Equilibrium Models and Variational Inequalities
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Table of contents
- Front CoverCover
- Equilibrium Models and Variational Inequalitiesiii
- Copyright Pageiv
- Prefacev
- Table of Contentsix
- List of Figuresxiii
- Chapter 1 Introduction1
- Part I MODELS11
- Chapter 2 Linear Models in Economics15
- 2.1 Open input-output model16
- 2.2 Generalizations20
- 2.3 Closed input-output model22
- Chapter 3 Linear Dynamic Models of an Economy29
- 3.1 Extended dynamic input-output model29
- 3.2 The von Neumann model of an expanding economy31
- Chapter 4 Optimization and Equilibria39
- 4.1 Linear programming problems39
- 4.2 Economic interpretation of optimality conditions43
- 4.3 Economic interpretation of the solution method45
- Chapter 5 Nonlinear Economic Equilibrium Models51
- 5.1 Cassel-Wald type economic equilibrium models51
- 5.2 General price equilibrium models52
- 5.3 Spatial price equilibrium models55
- 5.4 Imperfectly competitive equilibrium models60
- Chapter 6 Transportation and Migration Models69
- 6.1 Network equilibrium models69
- 6.2 Migration equilibrium models74
- Part II COMPLEMENTARITY PROBLEMS77
- Chapter 7 Complementarity with Z Properties81
- 7.1 Classes of complementarity problems81
- 7.2 Classes of square matrices and their properties83
- 7.3 Complementarity problems with Z cost mappings88
- Chapter 8 Applications95
- 8.1 Input-output models95
- 8.2 Price equilibrium models98
- 8.3 A pure trade market model101
- 8.4 Price oligopoly models102
- Chapter 9 Complementarity with P Properties105
- 9.1 Existence and uniqueness results105
- 9.2 Solution methods for CP’s with P properties111
- Chapter 10 Applications115
- 10.1 Walrasian price equilibrium models115
- 10.2 Oligopolistic equilibrium models121
- Part III VARIATIONAL INEQUALITIES127
- Chapter 11 Theory of Variational Inequalities131
- 11.1 Variational inequalities and related problems131
- 11.2 Existence and uniqueness results143
- Chapter 12 Applications149
- 12.1 Cassel-Wald equilibrium models149
- 12.2 Walrasian equilibrium models and their modifications150
- 12.3 Existence results in Walrasian equilibrium models157
- 12.4 Imperfect competition models159
- 12.5 Network and migration equilibrium models160
- Chapter 13 Projection Type Methods163
- 13.1 The classical projection method163
- 13.2 The projection methods with linesearch170
- 13.3 Modifications and extensions177
- Chapter 14 Applications of the Projection Methods181
- 14.1 Applications to variational inequalities181
- 14.2 Applications to systems of variational inequalities184
- Chapter 15 Regularization Methods191
- 15.1 The classical regularization method and its modifications191
- 15.2 The proximal point method193
- Chapter 16 Direct Iterative Methods for Monotone Variational Inequalities197
- 16.1 Extrapolation methods197
- 16.2 The ellipsoid method202
- Chapter 17 Solutions to Exercises205
- Bibliography229
- Index232
The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control.
This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.
- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field
- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models
- Covers the basics of theory and solution methods both for the complementarity and variational inequality problems
- The methods are illustrated by applications and exercises to economic equilibrium models
This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.
- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field
- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models
- Covers the basics of theory and solution methods both for the complementarity and variational inequality problems
- The methods are illustrated by applications and exercises to economic equilibrium models