Talk:Mathematical economics

Tautology

Reading the source on Popper, his complaints were that a complete mathematical (or philosophical) system could not make novel predictive statements without making assumptions so broad and forceful that the result could come from the assumptions itself. While this sounds the same as a rhetorical tautology (in the sense that we often see this when people make a defining statement and proceed to argue the truth value of the proposition from the defining statement), Popper clearly meant is as a philosophical constraint on theories.

My feelings for the why the link is proper stem from the History section on logical tautologies and the clear connection alluded by the (seven decades of economic methodology) sourcing. I may be wrong.

Protonk (talk) 21:12, 19 June 2008 (UTC)

What you want is quite clearly a tautology in the informal sense of the word. Tautology (logic) gives a precise definition in the context of formal logic. Most tautologies, when translated into a formal language such as first-order logic, become only what the article calls "validities", but not tautologies. I don't like this technical (ab)use of the word "tautology" at all, but it seems to be general practice. The following are tautologies:

He committed the crime or he didn't commit the crime.

Someone in this room committed the crime or nobody in this room committed the crime.

The following is unfortunately not a tautology:

Everybody in this room either committed the crime or did not commit the crime.

I am quite sure that Popper didn't want to make this distinction. If you feel that you must link to a formal(!) logic article, then it would have to be the (non-existent) one for validity. But I am quite sure that what Popper means is tautology in an informal sense. This is discussed, in passing, in tautology (rhetoric).

The best solution would be to add a discussion of the informal meaning to tautology (logic), but I am not going to do this because I only have a PhD in mathematical logic, while this is philosophical formal logic. --Hans Adler (talk) 21:34, 19 June 2008 (UTC)

Sorry for the delay. I don't have a phd in mathematical logic or otherwise formal logic (I actually don't have a phd in anything), but I'll try and make an argument nonetheless. Quotations are from Boland, L. A. (2006) Seven Decades of Economic Methodology. pp. 219-223 In: I. C. Jarvie, K. Milford, D.W. Miller Eds Karl Popper:A Centenary Assessment. London:Ashgate Publishing p. 219 unless otherwise noted. the full text of the article is available here.

Instead, the 1940s and 50s were the battle ground for the movement to make economics a mathematical science. A main criticism of mathematical economics was that mathematics could only provide tautologies – which were claimed to be statements or theorems that are true by virtue of their logical form rather than their empirical content. More correctly, a tautology is a statement which does not depend on the definition of its non-logical words but only on its logical words such as ‘and’, ‘or’, ‘is’ and ‘not’. Thus, a tautology is a statement which is true simply because one cannot conceive of a counter-example. For example, the statement ‘I am here or I am not here” is true regardless of who ‘I’ am or where ‘here’ is." "At the time of Hutchison’s [Here Hutchinson is an exponent of Popper's views] launch of testability-directed methodology, Paul Samuelson was beginning to write his Ph.D. thesis that promoted the mathematical basis for all economic theory. And Samuelson directly confronted the critics by saying that his version of mathematical economics could not be dismissed as a bunch of tautologies because he would require economic theorems to be testable and thereby conceivably false. For Samuelson, a testable theorem is ‘operationally meaningful’ by which he merely meant that it must be ‘refutable in principle’. To be refutable in principle, a theorem could not be a tautology. QED"

It is 100% possible that the confusion has arisen from my interpretation of this passage (and others), my communication of that interpretation on the page or my further confusion in attempting to explain it to you. If that is the case, I'm sorry. But as I see it this doesn't result in the proper link being to the current article on rhetorical tautologies. I notice that you are removing inappropriate internal links to logic articles. That is an important and valuable cleanup task. But I don't feel you are correct in this instance. At the very least (as you suggest above), a link to tautology_(rhetoric) is inappropriate. the tone and subject of the article don't match the intent of the source or the internal link (in my mind). A new article in logic (should I be correct about the link to rhetorical but incorrect about the link to logical tautology) might be appropriate, but such an article would be wholly out of my scope of competence. So, as I said, if the disagreement here is to the insufficient depth of knowledge I displayed about logic or the subject at hand, please accept my apologies. But as I see it, the link to tautology_(logic) is the proper reading of the source material. Protonk (talk) 16:54, 23 June 2008 (UTC)

Your quotation contains a perfectly reasonable definition of tautology. Until recently I never had a reason to concern myself with this notion, and naturally I thought that this was the definition in formal logic. Unfortunately I was wrong. In my opinion the confusion comes from the fact that formal logic uses a counterintuitive definition for the term. Our article tautology (logic) discusses only this counterintuitive term. It may be that some people, including Popper, work with a more liberal definition of the term. Such people may or may not know that the definition in formal logic is different. The important point for me is that so long as the article tautology (logic) discusses only one (unfortunate) meaning and this article uses the other (straightforward) meaning, such a wiki link contributes to the confusion. It's not about some esoteric distinction; it's a very straightforward problem, as if we were linking the word number from an article such as this one in a hypothetical world in which mathematicians use the word "number" only for positive integers and do not discuss anything else in that article.

