In other words, monetary policy should increase the size of the cake and leave the distributional choices to other policies. Second, it is crucial to think about this problem from a general equilibrium perspective. A monetary expansion can affect income and wealth through a number of channels.
It boosts financial assets that are held by the rich, but it also makes debt less onerous, thus helping the poor. It stimulates profits and capital markets, but it also raises employment, which is the main source of income for the poorest.