With the increasing interest in the use of millimeter wave bands for 5G cellular systems comes renewed interest in resource sharing. Properties of millimeter wave bands such as massive bandwidth, highly directional antennas, high penetration loss, and susceptibility to shadowing, suggest technical advantages to spectrum and infrastructure sharing in millimeter wave cellular networks. However, technical advantages do not necessarily translate to increased profit for service providers, or increased consumer surplus. In this paper, detailed network simulations are used to better understand the economic implications of resource sharing in a vertically differentiated duopoly market for cellular service. The results suggest that resource sharing is less often profitable for millimeter wave service providers compared to microwave cellular service providers, and does not necessarily increase consumer surplus.