Yes, the problem should be fixed on the logic side, but as I said I am not qualified for this, either. I thought that we could fix this by not linking. You don't seem to be happy with this, but I don't know what to do. I can't write the obvious other meaning into the article without any sources, and I already checked my books: They all use the weird meaning. --Hans Adler (talk) 18:36, 23 June 2008 (UTC)

thanks for the reply. I am happy with not linking, though not as happy as I would be were there an article to link to. I think in order to not impute an incorrect meaning into this article (linking to rhetoric) and not generate unnecessary confusion linking to the logic article, we can find a second best solution by temporarily removing the link. Thanks for your help. Protonk (talk) 18:48, 23 June 2008 (UTC)

Copyedit

Hi Protonk, I'm not your GAN reviewer, but I can help you get past the "well-written" criterion. Economics isn't my field, but I'm a fan of game theory and other applications of the field. Feel free to disagree; please put any responses directly under the bullet point that you're responding to. I don't generally cover images or endsections when I copyedit. I'm doing a little more than I usually do for a WP:GAN article because I could easily see this article heading to FAC in the future.

Lead section:

• I removed the Mathematical problem link; I didn't think that page added anything to this article.
• What makes "What use is Economic Theory?" a reliable source? Since most of economics these days has a heavy math component, it should be possible to find peer-reviewed papers to say what you want to say.
• There were two links to Model (economics); I removed the first link.
• I think it's likely your GAN reviewer will want a longer lead section. See WP:LEAD.

Mathematical_economics#History:

• Flavors of English other than British should only use single-quotes when necessary inside of double-quotes; I'll make the changes. (And I will generally make the case to use double-quotes in British English articles, too.)
• It's fine to use a quote to convey the consensus of the field, or the precise or witty language of the leaders of the field. I didn't think the Sheila Dow quote fit that description, so I reworded it.
• I inserted commas before conjunctions joining two independent clauses.
• I inverted the order of "engineering problems" because of potential ambiguity, but please change it if I guessed wrong.
• I went with "Operations research, a newly formed discipline which influenced and was influenced by mathematical economics". To say that it arose from economics is contradicted by the sources over at that article (and by my one operations research professor at college); it initially was concerned more with logistics and engineering.
• I added the word "paradigm", and having done that, I felt that "and an attempt to turn economics into a normal science" was probably redundant. Let me know if there's some deeper concept from Kuhn's work that you want to work into the text.

Mathematical_economics#Application:

• I took out "According to the Editors, each is a non-specialist journal" because it seemed to be implied by "diverse" in the next sentence, but feel free to revert. This is a judgment call, but if it were my article, I would give more than just saying "non-specialist" or "diverse"; I would list the subject areas accepted or solicited by the journals.
• This is a little beyond "copyediting", but the part of this article I would like to see expanded for GAN, and that would probably have to be expanded for FAC, is the sentence "Mathematical economics provides methods to model behavior in diverse, real world situations, including international climate agreements, reactions to changes in divorce laws, and pricing in the futures markets for commodities." This seems to me to need a section to itself, justifying and illustrating that proposition.
• "mathematically competent professionals are needed in industry and government for dealing with the subject" seems ambiguous to me. Do you mean that you probably can't get a job without the mathematical background, or that these people are or were in high demand at some time (specify the time)?
• "Graduate programs in economics and finance programs in graduate schools of management require strong undergraduate preparation in mathematics": the reference, a presentation by Sheila Dow, doesn't establish this (probably). A few links to entrance requirements on university websites that are known for strong economics programs would work for me; even better would be some reliable source that summarizes this information.
• "empirical interpretation" is not a common phrase (12k Google hits). Is that the way your sources describe it, or did they say "interpretation of empirical data"?
• I think the "Warwick Department of Economics" probably won't qualify as a reliable source, and the sentence will have to go. If it does qualify, then you want to change the word "recent" to "in 2008". But a departmental study could be used to answer questions about what that university is looking for in applicants.

Mathematical_economics#Criticism of mathematical economics

• Looks good.

Mathematical_economics#Mathematical economics applications and the section after:

• One of the style guidelines specifically mentioned at WP:Good article criteria is WP:Embedded list; check it out. Raw lists (including in See also) can be very useful in B-class articles by letting everyone know which other articles to look at; material often flows between articles. When you get up to the GA level of maturity, you're supposed to be largely finished with this process of shifting information in and out of this article, and most wikilinks should be either discarded or worked into the proper section, accompanied by context. When you really do want a list, it's better if the list looks more like the lists in WP:Embedded list, or sometimes lists work best when they're converted into tabular form.

Okay that's it. Best of luck with your review, and I'll be happy to answer questions. I enjoyed learning more about the subject. - Dan Dank55 (talk)(mistakes) 02:43, 16 August 2008 (UTC)

• thanks for the questions and updates. I just got back from being out of town, so I'll try to answer these questions more fully later tonight or tomorrow. Thank you for your help and attention to detail. :) Protonk (talk) 02:29, 16 August 2008 (UTC)

Some reponses to questions above:

• "what use is economic theory" is used in here for two reasons. One, I can't find (or don't know of) too many histories of economic theory (or encyclopedias of economic theory) aside from the new palgrave (and the Handbook of Economics, which each volume is 3 weeks away on interlibrary loan), so introspective discussions of 'mathematical economics' as a concept are hard to come by. Two, Hal Varian is a reliable source on economics, no matter the venue. I shouldn't probably find out what conference he gave that talk at and cite it properly.

