I think the best candidate would be monopolistic competition as introduced by
Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity,
in which two models are introduced. One central theme was product variety and the endogenous determination of the number of product varieties.
There are many models formulated within the monopolistic competition framework in diverse areas of economic theory including
- International Trade (Krugman)
- Economic Geography (Henderson,Fujita,Krugman,Venables)
- Economic Growth (Smulders, De Groot)
- Macroeconomics (see for example Blanchard and Kiyotaki 1987)
The welfare analysis has centered around the question whether there is too much or too little product variety in equilibrium. The problem is that there are counteracting forces in equilibrium. Because of setup costs, revenues may fail to cover the costs of a socially desirable product. As a result some products may be produced at a loss at an optimum. This force tends towards too few products. On the other hand firms hold back output making price higher than marginal costs, which gives an incentive to entry, which creates a tendency towards too many products.
The different models therefore vary with respect to whether the first best social optimum is a case of too many or too few varieties depending on the specifics of the model and how the influence the balance of the counterveiling forces.
A representative selection of the literature on monopolitistic competition is collected in book
Brakman and Heijda (2003) The Monopolistic Competition Revolution in Retrospect,
chapter one of which has a textbook example of a general equilibrium monopolistic competition model ala Dixit and Stiglitz.