ECON 24410

Econ 24410 - Advanced Microeconomic Theory in a Mathematical Mode. H. Sonnenschein.
This ten week course will be an introduction to microeconomic theory in a "mathematical mode". The approach will be quite abstract and for a select group of adventuresome students who have the appropriate preparation, inclinations, and aspirations. Students should be "comfortable" with intermediate level "mathematical analysis" and have completed a rigorous intermediate course in price theory.  A good deal of time will be spent developing "mathematical structure" at the cost of time spent explaining applications to substantive economic analysis. The "level" will be similar to what one sees in leading economics departments in Ph.D. courses in microeconomics and mathematical economics.
We will begin with the standard theories of consumer and producer behavior, which will include a quick review of the implicit function theorem and elementary analysis(continuity, differentiability, etc.) plus some convex analysis.  We will next state and prove the basic theorems of welfare economics; again, this will require the introduction of basic results from convex analysis.  After presenting some elementary fixed point theory we will use that theory to establish the existence of Arrow-Debreu Equilibrium under rather general assumptions.  We will next prove theorems on the structure of multi market excess demand functions.  Finally, we will present some elementary measure theory, prove Sard's Theorem, and present Debreu's result on the generic finiteness of the Arrow-Debreu equilibrium price set. Autumn 2012.

This is the first time that this course has been offered at the U of C; although, much of the material is presented in the graduate sequence in price theory.  The course is (for some) a good way to put toes in the water in order to explore and or prepare oneself for Ph.D. study in Economics and or Finance in a "protected environment".  (The term "protected environment" refers to the fact that enrollment will be limited and that students will not be preparing for a "core" exam.  Also, there will be the time and flexibility to allow students to review the mathematics that they "need", but may have not yet learned properly.)  A significant amount of the material to be presented was influenced by scholars at the University of Chicago: Kenneth Arrow and Gerard Debreu began some of the most important work here as members of the Cowles Commission, and the "style" plus the substance of much of what will be presented owes a great debt to Gerard Debreu. There will be time to discuss the "mathematical mode" in Economics.  In addition, I am hopeful that the small size of the class will allow students to present some of the material themselves and perhaps to begin customized projects.  For much of the course, we will "use" two standard texts(by Mas-Colell, Whinston, and Green and Jehle and Reny) plus a third that will be available in preprint(by David Kreps.)  For anybody interested in checking out the "level" of what "we are up to", you may wish to take a quick look at the Mas-Colell, et al text(much available), plus Gerard Debreu's Mathematical Economics(including the introduction.)