Talk:General equilibrium
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In this view, static equilbrium is totally unsuited for modelling real economies, apart perhaps from traditional societies which have remained stable for centuries.
- By "traditional" are we talking the time of Adam Smith, or Ancient Greece, or what? I'm curious what might be considered a successful application of static equilibrium analysis to a traditional society. If there are no alleged successes along these lines, perhaps even this claim about static equilibrium analysis is too optimistic, and should be toned down. --Ryguasu
"Some think this implies that the Arrow-Debreu model lacks empirical content. At any rate, Arrow-Debreu equilibria cannot be expected to be unique, stable, or determinate." I removed "determinate" as I think it doesn't belong here. The SMD does imply that uniqueness or tatonnement stability is not guaranteed but it doesn't say anything about local uniqueness - which is what I understand 'determinate' to refer to. In fact the index theorem tells us that the number of equilibria is finite and odd (so no continuums). Some folks do think that this gives back some empirical relevence to GE - as long as shocks are not too large we can just focus on local equilibria -- Radek
Radek, I think you are mistaken. Recall that the Arrow-Debreu model uses topological arguments. It is thus supposed to be consistent with a generalized Leontief technology, in which firms in each industry choose among (linear combinations of) fixed coefficient processes. It is my understanding that in this case, Arrow-Debreu equilibrium paths can be indeterminate, that is, lie along a continuum. (You're correct about the meaning of the term "determinate". If I recall correctly, Dixit, for example, argues this conclusion in a late 1970s paper in Oxford Economic Papers. You may be correct in that this is not an implication of the SMD results. I did not change the page because I am not totally confident of my position here. -- RLV
There may be something to what you say, but I can't find the Dixit paper you refer to. Here's all Dixit's papers from OEP, if you have JSTOR access:
The only one that appears to be relevant here is "The Accumulation of Capital Theory" (partly a book review). Skimming it quickly I don't see its connection. The only 'indeterminancy' that shows up there is the usual indeterminacy of the prices due to Walras' Law (you get a normalization). I'll read it more carefully though. And I'm pretty sure that indeterminacy is not an implication of SMD. Usually when it pops up it's in some kind of intertemporal setting with funky capital accumulation (like in a weird OLG model).
Oh, and with respect to your other edit, I'd use the term "strong" rather than "arbitrary" in the sentence "As well as arbitrary restrictions on excess demand functions..." since the restrictions do have an economic interpretation in terms of the weak axiom or whatever, hence are not arbitrary, just very strong.radek
Radek, I'm glad that you expanded on the two fundamental theorems. I added something about indeterminacy that seems to be in tension with your comments on the index theorem. You might find the Mandler reference of interest. (He's written about this elsewhere, too.)
Ok, that sounds about right - with production (especially non convexities) and time weird things can happen. Thanks for the pointer, I'll check that paper out. radek 02:07, 15 February 2006 (UTC)
I don't have access to Mandler's book but I read (quickly, didn't work through the proofs or nothing) some of the related papers on his website (should we add a cite?). I think I get the basic gist of how it works - set of endowments which make for non regular economy is measure zero, but with spot markets and time, under certain conditions, agents can sort of 'manipulate' their endowments (this is related to price taking assumption) in such a way that the beginning of period endowments converge precisely to that set of measure zero, hence you can get indeterminacy. Two thoughs on this: first, I think this is substantial enough that we might want a seperate section on indeterminacy rather than putting it under uniqueness. Then, a good portion of it should go under "Unresolved problems" since this is fairly recent research and more along the lines of "ok, the ball's in your court now" and the issue isn't completly settled (in fact Mandler's got another paper on there which derives some more optimistic conclusions). Any thoughts? And thanks for looking and writing this up.radek 22:41, 15 February 2006 (UTC)
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[edit] Changes in section on Walras
I removed the sentence "Many think Walras was unsuccessful and the later models in this series inconsistent." since "many think" is very umbigous and sort of, well, weasely. Who are these many? Citations? References? (And unsuccesful /= some people don't like it) I replaced it with a short description of what Walras got wrong. I can't be sure that this is what the original referred to so please, discuss here, or clarify in the main article. Same with regards to "inconsistent" - however, if by this is just meant that Walras' didn't solve every general equilibrium problem that can possibly arise, I think it'd be better to just leave it out.radek 21:40, 25 December 2005 (UTC)
On such points. I simply don't see why silly conterversies generated by researchers that have made no contribution to general equilibrium theory, and who obviousely don't understand it should be given such prominance here. In particular, I don’t see why the nonsense by Georescu-Roegen should be highlighted here. Rabee Tourky
Georgescu-Roegen discovered the non-substitution theorem. As far as I am concerned, this theorem is an element of what Walsh and Gram call classical general equilibrium. Georgescu-Roegen also helped develop and criticize activity analysis. So I don't know how one who is aware of the development of GE theory can say he made no contribution to it. Furthermore, when one quotes Georgescu-Roegen, one is not performing original research, but only noting the existence of a pre-existing view. I intend to restore the "nonsense" sometime or other when I get around to it. -- Robert
