The Sonnenschein-Mantel-Debreu theorem.

[Nusocialist]

I'm currently arguing with a cappie about this. I read Steve Keen's Debunking economics and he claims multiple equilibria is a very important flaw in Neoclassical economics but this guy denies it.

Does anyone have any knowledge or resources on this?

[ComradeRed]

It is well known that only under certain conditions the market demand will possess the properties of individual demand. The main condition is that the utility functions have Gorman form, which Keen correctly identifies.

In behavioral terms, this functional form implies that agents are allowed to differ only to a limited extent.

Keen argues that the necessary assumptions are unrealistic (see pg. 27 of his book) and that this demonstrates that methodological individualism is flawed...since society is something more than the sum of its parts.

If you actually look closely you can quote the economists that Keen quotes, which is pretty damning quotes in and of itself since it's vulgar economists admitting they fucked up.

[edit] Wikipedia actually had a surprisingly accurate history of this theorem in Marginalism and how it spawned from the cambridge capital contraversy:
Problems with making the neoclassical general equilibrium theory compatible with an economy that develops over time and includes capital goods. This was explored in a major debate in the 1960s—the "Cambridge capital controversy"—about the validity of neoclassical economics, with an emphasis on the economic growth, capital, aggregate theory, and the marginal productivity theory of distribution. There were also internal attempts by neoclassical economists to extend the Arrow-Debreu model to disequilibrium investigations of stability and uniqueness. However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to insure that the equilibrium is stable and unique are quite restrictive. From This cached image of the marginalism page (http://72.14.253.104/search?q=cache:9qTBDpg37MoJ:en.wikipedia.org/wiki/Neoclassical_economics+debunking+economics+Sonnens chein-Mantel-Debreu+Theorem&hl=en&ct=clnk&cd=2&gl=us&client=firefox-a).

[McCaine]

Originally posted by [email protected] 16, 2007 05:24 pm
It is well known that only under certain conditions the market demand will possess the properties of individual demand. The main condition is that the utility functions have Gorman form, which Keen correctly identifies.

In behavioral terms, this functional form implies that agents are allowed to differ only to a limited extent.

Keen argues that the necessary assumptions are unrealistic (see pg. 27 of his book) and that this demonstrates that methodological individualism is flawed...since society is something more than the sum of its parts.

If you actually look closely you can quote the economists that Keen quotes, which is pretty damning quotes in and of itself since it's vulgar economists admitting they fucked up.

[edit] Wikipedia actually had a surprisingly accurate history of this theorem in Marginalism and how it spawned from the cambridge capital contraversy:
Problems with making the neoclassical general equilibrium theory compatible with an economy that develops over time and includes capital goods. This was explored in a major debate in the 1960s—the "Cambridge capital controversy"—about the validity of neoclassical economics, with an emphasis on the economic growth, capital, aggregate theory, and the marginal productivity theory of distribution. There were also internal attempts by neoclassical economists to extend the Arrow-Debreu model to disequilibrium investigations of stability and uniqueness. However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to insure that the equilibrium is stable and unique are quite restrictive. From This cached image of the marginalism page (http://72.14.253.104/search?q=cache:9qTBDpg37MoJ:en.wikipedia.org/wiki/Neoclassical_economics+debunking+economics+Sonnens chein-Mantel-Debreu+Theorem&hl=en&ct=clnk&cd=2&gl=us&client=firefox-a).
Yeah, basically the issue can be summarized as that the conditions under which the aggregation of individual demand is possible are so restricted as to be nonexistent in practice. This, in turn, voids a very large amount of assumptions made in orthodox economics, in particular those relating to macro-behavior in markets and so-called 'perfect competition'.

[Nusocialist]

Originally posted by McCaine+September 18, 2007 02:54 pm--> (McCaine @ September 18, 2007 02:54 pm)
[email protected] 16, 2007 05:24 pm
It is well known that only under certain conditions the market demand will possess the properties of individual demand. The main condition is that the utility functions have Gorman form, which Keen correctly identifies.

In behavioral terms, this functional form implies that agents are allowed to differ only to a limited extent.

Keen argues that the necessary assumptions are unrealistic (see pg. 27 of his book) and that this demonstrates that methodological individualism is flawed...since society is something more than the sum of its parts.

If you actually look closely you can quote the economists that Keen quotes, which is pretty damning quotes in and of itself since it's vulgar economists admitting they fucked up.

[edit] Wikipedia actually had a surprisingly accurate history of this theorem in Marginalism and how it spawned from the cambridge capital contraversy:
Problems with making the neoclassical general equilibrium theory compatible with an economy that develops over time and includes capital goods. This was explored in a major debate in the 1960s—the "Cambridge capital controversy"—about the validity of neoclassical economics, with an emphasis on the economic growth, capital, aggregate theory, and the marginal productivity theory of distribution. There were also internal attempts by neoclassical economists to extend the Arrow-Debreu model to disequilibrium investigations of stability and uniqueness. However a result known as the Sonnenschein-Mantel-Debreu theorem suggests that the assumptions that must be made to insure that the equilibrium is stable and unique are quite restrictive. From This cached image of the marginalism page (http://72.14.253.104/search?q=cache:9qTBDpg37MoJ:en.wikipedia.org/wiki/Neoclassical_economics+debunking+economics+Sonnens chein-Mantel-Debreu+Theorem&hl=en&ct=clnk&cd=2&gl=us&client=firefox-a).
Yeah, basically the issue can be summarized as that the conditions under which the aggregation of individual demand is possible are so restricted as to be nonexistent in practice. This, in turn, voids a very large amount of assumptions made in orthodox economics, in particular those relating to macro-behavior in markets and so-called 'perfect competition'. [/b]
The guy I ws talking too kept disputing this and simply saying it just made things a little messier and wasn't really important. He even claimed social indifference curves are not used any more.

He said stuff like this.

This is simply wrong. Multiple equilibria makes theory more messy, nothing more. And I don't know where you got the idea that the "social demand" model assumes all agents are considered the same, but that is just not the case. There are representative agent models, but there are many models without that assumption.

[ComradeRed]

Originally posted by [email protected] 18, 2007 06:48 pm
This is simply wrong. Multiple equilibria makes theory more messy, nothing more.
Yes! That's the damn point! In order for economics to work practically in real life situations, it would be so needlessly complicated that it would be absurd.

The vulgar economists reply with the assumption that all agents are, according to their calculations, identical so they can add up the individual demand curves to get the aggregate demand curve.


And I don't know where you got the idea that the "social demand" model assumes all agents are considered the same, but that is just not the case. It's from the Sonnenschein-Mantel-Debreu theorem...he should know this.

The entire point of the theorem is to assume that all the agents are "similar enough" (i.e. identical) so you can simply add up individual demand curves to yield the aggregate demand curve.


There are representative agent models, but there are many models without that assumption. None of which are used in practice, and rarely used in theory.