I find it somewhat curious that economists don't seem to use gauge theories at all in modeling markets (I may be wrong and they actually do but I couldn't find much in economic publications) For those that are unfamiliar with the math, gauge theories are an application of group theory in which things that are local can be related to global quantities via a transformation. It seems like this situation comes up all the time in economics, buying/selling is a local phenomenon but we would like to ask questions about global parameters that are related to it. Here is a paper about using gauge theory in econ from a physics person:

http://www.iop.org/EJ/article/0305-4...ja33001l2.html

If you want to skip the math, here is the end result:

Is this useful, and if not, why? Austrians can also explain why this is 100% wrong and why it should be obvious to a 5th grader.

This does not strike me as useful. At first sight, the symmetry is not the powerful and is almost trivial. I have not seen another sight.

I'm no professional economist, it just strikes me as a little far fetched that anyone out there is trying to prove something and running into the problem whereby if you use dollars your theorem makes sense, but if you use pennies it does not.

Actually, no. The fundamental property that he is talking about, that the quantity of money is irrelevent, is a fundamental result of Austrian analysis. It is in sharp contrast to, for example, monetarists, who believe that the money supply must grow with the economy or else aggregate economic problems will result.

He is, however, completely wrong in a couple things. First of all, it certainly does matter whether or not there are one share or two shares; two shares can be sold to two people, one share cannot. His point really only applies specifically to money. And that means that there is a fundamental unit; the unit of the money.

His specific example is perhaps trivial, but the point is that you can use gauge theory to restrict the class of functions you can use to successfully describe markets. I think he used that one since he obviously doesn't know enough about real markets to come up with a gauge transformation that would be of real significance. He is not saying that the one he specified is all you need to create new economics.

max maybe you can tell me whether this is related to specifying functions are homogeneous degree 0, 1, etc. economists often make use of those properties.

That wasn't really the point of the paper. He just picked an obvious gauge symmetry he understood and had to be true. Also, what you said about monetarists has to be wrong. I know nothing about monetarists, but this example of gauge invariance has nothing to do with policy. It is just the trivial statement that the functions used to describe markets should be scale invariant ie the same if you use dollars or cents. There is no way an entire modern school of economics can disagree with this.

I don't think you are understanding the overall point. It doesn't matter that the symmetries aren't exact, it is that they are only slightly broken. Like parity (or better yet CP) in physics. A standard model that preserves CP is still very close to correct. The effects of your objections clearly would be small.

I am not sure what you mean by degree here.

Obviously, because you are wrong. Monetarists like Milton Friedman claim that the money supply must grow with the economy or else aggregate economic problems will develop.

They do subscribe to the quantity theory of money, though, so at least they have that going for them.

Again, this gauge invariance has nothing to do with policy. I don't care about what monetarists say about what should be done to the money supply in the future. This is simply a transformation from dollars to cents. If you don't understand what a gauge transformation or honestly think that Friedman would say that this transformation will cause a huge change in meaningful observables there is not much I can do to help you.

Max, see here:

http://en.wikipedia.org/wiki/Homogeneous_function

Max,

Mea culpa. I was being stupid. I see your point now.

My apologies.

Oh, you meant in just the normal math sense, I thought it may have been an economics term. I'll respond to you in a bit, want to make sure I get the math right.

Cool. I think the problem with his example is that it is too trivial. Pretty much any economist will automatically restrict themselves to functions of this kind even if they don't know any gauge theory. The question is whether it is possible to find a more complicated version that can restrict something in a more non-trivial way. It may or may not be possible, I was basically wondering if this sort of thinking is on the radar in economics. Or if not, perhaps people have tried it and run into catastrophic problems.

Well, decimalization, which is a form of redenomination, did close the bid/ask spreads at the stock exchanges, decreasing transaction costs. There could be a general equivalent.

Gauge theory is a more general idea that could be used regardless of the degree of the particular equations you are using. I don't really see a relation.

It seems that one of the examples you gave above -- of results being invariant to measuring in dollars or cents -- can be dealt with by specifying (or proving) that functions are homogenous degree 0 wrt some arguments. For example, profits functions are homogenous degree 0 wrt prices. Maybe you could give another example of how gauge theory could be used.

Oh i see what you mean now. I think the issue is again that his example is too simple. Nobody would ever really think about writing a profit function that doesn't have that property. Let me think a bit more and try to come up with a gauge theory example that could be useful. It will be wrong, or not usable since I don't know enough about econ, but hopefully it will give you an idea of the concept.

I doubt anybody here cares, but here is a paper by a "known" physicist about the sort of thing I was thinking about when I made this thread.

http://arxiv.org/abs/0902.4274

I've only skimmed it (not sure why there are so few equations) but it is conceptually appealing to me. Not sure if any economists even bothered to read it.

I don't suppose anyone would feel like rewriting this in plain(er) English?

To start with I'm confused about what the unit of measurement is within a local symmetry group. Isn't it, essentially, money?

That sounds like money.

Second, what are examples of the bolded part of the first above quote? Is it something abstract or is it something I would recognize as easily measurable?

/edit I know differential and integral calculus, as well as linear and even multilinear algebra, but I've never studied differential geometry, or at least that I can remember.

It will be similar to what we call price, but fully gauge invariant. I'm not 100% sure what that even means though (or if this is even actually what is normally called gauge invariance), for instance, will it be obvious to tell situations with arbitrage like it is with normal money?

I think he is talking about something more general. Are you asking for an example from math? Trivial fiber bundles are locally just a simple product space but can have multiple (and nontrivial) global topologies. The standard example is a mobius strip and how you have to look at global properties to see that it isn't a cylinder.

economists aren't even smart enough to realize that a lot of the models they already have are BS and you want them to start using tensors and **** like that?

GL

Many, many economists know how and when to use tensors.

Guess I'm showing my ignorance then, I've never done any grad level econ obv.

Well, neither have I but I am assuming. Tensors come up in sophomore level math and physics classes so I would guess that quite a few (if not most) professional economists understand what they are. It isn't a super hard topic fwiw.

Dude I don't know where the hell you went to high school but we sure didn't ever discuss tensors in any class I have ever taken, nor in my college undergrad courses on multivariable calc, diff eq, and linear algebra. I only even know what they are because I heard them used in some advanced physics thing I was trying to read once so I looked up what they were.

Who here learned about tensors in high school? I would be SHOCKED to learn it was more than like...one of you.