Abstract
This paper analyzes the capacity choice issue under a price-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 public firm chooses over-capacity irrespective of the degree of product differentiation and the degree of importance of the relative performance of the private firm. In contrast, we find that the difference between the output and capacity levels of the private firm strictly depends on both the degree of product differentiation and the degree of importance of its relative performance. More precisely, the private firm chooses over-capacity when the degree of importance of its relative performance is high relative to the degree of product differentiation, whereas it chooses under-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 price-setting mixed duopoly
In this paper, taking into account that the objective function of the private firm is its relative profit, we consider the impact of the degree of importance of its relative performance on the difference between their output and their capacity levels of both the public firm and the private firm in a pricesetting mixed duopoly
When the degree of importance of the private firm’s relative performance is high relative to the degree of product differentiation, the private firm aggressively behaves in the market in the case wherein it is a relative-profit-maximizer rather than in the case wherein it is only a profit-maximizer, implying its relatively low price level and its high output level
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 price-setting mixed duopoly. The main purpose of this paper is to check the robustness of the results to the difference between the output and capacity levels of both the public firm and the private firm, which was obtained in Bárcena-Ruiz and Garzón [7]. The goods of both firms are restricted to being substitutable, we show that the difference between the output and capacity levels of the private firm changes in accordance with the degree of importance of its relative performance and the degree of product differentiation. Each firm’s equilibrium price level is relegated to the Appendix
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