Intriligator M.D., Arrow K.J. — Handbook of Mathematical Economics (vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ

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Intriligator M.D., Arrow K.J. — Handbook of Mathematical Economics (vol. 1)

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Название: Handbook of Mathematical Economics (vol. 1)

Авторы: Intriligator M.D., Arrow K.J.

Аннотация:

The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.
Volume 2 elaborates on Mathematical Approaches to Microeconomic Theory, including consumer, producer, oligopoly, and duality theory, as well as Mathematical Approaches to Competitive Equilibrium including such aspects of competitive equilibrium as existence, stability, uncertainty, the computation of equilibrium prices, and the core of an economy.

Язык:

Рубрика: Экономика и финансы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 378

Добавлена в каталог: 01.03.2007

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Предметный указатель

"Almost everywhere" property      179
"Darwinian" selection function      274—277
$\omega$ -limit point      103 105
$\omega$ -limit set      103
$\sigma$ -additive function      175
$\sigma$ -algebra      171 175 177 190
$\varepsilon$ -net      30
$\varepsilon$ -sphere ( $\varepsilon$ -neighborhood)      19 56
a-finite set function      175
Absolutely continuous function      192
Absolutely continuous set function      192
Active learning in stochastic control      122 124 133 see
Actuarially fair price      230
Adaptive control      111 133—134
Adaptive control, N-period      135 144
Adaptive search      227
Additive set function      173—175
Additive set function, finitely      172 174
Additive uncertainty      125—126
Adverse selection      214 229
Aggregate demand      7 162 207—208
allocation      55 160 344
Allocation, feasible      344
Arc-connected metric space      36
Arrow — Debrcu theorem      364
Ascoli's theorem      33
Asymptotically stable equilibrium      105
Asymptotically stable equilibrium, locally      00
Atomless measure space      161 179 207
Atomless probability measure      161
Auctions and bids      317
Balanced family of subsets      301
Balanced game      300
Bargaining point      303
Bargaining set      299 303 321
Bilateral monopoly      315—316
Bolzano — Weierstrass property      31
Boolean algebra      170
Bordered Hessian Theorem      63
Borel sets class of      172
Borel — Cantelli lemma      224
Boundary point of a set      21
Bounding hyperplane      38
Brouwer fixed point theorem      4 50
Brownian motion      260—264 267
Budget set      342 344
Business games      316
C-game      299
Cantor intersection theorem      26
Carathcodory's theorem      40
Catastrophe point      108
Cauchy sequence      23 28
Cellina's theorem      368
Characteristic function      292—293
Characteristic function, with side payments      293
Chow's algorithm      151
Classical programming problem      53 59 61 66 76
Classical programming problem, geometric interpretation of      63
Classical programming problem, solution to      62 77
Closed orbit      102—103
Closed set      21
Closed-loop policy      122—124
Closure of a set      21
Coalition      163 178
Commodity bundle      332
Commodity space      332
Compact metric space      30—31
Compact set      30 33 40 47 51 167 198
Comparative statics      76 82
Comparative statics, for the firm      87
Comparative statics, theorem      78
Competitive equilibrium      50
Competitive industry under uncertainty      258—260
Complement of a set      16
Complementary slackness conditions of linear programming      75
Complementary slackness conditions of nonlinear programming      68—69
Complementary slackness theorem      74 81 85
Complete space      23—24 26 31
Composition of functions      16
Concave function      44 56n
Concave function, strictly      56n
Concave programming      69—70
Conjugate gradient method in control theory      112
Connected metric space      36
Constraint, functions      60 63 66 69n 73
Constraint,constants      60 62 73
Constraint,vector      66
Consumption under uncertainty      236—247
Consumption under uncertainty, multiperiod      242—247
Contingent demand      314
Continuous curve in a topological space      36
Continuous function      28
Continuous function, uniformly      28
Continuum economy      7 162—165 179 196
Contract curve      3 315
Contraction      50
Contraction mapping theorem      50
Contraction mappings      214
Contraction operator      243
Control theory      111
Convergence of points      23
Convergence, almost everywhere      194—195 201
Convergence, almost uniform      194
Convergence, in distribution      200—201
Convergence, in mean      195
Convergence, in measure      194 196 201
Convergence, point-wise      194
Convergence, uniform      194
Convergence, weak      196—197
Convex function      69n
Convex function, quasiconvex      70n
Convex hull      40—41
Convex set      37—40 51 56 207
Convexity      36—37
Convexity of preferences      162 207—208
Cooperative form (characteristic function form)      286 291—294
Cooperative solutions      299
Core      3 163 299—301 319—321
Core, $\varepsilon$ -core      299 305
Core, $\varepsilon$ -core, strong $\varepsilon$ -core      305
Core, $\varepsilon$ -core, weak $\varepsilon$ -core      305
Core, inner core      299 305—306
Core, least core      305
Core, near core      305
Correspondence      205—208
Correspondence between sets      46
Correspondence between sets, a fixed point of      51
Correspondence between sets, composition of      46
Correspondence between sets, cross product of      46
Correspondence between sets, graph of      46
Correspondence between sets, hemi-continuity of      46
Correspondence between sets, is closed      46—47 51
Correspondence between sets, is compact valued      46—49
Correspondence between sets, is continuous      49
Correspondence between sets, is lower hemi-continuous      48
Correspondence between sets, sum of      46
Correspondence between sets, upper hemi-continuity      46—48
Correspondence, integrable selection of      206
Correspondence, integrably bounded      207
Correspondence, integral of      206
Correspondence, measurable      206
Countable set      24—25
Counter objection      303
Cournot, aggregation condition      84
Cournot, duopoly model      290 295 311
Cournot, solution      2 50
Cover of a set      29
Cycles      see “Closed orbits”
Debreu — Gale — Nikaido theorem      338
Decreasing sequence of sets      26

