Equilibrium Models and Variational Inequalities (eBook)

Front Cover 1
Equilibrium Models and Variational Inequalities 4
Copyright Page 5
Preface 6
Table of Contents 10
List of Figures 14
Chapter 1 Introduction 16
Part I MODELS 26
Chapter 2 Linear Models in Economics 30
2.1 Open input-output model 31
2.2 Generalizations 35
2.3 Closed input-output model 37
Chapter 3 Linear Dynamic Models of an Economy 44
3.1 Extended dynamic input-output model 44
3.2 The von Neumann model of an expanding economy 46
Chapter 4 Optimization and Equilibria 54
4.1 Linear programming problems 54
4.2 Economic interpretation of optimality conditions 58
4.3 Economic interpretation of the solution method 60
Chapter 5 Nonlinear Economic Equilibrium Models 66
5.1 Cassel-Wald type economic equilibrium models 66
5.2 General price equilibrium models 67
5.3 Spatial price equilibrium models 70
5.4 Imperfectly competitive equilibrium models 75
Chapter 6 Transportation and Migration Models 84
6.1 Network equilibrium models 84
6.2 Migration equilibrium models 89
Part II COMPLEMENTARITY PROBLEMS 92
Chapter 7 Complementarity with Z Properties 96
7.1 Classes of complementarity problems 96
7.2 Classes of square matrices and their properties 98
7.3 Complementarity problems with Z cost mappings 103
Chapter 8 Applications 110
8.1 Input-output models 110
8.2 Price equilibrium models 113
8.3 A pure trade market model 116
8.4 Price oligopoly models 117
Chapter 9 Complementarity with P Properties 120
9.1 Existence and uniqueness results 120
9.2 Solution methods for CP’s with P properties 126
Chapter 10 Applications 130
10.1 Walrasian price equilibrium models 130
10.2 Oligopolistic equilibrium models 136
Part III VARIATIONAL INEQUALITIES 142
Chapter 11 Theory of Variational Inequalities 146
11.1 Variational inequalities and related problems 146
11.2 Existence and uniqueness results 158
Chapter 12 Applications 164
12.1 Cassel-Wald equilibrium models 164
12.2 Walrasian equilibrium models and their modifications 165
12.3 Existence results in Walrasian equilibrium models 172
12.4 Imperfect competition models 174
12.5 Network and migration equilibrium models 175
Chapter 13 Projection Type Methods 178
13.1 The classical projection method 178
13.2 The projection methods with linesearch 185
13.3 Modifications and extensions 192
Chapter 14 Applications of the Projection Methods 196
14.1 Applications to variational inequalities 196
14.2 Applications to systems of variational inequalities 199
Chapter 15 Regularization Methods 206
15.1 The classical regularization method and its modifications 206
15.2 The proximal point method 208
Chapter 16 Direct Iterative Methods for Monotone Variational Inequalities 212
16.1 Extrapolation methods 212
16.2 The ellipsoid method 217
Chapter 17 Solutions to Exercises 220
Bibliography 244
Index 247