Mathematical economic theory : pure and mixed types of economic mechanisms

목차 (Table of Contents)

• CONTENTS
• Introduction to the series = ⅴ
• Preface = ⅶ
• List of notation = xix
• PART Ⅰ. STATIC MODELS OF ECONOMIC INTERACTION
• Chapter 1 INTERACTION AND THE ECONOMIC MECHANISM
• 1.1 Elements of economic systems = 3
• 1.2 Examples of coordinating mechanisms = 8
• 1.2.1 Coordinating by flexible prices = 8
• 1.2.2 Coordinating mechanism with quotas = 12
• 1.2.3 Mixed coordinating mechanisms with nonflexible prices = 15
• 1.2.4 Mixed mechanism with fixed and flexible prices = 17
• 1.2.5 Matching mechanisms with adjustment of utility function = 18
• 1.2.6 Coordinating mechanism with fixed prices and quotas. Requirements on quotas = 19
• Chapter 2 CONSUMPTION MODELS
• 2.1 An elementary model of consumer choice under constraints = 23
• 2.2 Consumer choice and preference = 26
• 2.3 Demand function and consumer choice under a budget constraint = 35
• 2.4 Consumer choice under quotas = 41
• 2.5 Choice and demand under total shortage = 46
• 2.6 Choice and demand under partial shortage = 57
• Chapter 3 EXCHANGE MODELS
• 3.1 Transaction model = 66
• 3.2 Equilibrium in a model with fixed prices and rigid quotas (q-equilibrium) = 70
• 3.3 An exchange model with flexible quotas = 74
• 3.4 Generation of flexible quotas = 80
• 3.5 Exchange models with quotas and ranges of prices = 83
• 3.6 Exchange model with flexible prices = 87
• Chapter 4 PRODUCTION MODELS
• 4.1 Producer model. A technological description of production = 97
• 4.2 Models of production system. Technological aspects = 104
• 4.2.1 Description of production system and its efficiency = 104
• 4.2.2 Input-output Leontieff models = 112
• 4.3 A disequilibrium model of the production system = 116
• 4.3.1 A normal production unit and its properties = 117
• 4.3.2 Coordinated functioning of a normal production system = 120
• 4.3.3 Quasi-equilibrium and efficiency = 128
• Chapter 5CHANGING OF NET OUTPUTS IN A PRODUCTION SYSTEM WITH FIXED PRICES
• 5.1 Monotonic increase of net outputs in quasi-equilibria = 133
• 5.2 Nonmonotonic changes of net outputs in a production system = 145
• 5.3 Production system of units with complementary inputs = 148
• Chapter 6 CLOSED PRODUCTION SYSTEMS
• 6.1 An equilibrium model of a production system = 153
• 6.2 A closed production model with fixed prices and quotas = 159
• Chapter 7 CLOSED MODELS OF ECONOMIC SYSTEMS
• 7.1 A model of coordinated functioning with fixed prices and consumer's quotas = 166
• 7.2 Models of an economy with flexible prices. Basic notions = 169
• 7.2.1 Examples of economies with flexible prices = 169
• 7.3 Semi-equilibrium in an economic system = 175
• 7.4 Existence of equilibrium in the economy $$\varepsilon_{2}$$ = 186
• 7.5 Efficiency of equilibria = 194
• 7.6 Special kinds of closed models = 202
• 7.6.1 Pair interactions and efficient states = 202
• 7.6.2 Contracted states = 205
• 7.7 A model of an economy with fixed budgets = 211
• 7.8 A model of joint functioning of mixed mechanism : flexible and fixed prices and quotas = 224
• PART Ⅱ. DYNAMIC MODELS OF ECONOMIC INTERACTION
• Chapter 8 SUPER-LINEAR MAPPINGS AND MODELS OF VON NEUMANN TYPE
• 8.1 Duality of super-linear mappings = 240
• 8.1.1 The simplest properties of super-linear mappings = 240
• 8.1.2 Super(sub)differentials and super(sub)linear functions = 244
• 8.1.3 Matched four-tuples = 249
• 8.2 Von Neumann-type models of economic dynamics = 252
• 8.2.1 Main definitions = 253
• 8.2.2 Characteristics of paths = 256
• 8.3 Exchange mapping = 260
• 8.3.1 Description of exchange mapping = 260
• 8.3.2 Mapping conjugate with respect to an exchange mapping = 262
• 8.3.3 The maximal gain as utility function = 268
• 8.3.4 The minimal production costs as utility function = 274
• 8.4 An equilibrium for mixed mechanism described by super-linear mappings = 280
• 8.4.1 Description of the economy = 280
• 8.4.2 Existence of a weak equilibrium = 285
• 8.4.3 Description of matched four-tuples for some mappings = 292
• 8.4.4 Four-tuples matched with respect to intersections and sums = 296
• 8.4.5 Matched four-tuples for mixed exchange mappings = 298
• 8.4.6 Matched four-tuples for fixed prices exchange mapping = 302
• 8.4.7 Weak equilibrium under free exchange = 309
• 8.4.8 Weak equilibrium under direct distribution = 310
• 8.4.9 Weak equilibrium under fixed prices exchange = 312
• 8.4.10 Exchange under special quotas = 313
• Chapter 9 EFFICIENT PATHS IN REPRODUCTION MODELS
• 9.1 Reproduction models = 315
• 9.1.1 Description of models = 315
• 9.1.2 Some particular models = 319
