In the country of Economica, the total labor force consists of workers. 400 of these workers are unemployed, and thus the current unemployment rate is 4.0%. This year, 200 workers will lose their jobs, 170 workers will return to the labor force after an absence, 100 workers will voluntarily leave their jobs, and 500 new workers will enter the labor force. At the same time, 933 workers will find jobs, and 300
workers will retire or leave the labor force for other reasons.
a. At the end of the year, the labor force will consist of ----
workers,
assuming no other changes occur.
Solution:
To calculate the size of the labor force at the end of the year, we need to add up all the changes that will occur during the year:
Starting labor force = Total workers = 10000
Workers who will lose their jobs = -200
Workers who will return to the labor force = +170
Workers who will voluntarily leave their jobs = -100
New workers who will enter the labor force = +500
Workers who will find jobs = +933
Workers who will retire or leave the labor force = -300
Ending labor force = Starting labor force + (changes)
= 10000 - 200 + 170 - 100 + 500 + 933 - 300
= 11003
Therefore, at the end of the year, the labor force in Economica will consist of 11,003 workers.
b. The unemployment rate will be---%.
(Round your responses to one decimal place.)
Solution:
To calculate the unemployment rate at the end of the year, we need to calculate the number of unemployed workers and then divide by the total labor force:
Unemployed workers at the beginning of the year = 400
New workers who will enter the labor force = +500
Workers who will find jobs = -933
Unemployed workers at the end of the year = Unemployed workers at the beginning of the year + (changes)
= 400 + 500 - 933
= -33
Note that the result is negative. This means that there are fewer unemployed workers at the end of the year than at the beginning, which is a good thing.
However, we need to adjust for the fact that the unemployment rate cannot be negative. To do this, we assume that the number of unemployed workers at the end of the year is zero. This means that all the new workers who entered the labor force found jobs, and all the workers who lost jobs or voluntarily left the labor force were not seeking employment.
Adjusted ending labor force = Ending labor force - number of unemployed workers
= 11003 - 33
= 10970
Unemployment rate = number of unemployed workers / adjusted ending labor force
= 0 / 10970
= 0% (rounded to one decimal place)
Therefore, the unemployment rate at the end of the year in Economica will be 0%.
To calculate the final number of workers in the labor force, we need to consider the changes in the labor force throughout the year.
Starting with the initial number of workers in the labor force, we subtract the workers who will lose their jobs, add the workers returning to the labor force, subtract the workers voluntarily leaving their jobs, and add the new workers entering the labor force.
Here is the calculation:
Initial labor force = Total labor force - Unemployed workers
Initial labor force = Total labor force - 400
Labor force at the end of the year = Initial labor force - Workers losing jobs + Workers returning + New workers entering - Workers leaving
Labor force at the end of the year = (Total labor force - 400) - 200 + 170 + 500 - 100
Simplifying the equation:
Labor force at the end of the year = Total labor force - 400 - 200 + 170 + 500 - 100
Labor force at the end of the year = Total labor force - 30
Therefore, the labor force at the end of the year will consist of (Total labor force - 30) workers.
To find the number of workers in the labor force at the end of the year, we need to calculate the net change in the labor force. We can calculate this by taking the initial labor force and adding the number of new workers, subtracting the number of workers who lost their jobs or left voluntarily, and then adding the number of workers who returned to the labor force.
Initial labor force: Total workers - Unemployed workers = Labor force
Labor force at the beginning of the year: Total workers - Unemployed workers = 400 workers
New workers: 500 workers
Workers who lost their jobs: 200 workers
Workers who left voluntarily: 100 workers
Workers who returned to the labor force: 170 workers
Net change in the labor force = New workers - (Workers who lost jobs + Workers who left voluntarily) + Workers who returned to the labor force
Net change in the labor force = 500 - (200 + 100) + 170
Net change in the labor force = 370 workers
Therefore, to find the labor force at the end of the year, we add the net change to the initial labor force:
Labor force at the end of the year = Initial labor force + Net change in the labor force
Labor force at the end of the year = 400 + 370
Labor force at the end of the year = 770 workers