Question: Even though most Americans who become unemployed are only unemployed for a short period of time, when you look at who is unemployed at a given moment in time, you'll find that most of the unemployed have been without a job for quite a while. Let's imagine a simple economy to see how to resolve this paradox. In this economy, there are two types of workers: Type A workers take one month to find a new job and Type B workers take 10 months to find a new job. Each month, let's assume that one Type A and one Type B worker lose their jobs. Notice that we're assuming that half of all people who lose their jobs today will find new jobs in a month. But, as we shall see, this implies that most of the unemployed will have been unemployed for a long period.
a. In the long run (or "steady state"), there will be 11 workers out of work in this simple society at any given point in time. Show that this is true by keeping track of the "pool" of unemployed workers in this society for two years. You can start off assuming that the pool is empty at time zero-that no one is unemployed-but you'd get the same steady state answer regardless of your starting point. You can prove that 11 will be out of work just with pencil and paper or much more quickly with Excel. To help you out, here's an example of what the pool of unemployed will look like in month 7. Keep going with this calculation until you see that the number of workers in the pool no longer changes month to month-this is called the "steady state."
b. In the steady state-that is, when your pool starts having the same numbers every month-how many of the 11 workers in the unemployment pool have been unemployed for "one month"? How many of the 11 workers in the unemployment pool have been unemployed for more than one month?
c. If you see an economy where most currently unemployed workers have been out of work for a long time, does this mean that most people who have been unemployed in the last few years were unemployed for a long time? How does this example illustrate your answer?