Using data from the Consumer Expenditure Survey, we first document that the recent increase in income inequality in the U.S. has not been accompanied by a corresponding rise in consumption inequality. Much of this divergence is due to different trends in within-group inequality, which has increased significantly for income, but little for consumption. We then develop a simple framework that allows us to characterize analytically how within-group income inequality affects consumption inequality in a world in which agents can trade a full set of contingent consumption claims, subject to endogenous constraints emanating from the limited enforcement of intertemporal contracts. Finally, we quantitatively evaluate, in the context of a calibrated general equilibrium production economy, whether this set-up, or alternatively a standard incomplete markets model, can account for the documented stylized consumption inequality facts from the U.S. data.