The paper investigates how product market competition affects the firms' decision to hire altruistic or selfish employees in a mixed duopoly where a public and a private firm compete against each other on prices and quality. When firms offer similar services, so that product competition is fierce, both firms benefit from hiring altruistic employees even if it leads to lower prices. Conversely, when firms offer sufficiently differentiated services, the private firm prefers to hire selfish employees as starting a price war with the public firm is not profitable. However, the private firm would hire altruistic employees if it faced another private firm. Therefore, when firms offer differentiated products, customers may benefit from the privatization of the public firm, especially when the employees' degree of altruism is high.