• Regarding your rewording of normal science' to paradigm. That is probably ok for now because I didn't have too much content to go on with the normal science bit. I'll re-insert it with some content when I can find a source talking about the transition of economics from some Baconian style inquiry to a narrow, normal science.

• "Mathematical economics provides methods to model behavior in diverse, real world situations, including international climate agreements, reactions to changes in divorce laws, and pricing in the futures markets for commodities"--That sentence was meant (at the time) as a kind of end to a section with some examples for flair. I'll take a look at the article itself and see if I can't make a small section from that. The papers (and website) linked are pretty interesting.

• the warwick paper. that is probably not an impeccable source, but again the author is pretty reliable. I have to see the 'followon' paper in Econometrica (here), maybe that is helpful (although it seems like that is more of a cautionary tale to university hiring committees.

• You are right about operations research. Not sure why I worded the sentence that way.

• "Graduate programs in economics and finance programs in graduate schools of management require strong undergraduate preparation in mathematics" I will look for a source on this, because it is certainly true. I feel slimy enough linking one course catalog in this article, I probably won't link another. Wow. I guess Sheila C. Dow wrote a book on methodology: Economic Methodology:An Inquiry (link). Maybe I should check that out of the library. :)

• "mathematically competent professionals are needed in industry and government for dealing with the subject" -Reworded.

Thanks for the help so far. I'll see what I can check out of the library. Protonk (talk) 02:54, 16 August 2008 (UTC)

More

Very nice work. I'm not good with advice on images, but it seems to me that a couple more images that should be easy to find might help nail the WP:GAN. You might illustrate your sentence "Much of classical economics can be presented in simple geometric terms or elementary mathematical notation" with a simple supply-demand curve, contrasted with some more intricate 3-D plot. If that seems too dry, most of the articles on notable economists have pictures you could borrow. - Dan Dank55 (talk)(mistakes) 02:24, 18 August 2008 (UTC)

Thanks for the continuing help. I'll try to gin something up in inkscape, but I can't think of a good visual for modern mathematical economic concepts. Take the Edgeworth box portrayed in the article. The concept there works fine with more than two actors, but the box becomes vectors in Rⁿ space. Maybe the black-scholes smile? Protonk (talk) 03:51, 18 August 2008 (UTC)

Or the "Heat equation, to which the Black–Scholes PDE can be transformed." Wikipedia economics articles have very few images, I see, but math articles have tons of 2-D and 3-D representations. - Dan Dank55 (talk)(mistakes) 04:15, 18 August 2008 (UTC)

That's a really good idea. I just picked up a book on partial differential equations and the heat equation is the first thing discussed. Protonk (talk) 04:20, 18 August 2008 (UTC)

• The addition of Adam Smith was appropriate, I thought. Reviewers at GAN and especially FAC tend to like historical contexts, especially historical contexts they understand; throwing in a portrait of Adam Smith and one of the 19th-century guys will help your case, I think.
• I don't understand what the sentence that includes "as the highest level of mathematical technique" means.
• What you've done covers my concerns (and a lot more), except for the list of economists. It's actually easier to review for FAC than for GAN because GAN is more flexible, but it's hard to guess how flexible. At FAC, you'd probably want to turn that list into a table, perhaps with the birth and death dates in the second column and a one (or at most two) sentence description of their importance in the third column. Btw, even the See also section would probably be too long for FAC (although it's probably fine for GAN). At FAC, the reviewers (if they're diligent and consistent) would look at the links and think about whether any of them could be moved up into the text, perhaps as a See also link directly below the relevant heading or subheading, or perhaps just as a link, with text that explains the relationship of the link to this article.
• In summary, a very nice article. Your GAN reviewer might have a few requests but I don't see any big problems at GAN here.

- Dan Dank55 (talk)(mistakes) 13:10, 18 August 2008 (UTC)

List of economists

I see what you mean about that. I'm going to try and flesh out the early 20th century history bit first and then I'll try to come up with a short blurb for each economist on the list (and prune as necessary). Protonk (talk) 14:32, 18 August 2008 (UTC)

Structure

On the advice of Jay Henry, I've checked out a few mathematical economics textbooks to get a feel for the basic structure of a course on the matter.

This is from:

• Nicola, PierCarlo (2000). Mainstream Mathermatical Economics in the 20th Century. Springer. ISBN 354067084X.

I:Prolegomena
 1. Cournot, Walras and Edgeworth
II:The founding Years (1900-1949)
 2. Pareto and General equlibrium
 3. Classical General equilibrium
 4. Wald and existence proofs
 5. Early game theory
 6. Early multi-sectoral growth
 7. Dynamic modeling
 8. Iring Fischer and Interest theory
 9. Widening General Equilibrium Theory
 10. Applied general equilibirum
III: Extensions, Fitness and formalism (1950 on)
 11. Walras ''cum'' Leontief
 12. From classical to modern analysis
 13. Linear programming and extensions
 14. Consumer's analysis
 15. Firm's analysis
 16. General competitive equlibrium
 17. Stability and more
 18. Regular economics
 ... it continues for a while

