Capacity Choice in a Price-Setting Mixed Duopoly with Network Effects

Abstract

This paper explores the capacity choice for a public firm that is a welfare-maximizer and for a private firm that is a pure-profit-maximizer in the context of a price-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 that firm. In this paper, we show that the public firm chooses over-capacity irrespective of the strength of network effects and the demand parameter, and that the difference between the output level and capacity level of the private firm strictly depends on the values of both the strength of network effects and the demand parameter. More precisely, the private firm chooses over-capacity when the strength of network effects is high relative to the demand parameter, while it chooses under-capacity otherwise.

Capacity Choice in a Quantity-Setting Mixed Duopoly with Network Effects

“…TEL 44 capacity levels of both public and private firms in the case of price-setting mixed duopolies obtained by Nakamura [7]. More precisely, we ascertain whether or not the differences between the output and capacity levels of both the public firm and private firm depend on the strength of network effects à la Katz and Shapiro [8] and Hoernig [9] and the degree of product differentiation in a quantity-setting mixed duopoly 4 .…”

“…More precisely, we ascertain whether or not the differences between the output and capacity levels of both the public firm and private firm depend on the strength of network effects à la Katz and Shapiro [8] and Hoernig [9] and the degree of product differentiation in a quantity-setting mixed duopoly 4 . In this paper, we show that in quantity competition with the network effects à la Katz and Shapiro [8], Hoernig [9], and Nakamura [7], a social welfare-maximizing public firm chooses under-capacity irrespective of the degree of product and strength of network effects, whereas an absolute profit-maximizing private firm chooses over-capacity irrespective of the degree of product differentiation and strength of network effects, which is strikingly different from the results in price competition obtained in Nakamura [7]. The intuition behind the result that the difference between the quantity and capacity levels of a social welfare-maximizing firm is always positive can be explained as follows: In quantity competition with network effects, regardless of the degree of product differentiation and strength of network effects, a public firm attempts to increase the quantity level of the rival private firm in order to enhance social welfare.…”

“…5 In the model employed in this paper, the parameters are a, b, c, and n. The economic meanings of such parameters are given in the following body of this paper. [5], Barcena-Ruiz and Garzon [6], Tomaru et al [10], Nakamura and Saito [14], and Nakamura and Saito [15], we assume that the cost function is given by 7 This cost function implies that if each firm's output level equals its capacity level, i i q x = , then the long-run average cost is minimized. The profit of firm i is given by ( )…”

“…Subsequently, Ogawa [5] and Bárcena-Ruiz and Garzón [6] extended the model introduced in Nishimori and Ogawa [3] to quantity-setting and price-setting mixed markets with differentiated goods, respectively. 3 The area of the demand parameter considered in this paper corresponds to that wherein the goods produced by both the social welfaremaximizing public firm and the absolute profit-maximizing private firm are substitutable, which is similar to the price-setting mixed duopoly with network effect considered in Nakamura [7].…”

“…1 Similar to the works on the capacity selection issues in private oligopolies composed of private firms only, such as the seminal works of Dixit [1] and Brander Spencer [2], studies exist in the context of mixed oligopolistic markets composed of both public and private firms that broadly investigate the capacity choice problems 2 . Most recently, Nakamura [7] investigated the capacity choice problems in a price-setting mixed duopoly with network effects in the fashion of Katz and Shapiro [8] and Hoernig [9], and showed that a public firm chooses over-capacity, whereas the difference between the quantity and capacity levels of a private firm strictly depends on both the degree of product differentiation and strength of network effects. 3 In this paper, in a quantity-setting mixed duopoly with network effects, we confirm the robustness of the results of the difference between the quantity and 1 Similar to a private duopoly composed of private firms only, since the network effect such that a firm's client gets surplus increases along with the number of other clients of the firm can be observed in the representative real world mixed oligopolistic industries including the airline, rail, telecommunications, natural gas, electricity, steel, and overnight-delivery, as well as in the services including banking, home loans, health care, life insurance, hospitals, broadcasting, and education, it is important to consider the capacity choice problems of both the public and private firms in a mixed duopoly with network effects.…”