Luptácik Mathematical Optimization and Economic Analysis

1. Auflage 2009
ISBN: 978-0-387-89552-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 36, 294 Seiten

Reihe: Springer Optimization and Its Applications

'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.

Autoren/Hrsg.

Luptácik, Mikulás

Inhaltsverzeichnis

1;Contents;7
2;Preface;11
3;Part I: Single-Objective Optimization;14
3.1;1 Scarcity and Efficiency;15
3.1.1;1.1 The Mathematical Programming Problem;16
3.1.2;1.2 Mathematical Programming Models in Economics;16
3.1.3;1.3 Classification of Mathematical Programming Problems;30
3.1.4;References and Further Reading;34
3.2;2 Kuhn-Tucker Conditions;37
3.2.1;2.1 The Kuhn-Tucker Theorem;37
3.2.2;2.2 Rationale of the Kuhn-Tucker Conditions;43
3.2.3;2.3 Kuhn-Tucker Conditions and a Saddle Point of the Lagrange Function;44
3.2.4;2.4 Kuhn-Tucker Conditions for the General Mathematical Programming Problem;45
3.2.5;2.5 The Kuhn-Tucker Conditions and Economic Analysis;48
3.2.6;References and Further Reading;68
3.3;3 Convex Programming;71
3.3.1;3.1 Basic Definitions and Properties;72
3.3.2;3.2 Kuhn-Tucker Conditions for a Convex Programming Problem;80
3.3.3;3.3 Duality Theory;85
3.3.4;3.4 Economic Interpretation of Duality in Convex Programming;90
3.3.5;References and Further Reading;96
3.4;4 Linear Programming;98
3.4.1;4.1 The General Linear Programming Problem;98
3.4.2;4.2 Implications of Linearity Assumption for Economic Analysis;102
3.4.3;4.3 Duality in Linear Programming;104
3.4.4;4.4 The More-for-Less Paradox;112
3.4.5;4.5 Computational Procedure: The Simplex Method;118
3.4.6;4.6 Some Applications of Linear Programming in Economics;130
3.4.7;References and Further Reading;143
3.5;5 Data Envelopment Analysis;146
3.5.1;5.1 Productivity and Technical and Allocative Efficiency;147
3.5.2;5.2 Basic DEA Models;150
3.5.3;5.3 Production Technologies and Efficiency Measurement;178
3.5.4;5.4 Technical versus Environmental Efficiency, or How to Measure Ecoefficiency;188
3.5.5;References and Further Reading;195
3.6;6 Geometric Programming;198
3.6.1;6.1 The Principle of Geometric Programming;199
3.6.2;6.2 The Theory of Geometric Programming;200
3.6.3;6.3 Models of Geometric Programming in Economics;206
3.6.4;6.4 Transformation of Some Optimization Problems into Standard Geometric Programming Models;217
3.6.5;References and Further Reading;220
4;Part II: Multiobjective Optimization;222
4.1;7 Fundamentals of Multiobjective Optimization;223
4.1.1;7.1 Examples of Multiobjective Programming Models in Economics;224
4.1.2;7.2 Kuhn-Tucker Conditions for the Multiobjective Programming Problem;235
4.1.3;7.3 Duality for Multiobjective Optimization Problems;242
4.1.4;7.4 Behavior of the Firm Facing a Bicriteria Objective Function under Regulatory Constraint;245
4.1.5;References and Further Reading;247
4.2;8 Multiobjective Linear Programming;252
4.2.1;8.1 Linear Vector Optimization Problems;252
4.2.2;8.2 Duality in Multiple-Objective Linear Programming;257
4.2.3;8.3 Interactive Procedures and the Zionts-Wallenius Method;266
4.2.4;8.4 The Leontief Pollution Model with Multiple Objectives;271
4.2.5;References and Further Reading;276
4.3;9 Multiobjective Geometric Programming;279
4.3.1;9.1 Vector Minimization Problems in Geometric Programming;279
4.3.2;9.2 Duality for Multiobjective Geometric Programming in Parametric Form;283
4.3.3;9.3 A Nonlinear Model of Environmental Control;288
4.3.4;9.4 Optimal Behavior of a Monopolist Facing a Bicriteria Objective Function;291
4.3.5;References and Further Reading;295
5;Index;296