The Fair Wage model in the study explains why wages and employment don't always move together in the economy. By adding real wage rigidities to the traditional sticky price model, the researchers found that this new approach helps to better understand structural unemployment and labor market dynamics. The model also shows that real wage rigidity can smooth out cost changes, leading to stronger and longer-lasting effects of monetary policy on the economy. Overall, the study suggests that including fair wages in economic models can improve our understanding of how the economy works.