Talk:Comparative statics

Fair use rationale for Image:Pyat rublei 1997.jpg

Image:Pyat rublei 1997.jpg is being used on this article. I notice the image page specifies that the image is being used under fair use but there is no explanation or rationale as to why its use in this Wikipedia article constitutes fair use. In addition to the boilerplate fair use template, you must also write out on the image description page a specific explanation or rationale for why using this image in each article is consistent with fair use.

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BetacommandBot 11:23, 6 July 2007 (UTC)

It's irrelevant anyway

Besides, what's the purpose of a picture of a ruble on the comparative statics page? --Rinconsoleao 12:47, 6 July 2007 (UTC)

Dubious assertion on cardinal vs. ordinal

At 02:00, 27 September 2010 the following was put in by an editor who has not edited since the end of 2010:

Another limitation is that results are cardinal rather than ordinal; that is, results are not robust to a monotone transformation of the objective function. For economic applications, ordinal results are preferred. In particular, monotone strictly increasing transformations of a utility function represent the same preference relation.

Paul Milgrom and Chris Shannon developed a theory and method for comparative statics analysis using only conditions that are ordinal. The method uses lattice theory and introduces the notions of quasi-supermodularity and the single-crossing condition. The central theorem of monotone comparative statics is:

Suppose $p:R^{n}\times R^{m}\rightarrow R$ and let $x^{*}(q)=\arg \max p(x;q)$. Suppose $|x^{*}(q)=1|\forall q$, 'p' is quasi-supermodular in 'x' and satisfies the single-crossing property. Then

$q\geq r\implies x^{*}(q)\geq x^{*}(r).$

The link to the source is dead.

I have two problems with this:

(1) The statement of the theorem is not accompanied by any verbal explanation, and I can't see why it's relevant in the absence of a lot more explanation.

(2) The assertion that results are cardinal rather than ordinal; that is, results are not robust to a monotone transformation of the objective function is just wrong, unless it's intended to mean something that I'm not catching. If you optimize a monotone increasing transformation of a utility function you'll get exactly the same first-order conditions as if you optimize the untransformed utility function, and so the comparative statics will be exactly the same.

Unless someone objects, I'm going to delete the above-quoted passage in a few days. Duoduoduo (talk) 19:40, 27 April 2012 (UTC)

References