Dynamic job search model with discrete wage: A model economy runs for an infinite number of periods. The total population is 1. At the beginning of period 1, everyone is unemployed. A job-finding rate is a = 0.1 Once a person finds a job, she keeps it forever. It means that a job separation rate is zero. Answer the following questions. Unemployment rate in the period 1 and period 5. Aggregate and average unemployment duration. Prove that Du = a 1 + a(1 a) 2+ a(1 a) 3 + ... = 1