Due to the greater path loss, shadowing, and increased effect of blockage in millimeter wave cellular networks, base station sharing among network service providers has the potential to significantly improve overall network capacity. However, a service provider may find that despite the technical gains, sharing actually reduces its profits because it makes price competition between service providers tougher. In this work, a weighted scheduling algorithm is described, which gives greater control over how the airtime resource is allocated within a shared cell. It is shown that, under certain market conditions, there exist scheduling weights such that base station sharing is more profitable than not sharing for both service providers in a duopoly market, while still achieving almost as much network capacity as in a conventional base station sharing scenario. Thus, both technical and economic benefits of base station sharing may be realized simultaneously.