A MARKET WITH A SOCIAL CONSUMPTION EXTERNALITY

We model a spatial market in which the utility of each consumer is affected by the collection of consumers who buy precisely the same product. The marginal contribution of another consumer x’s purchase on consumer y depends on |y - x|. This marginal contribution declines as |y - x| increases and can be negative. This way of modeling preferences fits goods that signal something about a consumer’s place in society; clothing styles, automobiles, and jewellry are examples. For a given number of firms and a given overall market size, we find the unique symmetric equilibrium and also derive comparative statics results on the optimal number of firms, the largest number of firms the market can support and the behavior of profits per firm as the number of firms increases