Talk:Comparative statics

Fair use rationale for Image:Pyat rublei 1997.jpg
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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)