Optimization In Economic Theory

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Author: Avinash K. Dixit
Publisher: Oxford University Press on Demand
ISBN: 9780198772101
Size: 48.27 MB
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Optimization In Economic Theory by Avinash K. Dixit


Original Title: Optimization In Economic Theory

Building on a base of simple economic theory and elementary linear algebra and calculus, this broad treatment of static and dynamic optimization methods discusses the importance of shadow prices, and reviews functions defined by solutions of optimization problems. Recently revised and expanded, the second edition will be a valuable resource for upper level undergraduate and graduate students.

Mathematical Optimization And Economic Analysis

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Author: Mikulás Luptácik
Publisher: Springer Science & Business Media
ISBN: 0387895523
Size: 19.91 MB
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Mathematical Optimization And Economic Analysis by Mikulás Luptácik


Original Title: Mathematical Optimization And Economic Analysis

"Mathematical Optimization and Economic Analysis" is a self-contained introduction to various optimization techniques used in economic modeling and analysis such as geometric, linear, and convex programming and data envelopment analysis. Through a systematic approach, this book demonstrates the usefulness of these mathematical tools in quantitative and qualitative economic analysis. The book presents specific examples to demonstrate each technique’s advantages and applicability as well as numerous applications of these techniques to industrial economics, regulatory economics, trade policy, economic sustainability, production planning, and environmental policy. Key Features include: - A detailed presentation of both single-objective and multiobjective optimization; - An in-depth exposition of various applied optimization problems; - Implementation of optimization tools to improve the accuracy of various economic models; - Extensive resources suggested for further reading. This book is intended for graduate and postgraduate students studying quantitative economics, as well as economics researchers and applied mathematicians. Requirements include a basic knowledge of calculus and linear algebra, and a familiarity with economic modeling.

Mathematics For Stability And Optimization Of Economic Systems

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Author: Yasuo Murata
Publisher: Academic Press
ISBN: 1483271293
Size: 10.43 MB
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Mathematics For Stability And Optimization Of Economic Systems by Yasuo Murata


Original Title: Mathematics For Stability And Optimization Of Economic Systems

Economic Theory and Mathematical Economics: Mathematics for Stability and Optimization of Economic Systems provides information pertinent to the stability aspects and optimization methods relevant to various economic systems. This book presents relevant mathematical theorems sufficient to develop important economic systems, including Leontief input–output systems, Keynesian dynamic models, the Ramsey optimal accumulation systems, and von Neumann expanding economic systems. Organized into two parts encompassing nine chapters, this book begins with an overview of useful theorems on matrices, eigenvalue problems, and matrices with dominant diagonals and P-matrices. This text then explores the linear transformations on vector spaces. Other chapters consider the Hawkins–Simon theorem concerning non-negative linear systems. This book discusses as well the dual linear relations and optimization methods applicable to inequality economic systems. The final chapter deals with powerful optimal control method for dynamical systems. This book is a valuable resource for mathematicians, economists, research workers, and graduate students.

Mathematical Methods Of Game And Economic Theory

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Author: Jean-Pierre Aubin
Publisher: Courier Corporation
ISBN: 048646265X
Size: 43.19 MB
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Mathematical Methods Of Game And Economic Theory by Jean-Pierre Aubin


Original Title: Mathematical Methods Of Game And Economic Theory

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.

Dynamic Optimization And Mathematical Economics

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Author: Pan-Tai Liu
Publisher: Springer Science & Business Media
ISBN: 1468435728
Size: 80.39 MB
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Dynamic Optimization And Mathematical Economics by Pan-Tai Liu


Original Title: Dynamic Optimization And Mathematical Economics

As an outgrowth of the advancement in modern control theory during the past 20 years, dynamic modeling and analysis of economic systems has become an important subject in the study of economic theory. Recent developments in dynamic utility, economic planning, and profit optimiza tion, for example, have been greatly influenced by results in optimal control, stabilization, estimation, optimization under conflicts, multi criteria optimization, control of large-scale systems, etc. The great success that has been achieved so far in utilizing modern control theory in economic systems should be attributed to the effort of control theorists as well as economists. Collaboration between the two groups of researchers has proven to be most successful in many instances; nevertheless, the gap between them has existed for some time. Whereas a control theorist frequently sets up a mathematically feasible model to obtain results that permit economic interpretations, an economist is concerned more with the fidelity of the model in representing a real world problem, and results that are obtained (through possibly less mathematical analysis) are due largely to economic insight. The papers appearing in this volume are divided into three parts. In Part I there are five papers on the application of control theory to economic planning. Part II contains five papers on exploration, exploita tion, and pricing of extractive natural resources. Finally, in Part III, some recent advances in large-scale systems and decentralized control appear.

Optimization In Economics And Finance

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Author: Bruce D. Craven
Publisher: Springer Science & Business Media
ISBN: 0387242805
Size: 56.18 MB
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Optimization In Economics And Finance by Bruce D. Craven


Original Title: Optimization In Economics And Finance

Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book.

Practical Mathematical Optimization

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Author: Jan Snyman
Publisher: Springer Science & Business Media
ISBN: 9780387243481
Size: 41.27 MB
Format: PDF
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Practical Mathematical Optimization by Jan Snyman


Original Title: Practical Mathematical Optimization

It is intended that this book be used in senior- to graduate-level semester courses in optimization, as offered in mathematics, engineering, com puter science and operations research departments. Hopefully this book will also be useful to practising professionals in the workplace. The contents of the book represent the fundamental optimization mate rial collected and used by the author, over a period of more than twenty years, in teaching Practical Mathematical Optimization to undergradu ate as well as graduate engineering and science students at the University of Pretoria. The principal motivation for writing this work has not been the teaching of mathematics per se, but to equip students with the nec essary fundamental optimization theory and algorithms, so as to enable them to solve practical problems in their own particular principal fields of interest, be it physics, chemistry, engineering design or business eco nomics. The particular approach adopted here follows from the author's own personal experiences in doing research in solid-state physics and in mechanical engineering design, where he was constantly confronted by problems that can most easily and directly be solved via the judicious use of mathematical optimization techniques. This book is, however, not a collection of case studies restricted to the above-mentioned specialized research areas, but is intended to convey the basic optimization princi ples and algorithms to a general audience in such a way that, hopefully, the application to their own practical areas of interest will be relatively simple and straightforward.

An Introduction To Mathematical Analysis For Economic Theory And Econometrics

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Author: Dean Corbae
Publisher: Princeton University Press
ISBN: 1400833086
Size: 55.17 MB
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An Introduction To Mathematical Analysis For Economic Theory And Econometrics by Dean Corbae


Original Title: An Introduction To Mathematical Analysis For Economic Theory And Econometrics

Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory

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