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

Yasuhiko Nakamura

doi:10.4236/tel.2014.41007

Abstract

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.

Highlights

This paper investigates the capacity choice issue 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 network effects where the surplus that a firm’s client gets increases with the number of other clients of the firm
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]
This paper explored 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 network effects à la Katz and Shapiro [8] and Hoernig [9]

Summary

Introduction

This paper investigates the capacity choice issue 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 network effects where the surplus that a firm’s client gets increases with the number of other clients of the firm. 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. 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. More recently, Nakamura and Saito [14] and Nakamura and Saito [15] investigated the capacity choice of a public firm that is a social welfare-maximizer and a private firm that is a relative profit-maximizer in the context of quantity-setting and price-setting 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 and capacity levels of the private firm can change in accordance with the degree of importance of its relative performance.

Equilibrium Analysis

Conclusions