We analyze the relationship between income inequality and structural change in the sectoral composition of the tradable and the non-tradable sectors. We construct a small open economy two sector model where preferences imply non-linear Engel curves and we show that the relationship between income inequality and structural change crucially depends on the non-linearity of the Engel curves. We calibrate this model to the US economy in the period 1960-2010 and we show that it explains the observed patterns of structural change in terms of the sectoral composition of consumption and employment, it also explains the increase in inequality measured by the Gini index and, finally, it is consistent with the large reduction in the trade balance. From the analysis of several counterfactual exercises, we obtain the following insights: (i) income inequality contributes to explain structural change and reduces GDP when Engel curves are nonlinear; (ii) asset accumulation and the time path of GNP do not depend on the level of inequality, but on the evolution of income inequality; and (iii) a rising inequality implies a faster accumulation of assets, a larger growth of GNP and a fester deterioration of the trade balance.