This dissertation studies monetary policy design under different economic frameworks. The investigated frameworks include household heterogeneity, limitations to the policy response, and misalignments between the central bank and society's preferences concerning economic outcomes.In the first chapter of this dissertation, a tractable two-agent, sticky-price, sticky-wage model is built to investigate the gains of wage flexibility. The model extends the traditional two-agent new Keynesian model by allowing for consumption heterogeneity among those households with restricted access to mechanisms for sharing idiosyncratic income risk. It is shown how consumption and wage inequality across the two household types, as well as the dispersion of co...