Final answer:
The immediate change in the unemployment rate after an increase of 20 workers in the labor force would be an increase in unemployment by the same number, with the steady-state unemployment rate eventually stabilizing based on the existing rates of job finding and separations. The graph would show an initial spike in unemployment followed by a gradual approach to the new steady-state.
Step-by-step explanation:
When calculating the immediate change in the unemployment rate after an increase in the labor force by 20 workers, assuming no immediate job findings or separations, the number of unemployed would increase by 20 (since these workers are actively seeking work and haven't found jobs yet). The new labor force would be 520 workers (500 existing workers + 20 new workers). With no initial job findings, the 20 new workers are all unemployed, thus the immediate number of unemployed would be whatever the current number is plus 20.
The unemployment rate is defined as the number of unemployed persons divided by the number of persons in the labor force. With a job separation rate of 1.3% and a job finding rate of 25%, we can predict that in the long run, the labor market will reach a new steady-state unemployment rate determined by these ratios. The exact steady-state rate would require more specific data on the initial number of unemployed before adding the 20 workers.
Concerning the graph depicting how the unemployment rate evolves over time, we start with an immediate spike due to the increased labor force, followed by a decline towards a new steady-state as people find jobs or leave the labor market. This graph would show the unemployment rate starting at its original level, spiking up when the 20 new workers enter the labor force, and eventually settling down to its new steady-state determined by the rates of job finding and separations.