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. Calculate the following (Round up to ONE decimal place if needed. Enter only numbers) (a) What is the unemployment rate at t=1 in percentage? (b) What is the natural (steady state) unemployment rate in percentage? (c) 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

a)

We are given

Job separation rate=s=5%

Job finding rate=f=15%

Number of persons who loose job per period=Eo*s=800*5%=40

Number of persons who gets the job=Uo*f=200*15%=30

Number of unemployed persons after 1 year=U₁=200-30+40=210

Number of employed persons after 1 year=E₁=800-40+30=790

Unemployment rate after 1 year=U₁/(U₁+E₁)=210/(210+790)=21.0%

b)

Natural rate of unemployment is given as

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

c)

In this case

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

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

Job separation rate=s=8%

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%