Degrees of freedom (in linear programming problem)      61
Demand correspondence      49
Demand for cash balances      268—270
Demand for index bonds      270—271
Demand functions      81—82 342
Demand theorem      81—82
Dense set      24—26 37 166 198
Diameter of a set      26
Diffeomorphism      95 356
Diminishing marginal rate of substitution      37
Dirac measure      179
Directional derivative      104
Distribution of a function      199
Domain      15
Domination      302
Dual control      see “Adaptive control”
Dual problem      73 89
Dual problem, Kuhn — Tucker conditions for      74
Dual problem, Lagrangian function of      73 75
Dual problem, objective function of      75
Dual problem, primal problem to      73
Dual problem, solution to      74—75
Duality theorem      40 74
Duality theory      7 37
Dubins and Spanier's theorem      204—205
Duopoly      311—312 see
Dynamic programming      111
Dynamical systems      93—94 111
Effective set      303
Efficient market hypothesis      214 266—267
Endowment allocation      360
Engel aggregation condition      84
Equality constraints      59
Equicontinuous collection of functions      32—33
Equilibrium for an economy      364 367
Equilibrium of dynamical system      97
Equilibrium problem      332
Equilibrium theory      331
Euclidean distance      56n
Euclidean metric      17
Evolutionary theory      272
Excess demand      332
Excess of a coalition      304
Exchange economy      160 189 203
Exchange economy, perfectly competitive      160
Exchange economy, pure      41 344
Existence of a maximum      56
Existence of competitive equilibrium      50
Existence of equilibria      331
Existence theorem in linear programming      74
Experience rating      229
Extended price equilibrium      357
Extensive form      285—287
Externalities      322
Factor demand under uncertainty      254
False demand function      346 366
Farrell's speculator model      273
Fatou's lemma      189
Feasible vector (vector of instruments)      55 60 66
Feasible vector, to linear programming problem      72
Feedback policy      122—124
Finite partition      184
First-order conditions for local maximum theorem      57
Fixed point of function      49—50
flexibility      212
Flow of the differential equation      94
Fold catastrophe      109
Fold map      355
Free disposal equilibrium      338
Frobenius theorem      105
Full measure set      335
Function      15
Fundamental matrix equation of the theory of the firm      87
Fundamental matrix equation of the theory of the household      83
Game of pure opposition      306
Game of strategy      285
Game theory      2 6 285 287
Game with continuum of players      295 307
Game with perfect information      288
Gauss map      354
General equilibrium      13 318
Glivenko — Cantelli theorem      202
Global analysis      6 331
Global maximum      44 55—56
Global maximum, strict      55—56
Globally stable equilibria      101—102 106
Gradient method in control theory      112 120—121 143
Gradient system      104 106 109
Gradient system, local catastrophes of      108
Gradient vector      57 59 61 63 71 104
Graph of a function      16 44
Hamiltonian function      106
Hamiltonian system      106—107
Hausdorff's topology      203
Hessian matrix      58 64 78 81 83 88 106
Homeomorphism      28 108
Homeomorphism, ray preserving      337
Homogeneity condition      84
Homogeneous function of degree k      45
Homothetic function      45
Hyperplane      37
Identity mapping      182
Image of a set      55
Imbedding map      354
Imputation      297
Imputation set      296 319
Imputation set, externally stable      303
Imputation set, internally stable      303
Income effect      83
Income expansion path      343
Indifference curves      37 82n
Indifference surfaces      340
Indirect utility function      106
Indivisibilities      322
Inequality constraints      66
Inferior inputs      88n
Infinite economy      202
Insurance      227 230
Integrable measurable function      187—189 195 206
integral      186 206
Integration period      1
Interior of a set      20
Interior point      20
Inverse image      15
Inverse mapping theorem      334
Isolated community subset      359
Isometric spaces      17
Jacobian matrix      61 64
Jensen's inequality      222
Job search      218
Kakutani fixed point theorem      4 51 207
Kalman filter method      144 149
Kernel solution      299 304 321
Kinked oligopoly curve      313
Krein — Milman theorem      40 42
Kuhn — Tucker conditions      66 68 70—72 74—75 80—81 85 351
Kuhn — Tucker saddle point theorem      69
Lagrange multipliers      1 60—62 65—68
Lagrange multipliers, theorem on      60—61 66
Lagrangian function      60 65 67—68 73
Lebcsque measure      177—178 200
Lebesque number      30—31
Lebesque's theorem      189
Lebesque's theorem, generalization of      202
Level set      104
Liapunov function      101—102
Liapunov's theorem      180 204 207
Limit economies      183 200 202 204
Limit of a sequence      23
Limit point of a set      21

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