I think this is a little helpful, insofar as it points to some good ways to break the article history, applications and examples down. Nicola's breakdown is by no means the only one but I picked his book specifically because it made an attempt at grounding the chapters in history. Perhaps a new layout could be:

   * 1 History
          o 1.1 Marginalists and the roots of neoclassical economics
          o 1.2 General equilibrium and the interwar years
          o 1.3 Emergence of modern mathematical economics
            o 1.3.1 Econometrics
    * 2 Application
          o 2.1 Early Models of competition
            o 2.1.1 Perfect competition
            o 2.1.2 Monopoly
            o 2.1.3 Duopoly
          o 2.2 Models of equilibrium
            o 2.2.1 Walrassian equilibrium
            o 2.2.2 IS/LM
          o 2.3 Models of choice
            o 2.3.1 Game theory and oligopoly
            o 2.3.2 Public choice
          o 2.4 The theory of the firm
    * 3 Relationship to the discipline as a whole
          o 3.1 Mathematical economics as methodology
          o 3.2 Mathematical finance
          o 3.2 Views from inside and outside the professon (maybe, if I can find stuff)
    * 4 Criticism of mathematical economics
    * 5 Mathematical economists
          o 5.1 19th century
          o 5.2 20th century
    * 6 See also
    * 7 Notes
    * 8 External links

Thoughts?

Looking good. In my opinion, a nice structure might start by following the one included in the Historical Introduction of the Elsevier's Handbook of mathematical economics (written by Arrow and Intriligator, Vol. 1, p. 1):

  * 1 History
         o 1.1 The calculus-based marginalist period (1838-1947)
         o 1.2 The set-theoretic/linear models period (1948-1960)
         o 1.3 The current period of integration (1961-1984)

OK, maybe section 1.3 should not be named "current" since the quoted handbook was published in 1984! Nonetheless, whatever the title of that section be, I suggest to include at least these topics there: The theory of diversifiable risk sharing (as in Karl Borch's and Christian Gollier's work); and Social choice theory (as in Sen's work).

In section 1.2, an "Arrow-Debreu Model" subsection would be useful, since it has had a tremendous impact on microeconomic methodology over the last decades.

I agree with the mathematical economists section. French economist Maurice Allais deserves a special spot, of course.

Finally, I just want to say that the whole econometrics/mathematical economics marriage seems ackward to me... sure, it has a historical meaning, but nowadays there are very few mathematical economists who are profficient at econometrics and viceversa.--Forich (talk) 06:15, 15 October 2008 (UTC)

Econometrics

A question has been raised about the distinction between mathematical economics and econometrics in this article. I originally did not distinguish between the two but started to due to some sources making the distinction. What comes immediately to mind is the Stigler article (Stigler, George J. (April, 1995). "The Journals of Economics". The Journal of Political Economy. 103 (2). The University of Chicago Press: 339. ISSN 0022-3808. Retrieved 2008-08-17. {{cite journal}}: Check date values in: |date= (help); Unknown parameter |coauthors= ignored (|author= suggested) (help)). He notes a distinction between Econometrica and other mathematical economics journals and relates some stories about Keynes and other journal editors refusing to publish material that would today be considered econometrics in the AER and QJE. I'll see which other sources cited here distinguish between econometrics and mathematical economics. Protonk (talk) 20:41, 20 August 2008 (UTC)

Thanks for bringing the matter up. In further support of the distinction, there is JEL: C6 (under JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories). It lists some mathematical methods as applied to non-game-theory econ applications of "mathematical methods." Math methods are distinguished from other subcategories under "econometric methods." The JEL usages suggest at least the convenience of distingushing math econ and econometrics. --Thomasmeeks (talk) 20:07, 21 August 2008 (UTC)

• Oh, also Oskar R. Lange makes this split explicit in his review of economic modeling here. Protonk (talk) 20:59, 26 August 2008 (UTC)

It's been awhile, but let me extend congrats on well-deserved GA outcome. I did not press the point earlier, but there is a distinction in usage between 'mathematical economics' & 'econometrics'. The unwary reader might get the impression econometrics is a proper subset of math econ. Textbooks on the respective subjects indicate otherwise. Debreu's "mathemtatical economics" article in The New Palgrave does not even mention econometrics. It's true that Econometrica has always published a lot of math econ articles (in addition to articles on econometrics). Still, usage of the 2 terms is distinct. It is also reflected in the JEL codes as indicated above and in hierarchical The New Palgrave: A Dictionary of Economics#Subject Index (1987) where the articles are their respective headings. That subsection is ine history section of the article. There's really no need to go into the history of econometrics as such (unless it is merely to mention their co-development. --Thomasmeeks (talk) 21:40, 23 May 2009 (UTC)

Withdrawn GAN

I've withdrawn the GAN as I've discovered that the scope of the article doesn't come close to covering the scope of the subject. I'll expand it (as best I can) in the next week or so to look like the structure seen above. Any help is much appreciated. Also, anyone that can get Economic Methodology by Dow would be a help, as my interlibrary request for it got denied. Don't they KNOW I need to edit wikipedia?! Protonk (talk) 15:27, 21 August 2008 (UTC)

As an update, I've started a draft page, User talk:Protonk/Draft of mathematical economics for broad reworking of the history and applications sections. Changes are welcome there but it is prone to change rapidly. Protonk (talk) 20:11, 21 August 2008 (UTC)

General sources

Here are a few general sources that might be helpful in addition to those already in the article.

