Since 2000 developed countries like the US have seen a polarization of earnings. This paper explores a novel mechanism that can explain these recent trends in earnings inequality. I build a tractable general equilibrium model which differentiates three different types of tasks: manual, routine and cognitive. Workers are heterogeneous in skill and self select into the type of task they perform. Those doing cognitive tasks perform a managerial job and are susceptible to a superstar phenomenon. I use this model to look at the effects on labour composition and the earnings structure of an increase in competition between varieties, brought by participating in a more globalized economy. I find that this increases top income inequality due to a superstar effect. At the same time, there is a trickle down effect, increasing the number of manual jobs and reducing those of cognitive tasks, which then produces a polarization of earnings.