Concave Optimization for Microeconomic Theory

Preface These lecture notes grew out of several years of teaching a course on Advanced Microeconomics, first at the Indian Institute of Management, Ahmedabad and subsequently at the University of Witwatersrand, Johannesburg. When we were students at graduate schools in US (during the mid 1980's), a typical first year graduate Microeconomics course, revolved around Hal Varian's classic on the subject: Microeconomic Analysis (first edition). The purpose of such a course was to provide a bridge between a typical undergraduate Microeconomics course and Gerard Debreu's seminal contribution: Theory of Value. Most of advanced economic theory which culminated in research at the frontier, was until that point in time, inextricably bound to the existence and optimality results of the Arrow-Debreu general equilibrium model and its immediate extensions. Thus, a course on graduate microeconomics such as the one prescribed in Varian's book, served an important need to make the transition from undergraduate economic theory to advanced economic theory, less hostile for the students. As teachers of graduate microeconomics in the late 1980's and early 1990's, many of us (including myself) were ardent adherents of the cause espoused by Varian's Microeconomic Analysis. However, by the mid 1990's it had become apparent, that research dealing with the existence and optimality properties of competitive and related equilibria, was no longer the sole preoccupation of economic theory. Further, the volume of academic output on each topic that was covered by a standard graduate level text book in Microeconomics, had become so enormous, that each topic started evolving as a separate course in its own right (as for instance Information Economics), and sometimes (as in the case of game theory) as a separate subject altogether. While teaching from standard graduate texts on Microeconomics, I as an instructor, could not miss the feeling, that neither the students nor the instructor, were deriving very little by nibbling bits and pieces from sundry topics. Such courses were contributing marginally more than what a good dictionary on economic theory would do, and by then there were several such dictionaries available in the market. As an instructor, I was beginning to realize, that a first year graduate microeconomic theory course could survive and flourish, only if it centered on teaching students the tools of optimization theory along with a few robust applications. Optimization theory (: much more than fixed point theory) was the technique that pervaded most topics discussed in microeconomics, and for …