1. How do economists find equilibrium in the market?

Answer: No way. Because it is not observable. Then are the economic models wrong? In some sense, all models are wrong. But they can be useful for explanation and prediction.

2. As of Aug 2018, from the BLS employment data, why is there a seemingly contradictory pattern observed in the U.S. labor market?

Unemployment Rate Labor Force Participation Rate Employment-Population Ratio