<p>I think the best candidate would be monopolistic competition as introduced by</p>
<blockquote>
<p>Dixit and Stiglitz (1977) Monopolistic Competition and Optimum Product Diversity,</p>
</blockquote>
<p>in which two models are introduced. One central theme was product variety and the endogenous determination of the number of product varieties.</p>
<p>There are many models formulated within the monopolistic competition framework in diverse areas of economic theory including</p>
<ol>
<li>International Trade (Krugman)</li>
<li>Economic Geography (Henderson,Fujita,Krugman,Venables)</li>
<li>Economic Growth (Smulders, De Groot)</li>
<li>Macroeconomics (see for example Blanchard and Kiyotaki 1987)</li>
</ol>
<p>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.</p>
<p>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.</p>
<p>A representative selection of the literature on monopolitistic competition is collected in book</p>
<blockquote>
<p>Brakman and Heijda (2003) The Monopolistic Competition Revolution in Retrospect,</p>
</blockquote>
<p>chapter one of which has a textbook example of a general equilibrium monopolistic competition model ala Dixit and Stiglitz.</p>

CC BY-SA 4.0
2020-12-17T21:08:44.163Z
+1 in this case -1 without explanation  seems frivolous.
1muflon1
CC BY-SA 4.0
2020-12-17T21:11:27.330Z
Agreed explanation of downvoting behavior would be constructive.
Jesper Hybel
CC BY-SA 4.0
2020-12-17T22:54:36.570Z
I think the OP was explicitly asking for a general equilibrium framework.
Bayesian
CC BY-SA 4.0
2020-12-18T01:59:51.303Z
Why would you assume Monopolistic Competition to be incompatible with general equilibrium?
Jesper Hybel
CC BY-SA 4.0
2020-12-18T02:22:22.267Z
Indeed, monopolistic competition is the instrumental corner stone of, e.g. Krugman's NEG, and general equilibrium theory is what makes economic geography *New*.
keepAlive
CC BY-SA 4.0
2020-12-18T03:05:10.373Z
My thoughts exactly. Offcourse there exist an early literature critical of MC as GE. And first attempt at making MC compatible with GE is to my knowledge Negishi (1961). Bonnano (1990) GENERAL EQUILIBRIUM THEORY WITH
IMPERFECT COMPETITION, summarizes this discussion.
Jesper Hybel
CC BY-SA 4.0
2020-12-18T03:11:59.507Z
Thisse and Fijuta (2002) states "Most of the contributions to location
theory by industrial organization deal with partial equilibrium models. Although
a comprehensive general equilibrium model with imperfect competition has so
far been out of reach and is likely to remain so for a long time (Bonanno 1990),
speciﬁc models have been developed that, taken together, have signiﬁcantly
improved our understanding of how the spatial economy works.
Jesper Hybel
CC BY-SA 4.0
2020-12-18T03:19:17.817Z
Given the depth of this literature I do not think it is a simple matter to define exactly how it is these models fail to be GE models in comparison to the modern GE models with perfect competition by Arrow, Debreau and others.
Jesper Hybel
CC BY-SA 4.0
2020-12-18T03:24:23.173Z
Dixit-Stiglitz model should not be considered GE because the income is taken as exogenously given (afaik).
Dayne
CC BY-SA 4.0
2020-12-18T04:01:27.223Z
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)
Jesper Hybel
CC BY-SA 4.0
2020-12-18T04:01:41.537Z
It is true, that in the Dixit & Stiglitz (1977) models income are taken exogenously, but endogenizing this do not seem to be the main problem. Based on a fast read income is also endogenized in th textbook model given in chapter 1 of Brakman and Heijda (2003) which is otherwise a straight up version of Dixit & Stiglitz (1977). But offcourse I could be misunderstanding.
Jesper Hybel
CC BY-SA 4.0
2020-12-18T04:02:07.847Z
So as far as I can see it it fair as you say @Dayne that DS(1977) is not GE but to dismiss the entire monopolistic competition framework as incompatible with GE in current theory is just far from trivial.
Jesper Hybel
CC BY-SA 4.0
2020-12-18T04:55:28.460Z
@Dayne Indeed, having an exogenous income necessarily boils down to "partializing your considerations". But such choice is arbitrary and *clearly not* inherent to MC. Models are not religious frozen objetcs, you can do whatever you like and combine/describe/endogenize things as you wish (!)
keepAlive
CC BY-SA 4.0
2020-12-18T04:59:58.837Z
First this is a very fruitful discussion. Now I completely agree that just because income is exogenous that doesn't make a huge impact. But the way OP has asked the question a larger discussion should be considered where income is endogenous. Introducing a number of new choices will change labor market dynamics and the welfare impacts will be asymmetrical as income distribution as well as level of income may get affected (what if choices increased solely by higher imports) - which maybe be appropriately in a GE setting.
Dayne
CC BY-SA 4.0
2020-12-18T08:56:42.027Z
I am not saying that MC and GE are necessarily incompatible, but I wouldn't consider DS'77 as GE. I also don't see immediately how MC per se connects to product innovation. See the Arrow paper on innovation and competition.
Bayesian
CC BY-SA 4.0
2020-12-18T09:43:35.990Z
Just to clarify: The contribution of DS77 is to make N the number of goods endogenous.  In that sense it can be argued that the model explains product innovation.
Jesper Hybel
CC BY-SA 4.0
2020-12-17T19:58:45.097Z
2020-12-18T02:03:33.767Z
2020-12-18T02:03:33.767Z
Jesper Hybel
<p>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.</p>
<p>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?</p>
<p>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?</p>

