Abstract This paper puts to scrutiny the way monetary policy propagates its effects and the way it should be conducted, focusing on the behavior of consumers. Specifically, it considers a price elasticity of demand that increases with the level of consumption as is observed in the data. A realistic demand structure has remarkable implications for monetary policy. Three main results stand out. First, it can amplify the real effects of monetary and technology shocks. Second, it can weaken the ability of a simple Taylor rule to stabilize the economy. Third, it can attenuate the trade-off in the stabilization of output and inflation. These findings provide support to the notion of a dual mandate for the central bank. They are based on a novel mechanism of intertemporal substitution, whereby consumers have a weak incentive to smooth out the effects of income fluctuations. The mechanism lends itself to addressing questions of stabilization policy and business cycle analysis.