Unemployment and the Labor Market $$ End of Chapter Problem

The steady$-$state rate of unemployment is $\frac{U}{L}=\frac{s}{s+f}.$ Suppose that the unemployment rate does not begin at this level. Use this

relationship to show that unemployment will evolve over time and reach this steady state.

a$.$ The change in the number of people who become unemployed $(U_{t+1})$ is the difference between the number of employed

people losing their current jobs and the number of unemployed people finding new jobs. The number of employed people

losing their jobs can be expessed as

b$.$ The number of unemployed people finding new jobs can be expressed as

c$.$ The change in the number of unemployed is therefore $U_{t+1}=$