I think that it is often assumed that monetary policies have little or no impact on inequality. At least in the public the monetary policy is not seen as a political question the same way that fiscal policy is.
Let us consider two different ways the fed can stimulate the economy:
QE. The feds buy back US treasury bonds from banks. Say the house prices are so high that the average consumer can not afford to buy a house even if the interest rates are zero. Instead the banks move the money into the stock market. The stock prices go up. The ones selling the stocks to the banks are the richest. They use the money to buy US built luxury yatchs. This employs more people. The increased consumption of the newly employed people show up in the CPI but not the yatchs.
Helicopter money. Every US citizen gets a certain amount of USD. Most of this is spent and shows up in the CPI. Increased spending means more employment.
The two different strategies can result in the same inflation and low unemployment. However in the strategy 1 the rich now owns a lot of luxury yatchs so the effect on inequality is not the same.
It therefore seems that in an already inequal society the choice of monetary policy can worsen the wealth inequality?
Am I wrong in my reasoning?