DISCONTINUITY PROBLEMS IN A GENERALIZED PRICE LEADERSHIP MODEL

1. Introduction There exists substantial evidence that price leadership is a common form of market structure. By contrast, theoretical treatments of this phenomenon are rare. This paper attempts to extend in three directions the existing treatments of the price leadership model. Firstly, it provides a mathematical statement of the model, generalizing existing geometrical and literary approaches, and extending the mathematical version of Hadar (1971, pp. 115–117). Secondly, it admits of the possibility of many followers, rather than adopting the conventional assumption of just one follower, or an anonymous aggregate of followers regarded as a competitive fringe. An essential feature of the analysis is that the output of each firm is a significant part of total market output. Thus the smooth continuous supply curve which emerges when followers are massed together in a competitive fringe is no part of the analysis. Thirdly, the paper attempts to take seriously the problems of discontinuity which arise in this type of market when a follower is forced out of business: a matter which is frequently ignored in the theorizing of economists.