Simple Unemployment Math

We are constantly reminded by Obama's detractors, and rightly so, of the national unemployment rate, yet I wonder as to whether most people understand what the unemployment rate is. Undoubtedly, some believe it reveals what percentage of the total population of Americans are jobless. Others think it describes how many people who are capable of working are jobless. The unemployment rate is a description of neither.

The number U of people who are unemployed are people who are not working and are active searching for a job. The labour force L is the sum of the number E of people who are employed and the number U who are unemployed. The unemployment rate u is the ratio of those who are unemployed U to the labour force L, where U is the numerator and L is the denominator. Hence:

u = U/L, L = E + U, u = U/(E + U)

Naturally, the employment rate e is the ratio of those who are employed E to the labour force L, again where E is the numerator and L is the denominator. Since the employment and unemployment rates are fractions, they add to 1. Hence:

e = E/L, 1 = e + u, e = E/(E + U)

Many people confuse the labour force with what's known as the working-age population. The working-age population N is, essentially, everyone capable of working between the ages of 15 and 65. It is the broadest quantity thus far, being the sum of those who are employed E, unemployed U, and excluded X from the labour force. Hence:

N = (E + U) + X, N = L + X

Finally, the participation rate p is the ratio of the labour force L to the working-age population N. Hence:

p = L/N = 1 - X/N