• 9.2 Efficient paths of the model M(A$$_t$$, C$$_t$$) = 322
• 9.2.1 Analysis of modified models = 322
• 9.2.2 Paths with a characteristic as an equilibrium in the case of free exchange = 327
• 9.2.3 Paths with a characteristic as the generalized equilibrium = 328
• 9.2.4 Necessary and sufficient conditions = 331
• 9.3 Efficient paths under free exchange = 335
• 9.3.1 Characteristics under free exchange = 335
• 9.3.2 Some auxiliary results = 336
• 9.3.3 Proof of Theorem 9.4 = 340
• 9.3.4 Properties of efficient paths under free exchange = 343
• 9.3.5 Another view on efficient paths and its characteristics = 345
• 9.4 Efficient paths in the model N$$_1$$, = 350
• Chapter 10 EFFICIENT FUNCTIONS
• 10.1 Efficient functions in the von Neumann-Gale model = 356
• 10.1.1 Optimality with respect to efficient functions = 356
• 10.1.2 Some properties of efficient functions = 358
• 10.2 Efficient functions in models associated with simplest reproduction models = 364
• 10.2.1 Efficient functions for reproduction models with linear production mappings = 364
• 10.2.2 Efficient functions for reproduction models with Leontieff production mappings = 369
• Chapter 11 THE EQUILIBRIUM MECHANISMS OF PATH DESIGNING
• 11.1The equilibrium mechanisms of models NC(A$$_t$$) = 374
• 11.1.1 Notion of equilibrium mechanisms = 374
• 11.1.2 The first kind mechanism = 378
• 11.1.3 Some applications of the equilibrium mechanism = 386
• 11.1.4 Equilibrium mechanisms for the model N$$_1$$(A$$_t$$, B$$_t$$) = 389
• 11.1.5 Direct control mechanisms = 390
• 11.2 Stability of equilibrium mechanisms = 393
• 11.2.1 Forecast and market prices = 393
• 11.2.2 Analysis of stability of equilibrium mechanisms = 395
• 11.3 Growth rates = 400
• 11.3.1 Definition of growth rates = 400
• 11.3.2 Main properties of growth rates = 402
• 11.4 Equilibrium market mechanisms = 408
• 11.4.1 The financial market = 408
• 11.4.2 The commodity market = 409
• 11.4.3 Efficient paths and mechanisms of the financial market = 412
• 11.4.4 Efficient paths and mechanisms of the commodity market = 416
• Chapter 12 DYNAMIC EQUILIBRIUM WITH FLEXIBLE PRICES
• 12.1 Dynamic equilibrium model with flexible prices = 420
• 12.1.1 Dynamics of the model = 420
• 12.1.2 Goals of units = 423
• 12.1.3 Definition of equilibrium = 426
• 12.2 Proof of the existence of an equilibrium in the model M$$_{\varepsilon}$$ = 430
• 12.2.1 Modified model of reproduction = 430
• 12.2.2 Special von Neumann-type model = 432
• 12.2.3 Some auxiliary results = 438
• 12.2.4 Efficient paths of the model $$\tilde{M}$$ = 441
• 12.2.5 One special model with fixed budgets = 449
• 12.2.6 Proof of Theorem 12.1. = 450
• Chapter 13 ESTIMATES OF THE GROWTH OF PATHS
• 13.1 Growth rate in von Neumann-type models = 452
• 13.1.1 Asymptotically efficient paths = 452
• 13.1.2 Existence theorem = 455
• 13.2 Estimates of the growth of paths designed by equilibrium mechanisms = 456
• 13.3 Examples of designing of equilibrium mechanisms = 466
• 13.3.1 Efficient functions and matched four-tuples = 466
• 13.3.2 Particular cases = 470
• Chapter 14 ASYMPTOTIC PROPERTIES OF PATHS OF THE MODEL M$$_1$$((B$$\phi$$)$$_t$$)
• 14.1 Turnpike theorem for M$$_1$$((B$$Phi$$)$$_t$$) = 478
• 14.1.1 Formulation of the theorem = 478
• 14.1.2 Lemmas = 484
• 14.1.3 Proof of Theorem 14.1 = 489
• 14.2 Turnpike theorem for models with constant technologies = 493
• 14.2.1 Turnpike theorem for von Neumann -Gale models = 493
• 14.2.2 Stationary reproduction models = 498
• 14.2.3 The case when a turnpike is a ray = 504
• 14.2.4 Model with conservation matrices = 510
• 14.2.5 Two-product models = 515
• Chapter 15 EQUILIBRIUM MECHANISMS IN A TWO-SECTOR MODEL
• 15.1 Paths designed by using equilibrium mechanisms and their asymptotics = 520
• 15.1.1 Description of the model = 520
• 15.1.2 Geometrical interpretation = 527
• 15.1.3 Path designing = 529
• 15.1.4 Efficient paths = 531
• 15.1.5 Asymptotic behaviour = 535
• 15.1.6 Sufficient conditions of asymptotic efficiency = 542
• 15.1.7 Necessary conditions for asymptotic efficiency = 544
• 15.2 Examples of equilibrium mechanisms in a two-sector model = 555
• 15.2.1 Financial market mechanism = 555
• 15.2.2 Commodity market mechanism = 556
• 15.2.3 Growth rates = 558
• Appendices
• Appendix 1 Multi-valued mappings = 563
• Appendix 2 Non-smooth and convex analysis = 566
• Appendix 3 Analysis of the two-sector reproduction model = 570
• Appendix 4 Numerical experiments with a two-sector reproduction model = 576
• Appendix 5 Exercises and problems = 579
• Bibliography = 595
• Subject index = 605