This paper provides an analytically tractable general-equilibrium model of money demand with micro-foundations. The model is based on the incomplete-market model of Bewley (1980) where money serves as a store of value and provides liquidity to smooth consumption. The model is applied to study the effects of monetary policies. It is shown that heterogeneous liquidity demand can lead to sluggish movements in aggregate prices and positive responses from aggregate output to transitory money injections. However, permanent money growth can be extremely costly: With log utility function and an endogenously determined distribution of money balances that matches the household data, agents are willing to reduce consumption by 8% (or more) to avoid 10% annual inflation. The large welfare cost of inflation arises because inflation destroys the liquidity value and the buffer-stock function of money, thus raising the volatility of consumption for low-income households. The astonishingly large welfare cost of moderate inflation provides a justification for adopting a low inflation target by central banks and offers an explanation for the empirical relationship between inflation and social unrest in developing countries.