Monday, July 1, 2013

A couple marginalism thoughts from reading Agnar Sandmo

1. Grant is right - this book does a great job reviewing the contributions of pre-marginalists like von Thunen, Cournot, Dupuit, and Gossen. I knew von Thunen from my undergraduate history of thought class (I did my paper on spatial economics, which goes back to him), and of course Cournot is familiar. I knew Dupuit somewhat through Grant and didn't know Gossen at all. Sandmo is excellent at outlining precisely what each contribute, what each missed, etc. It is impressive in most cases how much more they actually perceived than the marginalists themselves.

2. Here's a nice quote from Jevons that drives home the stupidity of the cardinal/ordinal arguments, because everyone agrees that preferences themselves are ordinal even if we choose cardinal functions to represent them. He writes: "To me it seems that our science must be mathematical, simply because it deals with quantities. Wherever the things treated are capable of being greater or less, there the laws and relations must be mathematical in nature". Of course some things go beyond this ordinality (like prices or quantities), but in terms of preferences, as I've said many times on here before, the preference relations are ordinal, the utility functions (which nobody believes actually exist but are a modeling convenience) are what's cardinal.

3. Menger is presented by Sandmo as being unaware of the advantages of modeling with continuous, cardinal utility functions. The sketch on these authors is sometimes brief so it's not clear why, but he refers to it as something that he was not aware of. It's amazing to see the simply things that early scholars missed, just because it hadn't been discussed much before (Jevons, for example, is described as being just one very easy step shy of a full general equilibrium model of the sort that Walras had. Jevons wasn't a dummy any more than Menger was, but sometimes coming up with this stuff for the first time is tough). So does anyone know if this is true? Does anyone know, for example, if Menger actually said "well you could do it ordinally and you could do it cardinally and ordinally is definitely the right way to do it" - because if he didn't make such a ruling it seems to me (1.) Sandmo is likely right, and (2.) a lot of the Austrian preoccupation with this question is window dressing after the fact on a point that was never particularly important to Menger in principle the way it is important now as a principle. 

17 comments:

  1. Out of curiosity, does Agnar Sandmo's book cite anything by Samuel Hollander?

    But speaking of ordinal utility and cardinal utility...does Sandmo deal with the founding fathers of S.E.U. theory (Bruno de Finetti, F.P. Ramsey, and L.J. Savage) in at least one footnote and with Daniel Ellsberg's critique of S.E.U. theory, only in passing?

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    1. Not yet but they would come later - I'm in the late nineteenth century at this point.

      There is only a chapter or two on post-Keynes economics and I think that focuses on the macro wars and the rise of econometrics.

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    2. I see. Did you see the names of de Finetti, Ramsey, and Savage in the bibliography of the book? And would it be fair for me to guess that Ellsberg's name was absent?

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  2. Does it mention Senior as a pre-marginalist? I thought he was quite important too.

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    1. Those are the four he mentioned in a chapter dedicated to the question. Senior came up in passing before. More precedents were discussed than just those four but they were focused on as the cases that really could have been "the marginal revolution" if intellectual history had played out differently. A lot of it was presented as a sociological problem. They were not operating in communities of economists, they were not writing for economists in a lot of cases and they just weren't taken up by others.

      I'm not deeply familiar with Senior - if you've got the time/interest I'd be interested in hearing about the sense in which he anticipated marginalism.

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    2. Seniors system is based around utility, it's fairly similar to other later types of marginalism.

      Rather than me explaining it, it's easy to read what he wrote, his explanation of his marginalist system is only a few pages long:
      http://oll.libertyfund.org/?option=com_staticxt&staticfile=show.php%3Ftitle=116&chapter=36047&layout=html&Itemid=27

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  3. There is empirical evidence that human preferences are only partially ordered. Some people think that that means that they are irrational, but that's an antiquated notion of rationality. It is notable, I think, that Keynes regarded probabilities as partially ordered.

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    1. Have you read A Treatise on Probability, Min?

      Or any of the following articles?

      http://bjps.oxfordjournals.org/content/44/2/357.full.pdf+html

      http://dx.doi.org/10.1080/02698599408573487

      http://www.torrossa.it/resources/an/2569189

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  4. That's the only thing of Keynes that I have read. :)

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    1. Seriously?

      That's cool but weird :)

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    2. Min: I see. Are you a mathematician by training, or what? Have you seen any of the articles that I linked you to in the previous comment I had before?

      Daniel Kuehn: How is it weird? A Treatise on Probability was actually supposed to be J.M. Keynes's second publication after Indian Currency and Finance, but that didn't happen thanks to the assassination of Archduke Ferdinand of Austria. It had to be delayed for publication due to censorship issues, and only came out in 1921. Also, as you ought to know, Daniel Kuehn, his 1921 book is actually of immense importance to his later thought...there is a reason he has two footnotes in The General Theory referring to Chapter VI of A Treatise on Probability.

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    3. It's weird because it is harder to obtain and more peripheral to what most people think of when they think of Keynes.

      How many people do you know who have only read the TP?

      Min is my first. Do you know any others? The relative lack of such people seems as good a reason as any for calling it "weird" :)

      I'm certainly not arguing that there aren't important ideas in the TP.

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    4. Daniel Kuehn: Fair enough. There aren't that many people that have read A Treatise on Probability cover to cover, and properly understand it. I can name three people off the top of my head, and two of the three I have corresponded with. Two of the three, IIRC, read A Treatise on Probability as their very first book by J.M. Keynes.

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  5. I think some Austrians put a lot of weight on the cardinal v. ordinal point because they don't really get why other economists use cardinal measures just for the sake of illustration/modelling. Fortunately, all the effort bloggers have put into correcting this misinterpretation has paid off -- I don't think many Austrians still think this is true (or, maybe the benefit is that young Austrians have paid attention and moved away from the Auburn sect). Menger may not have discussed the use of cardinality for modeling because he didn't do much quantitative modeling. I don't think that he was unfamiliar with it (or he could have been, but I don't think it matters that much); he was approaching economics from a fundamentally different angle than Walras. Menger wasn't interested in exploring general equilibrium. He wanted to develop a causal theory of value and prices -- Walras' GE construction, as far as I know, wasn't interested in the causal process. Some of this, I think, has to do with Menger's preoccupation with the role of time.

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  6. Min: I agree re: partial ordering. The best example I know is Razian incommensurability. Suppose you don't prefer Darwin to Mozart, nor Darwin to Mozart. Are you then indifferent between the two? If so then a hypothetical Darwin-ALT who was Darwin with a little bit more musical ability than the actual Darwin would be strictly preferred to Mozart. This is not so, obviously. We are not indifferent between the two - they are incommensurable.

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