Price competition, quality and income disparities

A market is considered, the demand side of which consists of a large number of consumers with identical tastes but different income levels, and the supply side, of two firms selling at no cost products which are relatively close substitutes for each other. Consumers are assumed to make indivisible and mutually exclusive purchases. A full characterization of the demand structure and the non cooperative market solution is given, and the dependence of the latter on income distribution and quality parameters is analyzed.