For a classic discussion: F.Y. Edgeworth (2008), "mathematical methods in political economy," The New Palgrave Dictionary of Economics, 2nd Edition, earlier (with "method" in the title) at (1987) The New Palgrave: A Dictionary of Economics , v. 3, pp. 404-05, and (1987) Palgrave's Dictionary of Political Economy

For later treatment: Gerard Debreu (2008), "mathematical economics," (Abstract.) The New Palgrave Dictionary of Economics, 2nd Edition.

The JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories list some mathematical methods as applied to non-game-theory applications under JEL: C6. Game theory has its own subbategories. --Thomasmeeks (talk) 20:13, 21 August 2008 (UTC)

GA Review

This review is transcluded from Talk:Mathematical economics/GA1. The edit link for this section can be used to add comments to the review.

I will review the article. Give me a few hours to read it over a few times. --Patrick (talk) 16:39, 19 September 2008 (UTC)

First read

After reading this a few times, I have to say this is a very good article. So far I only have a few comments. More, I think, are coming. I have not reviewed the sources yet.

• Does citation 3 cover the entire first part of the paragraph?

• Yes. Schumpeter talks a bit about Achenwall (but it kind of goes into a diversion), then begins to talk about Petty. Protonk (talk) 22:21, 21 September 2008 (UTC)

• There doesn't seem to be a pattern with redlinks and titles of published works. Some are linked, while others are not. While it's clear that some works will never have an article, there are others where it's a bit more likely.

• There wasn't a reason. I wikilinked those redlinked books while this was a userspace draft, just figuring that they were notable (they are). Someone will eventually make an article out of them. I tried to not wk link to anything that will "never" have an article. Protonk (talk) 22:21, 21 September 2008 (UTC)

Cheers. --Patrick (talk) 00:30, 20 September 2008 (UTC)

Copyediting

Protonk and Patrick, I'll be happy to give this a quick FAC-level copyedit if you like; let me know. I copyedited this article once before. The first think I see is that the lead is just a tiny bit too short per LEAD. I've had bad luck with trying to guess which facts in an article were most important to the editor; if you guys want to suggest what's important, I'll think about how to add it. - Dan Dank55 (send/receive) 21:49, 23 September 2008 (UTC)

• I think that is me being lazy. I updated the article and haven't updated the lead yet. the basic ideas are covered but I need to sit down and fix it up some night. Protonk (talk) 23:33, 23 September 2008 (UTC)

I'm totally happy with my big pile of 0.7 crap, so take your time :) - Dan Dank55 (send/receive) 00:00, 24 September 2008 (UTC)

Sorry about the delay in the final review. I was unexpectedly called for a business trip but I do think that this article should be put up for FA status. --Patrick (talk) 18:35, 27 September 2008 (UTC)

Final Review

GA review – see WP:WIAGA for criteria

---

Great article. I think this article should be put forward soon for FA status. Well done. --Patrick (talk) 18:33, 27 September 2008 (UTC)

1. Is it reasonably well written?

   A. Prose quality:

   B. MoS compliance:

2. Is it factually accurate and verifiable?

   A. References to sources:

   B. Citation of reliable sources where necessary:

   C. No original research:

3. Is it broad in its coverage?

   A. Major aspects:

   B. Focused:

4. Is it neutral?

   Fair representation without bias:

5. Is it stable?

   No edit wars, etc:

6. Does it contain images to illustrate the topic?

   A. Images are copyright tagged, and non-free images have fair use rationales:

   B. Images are provided where possible and appropriate, with suitable captions:

7. Overall:

   Pass or Fail:

Congrats on the GA

If you are interested in heading to A-class or FAC with this one, let me know, I'd love to help. - Dan Dank55 (send/receive) 20:42, 27 September 2008 (UTC)

• I'm looking to send it to A class review. I'm temporarily burned out on the article right now, but there is a lot of room for improvement. I did enjoy discovering that...I have a LOT to learn about economics, although writing this article is helping me in my Mathematical econ. class. :) Protonk (talk) 21:33, 27 September 2008 (UTC)

Waiting works for me, A-class works for me. I've got 0.7 stuff til Oct 20. - Dan Dank55 (send/receive) 21:54, 27 September 2008 (UTC)

For the record, there is currently no FA general-field article in Econ. The only current general-field WP:Good article-rated in Econ is here per http://en.wikipedia.org/wiki/Wikipedia:Good_articles/Social_sciences_and_society#Economics_and_business -- a stunning achievement -- with most of the non-minor Edits due to Protonk, which took the article from here to here (that is, shortly after GA status). Protonk continued making careful, not-infrequent Edits thereafter. P's last 1.5 sentences above evince an attitude that doubtless contributed to the success of the outcome. -- Thomasmeeks (talk) 22:26, 19 July 2010 (UTC)

Above are updated & added links, an added last phrase, and 2 sentences. --14:09, 22 December 2010 (UTC)(UTC)

In mathematical economics, GA status was awarded yesterday to the Shapley–Folkman lemma, which describes the head-aches of non-convex sets, largely motivated by economic applications. Editing (especially copy editing) would be welcome! Cheers, Kiefer.Wolfowitz (talk) 09:52, 20 January 2011 (UTC)

Odd Paragraph

Is it just me, or does the following paragraph fail to relate to the topic:

Around the end of the 19th century, the effort to place mathematics on secure logical foundations reached its most ambitious heights with the publication of Principia Mathematica by Russell and Whitehead. In 1918, David Hilbert continued the call for a complete axiomatic system in mathematics.[9]. Although the ultimate goal of a complete, consistent and self-contained mathematical system was ultimately shown by Godel to be unachievable, economists continue to regard mathematical rigor as a desirable objective.

