Algorithm designers increasingly optimize not only for accuracy but also for fairness across pre-defined groups. We study the tradeoff between fairness and accuracy by characterizing a fairness-accuracy frontier, which consists of the optimal points across a broad range of preferences over fairness and accuracy. A simple property of the algorithmic inputs, group-balance, qualitatively determines the shape of the frontier. We further study an information-design problem where the designer flexibly regulates the inputs, but the algorithm is chosen by another agent. Excluding informative inputs can be optimal in general but is strictly suboptimal if the designer has access to group identity.