This paper studies the behavior of the economy and the efficacy of monetary policy under zero nominal interest rates, using a model with population growth that nests, as a special case, a more conventional specification in which there is a single infinitely lived representative agent. The paper shows that with a growing population, monetary policy has distributional effects that give rise to a real balance effect, thereby eliminating the liquidity trap. These same distributional effects, however, can also work to make many agents much worse off under zero nominal interest rates than they are when the nominal interest rate is positive.