I think it should be removed 70.61.48.113 (talk) 19:42, 29 March 2009 (UTC)

Criticisms of mathematical economics

I'll make a few comments:

• The (lead) discussion of Hayek's assertions is not helpful to the reader. It should be removed (as a cranky theory, imho) or expanded.
• The discussion seems to reflect the obsessions of the 1950s (Popper and Friedman, etc.), but don't discuss contemporary discussions of mathematical economics.
• One of the main criticisms of mathematical economics was by Marxism-Leninism. There was a nice article in Journal of Political Economy called "Karl Marx and Mathematical Economics" , about the Communist campaigns against mathematics (more advanced than used in Das Kapital):

Karl Marx and Mathematical Economics, Leon Smolinski, The Journal of Political Economy, Vol. 81, No. 5 (Sep. - Oct., 1973), pp. 1189-1204.
Any biography of Leonid Kantorovich discusses the problems of using mathematics, in the U.S.S.R. which was most intense during the time of Stalin; he has an autobiographical essay "My Journey in Science" which recounts him being denounced and compared to "the fascist Pareto" during the most repressive years.

• Another problem of mathematical economics stems from the Humboldtian sibling rivalry between the natural sciences versus humanities & social-sciences. In some European countries, especially Sweden, social scientists have long received inferior mathematical education while in gymnasium.
• There is a related problem, worth mentioning: In England, economics grew out of moral philosophy, and was conceived as a non-historical and a priori science. Edgeworth and Marshall were hostile towards (German) economic history, and took various actions against the development of statistical methods. (Mirowski's book of Edgeworth's writings discusses this.)

Thanks. Kiefer.Wolfowitz (talk) 21:21, 12 January 2010 (UTC)

This is about 6 months late, but I'll attempt a reply. I don't think Hayek's criticism is cranky or iconoclastic in this regard. I'll agree that the LEDE is too short and a longer lead might not put so much focus on the that particular criticism. However, the core critique that human behavior is not well modeled by physics remains--especially after the financial crisis of 2007/8.

As for the historical school and "physics envy" points, I agree completely. I don't know if I'll make any substantial revisions to the article, but please feel free to update or fix it as necessary. Protonk (talk) 20:03, 13 July 2010 (UTC)

Uh Hayek is a nobel prize laureate. You can disagree with him but his ideas were obviously important at one time or another. Actually it is quite amusing how you talk so highly of Marx with his theories have been proven to be an abject failure. Hayek has been vindicated in many regards and well respected by esteemed economist such as Milton Friedman. —Preceding unsigned comment added by Sabaton10 (talk • contribs) 11:57, 15 September 2010 (UTC)

Editor Sabaton10, your comments puzzle me. Kantorovich was denounced as a mathematical fascist by Stalinists; these same criticisms are parroted by many anti-math leftist economists in "western" countries. My stating that these criticisms are common (like the common cold) does not imply their validity, unless you wrongly impute to me a belief (shudder!) that Stalin or The Monthly Review or URPE be infallible --- a false belief that I disavow. I suggest you read Smolinski, who describes the Stalinist campaign. Thanks, Kiefer.Wolfowitz (talk) 23:51, 15 September 2010 (UTC)

I added references that discuss the Communist/Stalinist campaigns against mathematical economics, previously noted: Kantorovich and Polyak. Kantorivich's abbreviation of prices as O.O.O. was particularly brave/humorous during Stalin's dictatorship. Kiefer.Wolfowitz (talk) 23:49, 11 December 2010 (UTC)

Use of honorifics/titles with names

I tentatively added "Sir" to both R.G.D. Allen and John Hicks's names in the list of MEs to be consistent with its use for Mirrlees. (Their WP articles show them as having been knighted, although Hicks's article doesn't give his specific honor/order. Their articles also refer to them as "Sir" in the lead sentence.)

I have no strong feelings one way or the other about whether to use of honorifics and titles for British (and possibly other) economists, e.g., Lord J.M. Keynes (1st Baron Tilton). Clearly, though, usage should be consistent throughout the article, especially in such a list. --Jackftwist (talk) 19:37, 13 July 2010 (UTC)

• I'd prefer not to have a list of economists, especially since what constitutes a mathematical economist has changed so radically over the past 100 years. But I don't have the motivation to remove the lists made by other folks. I also am ignorant of the particulars of our MOS for names, so I'll defer to your judgment on that subject. Protonk (talk) 19:59, 13 July 2010 (UTC)

• Consistency in a list might begin by at least not adding an honorific not already in the title. The New Palgrave does not use such in titles. And it has strong British roots. Usage within the article is different from its title. Wikipedia:Naming conventions (royalty and nobility)#British nobility says

4. Titles of Knighthood such as Sir and Dame are not normally included in the article title: e.g. Arthur Conan Doyle, not "Sir Arthur Conan Doyle" (which is a redirect). However, Sir may be used in article titles as a disambiguator when a name is ambiguous and one of those who used it was knighted, e.g. Sir Arthur Dean. A person's full title (including both prefix and post-nominals) should be given in the article itself. (Remember that honorary knights – roughly, those not from the Commonwealth – are not called Sir, and that knights bachelor have no post-nominals.)

