In the basic recommendation paradigm, the most (predicted) relevant item is recommended to each user. This may result in some items receiving lower exposure than they "should"; to counter this, several algorithmic approaches have been developed to ensure item fairness. These approaches necessarily degrade recommendations for some users to improve outcomes for items, leading to user fairness concerns. In turn, a recent line of work has focused on developing algorithms for multi-sided fairness, to jointly optimize user fairness, item fairness, and overall recommendation quality. This induces the question: what is the tradeoff between these objectives, and what are the characteristics of (multi-objective) optimal solutions? Theoretically, we develop a model of recommendations with user and item fairness objectives and characterize the solutions of fairness-constrained optimization. We identify two phenomena: (a) when user preferences are diverse, there is "free" item and user fairness; and (b) users whose preferences are misestimated can be especially disadvantaged by item fairness constraints. Empirically, we prototype a recommendation system for preprints on arXiv and implement our framework, measuring the phenomena in practice and showing how these phenomena inform the design of markets with recommendation systems-intermediated matching.