Talk:Sonnenschein–Mantel–Debreu theorem

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This is meant to be a start. Please edit, contribute, and clarify. I've shied away from presenting a mathematical version of a theorem as it's quite complicated and probably not very useful to a casual reader.

This is completely opaque to anyone without significant formal training in economics. Though the page does in fact refer to a significantly complex mathematical theorem, the implications for the discipline of economics are not even close to being understandable. —Preceding unsigned comment added by Valkyryn (talk • contribs) 03:13, 5 November 2008 (UTC)[reply]

Honestly, the implications for the discipline of economics are not that clear even to the economists themselves. The theorem basically means that there could be multiple equilibria. So it sort of depends on how you view the problem of multiple equilibria. If you're an optimist then you shrug your shoulders; as long as there's only a finite number of them we can still use the model to analyze moderate and small shocks and in fact the possibility of multiple equilibria is just a realistic feature, not a bug. If you're a pessimist then you conclude that the theorem implies that the world is too complex and unpredictable for us to be able to say anything concrete about it, give up, and go home. That's at least how I view it.

This is a very obscure subject. Therefore it is not appropriate for someone to read it BEFORE they have done the reading on more elementary economic concepts. Perhaps some "explanations for beginners" could be added, but the nature of the topic means that it will be difficult for the casual reader. LarryStevens (talk) 23:40, 18 February 2009 (UTC)[reply]

What SMD is saying is that general equilibrium theory does not necessarily have unique solutions that can be obtained by aggregating individual economic agents behaviours. Kirman explains that SMD demonstrates this at length and concludes "that general equilibrium theory and the demand theory contained in it have not provided a model that has empirically testable content and thus will allow us to explain economic phenomena". http://www.umass.edu/preferen/Class%20Material/Readings%20in%20Market%20Dynamics/Kirman%20HOPE%202006.pdf The WP article reads as though there is an escape for general equilibrium theory from the ramifications of SMD, and there isn't. Gjocopa (talk) 19:38, 27 December 2013 (UTC)[reply]

I don't think the way Hahn is quoted in the first paragraph is correct. The original quote is "Results most damaging to neoclassical theory have recently been proved ...". "Most damaging" is not the same as "... the most dangerous" Jomichell (talk) 17:01, 17 May 2016 (UTC)[reply]

You're right, I just fixed it :) Montgolfière (talk) 03:33, 15 July 2019 (UTC)[reply]

The last 50 years in growth theory and the next 10 RM Solow - Oxford review of economic policy, 2007

> We know from the Sonnenschein–Mantel–Debreu theorems that the sole empirical implication of a classical general-equilibrium genealogy is that excess-demand functions are continuous and homogeneous of degree zero in prices, and satisfy Walras’s Law. Those conditions can be imposed directly on a large class of macroeconomic models. I have made this point in another context, the example being the monetary macro-models of James Tobin (see Solow, 2004). It applies just as forcefully here. The cover story about ‘microfoundations’ can in no way justify recourse to the narrow representative-agent construct. Many other versions of the neoclassical growth model can meet the required conditions; it is only necessary to impose them directly on the relevant building blocks. pony in a strange land (talk) 18:43, 30 December 2022 (UTC)[reply]