This paper explores the capacity choice for a public firm that is a social welfare-maximizer and a private firm that is an absolute profit-maximizer in the context of a quantity-setting mixed duopoly with a simple mechanism of network effects where the surplus that a firm’s client gets increases with the number of other clients of the firm. In this paper, we show that the social welfare-maximizing public firm chooses under-capacity irrespective of both the degree of product differentiation and strength of network effects, whereas the absolute profit-maximizing private firm chooses over-capacity irrespective of both the degree of product differentiation and strength of network effects, which is strikingly different from the results on the capacity choice problems for public and private firms obtained in price-setting mixed duopolistic markets in the existing literature.