Question

A labour market has 50,000 people in the labour 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 labour 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

$Solution$

Let : $L=labor \ force ,\ e=employment, \ u=unemployment \\ L=e+u,\ so\ e=l-u\ ,u=l-e\\ \frac{u}{l}\ =unemployment \ rate,\frac{e}{l}=employment \ rate$

$S=rate \ of \ employed \ losing \ jobs\\ f=unemployed \ who \ get\ jobs$

$Steady \ state \ unemployment \ rate \ :\frac {u}{l}=\frac{s}{[s+f]}$

B)$\frac{u}{50000}=\frac{0<q<1}{(0<q<1+0<p<1)}$

C) $\frac{u}{50000}=\frac {0.32}{[0.08+0.32]}\\$

$0.4u=16000\\ u=4000$