Capacity Choice in a Private Duopoly: A Unilateral Externality Case

Abstract

This paper studies capacity choice in a quantity-setting and price-setting private duopoly with differentiated goods wherein either of two firms has a price-raising effect on the price level of the product of the opponent firm. In both quantity-setting and price-setting competition, whether the price-raising effect of the product of one firm on the price level of the other firm’s product is strong or weak strictly depends on the differences between the quantities and capacity levels of both firms. More precisely, in the quantity-setting competition, when the price-raising effect is sufficiently strong, both firms choose under-capacity, whereas when such an effect is sufficiently weak, both firms choose overcapacity. Furthermore, in the price-setting competition, when the price-raising effect is sufficiently strong, both firms choose over-capacity, whereas when such an effect is sufficiently weak, both firms choose under-capacity. Therefore, the presence of the price-raising effect as the unilateral externality strikingly changes the difference between each firm’s quantity and capacity level in the contexts of both the quantity-setting competition and the price competition in a private duopoly with differentiated goods.