Somdeb Lahiri
I obtained a M.Stat (Statistical Economics) from Indian Statistical Institute Calcutta in 1981 and a Ph.D in (Applicable) Mathematical Economics from the University of Minnesota in 1986. I was a Professor of Economics at the School of Petroleum Management, PD Energy University (PDEU) and am currently an Adjunct Professor in the School of Management Studies, Lok Jagruti (LJ) University, Ahmedabad. My current research (https://sites.google.com/view/somdeblahiri/somdeb-lahiri/current-research) interests are in microeconomic theory, decision theory, (applicable) mathematical economics and linear economic models (linear economics). My personal website is available at: https://sites.google.com/view/somdeblahiri/somdeb-lahiri
On October 12, 1987, I was privileged to tie the knot with Dr. (Ms.) Rajyashree Khushu-Lahiri (June 23, 1959 to August 3, 2014), whose scholarship and academic achievements outshines my own, by leaps and bounds (https://www.iitk.ac.in/hss/data/Lecture.pdf). This is what tying the knot meant and means to us: https://m.youtube.com/watch?v=uc6cQdMY8iA
Phone: +919974353365
On October 12, 1987, I was privileged to tie the knot with Dr. (Ms.) Rajyashree Khushu-Lahiri (June 23, 1959 to August 3, 2014), whose scholarship and academic achievements outshines my own, by leaps and bounds (https://www.iitk.ac.in/hss/data/Lecture.pdf). This is what tying the knot meant and means to us: https://m.youtube.com/watch?v=uc6cQdMY8iA
Phone: +919974353365
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(i) Primacy of "scientific temper" in public life and thought.
(ii) People are more important than dogmas.
(iii) The willingness to learn as such, and in particular, from past mistakes so as to be able to take corrective actions.
(iv) A mixed economy with its "commanding heights" being under public or state control.
(v) Anti-imperialism and world peace.
and last but not the least,
(vi) Bottomless compassion for the poor, weak and socially disadvantaged people.
These principles are very similar to the views of Nehru, and it is not just a "mere coincidence" that they are similar.
As an immediate corollary of the above, it follows that, the “intelligentsia” have a significant role to play in the progress of Leninism as we understand it. Such a role of the intelligentsia in a “vanguard” party would be realistic only to the extent that the party represents the masses, and not just a section of society or a social class, and it appears that Nehru was the first person to realize this. It would be grossly “unrealistic” to assume otherwise and I think events beginning with the ones in the twentieth century provides enough evidence for such a conclusion. The “unrealistic nature of the assumption” about the role to be played by the intelligentsia in the “vanguard “party if it were to only represent the “proletariat”, is the extent of “altruism” and “generosity” expected from the former group, while representing a section of society, that did not include them in its entirety. In a way, this realization that the “vanguard” party of the progressive forces should represent the (exploited?) masses and not just the proletariat, was a significant contribution of Nehru to Leninism.
(i) Primacy of "scientific temper" in public life and thought.
(ii) People are more important than dogmas.
(iii) The willingness to learn as such, and in particular, from past mistakes so as to be able to take corrective actions.
(iv) A mixed economy with its "commanding heights" being under public or state control.
(v) Anti-imperialism and world peace.
and last but not the least,
(vi) Bottomless compassion for the poor, weak and socially disadvantaged people.
These principles are very similar to the views of Nehru, and it is not just a "mere coincidence" that they are similar.
As an immediate corollary of the above, it follows that, the “intelligentsia” have a significant role to play in the progress of Leninism as we understand it. Such a role of the intelligentsia in a “vanguard” party would be realistic only to the extent that the party represents the masses, and not just a section of society or a social class, and it appears that Nehru was the first person to realize this. It would be grossly “unrealistic” to assume otherwise and I think events beginning with the ones in the twentieth century provides enough evidence for such a conclusion. The “unrealistic nature of the assumption” about the role to be played by the intelligentsia in the “vanguard “party if it were to only represent the “proletariat”, is the extent of “altruism” and “generosity” expected from the former group, while representing a section of society, that did not include them in its entirety. In a way, this realization that the “vanguard” party of the progressive forces should represent the (exploited?) masses and not just the proletariat, was a significant contribution of Nehru to Leninism.
