Question

Suppose that unemployed workers find jobs at the rate of 15% per period and the job separation rate for employed workers is 5% per period. Assume the size of the labor force is fi xed at 1000. At period t=0, number of unemployed U0 = 200 and employed E0 = 800.Starting from the steady state where the unemployment rate is at its natural rate, suppose that suddenly the job finding rate falls to 10% and separation rises to 8%, what will be the unemployment rate of one period after in percentage?

Answer 1

We are given

Given

Job separation rate=s=5%

Job finding rate=f=15%

Natural rate of unemployment can be calculated as

Natural rate of unemployment (steady state)=s/(s+f)=5%/(5%+20%)=20.0%

Now, consider the new new scenario which starts with steady state,

Number of unemployed persons in steady state=Us=1000*20%=200

Number of employed persons in steady state=Es=1000-200=800

New job separation rate=s=8%

New job finding rate=f=10%

Number of persons who loose job=Es*s=800*8%=64

Number of persons who gets the job=Us*f=200*10%=20

Number of unemployed persons after 1 year=U₁=200-20+64=244

Number of employed persons after 1 year=E₁=800-64+20=756

Unemployment rate after 1 year=U₁/(U₁+E₁)=244/(244+756)=24.4%