Dress to impress: Brands as status symbols

•We model the market for pure status goods.•Market can be Monopoly or Contestable.•Taxation or subsidy may be optimal, depending on parameters.

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 stratified 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 extant literature, subsidies may be socially optimal, depending on the parameters, in both market structures.