Segmenting the market: The monopolist's optimal product mix

In an industry producing products which differ in quality, to consumers who vary in their willingness to pay, it may happen that only a bounded number of producers can coexist at (noncooperative price) equilibrium; in other words, the industry is a natural oligopoly. We are here concerned with a special example, in which only one producer can survive. Our focus of interest in the present paper is to examine this monopolist's optimal product range. Depending on the dispersion of consumers' willingness to pay (income), either (i) the monopolist will find it optimal to segment the market completely, offering the maximum number of products permitted or (ii) the monopolist will offer only a single product. The precise nature of this switch of policy, which occurs at a certain critical distribution of consumer incomes (willingness to pay), is explored fully.