<preferences><general-equilibrium><choice-theory><welfare><innovation>
Market with changing number of goods and services
Ishan Kashyap Hazarika
# Market with changing number of goods and services

(Asked by: username_0 on 2020-12-17)

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?

**Tags:** preferences, general-equilibrium, choice-theory, welfare, innovation

---

## 1 answers

### Answer by username_1 on 2020-12-17. Score: 5

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.

> **Comments:**
> **username_2**: +1 in this case -1 without explanation  seems frivolous.  
> **username_1**: Agreed explanation of downvoting behavior would be constructive.  
> **username_3**: I think the OP was explicitly asking for a general equilibrium framework.  
> **username_1**: Why would you assume Monopolistic Competition to be incompatible with general equilibrium?  
> **username_4**: Indeed, monopolistic competition is the instrumental corner stone of, e.g. Krugman's NEG, and general equilibrium theory is what makes economic geography *New*.  
> **username_1**: My thoughts exactly. Offcourse there exist an early literature critical of MC as GE. And first attempt at making MC compatible with GE is to my knowledge Negishi (1961). Bonnano (1990) GENERAL EQUILIBRIUM THEORY WITH IMPERFECT COMPETITION, summarizes this discussion.  
> **username_1**: Thisse and Fijuta (2002) states "Most of the contributions to location theory by industrial organization deal with partial equilibrium models. Although a comprehensive general equilibrium model with imperfect competition has so far been out of reach and is likely to remain so for a long time (Bonanno 1990), speciﬁc models have been developed that, taken together, have signiﬁcantly improved our understanding of how the spatial economy works.  
> **username_1**: Given the depth of this literature I do not think it is a simple matter to define exactly how it is these models fail to be GE models in comparison to the modern GE models with perfect competition by Arrow, Debreau and others.  
> **username_5**: Dixit-Stiglitz model should not be considered GE because the income is taken as exogenously given (afaik).  
> **username_1**: 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)  
> **username_1**: It is true, that in the Dixit & Stiglitz (1977) models income are taken exogenously, but endogenizing this do not seem to be the main problem. Based on a fast read income is also endogenized in th textbook model given in chapter 1 of Brakman and Heijda (2003) which is otherwise a straight up version of Dixit & Stiglitz (1977). But offcourse I could be misunderstanding.  
> **username_1**: So as far as I can see it it fair as you say @Dayne that DS(1977) is not GE but to dismiss the entire monopolistic competition framework as incompatible with GE in current theory is just far from trivial.  
> **username_4**: @Dayne Indeed, having an exogenous income necessarily boils down to "partializing your considerations". But such choice is arbitrary and *clearly not* inherent to MC. Models are not religious frozen objetcs, you can do whatever you like and combine/describe/endogenize things as you wish (!)  
> **username_5**: First this is a very fruitful discussion. Now I completely agree that just because income is exogenous that doesn't make a huge impact. But the way OP has asked the question a larger discussion should be considered where income is endogenous. Introducing a number of new choices will change labor market dynamics and the welfare impacts will be asymmetrical as income distribution as well as level of income may get affected (what if choices increased solely by higher imports) - which maybe be appropriately in a GE setting.  
> **username_3**: I am not saying that MC and GE are necessarily incompatible, but I wouldn't consider DS'77 as GE. I also don't see immediately how MC per se connects to product innovation. See the Arrow paper on innovation and competition.  
> **username_1**: Just to clarify: The contribution of DS77 is to make N the number of goods endogenous.  In that sense it can be argued that the model explains product innovation.  

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