In this paper, we analyze the level of media plurality in a market with two private news firms (private duopoly) and in a market with a private news firm and a public news firm (mixed duopoly). In the private duopoly news firms maximize profits. In the mixed duopoly, the private news firm maximizes profits, while the public news firm maximizes social welfare. We show that, in spite of the public news firm maximizing social welfare, neither media plurality nor social welfare needs to be higher under the mixed duopoly compared with the private duopoly. This will depend on the relation between the costs of adapting news to readers' political preferences, the intensity of the readers' political preferences, and the size of the advertising market.