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In the General Equilibrium framework of Arrow, Debreau and others, there are a fixed number of commodities, which I feel is a valid assumption in the short run but maybe not in the long run.

Over time, new products are introduced and old products seize to exist in the market. What are some models that address such markets? What are the welfare implications?

On a somewhat similar line, for example a smartphone was not available for most people earlier, but not only that, many people didn't even imagine such a device. Was the smartphone in their Choice Set earlier? If not, and if the introduction of the smart phone changes the Choice Set, can the welfare of a consumer before and after the introduction of the smart phone be compared (does it even make sense), as the preference relation is usually defined for a particular Choice Set?

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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

  1. International Trade (Krugman)
  2. Economic Geography (Henderson,Fujita,Krugman,Venables)
  3. Economic Growth (Smulders, De Groot)
  4. 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.

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    $\begingroup$ I think the OP was explicitly asking for a general equilibrium framework. $\endgroup$
    – Bayesian
    Dec 17, 2020 at 22:54
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    $\begingroup$ Why would you assume Monopolistic Competition to be incompatible with general equilibrium? $\endgroup$
    – Jesper Hybel
    Dec 18, 2020 at 1:59
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    $\begingroup$ Indeed, monopolistic competition is the instrumental corner stone of, e.g. Krugman's NEG, and general equilibrium theory is what makes economic geography New. $\endgroup$
    – keepAlive
    Dec 18, 2020 at 2:22
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    $\begingroup$ Dixit-Stiglitz model should not be considered GE because the income is taken as exogenously given (afaik). $\endgroup$
    – Dayne
    Dec 18, 2020 at 3:24
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    $\begingroup$ In the Negishi model firm profits are channeled back to workers. And he proves existence of equilibrium (so what is meant by GE?). The problem according to Bonnano is that: One of Negishi's assumptions is that the production set of every firm is convex and contains the origin, which implies decreasing or constant returns to scale. Negishi (1961, p. 199) himself felt uncomfortable about making this assumption'considering the fact that monopolistic competition has much to do with so-called increasing returns (Sraffa, 1926) $\endgroup$
    – Jesper Hybel
    Dec 18, 2020 at 4:01

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