We present a tractable heterogeneous-agent version of the New Keynesian (NK) model that allows us to study the interaction between inequality and monetary policy. Though formulated as a precautionary-saving model a` la Huggett-Aiyagari, its reduced form is a two-agent model with a highly concentrated wealth distribution. When prices are sticky and wages flexible, as in the textbook representative- agent model, monetary policy affects the distribution of consumption, but has no effect on output as workers choose not to change their hours worked in response to wage movements. This highlights a transmission mechanism of the textbook model that we find implausible: in response to a monetary stimulus, the represen- tative worker’s labor supply is greatly affected by the profits she receives. First, the lower profits induced by higher wages raise labor supply through a wealth effect and, second, the mere presence of profits reduces the negative income effect of a wage rise. When wages are rigid, in contrast, our model exhibits plausible responses of output and hours worked to monetary policy shocks.