Market Size and Substitutability in Imperfect Competition: A Bertrand-Edgeworth-Chamberlin Model
构建了一个连接张伯伦与伯特兰-埃奇沃思价格竞争模型的框架，研究竞争者数量（市场规模）和产品替代程度对均衡存在性的影响，发现足够多的竞争者能确保均衡存在，而高替代性则可能导致均衡不存在。
Competition is often associated with the idea that there are many traders in the market or that each price maker is small as compared to the market. This paper introduces this notion of market size in a model of price competition with imperfect substitutes by constructing a model which creates a bridge between the Chamberlin and Bertrand-Edge worth lines of work on price competition. We investigate the role of two fundamental parameters in the existence of an equilibrium: the market size, given by the number n of competitors, and the degree of substitutability. We prove that: (a) For a given number of n ≦ 2 of competitors, a sufficiently large but finite degree of substitutability entails nonexistence. This thus generalizes the Bertrand-Edgeworth nonexistence result, which applies only to perfect substitutes, (b) Conversely for a given upper bound on the degree of substitutability, a sufficiently large number of competitors ensures existence, which thus introduces a significant role for market size in models of imperfect competition. We finally investigate the proximity of an equilibrium (when it exists) to a "competitive outcome", and we find that both high substitutability and large market size are a condition for competitiveness.