Consider an environment where an agent could be either employed E or unemployed U. Let’s normalize E + U = 1, so that E and U are interpreted as the fraction of people employed and unemployed at any given point in time, respectively. Conditional on being employed today, the probability of being fired is δ=.05; and conditional on being unemployed today, the probability of finding a job is ω=.5
a) What is the probability of staying employed? (b) What is the probability of not finding a job? (c) Suppose that we know that today (Monday) the fraction of people who are employed is 0.95, what is the fraction of people employed tomorrow (Tuesday)? (d) What is the steady state level of employment?