I know little about Wikipedia but I do know rather more about general equilbrium theory. This article is not a very well-rounded presentation of the topic: it is short on the accomplishments of GET and long on criticisms by rather obscure people, as the bibliography makes clear. The whole thing has a very dated and superficial quality. One would be left with the impression that forward markets in all contingent commodities at the beginning of time (as in Debreu) was actually required for complete markets, when it is a classical result of Arrow that all one needs are enough assets to sucessfully transfer purchasing power across the various states, vastly reducing the requred number of markets. The more recent, but not all that recent, literature shows that repeated trade in long lived assets serves to further reduce the number of assets required for spanning in a major way, and this has provided the theoretical underpinnings of modern derivative asset pricng, which in turn has had a substantial effect on the operation and efficiency of modern financial markets. There is no mention anywhere of computational general equilibrium (CGE) models, a major strand of modern empirical work, which has existed for more than thirty years. There ought to be more recognition that modern dynamic macroeconomic theory is entirely founded on general equilibrium principles, and thereby micro and macro, the two major strands of economics, have been reunited (for better or worse.) Where are discussions of the latest advances: for instance the recent results showing that unlike what one might conclude from Sonnenschein-Mantel-Debreu result, the equilibrium manifold allows one to recover all information about the underlying economy? Who are you people and why do you think you are competent to write about this field? The discussion of Sraffa is completely out of place; whatever his contributions and his effect on your thinking, he has had almost no effect on general equilibrium theory. I think the first occurence of the word decreasing in the paragraph of concern should be increasing. It is hard to say what the paragraph is saying, but comparing the beginning of it with the end of it, I would say there has been a confusion of a movement of a curve with a movement along it. It is unclear whether the problem is confusion in Sraffa's mind or that of the author of this paragraph. It would be a good idea to split the entire article into a section on positive issues and one on normative ones. There is no discussion of the limit results associating the competitive equilibria of large economies with solution concepts of cooperative game theory other than efficiency (core, value, bargaining set) and those solution concepts of noncooperative game theory (Nash equilibrium). A discussion of the special issues that arise (indeterminacy or not) when there is unending time and/or an infinite number of consumers would be interesting. For people who seem so intent on digging up criticisms of general equilibrium theory you ignore some of the more pertinent ones; in your discussion of incomplete markets you emphasize that there might be constrained efficiency, but of course the striking result is that generically there isn't. The one paragraph that does somewhat vaguely refer to extending the Arrow-Debreu contingent commodity device unfortunately refers to temporary equilibria, which is then confounding a rather different and much less mainstream strand of literature.
Please, expand and edit, though it's a good idea to register. Oh, and you should've seen the article a year ago.radek 03:27, 26 April 2006 (UTC)
[edit] Expanded on the two theorems, existance, uniqueness and stability
I provided more details on these aspects of GE, since most research, whether theortical or empirical, as well as most controversies/misunderstandings revolve around them. I tried to keep it as non-technical as possible. Ideally I think this article should have a short verbal/intuitive description of each issue and provide links to more specialized articles for the more technically minded. However, some of these articles do not exist yet (existance, uniqueness, stability) or are inadequate (the two theorems). In particular the section on uniqueness is rather long - partly because it is the most complicated and also because it's the one issue where a lot of people seem to be really confusing things. Relatedly I'll try to write up an article on DMS theorem which it seems like a lot of folks who've never read it refer to for one reason or another often erronously. Cheers.radek 21:05, 17 January 2006 (UTC)
I created a relevant article on Sonnenschein-Mantel-Debreu Theorem. It's sorta rough so any constructive edits are appreciated.radek 08:19, 26 March 2006 (UTC)
I don't think your sentence about getting uniqueness with assumptions weaker than weak axiom of revealed preference or the gross substitutes property is correct, whatever it was intended to mean, which isn't clear, so I eliminated it and replaced it with another which connects with your discussion of the index theorem. There is a lack of precison in much of this discussion: a reader who did not know better would be unable to distinguish WARP for the individual, which follows from simple rationality, from WARP in the aggregate, which is the very strong assumption needed for uniqueness.
That's fine. The imprecision is due to the trade off between too much technical detail and covering the major aspects. The general point was that WARP for excess demand functions and/or gross substitution (although for this one, only in the exchange economy case) are sufficient but not necessary for uniquenees.radek 03:08, 11 April 2006 (UTC)
- The article claims that the two welfare theorems say nothing about existence. However, I believe that the second theorem establishes existence under certain circumstances. am I correct?
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- The assumptions needed for existance and for the second theorem are essentially the same. But the theorems are different in principle.
It is not possible as a matter of logic and its definition to have global stability when there is more than one equilbrium. I think the way it now reads reflects what the original author wishes to say (though the term system stability is not as familar a one as global stability.) The article is a much better one than when last I looked. The reference to CGE models is very appropriate; discussion of cutting edge developments in GE theory is still lacking.
Temporary equilibrium is distinct from sequential equilibrium, which is not clear from the article. I have made a quick effort to draw the distinction -- sequential equilibria are sequences of prices that simultaneously clear all markets, including those not yet open, while temporary equilibria are conditional on expected future prices which need not be market clearing. It is a technical difference but it is one that has prevented temporary equilibria from having much impact.
[edit] Experimental economics
I added a sentence refering to some results in experimental economics in the Unresolved Problems section, but I'm not entirely satisfied with the setting. Genererally Vernon-Smith type results are more applicable to Partial rather than General equilibrium models (for obvious reasons) so I'm not sure it's completely relevant. On the other hand the criticism was the standard one about rationality, information and competition being unrealistic assumptions and Smith's experimental work suggests for whatever reason markets do tend to function as if these assumptions held. So it addresses the criticism. Thoughts and edits are appreciated.radek 03:38, 19 March 2006 (UTC)
[edit] Just wondering
"Georgescu-Roegen cites as an example a paper that assumes more traders in existence than there are points in the set of real numbers." - What is the paper that GR is referring to? I'm suspicious that it should be "integers" or "rational numbers" (i.e. that the paper assumes there's a continuum of traders) rather than "real numbers".radek (talk) 15:52, 6 December 2007 (UTC)
