Question

Consider a setting similar to that in Question 2 (u = s/(s+f)), but assume that the unemployed can be divided into two groups: ”high-skilled” and ”low-skilled”. The number of high-skilled unemployed workers is denoted U1 and they find work at rate f1 each time period. The number of low-skilled unemployed workers is denoted U2 and their job-finding rate is f2, where f1> f2. L still denotes the total labour force and a fraction s of the employed are separated from their jobs every period.

a)  Assume that a fraction g of the unemployed are high-skilled. Derive an expression for the aggregate unemployment rate, u = U/L = (U1+U2)/L, in steady state. Hint: the flows in and out of U have to be equal in steady state. u is to be expressed in terms of s, g, f1 and f2.

b) Compute the unemployment rate when s = 0.01, f1= 0.25, f2 = 0.15 and g = 0.9.

c)  What happens to unemployment if the fraction of high-skilled unemployed, g, decreases to 0.5?

Answer 1

Solution:-

Given that

a)

Let fraction g of unemployed are high skill

$u_1=gu$

$u_2=(1-g)u$

At the steady state

$f_1u_1+f_2u_2=SE$

$f_1gu+f_2(1-g)u=s(L-u)$

$[f_1g+f_2(1-g)]u=s(L-u)$

$\frac{[f_1g+f_2(1-g)]}{s}=\frac{L}{u}-1$

$\frac{L}{u}=\frac{[f_1g+f_2(1-g)]}{s}+1$

$u^*=\frac{u}{L}=\frac{s}{f_1g+f_2-f_2g+s}$

b)

Assuming s = 0.01, f1 = 0.25, f2 = 0.15, g = 0.9

$u^*=\frac{0.01}{0.225+0.15-0.135+0.01}$

$u^*=\frac{0.01}{0.25}$

$u^*=0.04$

c)

Assuming g = 0.5

$u^*=\frac{u}{L}=\frac{s}{f_1g+f_2-f_2g+s}$

$u^*=\frac{0.01}{0.125+0.15-0.075+0.01}$

$u^*=\frac{0.01}{0.21}$

$u^*=0.048$

As the fraction of high skill unemployed rises then steady state unemployment decreases