Recall that the steady state unemployment rate is u=s/s+f

Assume that the unemployment rate in period 1 does not coincide with u Show that in the long run the unemployment rate will converge to its steady state value(u)

hint: show that when the unemployment rate is higher than u unemployment will decrease in the following period and when it is lower than u it will increase notice that the evolution of the number of unemployed workers over time can be expressed as Ut+1=(1-f)*Ut + s* Et

You can use this equation and change it at convenience in order to describe how the evolution of the unemployment rate over time