We analyzed the market for indivisible, pure status goods. Firms produce and sell different brands of pure status goods to a population that is willing to signal individual abilities to potential matches in another population. Individual status is determined by the most expensive status good one has. There is a strati.ed equilibrium with a finite number of brands. Under constant tax rates, a monopoly sells different brands to social classes of equal measure, while in contestable markets, social classes have decreasing measures. Under optimal taxation, contestable markets have progressive tax rates, while a monopoly faces an adequate flat tax rate to all brands. In contrast with the literature, subsidies may be socially optimal, depending on the parameters, in both market structures.