When we were students at graduate schools 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 that 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 pre-occupation 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 much 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 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 most purposes, the optimization theory that was required, involved maximizing “one or more” concave objective function (s) subject to linear constraints. This is the central message that I have tried to convey, in the lectures that follow.
In preparing these lectures I have benefited immensely from the following sources:
(1) Concavity and Optimization in Microeconomics, by Paul Madden: Blackwell Publisher, 1986;
(2) Linear Programming and Economic Analysis, by Robert Dorfman, Paul Samuelson and Robert Solow: (The Rand Series), Mc Graw Hill, 1958;
(3) Resource Allocation Mechanisms, by Donald Campbell: Cambridge University Press, 1987;
(4) Lectures on Mathematical Economics, by J.S. Lane: London School of Economics and Political Science, 2001;
(5) An Introduction to Mathematical Finance: Options and other Topics, by Sheldon M. Ross: Cambridge University Press, 1999;
(6) On Market Games, by Lloyd Shapley and Martin Shubik: Journal of Economic Theory, Volume 1, pages 9 to 25, 1969;
(7) Cooperative Microeconomics: A Game-Theoretic Introduction, by Herve Moulin: Prentice Hall (Harvester Wheatsheaf), 1995.
To be able to comprehend and do justice to the ensuing lecture notes, the reader should have gone through a course on Advanced Calculus and some Linear Algebra. An appendix to these notes presents a development of Linear Algebra using analytical geometry. Our treatment though inspired by the chapter on Linear Algebra in:
(8) The Theory of Linear Economic Models, by David Gale, (New York) Graw Hill, 1960;
is based on:
(9) An Elementary Proof of a Result For Polyhedral Cones, by Somdeb Lahiri, Pure Mathematics and its Applications (PU.M.A), Volume 12, pages 310-325, 2001.
Our presentation in the appendix leads to a proof of the seminal result due to Farkas on the theorem of alternatives, which is applied in these lectures to establish the necessity of the first order conditions for a solution to a concave optimization problem.
Ideally, the reader should be familiar with matter covered in an intermediate microeconomics course as well. While the mathematical requirements are a definite prerequisite for these lectures, previous knowledge of intermediate microeconomics can in several instances be substituted by sufficient “mental maturity”, without doing considerable injustice to one’s understanding of what follows.
While I would like to thank all my students, both past and present, whom I have had the privilege of teaching Advanced Microeconomics, for making these “rough” lecture notes possible, at this point I would like to thank Gabor Szalontai, for pointing out numerous errors in the text and Ralitza Dobreva and Eugene Peterson (all at WITS) for fruitful participation in the class room discussions. It has been a delightful experience teaching Microeconomic Theory or Mathematical Economics to several batches of postgraduate students at WITS, for which I would like to thank them all. I would also like to thank Bruce Teubes, for raising some interesting questions, which probably indicates that these lecture notes require considerable polishing, before they can be deemed fit for unsupervised consumption. At IFMR, Chennai, I had the benefit of teaching from these notes to a batch of extremely gifted students, particularly Amrut Krishnan and Ganapathy Subramaniam. In a way they made teaching a delightful learning experience, and this acknowledgment would be incomplete without thanking them for having “tested” me all the way! Diptesh Ghosh made very interesting critical observations about these notes and suggested that the earlier version had too many “D’s”, representing several different concepts and thus leading to an inexcusable notational confusion. I have thus decided to represent a convex domain by X in these lecture notes, in order to alleviate some misery for the reader. I would like to thank him and all my other students and colleagues, for extending their “social service” to me by way of time spent on these notes, and I sincerely hope that this list continues to grow longer with the passage of time.
This Preface is my way of motivating the lectures that follow. Hence I would like to thank my wife, Rajyashree, for help in making this purpose linguistically clear and correct. Responsibility for errors that do remain, here as well as elsewhere, is obviously my own!
October 2006.