So, that guideline is to drop the "sir" in the article title. --Thomasmeeks (talk) 21:04, 13 July 2010 (UTC)

Criticisms of mathematical economics — or of non-empirical economics?

The "criticism" of Hayek can stay (although one wonders whether engineers have to suffer through such criticism of the role of calculus in their practices).

Most of the noted criticisms of mathematical economics are not criticisms of mathematical economics per se. They are rather criticisms of economics, as neglecting empirical theory construction and testing. Those criticisms should be moved off.

Could somebody find better criticisms of economics?

• Keynes's decadent sophistry shows the worst aspects of his Brittish upper-class breeding and public-school education.
• Heilbroner was a famous para-economist, but a half-coherent quote in an interview doesn't belong in an encyclopedia article.

For example, Martin Shubik wrote an entertaining criticism of microeconomics and the Oskar Morgenstern wrote a much sharper critique of actually existing economics in the 1970s. There was an American Economic Association blue-ribbon commission (c. 1993)that complained that grad programs rivaled McDonald's in their standardization, and rivaled metaphysical academies in their divorce from practice. Such criticisms would better serve the public than Keynes's snobbery and Heilbroner's dotage.

Sincerely, Kiefer.Wolfowitz (talk) 04:04, 12 December 2010 (UTC)

Agent-based computational economics

There is not citation saying that this is an important part of math econ. There is not citation of a competent good textbook in math econ with a chapter on agent based econ.

It's all very interesting, but computer experiments are as old as Schelling and Rapaport, and were old hat in the 1970s. At least Axelrod's updating of Rapapport had a theoretical point, correcting Mancur Olson et al on cooperation. (But see Smale for a math approach.)

Why not move the section to computational economics?

This is not the only article to feature agency/based econ, or what is sometimes called simulations by honest people, but this seems to be the least excusable.  Kiefer.Wolfowitz 20:55, 19 January 2012 (UTC)

Let me label points below if reference to them is necessary.

1T. May things have cooled since the above Edit. On the last 2 words the ("least excusable"), for the benefit of other readers, KW re-introduced computational economics (CE) to the Template:Economics sidebar. So, given the close relation of CE to agent-based computational economics (ACE), I’m a bit surprised that the above points would be raised in such manner. I have argued at Template talk:Economics sidebar#Proposed re-simplification of 'Technical methods' section from 7 to 4 links below heading that CE should be moved down there from the "Technical methods" section to help re-simplify that section. May KW's points indicate no stated opposition to such re-simplification (which would involve no backing off principle -- a lot has happened in the interim to warrant such resimplifacation).

2T. Per Applied mathematics#Economics, few of the math econ textbooks there have game theory sections. That does not mean that game theory is not a noteworthy part of math econ. Textbook references there on math methods of ACE include:

• John Stachurski, 2009. Economic Dynamics: Theory and Computation, MIT Press. Description and preview.
• Kenneth L. Judd, 1998. Numerical Methods in Economics, MIT Press. Description and chapter-preview links.

Of the latter, there is Avinash Dixit's testimonial:

"Judd's book is a masterpiece which will help transform the way economic theory is done. It harnesses the computer revolution in the service of economic theory by collecting together a whole array of numerical methods to simulate and quantify models that used to be purely algebraic and qualitative."

Dixit is author of among many other works the gem, Optimization in Economic Theory, 1990, 2nd ed., Oxford (description and contents preview), and so, well situated to comment on the matter. He is by no means dismissive of simulation used in ACE. Reasons why other math econ texts don't have much on CE/ACE may that the latter builds on the former & is distinctive enough to warrant separate treatment, just as game theory textbooks or economics handbooks do.

3T. Agent-based computational economics is a distinctive constituent and method of "computational economics" of which in math econ is important enough to warrant:

• referencing in JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories within: JEL: C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling, which includes:

JEL: C63 - Computational techniques; Simulation modeling

• an article "agent-based models", similarly JEL classified, in The New Palgrave Dictionary of Economics (there is no such article for "computational economics").
• the most recent of the 2-volume Handbook of Computational Economics: v. 2, 2006. Agent-Based Computational Economics, Elsevier (Description & and chapter-preview links).
• other supportive references at Mathematical economics#Agent-based computational economics, including by recent Nobel laureates in econ and leaders in math econ.

As to the last, I don't believe that most persons who peruse the links there would be very cautious about dismissing ACE, including economists, even if they don't choose to add it to their own repertoires. --Thomasmeeks 13:41, 16 March 2012 (UTC) [Correction per strikeout in last sentence above. 10:38, 20 March 2012 (UTC)]

Name one theorem (with a proof) in this area. If it doesn't have a theorem, how is it mathematical economics?

