The scarcity of talent is a tremendous challenge for firms in the globalized world. This paper investigates the role of labor market imperfection in open economies for the usage of talent in the production process of firms. For this purpose, I set up a heterogeneous firms model, where production consists of a continuum of tasks that differ in complexity. Firms hire low-skilled and high-skilled workers to perform these tasks. How firms assign workers to tasks depends on factor prices for the two skill types and the productivity advantage of high-skilled workers in the performance of complex tasks. I study the firms' assignment problem under two labor market regimes, which capture the polar cases of fully flexible wages and a binding minimum wage for low-skilled workers. Since the minimum wage lowers the skill premium, it reduces the range of tasks performed by high-skilled workers, which increases firm-level productivity and reduces the mass of active firms. Whereas trade does not affect the firm-internal assignment of workers to tasks in a setting with fully flexible wages, it renders high-skilled workers a scarce resource and reduces the range of tasks performed by this skill type with negative consequences for firm-level productivity, if low-skilled wages are fixed by a minimum wage. In this case, trade leads to higher per-capita income for both skill types and thus to higher welfare in the open than in the closed economy, whereas - somewhat counter-intuitive - inequality between the two skill types decreases, as more low-skilled workers find employment in the production process.