Imagine that the economy of Absurdia has a 100,000-person labor force.  The population includes another 100,000 persons who are otherwise voluntarily not working.  Of these, 10,000 are unemployed for the following reasons:  5,000 are unemployed due to a recession, there is no seasonal unemployment, 2,500 are frictionally unemployed, and the remaining 2,500 are structurally unemployed. 

Cyclically Unemployed	5,000
Seasonally Unemployed	0
Frictionally Unemployed	2,500
Structurally Unemployed	2,500
Total Unemployed	10,000

Unemployment rate = 10,000/100,000 = 10% 

The government of Absurdia decides to begin directly buying flugelhorns and steins from manufacturers in order to create demand.  The hope is this will stimulate demand enough to cause these employers to re-hire the laid off workers.   

The plan is successful and the number unemployed due to the recession decreases to zero.  But what about those who are frictionally unemployed?  Don’t they still need to go through the process of looking for the job, applying, interviewing, and eventually starting?  Even when the economy is at its best these things need to happen.  And so, frictional unemployment will remain as it is.  What about structural unemployment?  These workers worked in the now defunct lederhosen industry.  Their skills don’t fit well in either the flugelhorn or stein industries.  Barring retraining, they’re unemployable.  So, despite the governments direct spending, structural unemployment remains. 

Cyclically Unemployed	0
Seasonally Unemployed	0
Frictionally Unemployed	2,500
Structurally Unemployed	2,500
Total Unemployed	5,000

Unemployment rate = 5,000/100,000 = 5% 

Because some types of unemployment persist despite government attempts to counteract the business cycle, unemployment never actually reaches zero.  For Absurdia, an unemployment rate of 5% is deemed full employment. 

Here’s why… 

What if the government was determined to see the unemployment rate reach 3%?  There is no short-term solution for reducing frictional or structural unemployment.  And so, the numerator (the top number in the quotient) is irreducible.  But more spending might work in a back-hand way.  With cyclical unemployment now at zero, manufacturers looking to expand production to sell to the government must find workers elsewhere.  The structurally unemployed aren’t usable and frictional unemployment is normal.  But they can induce people who were voluntarily out of the labor force back in by offering higher wages. 

Would it be possible to lure enough workers into the labor force to achieve 3%?  Technically yes, but it would take a lot. 

Unemployment rate = 5,000/167,000 = 3% 

The problem with convincing two thirds of voluntarily idle workers to come back to work is that wages will have to increase dramatically.  And so, the tradeoff is that if we want to reduce the unemployment rate below that level that corresponds to zero cyclical unemployment, we’re going to cause wages to increase potentially leading to inflation. 

For this reason, the government defines full employment as the lowest rate of unemployment consistent with no wage-induced inflation.   

It would be so simple if this number were easy to observe.  But it isn’t.  We used to think the lowest possible unemployment rate was around 6%.  But more recently we’ve experienced rates half that without any inflation.  The reasons for this are a bit more than we need to cover.