The purpose of this problem is to show how the unemployment rate depends on both the number of people who become unemployed in any month and the amount of time they are unemployed. Suppose that the size of the labor force is 160 million people.
(a) During any month when the output gap is zero, two million people become unemployed, and they remain unemployed for four months before finding work. Compute the number of unemployed people in any month when the output gap is zero and the natural rate of unemployment.
(b) Suppose that a mild recession causes three million people to become unemployed in any month, but the amount of time it takes them to find work remains at four months. Compute the number of unemployed people during any month in this recession and the unemployment rate during this recession.
(c) Suppose that a more severe recession also causes three million people to become unemployed in any month but that the number of months that it takes to find work increases to eight months. Compute the number of unemployed people during any month in this recession and the unemployment rate during this recession.
(d) Suppose that when the economy recovers from the severe recession and the output gap returns to zero, the number of people who become unemployed during any month falls back to two million. However the severe recessions caused a decline in the skills of workers, and as a result it now takes people five months to find work. Compute the number of people now unemployed in any month when the output gap is zero and the new natural rate of unemployment.