Scientific publishing is rapidly shifting from a paper-based system to one of predominantly electronic distribution, in which universities purchase site licenses for online access to journal contents. Will these changes necessarily benefit the scientific community? By using basic microeconomics and elementary statistical theory, we address this question and find a surprising answer. If a journal is priced to maximize the publisher's profits, scholars on average are likely to be worse off when universities purchase site licenses than they would be if access were by individual subscriptions only. However, site licenses are not always disadvantageous. Journals issued by professional societies and university presses are often priced so as to maximize subscriptions while recovering average costs. When such journals are sustained by institutional site licenses, the net benefits to the scientific community are larger than if these journals are sold only by individual subscriptions.