It is an area of computational economics, often with strong ties to macroeconomics or industrial organization, I suppose.  Kiefer.Wolfowitz 14:21, 16 March 2012 (UTC)

4T. A question-begging demand, IMO, which Avinash Dixit (per his quotation at 2T above), presumably would be untroubled by, given his expertise in more conventional methods of optimization, which certainly includes theorems. The same Kenneth L. Judd whose whose CE-methods textbook Dixit recommends answers the above question in "Computationally Intensive Analyses in Economics," Handbook of Computational Economics, v. 2, ch. 17, pp. 881-893 (pre-pub PDF).

5T. A search of The New Palgrave Dictionary of Economics Online for "computational economics" brings up a link to "agent-based models" (a variant name of ACE) at the top of the hits list of 9 (http://www.dictionaryofeconomics.com/search_results?q=%22computational+economics%22&edition=current&button_search=GO) and per (3T) above, at JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories under JEL: C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling. Of course ACE is a method of mathematical economics. And of course ACE is related to macroeconomics and industrial organization among others, as the linked fn. for Mathematical economics#Agent-based computational economics exemplify, beginning with Leigh Tesfatsion, 2006. "Agent-Based Computational Economics: A Constructive Approach to Economic Theory," ch. 16, Handbook of Computational Economics, v. 2, Agent-based Computational Economics, pp. 831-880, Abstract and pre-pub PDF. For many other JEL Econ sub-areas that ACE has been applied to, see beginning of each remaining chapter therein (Description and chapter-preview links).

6T. Per (1T) above, other readers may still be interested as to why KW put computational economics (CE) in the Econ sidebar under a heading link to JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories if he did not think it was mathematical and important. By the measures of (5T), ACE is not only important in CE but the most important aspect of CE considered as an economic methodology. --Thomasmeeks (talk) 21:17, 18 March 2012 (UTC) --10:38, 20 March 2012 (UTC)

Dr. Krawczyk's comment on this article

Dr. Krawczyk has reviewed this Wikipedia page, and provided us with the following comments to improve its quality:

I am not certain whether ‘mathematical economics’ should have a separate entry in Wikipedia. The way I see it, this article provides many links to mathematical economics’ topics, which exist independently in Wikipedia. Also, there exist independent articles in Wikipedia which cover what this article purports to cover, e.g., “Walrasian auction”, “Cournot competition”, Krush-Kuhn-Tucker conditions, and more.

Here are my more detailed comments:

First para …

• “Calculus, difference and differential […] and other computational methods”

Calculus, difference and differential equations etc are not computational methods.

• “.. is its allowing formulation”

Grammar?

• “optimization problems as to goal equilibrium …”

Grammar?

• “Formal economic modeling began in the 19th century ..”

I would say “early 19th” to allow for Cournot’s works.

History … “… in (?) German universities…” At ?

You could mention that ‘statistics’ and ‘state’ have the same root.

• “… if there were n markets and n-1 markets cleared [..] that the nth market would clear…”

…than the nth market

• Nonlinear programming …

While Krush is mention in a link, he is missing from the article.

Finally, I would include in the list of the 20th century mathematical economists J. B. Rosen for his works on concave games and coupled constraint equilibrium (see e.g. http://www.jstor.org/stable/1911749?seq=1#page_scan_tab_contents)

and K. L. Judd https://en.wikipedia.org/wiki/Kenneth_Judd for his works on taxation and multiple contribution to computational economics.

We hope Wikipedians on this talk page can take advantage of these comments and improve the quality of the article accordingly.

Dr. Krawczyk has published scholarly research which seems to be relevant to this Wikipedia article:

• Reference 1: J.B. Krawczyk and K.L. Judd. A NOTE ON DETERMINING VIABLE ECONOMIC STATES IN A DYNAMIC MODEL OF TAXATION. Macroeconomic Dynamics, available on CJO2015. doi:10.1017/S1365100514000868.

• Reference 2: Contreras, J., J. B. Krawczyk, and J. Zuccollo. "Economics of collective monitoring: a study of environmentally constrained electricity generators." Computational Management Science (2015): 1-21.

ExpertIdeasBot (talk) 11:11, 28 May 2016 (UTC)

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@Luizpuodzius:

Como autorevisor caso tu interesses em traduzir e botar para EAB seria grato por isso. att 2804:14C:5BB1:8AF2:8DE1:61A8:EFA6:A1C2 (talk) 00:43, 25 November 2021 (UTC)

The purpose of Wikipedia

I have a background in math and not economics. The example in this article has cool math, but the function choices are made up, the constant choices are made up, and its conclusion is in complete disagreement with the empirical reality of corporate tax cuts and wage growth in the United States over the last 50 years. Does no one see a problem with this? Is the purpose of Wikipedia to provide truthful knowledge to the public, or to provide justification for crap policies to benefit corporations? Dudewaldo4 (talk) 11:51, 25 February 2022 (UTC)

• what you're describing is a problem with how economics uses math and not (as far as I know, it's been many years since I touched this article) a problem with how Wikipedia describes how economics uses math. Protonk (talk) 20:05, 25 February 2022 (UTC)