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) 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 employed each month? How many of the unemployed become employed each month?

(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) Let

l = Labor Force

e = Employment

u = unemployment

l = e+ u

So,

e = l – u and u = l – e

u/l= Unemployment Rate

s = the rate of job separation( the fraction of “employed” workers who lose jobs each month)

se = the number of “employed” workers who lose jobs each month

f = the rate of job finding: the fraction of “unemployed” workers who find jobs each month

fu= the number of “unemployed” workers who find jobs each month

In a steady-state labor market: fu = se

Write:

fu= s(l – u)

fu = sl – su

su + fu = sl

(s + f)u = sl

u/l = s / s+f ( this is steady state unemployment rate)

here s=p and f=q

hence unemployment rate=p/(p+q)

b) we need to find 'e' (defined in part a) for finding how many of the 50,000 in the labor force are employed and find 'fu'(defined in part a) to know the number of “unemployed” workers who find jobs each month. So, (q/(p+q))*50000 is the number of people who get employed every month.

c)u/l=p/(p+q)=  0.08/(0.08+0.32)=0.2 (unemployment rate)

f=q(the rate of job finding: the fraction of “unemployed” workers who find jobs each month)

u= l*unemployment rate=50000*0.2=10000

f=q=0.32

fu=0.32*10000=3200