We study optimal monetary policy in an analytically tractable Heterogeneous Agent New Keynesian model. In the model, the central bank has an incentive to reduce consumption inequality in addition to keeping economic activity at its efficient level and inflation stable.
The secular decline in real interest rates has created a challenge for monetary policy, now confronting the zero lower bound more often. An increase in the supply of safe assets reduces downward pressure on the natural interest rate. This allows monetary policy to reach price stability and full employment, but not without cost—permanently lower investment.