Previous research modeled academic journals as platforms connecting authors with readers in a two-sided market. This research used the same basic framework also used to study telephony, credit cards, video game consoles, etc. In this paper, we focus on a key difference between the market for academic journals and these other markets: journals vary in terms of quality, where a journal's quality determined by the quality of the papers it publishes. We provide a simple model of journal quality. As an illustration of the value of the model, we use it to address issues that have arisen in the recent debate concerning whether, in the Internet age, journals should become \open access" (freely available to readers, financed by author rather than subscriber fees). Among other issues, we examine (a) whether open-access journals would tend to publish more articles than traditional journals, moving further down the quality spectrum in order to boost revenue; (b) whether journal quality affects the profitability of adopting open access; and (c) whether submission fees or acceptance fees are better instruments to extract surplus from authors.