Assume that we can model the unemployment rate as Ut=a+ β Ut-1 a, β >0; t=1,2,3,...where Ut is the unemployment rate in period t. Labour economists refer to the steady state level of unemployment in...

Assume that we can model the unemployment rate as Ut=a+βUt-1  a,β>0; t=1,2,3,...where Ut is the unemployment rate in period t.

Labour economists refer to the steady state level of unemployment in this model as the natural rate of unemployment.

Solve this difference equation (assume that Uo is known), solve for the natural rate of unemployment, and determine the necessary and sufficient condition for Ut to converge to the natural rate of unemployment.