We construct a monetary economy in which agents face aggregate demand shocks and hetero- generous idiosyncratic preference shocks. We show that, even when the Friedman rule is the best interest rate policy, not all agents are satiated at the zero lower bound. Thus, quantitative easing can be welfare improving since it temporarily relaxes the liquidity constraint of some agents, without harming others. Moreover, due to a pricing externality, quantitative easing may also have beneficial general equilibrium effects for the unconstrained agents. Lastly, our model suggests that it can be optimal for the central bank to buy private debt claims instead of government debt.