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> I asked him what he was assuming for his supply and demand curves -- continuous, uniformly continuous, differentiable, continuously differentiable, infinitely

> I asked him what he was assuming for his supply and demand curves -- continuous, uniformly continuous, differentiable, continuously differentiable, infinitely differentiable, convex, pseudo-convex, quasi-convex, etc.? He said nothing. > Soon I got a call from my department secretary to call my Ph.D. advisor -- I was out of the econ course! What the hell? The first two semesters of microeconomic theory in graduate school go over all of that. Supply and demand are formalized down to set theory coming up (from Arrow's work!) If you are interested, the Mas-Colell/Whinston/Greene text is the bible all PhD students are forced through in microeconomics. Start at the set theory level, define what permits construction of a utility function, and get to defining supply and demand from there. Then get to game theory and other topics. You even have the theorems where free markets fail to be an efficient mechanism of allocation! We've known those things for decades, but economics is so politicized that it's hard for information out.

graycat 10y ago
I was a grad student in applied math and had done the basic research for my dissertation, solved the KTCQ problem, was polishing the research, and writing the illustrative software when my advisor suggested I take an econ course. The econ course was in the econ department, not my department, and was not an econ grad course! But, whatever the course was, the econ prof was apparently just terrified of my question! One way and another, maybe I've touched on much of what you mentioned. E.g., the optimization I studied, with the math rock solid, was a good start on game theory. Later, while in a part time job, to support us while my wife finished her Ph.D. and basically time-out from my Ph.D., I took a job in military systems analysis with a lot in game theory. So, I dug into parts of G. Owen's book on game theory which did the axiomatic utility function stuff and T. Parthasarathy and T. E. S. Raghavan which did a lot of fixed point theorems, Sion's result, Lemke's proof of Nash's result, etc. Sure, in the relatively general game theory the job had me in, I had to consider saddlepoint results, and apparently that is the core of equilibrium theory in econ. Once a tried a book on math econ, and it was just a lot of elementary regression analysis. Later I saw another such, by Tata?, and more advanced but still regression -- a place to see more about regression than want to know, and maybe the AI people should take a look. Later saw another such book, by Duffie, and early on it was heavily about the Kuhn Tucker conditions. I read the first chapter or two quickly and had some questions, went back, read carefully, and found a counterexample for every statement in that material. I did want to see a clean, solid, mathematical treatment of the Sharpe idea but didn't find that -- D. Luenberger, a good mathematician, has a book on finance that may have such a treatment. Thanks for the reference on micro. I copied that in my place for such things and will look at it if I get interested in econ after I exit from my startup! Well, nil nisi bonum.
- VHRanger 10y ago
  Most of the advanced math in economics in current research is either in econometrics or game theory. Not saying econ is math-less, far from it, but most of the time we can't simply solve our problems by applying advanced math like physics can. Equilibrium concepts in game theory are a tough thing. The holy grail is still getting a unifying concept of a "stable equilibrium" (see Kohlber & Mertens '86) which is pretty much a guaranteed Nobel (but I'm not sure it even exists, so many geniuses worked on the problem without success).

graycat 10y ago

I was a grad student in applied math and had done the basic research for my dissertation, solved the KTCQ problem, was polishing the research, and writing the illustrative software when my advisor suggested I take an econ course. The econ course was in the econ department, not my department, and was not an econ grad course! But, whatever the course was, the econ prof was apparently just terrified of my question! One way and another, maybe I've touched on much of what you mentioned. E.g., the optimization I studied, with the math rock solid, was a good start on game theory. Later, while in a part time job, to support us while my wife finished her Ph.D. and basically time-out from my Ph.D., I took a job in military systems analysis with a lot in game theory. So, I dug into parts of G. Owen's book on game theory which did the axiomatic utility function stuff and T. Parthasarathy and T. E. S. Raghavan which did a lot of fixed point theorems, Sion's result, Lemke's proof of Nash's result, etc. Sure, in the relatively general game theory the job had me in, I had to consider saddlepoint results, and apparently that is the core of equilibrium theory in econ. Once a tried a book on math econ, and it was just a lot of elementary regression analysis. Later I saw another such, by Tata?, and more advanced but still regression -- a place to see more about regression than want to know, and maybe the AI people should take a look. Later saw another such book, by Duffie, and early on it was heavily about the Kuhn Tucker conditions. I read the first chapter or two quickly and had some questions, went back, read carefully, and found a counterexample for every statement in that material. I did want to see a clean, solid, mathematical treatment of the Sharpe idea but didn't find that -- D. Luenberger, a good mathematician, has a book on finance that may have such a treatment. Thanks for the reference on micro. I copied that in my place for such things and will look at it if I get interested in econ after I exit from my startup! Well, nil nisi bonum.

VHRanger 10y ago
Most of the advanced math in economics in current research is either in econometrics or game theory. Not saying econ is math-less, far from it, but most of the time we can't simply solve our problems by applying advanced math like physics can. Equilibrium concepts in game theory are a tough thing. The holy grail is still getting a unifying concept of a "stable equilibrium" (see Kohlber & Mertens '86) which is pretty much a guaranteed Nobel (but I'm not sure it even exists, so many geniuses worked on the problem without success).