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.
Highlights
This paper investigates the capacity choice issue for a public firm that is a welfare-maximizer and for a private firm which is a pure-profit-maximizer in the context of a price-setting mixed duopoly with network effects where the surplus that a firm’s client gets increases along with the number of other clients of that firm1
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
Nakamura and Saito [28] and Nakamura and Saito [29] investigated the capacity choice of a public firm that is a welfaremaximizer and a private firm that is a relative-profitmaximizer in the context of quantity-setting and pricesetting mixed duopolies, respectively; their most important contribution in these two papers is to show that even though the relation between the goods produced by the two firms is restricted to being substitutable, the difference between the output level and capacity level of the private firm can change in accordance with the degree of importance of its relative performance6
Summary
This paper investigates the capacity choice issue for a public firm that is a welfare-maximizer and for a private firm which is a pure-profit-maximizer in the context of a price-setting mixed duopoly with network effects where the surplus that a firm’s client gets increases along with the number of other clients of that firm. In the context of a price-setting mixed duopoly, in addition to the relation between the goods produced by both firms and the degree of importance of the private firm’s relative performance, the strength of network effects plays an important role as a determinant of the difference between the output level and capacity level of the private firm. We formulate a price-setting competition model in a mixed duopoly with the capacity choice of both the public firm and the private firm and with an additional term that reflects network effects in the fashion of Katz and Shapiro [35] and Hoernig [36]9. In the equilibrium, we derive the subgame perfect Nash equilibrium under the additional “rational expectations” assumption: y0 q0 and y1 q1
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