This thesis utilizes quantitative macroeconomics to investigate three distinct topics. The first chapter focuses on designing an inflation target rule that effectively stimulates the economy when it reaches the lower bound. In the second chapter, a heterogeneous firm model is developed to provide a comprehensive explanation for three recently emerged phenomena in the United States economy: the decline in labor, the rise of market concentration, and the emergence of super-star firms and increased markups. The third chapter delves into a mechanism within the progressive labor tax system that reconciles economic growth with income equity.