Abstract
This paper studies capacity choice in a quantity-setting mixed duopoly with differentiated goods, when the objective function of the private firm is its relative profit. In this paper, we show that the differences between the output levels and capacity levels between both the public firm and the private firm strictly depend on both the degrees of product differentiation and of importance of the private firm’s relative performance. More precisely, we find that the public firm chooses over-capacity when both the degrees of importance of the private firm’s relative performance and of product differentiation are sufficiently high whereas it chooses under-capacity otherwise, and further the private firm chooses under-capacity when the degree of importance of its relative performance is high as compared the degree of product differentiation whereas it chooses over-capacity otherwise.
Highlights
This paper reconsiders the capacity choices of a public firm that is a welfare-maximizer and a private firm that is a relative-profit-maximizer in the context of a mixed duopoly
We show that the differences between the output levels and capacity levels between both the public firm and the private firm strictly depend on both the degrees of product differentiation and of importance of the private firm’s relative performance
This paper investigated the difference between the output and capacity levels of both the public firm and the private firm in a quantity-setting mixed duopoly with differentiated goods, in particular when the objective function of the private firm is its relative profit
Summary
This paper reconsiders the capacity choices of a public firm that is a welfare-maximizer and a private firm that is a relative-profit-maximizer in the context of a mixed duopoly. We first show that the public firm chooses over-capacity when both the degrees of importance of the private firm’s relative performance and of product differentiation are sufficiently high, whereas it chooses under-capacity otherwise. In this paper, it is shown that the difference between the output and capacity levels of the private firm strictly depends on both the degree of importance of the private firm’s relative performance and the degree of product differentiation. That is, when the degree of importance of the private firm’s relative performance is low relative to the degree of product differentiation, the private firm strategically chooses over-capacity in order to increase its payoff by enlarging its market share because its capacity level is negatively associated with the output level of the public firm. After both firms observe their capacity levels, they engage in quantity competition with each other
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