We develop a dynamic general equilibrium model to analyze the relationship between monetary policy, money demand, and unemployment. Our model succeeds in replicating the empirical fact of a downward sloping Phillips curve for low inflation rates and an upward sloping curve for high inflation rates. The reason is that low inflation rates make saving, as opposed to consumption, more attractive. Less consumption is associated with less output and therefore higher unemployment. To the contrary, when inflation exceeds a certain threshold, money is too costly to hold, which results in a decrease in output and an increase in unemployment.