Mathematical Optimization and Economic Analysis (eBook)
XIV, 294 Seiten
Springer New York (Verlag)
978-0-387-89552-9 (ISBN)
'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.
"e;Mathematical Optimization and Economic Analysis"e; 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.
Contents 7
Preface 11
Part I: Single-Objective Optimization 14
1 Scarcity and Efficiency 15
1.1 The Mathematical Programming Problem 16
1.2 Mathematical Programming Models in Economics 16
1.3 Classification of Mathematical Programming Problems 30
References and Further Reading 34
2 Kuhn-Tucker Conditions 37
2.1 The Kuhn-Tucker Theorem 37
2.2 Rationale of the Kuhn-Tucker Conditions 43
2.3 Kuhn-Tucker Conditions and a Saddle Point of the Lagrange Function 44
2.4 Kuhn-Tucker Conditions for the General Mathematical Programming Problem 45
2.5 The Kuhn-Tucker Conditions and Economic Analysis 48
References and Further Reading 68
3 Convex Programming 71
3.1 Basic Definitions and Properties 72
3.2 Kuhn-Tucker Conditions for a Convex Programming Problem 80
3.3 Duality Theory 85
3.4 Economic Interpretation of Duality in Convex Programming 90
References and Further Reading 96
4 Linear Programming 98
4.1 The General Linear Programming Problem 98
4.2 Implications of Linearity Assumption for Economic Analysis 102
4.3 Duality in Linear Programming 104
4.4 The More-for-Less Paradox 112
4.5 Computational Procedure: The Simplex Method 118
4.6 Some Applications of Linear Programming in Economics 130
References and Further Reading 143
5 Data Envelopment Analysis 146
5.1 Productivity and Technical and Allocative Efficiency 147
5.2 Basic DEA Models 150
5.3 Production Technologies and Efficiency Measurement 178
5.4 Technical versus Environmental Efficiency, or How to Measure Ecoefficiency 188
References and Further Reading 195
6 Geometric Programming 198
6.1 The Principle of Geometric Programming 199
6.2 The Theory of Geometric Programming 200
6.3 Models of Geometric Programming in Economics 206
6.4 Transformation of Some Optimization Problems into Standard Geometric Programming Models 217
References and Further Reading 220
Part II: Multiobjective Optimization 222
7 Fundamentals of Multiobjective Optimization 223
7.1 Examples of Multiobjective Programming Models in Economics 224
7.2 Kuhn-Tucker Conditions for the Multiobjective Programming Problem 235
7.3 Duality for Multiobjective Optimization Problems 242
7.4 Behavior of the Firm Facing a Bicriteria Objective Function under Regulatory Constraint 245
References and Further Reading 247
8 Multiobjective Linear Programming 252
8.1 Linear Vector Optimization Problems 252
8.2 Duality in Multiple-Objective Linear Programming 257
8.3 Interactive Procedures and the Zionts-Wallenius Method 266
8.4 The Leontief Pollution Model with Multiple Objectives 271
References and Further Reading 276
9 Multiobjective Geometric Programming 279
9.1 Vector Minimization Problems in Geometric Programming 279
9.2 Duality for Multiobjective Geometric Programming in Parametric Form 283
9.3 A Nonlinear Model of Environmental Control 288
9.4 Optimal Behavior of a Monopolist Facing a Bicriteria Objective Function 291
References and Further Reading 295
Index 296
| Erscheint lt. Verlag | 3.10.2009 |
|---|---|
| Reihe/Serie | Springer Optimization and Its Applications |
| Zusatzinfo | XIV, 294 p. 53 illus. |
| Verlagsort | New York |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Technik | |
| Wirtschaft ► Betriebswirtschaft / Management ► Planung / Organisation | |
| Wirtschaft ► Volkswirtschaftslehre ► Ökonometrie | |
| Schlagworte | Cost Minimization • data envelopment • Decision Problems • Decision Space • Distribution Function • Economic Analysis • Economic Optimization • Kuhn-Tucker Conditions • linear optimization • Luptacik • Mathematical Optimization • Mathematical Programming • Multi-Objective Optimization • Optimization • Profit M • Profit Miximization • Single-Objective Optimization |
| ISBN-10 | 0-387-89552-3 / 0387895523 |
| ISBN-13 | 978-0-387-89552-9 / 9780387895529 |
| Haben Sie eine Frage zum Produkt? |
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