Mathematical Methods For Economic Theory 2
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Mathematical Methods for Economic Theory 2
Author: James C. Moore
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-14
This is the second of a two-volume work intended to function as a textbook well as a reference work for economic for graduate students in economics, as scholars who are either working in theory, or who have a strong interest in economic theory. While it is not necessary that a student read the first volume before tackling this one, it may make things easier to have done so. In any case, the student undertaking a serious study of this volume should be familiar with the theories of continuity, convergence and convexity in Euclidean space, and have had a fairly sophisticated semester's work in Linear Algebra. While I have set forth my reasons for writing these volumes in the preface to Volume 1 of this work, it is perhaps in order to repeat that explanation here. I have undertaken this project for three principal reasons. In the first place, I have collected a number of results which are frequently useful in economics, but for which exact statements and proofs are rather difficult to find; for example, a number of results on convex sets and their separation by hyperplanes, some results on correspondences, and some results concerning support functions and their duals. Secondly, while the mathematical top ics taken up in these two volumes are generally taught somewhere in the mathematics curriculum, they are never (insofar as I am aware) done in a two-course sequence as they are arranged here.
Mathematical Methods of Game and Economic Theory
Author: Jean-Pierre Aubin
language: en
Publisher: Courier Corporation
Release Date: 2007-01-01
Mathematical economics and game theory approached with the fundamental mathematical toolbox of nonlinear functional analysis are the central themes of this text. Both optimization and equilibrium theories are covered in full detail. The book's central application is the fundamental economic problem of allocating scarce resources among competing agents, which leads to considerations of the interrelated applications in game theory and the theory of optimization. Mathematicians, mathematical economists, and operations research specialists will find that it provides a solid foundation in nonlinear functional analysis. This text begins by developing linear and convex analysis in the context of optimization theory. The treatment includes results on the existence and stability of solutions to optimization problems as well as an introduction to duality theory. The second part explores a number of topics in game theory and mathematical economics, including two-person games, which provide the framework to study theorems of nonlinear analysis. The text concludes with an introduction to non-linear analysis and optimal control theory, including an array of fixed point and subjectivity theorems that offer powerful tools in proving existence theorems.
The Fecundity of Mathematical Methods in Economic Theory
Author: H.W. Brand
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
The question of how far mathematical methods of reasoning and inves tigation are applicable in economic theorising has long been a matter of debate. The first part of this question needing to be answered was whether, outside the range of ordinary statistical methods, such application is in fact possible. In my opinion the controversy on this point has been a fruitful one, which has led, as might have been expected, to an affirmative answer. What, however, has not yet been decided - for the simple reason that hitherto it has not been investigated - is whether the application of mathematical methods to our science is expedient. From the point of view of economic methodology this seems to me the more important part of the question, although the only considerations hitherto brought to bear upon it have been of a rather general character, based on uncer tain ideas which have led to uncertain conclusions. That is why I welcome this attempt of Dr. Heinz W. Brand to bring the solution nearer by his present work. The conclusion he reaches here is that mathematical methods cannot unreservedly be employed in our science. The arguments which he carefully weighs, in the course of a criticism which is never destructive, are centred on his own criterion of asking whether it is not merely possible, but at the same time profitable, to apply mathematics in economic science.