Suppose that everyone who has looked for a job for more than six months gave up in despair and stopped looking. What would happen to the unemployment rate?

Unemployment rate would decrease.

Explanation:

This is a worrying situation to any country: decreasing unemployment rate, because people who does not look for a job is not considered unemployed, and not because there is more hired people.To be unemployed one must be actively looking for a job, which means must apply for jobs, must search opportunities, etc. When people stop looking, they are not longer considered unemployed by defintion, but  Discouraged Workers. Unemployment rate (U)  is calculated as indicated: .If unemployed people give up and stop looking for a job, they are still part of labor force, but they are not longer considered unmeployed, which yields in lower uneployment rates.