Question

The number of unemployed remains unchanged but the number of people in jobs looking for extra hours has increased. How does this affect the underutilization rate? Explain your answer

Answer 1

the number of unemployed is equal to those people who are willing to work at a given wage rate but cannot find jobs.

lets assume, at a particular point of time t, the number of people who are willing to work at the given wage rate = N

size of total labour force=L

hence the unemployment rate=(L-N)/L=U/L where L-N=U

lets assume people in are willing to work h hours per day at time t, hence total employable working hours per day=Lxh

total underutilised hours per day=Uxh

hence underutilisation rate at time t= Uxh/Lxh=U/L=L-N/L

hence at time t unemployment rate=underutilisation rate

let's suppose, at time (t+1), the unemployed people and total labour force remain the same. hence unemployment rate=U/L

but people in job are willing to work h+i hours per day, where i>0

now total potential labour hours per day=Nx(h+i)+Uxh

total underutilised hours per day= total potential labour hours-utilised labour hours=Nxh+Nxi+uxh-Nxh= N x i + u x h

hence underutilisation rate at time t+1 = {(N x i + U x h)}/{Nx(h+i)+Uxh}= (N x i +U x h)/ {(N+U)h + Ni}= {(N x i +U x h)/ {Lh + Ni}

how the underutilisation rate at time t= Uxh/Lxh

it is clear that underutilisation rate at time t+1 > underutilisation rate at time t

as( Uxh + Ni) /( Lxh + Ni )> Uxh/Lxh as Ni>0

intuitively, earlier the underutilised hours are those which were only from the unemployed labour force, but now some part of the hours which are being offered by the employed workforce is also being forgone. hence total underutilisation rate is more than the previous level.