Question

A labor market has 50,000 people in the labor force. Each month, a fraction p of employed workers become unemployed (0 < p < 1) and a fraction q of unemployed workers become employed (0 < q < 1).

(a) In terms of p and q, what is the steady-state unemployment rate?

(b) Under the steady-state, how many of the 50,000 in the labor force are employed and how many are unemployed each month? How many of the unemployed become employed each month? Hint: The Employment Rate is 1-(Answer to (a))

(c) Suppose p = 0.08 and q = 0.32. What is the steady-state unemployment rate and how many workers move from employment to unemployment each month?

Answer 1

a)

In this case,

L=50000

Job separation rate=s=p

Job finding rate=f=q

Number of persons who loose employment per period=p*(L-U)

Number of persons are employed per period=q*U

In steady state,

q*U=p*(L-U)

q*U=p*L-p*U

U*(p+q)=pL

U/L=u=p/(p+q) [steady state unemployment rate]

b)

Number of persons employed=E=L*(1-u)=50000*[1-p/(p+q)]=50000*q/(p+q)

Number of employed persons who loose employment each month=E*p

=[50000*q/(p+q)]*p=50000pq/(p+q)

Number of unemployed persons=U=L*u=50000*p/(p+q)

Number of unemployed persons who are employed each month=U*q

=[50000*p/(p+q)]*q=50000pq/(p+q)

c)

If p=0.08, q=0.32

Steady state unemployment rate= u=p/(p+q)=0.08/(0.08+0.32)=0.2 or say 20%

Number of employed persons who loose employment each month=50000pq/(p+q)

=50000*0.08*0.32/(0.08+0.32)=3200