We argue that demand composition between tradable and non-tradable goods and services affects monetary policy transmission. We document at the micro level that within Eurozone countries, richer households allocate a greater share of their consumption basket to non-tradable goods.  At the aggregate level, we show that non-tradable goods account for a larger share of total consumption in countries with higher income inequality. Finally, we show that output responses to identified monetary policy shocks are larger for economies with lower non-tradable consumption shares. We rationalize our micro and macro findings using a small open-economy heterogeneous-agent model with non-homothetic preferences. We then study the implications for optimal stabilization policy.