) If the economy has 500 workers in the labor force, calculate the unemployment rate.

Answer 1

To calculate the unemployment rate with a 1.3% job separation rate and a 25% job finding rate in a labor force of 500, we first find the number of separations, then consider the inverse of the job finding rate to estimate those remaining unemployed. Assuming all separations remain unemployed, the unemployment rate is roughly the number of separations (rounded) divided by the total labor force, resulting in an unemployment rate of 1.4%.

Step-by-step explanation:

To calculate the unemployment rate given the job separation and job finding rates, we need to understand how these rates affect the labor force. The rate of job separations (also known as the job destruction rate) measures the fraction of employment ending in a given time period, whereas the job finding rate is the fraction of the unemployed who find jobs during the period.

Given an economy with 500 workers in the labor force, if the job separation rate is 0.013 (1.3 percent) and the job finding rate is 0.25 (25 percent), we can calculate the number of people who are unemployed and then the unemployment rate. First, we determine the number of separations per period: 500 workers × 0.013 = 6.5 separations. Since we're dealing with discrete workers, we'd round this number to the nearest whole number.

Next, we need to establish the pool of unemployed. Because the job finding rate applies only to the unemployed, the inverse (1 - job finding rate) is the fraction of the unemployed not finding jobs, which remains unemployed. Therefore, if we assume all those who lost their job in the period contribute to the unemployment pool and do not find a job, we'll have a total number of unemployed persons equal to the separations, as anyone who becomes unemployed stays unemployed in this simplified example. In this case, assuming the separations are those who remain unemployed, we take the rounded number of separations as unemployment.

Finally, to calculate the unemployment rate::

1. Divide the number of unemployed people (rounded separation figure) by the total labor force.
2. Multiply by 100 to obtain the percentage.

Given that we have 500 workers in the labor force, and considering that approximately 7 workers are not finding jobs and therefore count as unemployed (after rounding 6.5 separations), the unemployment rate would be 7/500 = 0.014 or 1.4% unemployment rate when converted to a percentage by multiplying by 100.