We analyze differences in consumption and wealth that arise because of different degrees of rationality of households. In particular, we use a standard New Keynesian model and let a certain fraction of households be fully rational while the other fraction possesses less cognitive ability. We identify the rationality bias of boundedly rational agents, defined as a deviation from the fully rational benchmark, as the driver of consumption and wealth heterogeneity. It turns out that the rationality bias can be decomposed into three individual components: the consumption expectation bias, the real interest rate bias and the preference shock expectation bias. We show that for certain specifications of monetary policy the rationality bias can be eliminated because its individual components exactly offset each other although they are individually non-zero. However, it might not be desirable from a welfare perspective to eliminate the rationality bias as this comes along with high inflation volatility.