Under the assumption that a public firm provides goods or services to two markets and that a private firm provides goods or services to one market only, this study examines whether public firms should be privatized. It also investigates how the production quantity of a private firm changes when its degree of privatization increases. We find that when the market share of a duopoly market is large (small), partial privatization (nationalization) is socially preferable. We also find that the quantity produced by the private firm does not always increase along with the degree of privatization.