Sharing spectrum is a promising approach for expanding wireless access and increasing competition among wireless service providers. Indeed, this is a key motivation behind the recent regulations such as those for the 3.5 GHz band in the U.S. However, meeting this promise requires that service providers (SPs) have the incentives to invest in technology to be deployed in shared bands. This is not a forgone conclusion. Indeed by lowering entry barriers, sharing can promote more competition, but this also lowers revenue, making investment less attractive. In this paper, we study such scenarios for band of spectrum that is shared under a primary-secondary paradigm, by adopting a model developed by Liu and Berry in 2014. In their model, a primary SP and multiple secondary SPs compete for a common pool of customers using a shared band. In that work, any investments of the SPs was considered sunk, and it was shown that sharing improved both social welfare and consumer welfare over the case where the band was exclusively licensed to one SP. Here, we add an investment stage to this model, in which all of the SPs first decide on an investment level; given their investments, they again compete for customers. We characterize the sub-game perfect equilibrium of the resulting game and characterize the resulting consumer and social welfare. We show that a secondary SP needs a lower investment cost than a primary in order to enter the market. Moreover, at most one secondary SP will enter, even if multiple have low costs. Finally, we show that for large enough bandwidth, assigning the SP with the lower investment cost as the primary can provide more social welfare and consumer welfare than making it a secondary.