The majority of research to date investigating strategic tariffs in the presence of multinationals finds a knife-edge result where, in equilibrium, all foreign firms are either multinationals or exporters. Utilizing a model of heterogeneous firms, we find equilibria in which both pure exporters and multinationals coexist. We utilize this model to study the case of endogenously chosen tariffs. As is standard, Nash equilibrium tariffs are higher than the socially optimal tariffs. Unlike existing models with homogeneous firms, we find that non-cooperative tariffs promote the existence of low-productivity firms relative to the socially optimal tariffs. This highlights a new source of inefficiency from tariff competition not found in mod...